%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN475-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:15 AM UTC 2025
% Result : Unsatisfiable 0.57s 0.76s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN475-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:36:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.57/0.76 % SZS status Unsatisfiable
% 0.57/0.76 % SZS output start Proof
% 0.57/0.76 tff(c1_1_type, type, (
% 0.57/0.76 c1_1: $i > $o)).
% 0.57/0.76 tff(a1037_type, type, (
% 0.57/0.76 a1037: $i)).
% 0.57/0.76 tff(hskp19_type, type, (
% 0.57/0.76 hskp19: $o)).
% 0.57/0.76 tff(c0_1_type, type, (
% 0.57/0.76 c0_1: $i > $o)).
% 0.57/0.76 tff(a1008_type, type, (
% 0.57/0.76 a1008: $i)).
% 0.57/0.76 tff(c2_1_type, type, (
% 0.57/0.76 c2_1: $i > $o)).
% 0.57/0.76 tff(a1044_type, type, (
% 0.57/0.76 a1044: $i)).
% 0.57/0.76 tff(a1032_type, type, (
% 0.57/0.76 a1032: $i)).
% 0.57/0.76 tff(hskp17_type, type, (
% 0.57/0.76 hskp17: $o)).
% 0.57/0.76 tff(c3_1_type, type, (
% 0.57/0.76 c3_1: $i > $o)).
% 0.57/0.76 tff(ndr1_0_type, type, (
% 0.57/0.76 ndr1_0: $o)).
% 0.57/0.76 tff(hskp23_type, type, (
% 0.57/0.76 hskp23: $o)).
% 0.57/0.76 tff(hskp8_type, type, (
% 0.57/0.76 hskp8: $o)).
% 0.57/0.76 tff(a1003_type, type, (
% 0.57/0.76 a1003: $i)).
% 0.57/0.76 tff(hskp3_type, type, (
% 0.57/0.76 hskp3: $o)).
% 0.57/0.76 tff(a1040_type, type, (
% 0.57/0.76 a1040: $i)).
% 0.57/0.76 tff(hskp5_type, type, (
% 0.57/0.76 hskp5: $o)).
% 0.57/0.76 tff(hskp2_type, type, (
% 0.57/0.76 hskp2: $o)).
% 0.57/0.76 tff(a1002_type, type, (
% 0.57/0.76 a1002: $i)).
% 0.57/0.76 tff(hskp13_type, type, (
% 0.57/0.76 hskp13: $o)).
% 0.57/0.76 tff(hskp29_type, type, (
% 0.57/0.76 hskp29: $o)).
% 0.57/0.76 tff(a1001_type, type, (
% 0.57/0.76 a1001: $i)).
% 0.57/0.76 tff(hskp1_type, type, (
% 0.57/0.76 hskp1: $o)).
% 0.57/0.76 tff(hskp0_type, type, (
% 0.57/0.76 hskp0: $o)).
% 0.57/0.76 tff(a1023_type, type, (
% 0.57/0.76 a1023: $i)).
% 0.57/0.76 tff(a1000_type, type, (
% 0.57/0.76 a1000: $i)).
% 0.57/0.76 tff(hskp7_type, type, (
% 0.57/0.76 hskp7: $o)).
% 0.57/0.76 tff(a1045_type, type, (
% 0.57/0.76 a1045: $i)).
% 0.57/0.76 tff(hskp24_type, type, (
% 0.57/0.76 hskp24: $o)).
% 0.57/0.76 tff(a1010_type, type, (
% 0.57/0.76 a1010: $i)).
% 0.57/0.76 tff(a1005_type, type, (
% 0.57/0.76 a1005: $i)).
% 0.57/0.76 tff(a1006_type, type, (
% 0.57/0.76 a1006: $i)).
% 0.57/0.76 tff(hskp6_type, type, (
% 0.57/0.76 hskp6: $o)).
% 0.57/0.76 tff(a1041_type, type, (
% 0.57/0.76 a1041: $i)).
% 0.57/0.76 tff(hskp21_type, type, (
% 0.57/0.76 hskp21: $o)).
% 0.57/0.76 tff(hskp4_type, type, (
% 0.57/0.76 hskp4: $o)).
% 0.57/0.76 tff(a1004_type, type, (
% 0.57/0.76 a1004: $i)).
% 0.57/0.76 tff(a1043_type, type, (
% 0.57/0.76 a1043: $i)).
% 0.57/0.76 tff(a1052_type, type, (
% 0.57/0.76 a1052: $i)).
% 0.57/0.76 tff(hskp26_type, type, (
% 0.57/0.76 hskp26: $o)).
% 0.57/0.76 tff(a1048_type, type, (
% 0.57/0.76 a1048: $i)).
% 0.57/0.76 tff(hskp25_type, type, (
% 0.57/0.76 hskp25: $o)).
% 0.57/0.76 tff(a1026_type, type, (
% 0.57/0.76 a1026: $i)).
% 0.57/0.76 tff(hskp15_type, type, (
% 0.57/0.76 hskp15: $o)).
% 0.57/0.76 tff(hskp22_type, type, (
% 0.57/0.76 hskp22: $o)).
% 0.57/0.76 tff(hskp28_type, type, (
% 0.57/0.76 hskp28: $o)).
% 0.57/0.76 tff(a1033_type, type, (
% 0.57/0.76 a1033: $i)).
% 0.57/0.76 tff(1,assumption,(c2_1(a1044)), introduced(assumption)).
% 0.57/0.76 tff(2,plain,
% 0.57/0.76 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(3,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[2])).
% 0.57/0.76 tff(4,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(5,plain,
% 0.57/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(6,plain,
% 0.57/0.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[5])).
% 0.57/0.76 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.57/0.76 tff(8,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.57/0.76 tff(9,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.57/0.76 tff(10,plain,(
% 0.57/0.76 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[9])).
% 0.57/0.76 tff(11,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.57/0.76 tff(12,plain,
% 0.57/0.76 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(13,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[12])).
% 0.57/0.76 tff(14,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(15,plain,
% 0.57/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(16,plain,
% 0.57/0.76 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[15])).
% 0.57/0.76 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.57/0.76 tff(18,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.57/0.76 tff(19,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.57/0.76 tff(20,plain,(
% 0.57/0.76 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[19])).
% 0.57/0.76 tff(21,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.57/0.76 tff(22,assumption,(~hskp23), introduced(assumption)).
% 0.57/0.76 tff(23,plain,
% 0.57/0.76 (^[U: $i] : refl((hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(24,plain,
% 0.57/0.76 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[23])).
% 0.57/0.76 tff(25,plain,
% 0.57/0.76 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(26,plain,
% 0.57/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(27,plain,
% 0.57/0.76 (![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[26])).
% 0.57/0.76 tff(28,axiom,(![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.57/0.76 tff(29,plain,
% 0.57/0.76 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.57/0.76 tff(30,plain,
% 0.57/0.76 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.57/0.76 tff(31,plain,(
% 0.57/0.76 ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[30])).
% 0.57/0.76 tff(32,plain,
% 0.57/0.76 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.57/0.76 tff(33,assumption,(hskp2), introduced(assumption)).
% 0.57/0.76 tff(34,plain,
% 0.57/0.76 (((~hskp2) | (~c1_1(a1002))) <=> ((~hskp2) | (~c1_1(a1002)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(35,plain,
% 0.60/0.76 (((~c1_1(a1002)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1002)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(36,axiom,((~c1_1(a1002)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.60/0.76 tff(37,plain,
% 0.60/0.76 ((~hskp2) | (~c1_1(a1002))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.60/0.76 tff(38,plain,
% 0.60/0.76 ((~hskp2) | (~c1_1(a1002))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.60/0.76 tff(39,plain,
% 0.60/0.76 (~c1_1(a1002)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.60/0.76 tff(40,plain,
% 0.60/0.76 (((~hskp2) | c0_1(a1002)) <=> ((~hskp2) | c0_1(a1002))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(41,axiom,((~hskp2) | c0_1(a1002)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.60/0.76 tff(42,plain,
% 0.60/0.76 ((~hskp2) | c0_1(a1002)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.60/0.76 tff(43,plain,
% 0.60/0.76 ((~hskp2) | c0_1(a1002)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.60/0.76 tff(44,plain,
% 0.60/0.76 ((~hskp2) | c0_1(a1002)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.60/0.76 tff(45,plain,
% 0.60/0.76 ((~hskp2) | c0_1(a1002)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.60/0.76 tff(46,plain,
% 0.60/0.76 ((~hskp2) | c0_1(a1002)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.60/0.76 tff(47,plain,
% 0.60/0.76 (c0_1(a1002)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[46, 33])).
% 0.60/0.76 tff(48,assumption,(~ndr1_0), introduced(assumption)).
% 0.60/0.76 tff(49,plain,
% 0.60/0.76 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(50,plain,
% 0.60/0.76 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(51,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.60/0.76 tff(52,plain,
% 0.60/0.76 (ndr1_0 | (~hskp13)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.60/0.76 tff(53,plain,
% 0.60/0.76 (ndr1_0 | (~hskp13)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.60/0.76 tff(54,plain,
% 0.60/0.76 (~hskp13),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[53, 48])).
% 0.60/0.76 tff(55,plain,
% 0.60/0.76 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(56,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.60/0.76 tff(57,plain,
% 0.60/0.76 ((~hskp29) | ndr1_0),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.60/0.76 tff(58,plain,
% 0.60/0.76 ((~hskp29) | ndr1_0),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[57, 55])).
% 0.60/0.76 tff(59,plain,
% 0.60/0.76 ((~hskp29) | ndr1_0),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.60/0.76 tff(60,plain,
% 0.60/0.76 ((~hskp29) | ndr1_0),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.60/0.76 tff(61,plain,
% 0.60/0.76 ((~hskp29) | ndr1_0),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.60/0.76 tff(62,plain,
% 0.60/0.76 (~hskp29),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[61, 48])).
% 0.60/0.76 tff(63,plain,
% 0.60/0.76 ((ndr1_0 | (~hskp23)) <=> (ndr1_0 | (~hskp23))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(64,plain,
% 0.60/0.76 (((~hskp23) | ndr1_0) <=> (ndr1_0 | (~hskp23))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(65,axiom,((~hskp23) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.60/0.76 tff(66,plain,
% 0.60/0.76 (ndr1_0 | (~hskp23)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.60/0.76 tff(67,plain,
% 0.60/0.76 (ndr1_0 | (~hskp23)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.60/0.76 tff(68,plain,
% 0.60/0.76 (~hskp23),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[67, 48])).
% 0.60/0.76 tff(69,plain,
% 0.60/0.76 ((hskp29 | hskp23 | hskp13) <=> (hskp29 | hskp23 | hskp13)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(70,plain,
% 0.60/0.76 (((hskp29 | hskp23) | hskp13) <=> (hskp29 | hskp23 | hskp13)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(71,plain,
% 0.60/0.76 ((hskp29 | hskp23) <=> (hskp29 | hskp23)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(72,plain,
% 0.60/0.76 (((hskp29 | hskp23) | hskp13) <=> ((hskp29 | hskp23) | hskp13)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[71])).
% 0.60/0.76 tff(73,plain,
% 0.60/0.76 (((hskp29 | hskp23) | hskp13) <=> (hskp29 | hskp23 | hskp13)),
% 0.60/0.76 inference(transitivity,[status(thm)],[72, 70])).
% 0.60/0.76 tff(74,axiom,((hskp29 | hskp23) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.60/0.76 tff(75,plain,
% 0.60/0.76 (hskp29 | hskp23 | hskp13),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.60/0.76 tff(76,plain,
% 0.60/0.76 (hskp29 | hskp23 | hskp13),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[75, 69])).
% 0.60/0.76 tff(77,plain,
% 0.60/0.76 (hskp29 | hskp23 | hskp13),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.60/0.76 tff(78,plain,
% 0.60/0.76 (hskp29 | hskp23 | hskp13),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[77, 69])).
% 0.60/0.76 tff(79,plain,
% 0.60/0.76 (hskp29 | hskp23 | hskp13),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[78, 69])).
% 0.60/0.76 tff(80,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[79, 68, 62, 54])).
% 0.60/0.76 tff(81,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(82,plain,
% 0.60/0.76 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(83,plain,
% 0.60/0.76 ((hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002))) <=> (hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(84,plain,
% 0.60/0.76 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[83])).
% 0.60/0.76 tff(85,plain,
% 0.60/0.76 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[84, 82])).
% 0.60/0.76 tff(86,plain,
% 0.60/0.76 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(87,plain,
% 0.60/0.76 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.60/0.76 tff(88,plain,
% 0.60/0.76 (~c3_1(a1002)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[87, 81, 22, 47, 39, 32])).
% 0.60/0.76 tff(89,plain,
% 0.60/0.76 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(90,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[89])).
% 0.60/0.76 tff(91,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(92,plain,
% 0.60/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(93,plain,
% 0.60/0.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[92])).
% 0.60/0.77 tff(94,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.60/0.77 tff(95,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.60/0.77 tff(96,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.60/0.77 tff(97,plain,(
% 0.60/0.77 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.77 inference(skolemize,[status(sab)],[96])).
% 0.60/0.77 tff(98,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.60/0.77 tff(99,plain,
% 0.60/0.77 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(100,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[99])).
% 0.60/0.77 tff(101,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(102,plain,
% 0.60/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(103,plain,
% 0.60/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[102])).
% 0.60/0.77 tff(104,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.60/0.77 tff(105,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.60/0.77 tff(106,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.60/0.77 tff(107,plain,(
% 0.60/0.77 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[106])).
% 0.60/0.77 tff(108,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.60/0.77 tff(109,plain,
% 0.60/0.77 (((~hskp2) | c2_1(a1002)) <=> ((~hskp2) | c2_1(a1002))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(110,axiom,((~hskp2) | c2_1(a1002)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.60/0.77 tff(111,plain,
% 0.60/0.77 ((~hskp2) | c2_1(a1002)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.60/0.77 tff(112,plain,
% 0.60/0.77 ((~hskp2) | c2_1(a1002)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[111, 109])).
% 0.60/0.77 tff(113,plain,
% 0.60/0.77 ((~hskp2) | c2_1(a1002)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.60/0.77 tff(114,plain,
% 0.60/0.77 ((~hskp2) | c2_1(a1002)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.60/0.77 tff(115,plain,
% 0.60/0.77 ((~hskp2) | c2_1(a1002)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[114, 109])).
% 0.60/0.77 tff(116,plain,
% 0.60/0.77 (c2_1(a1002)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[115, 33])).
% 0.60/0.77 tff(117,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(118,plain,
% 0.60/0.77 ((hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002))) <=> (hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(119,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[118])).
% 0.60/0.77 tff(120,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[119, 117])).
% 0.60/0.77 tff(121,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(122,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.60/0.77 tff(123,plain,
% 0.60/0.77 (hskp19),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[122, 81, 47, 116, 39, 108, 88])).
% 0.60/0.77 tff(124,plain,
% 0.60/0.77 (((~hskp19) | (~c3_1(a1037))) <=> ((~hskp19) | (~c3_1(a1037)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(125,plain,
% 0.60/0.77 (((~c3_1(a1037)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1037)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(126,axiom,((~c3_1(a1037)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.60/0.77 tff(127,plain,
% 0.60/0.77 ((~hskp19) | (~c3_1(a1037))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.60/0.77 tff(128,plain,
% 0.60/0.77 ((~hskp19) | (~c3_1(a1037))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.60/0.77 tff(129,plain,
% 0.60/0.77 (~c3_1(a1037)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[128, 123])).
% 0.60/0.77 tff(130,plain,
% 0.60/0.77 (((~hskp19) | (~c1_1(a1037))) <=> ((~hskp19) | (~c1_1(a1037)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(131,plain,
% 0.60/0.77 (((~c1_1(a1037)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a1037)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(132,axiom,((~c1_1(a1037)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.60/0.77 tff(133,plain,
% 0.60/0.77 ((~hskp19) | (~c1_1(a1037))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.60/0.77 tff(134,plain,
% 0.60/0.77 ((~hskp19) | (~c1_1(a1037))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.60/0.77 tff(135,plain,
% 0.60/0.77 (~c1_1(a1037)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[134, 123])).
% 0.60/0.77 tff(136,assumption,(hskp13), introduced(assumption)).
% 0.60/0.77 tff(137,plain,
% 0.60/0.77 (((~hskp13) | (~c1_1(a1023))) <=> ((~hskp13) | (~c1_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(138,plain,
% 0.60/0.77 (((~c1_1(a1023)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(139,axiom,((~c1_1(a1023)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.60/0.77 tff(140,plain,
% 0.60/0.77 ((~hskp13) | (~c1_1(a1023))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.60/0.77 tff(141,plain,
% 0.60/0.77 ((~hskp13) | (~c1_1(a1023))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[140, 137])).
% 0.60/0.77 tff(142,plain,
% 0.60/0.77 (~c1_1(a1023)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[141, 136])).
% 0.60/0.77 tff(143,plain,
% 0.60/0.77 (((~hskp13) | c3_1(a1023)) <=> ((~hskp13) | c3_1(a1023))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(144,axiom,((~hskp13) | c3_1(a1023)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.60/0.77 tff(145,plain,
% 0.60/0.77 ((~hskp13) | c3_1(a1023)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.60/0.77 tff(146,plain,
% 0.60/0.77 ((~hskp13) | c3_1(a1023)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[145, 143])).
% 0.60/0.77 tff(147,plain,
% 0.60/0.77 ((~hskp13) | c3_1(a1023)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.60/0.77 tff(148,plain,
% 0.60/0.77 ((~hskp13) | c3_1(a1023)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.60/0.77 tff(149,plain,
% 0.60/0.77 ((~hskp13) | c3_1(a1023)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[148, 143])).
% 0.60/0.77 tff(150,plain,
% 0.60/0.77 (c3_1(a1023)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[149, 136])).
% 0.60/0.77 tff(151,plain,
% 0.60/0.77 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(152,plain,
% 0.60/0.77 ((hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023))) <=> (hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(153,plain,
% 0.60/0.77 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[152])).
% 0.60/0.77 tff(154,plain,
% 0.60/0.77 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[153, 151])).
% 0.60/0.77 tff(155,plain,
% 0.60/0.77 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(156,plain,
% 0.60/0.77 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.60/0.77 tff(157,plain,
% 0.60/0.77 (~c0_1(a1023)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[156, 81, 22, 150, 142, 32])).
% 0.60/0.77 tff(158,plain,
% 0.60/0.77 (((~hskp13) | (~c2_1(a1023))) <=> ((~hskp13) | (~c2_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(159,plain,
% 0.60/0.77 (((~c2_1(a1023)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(160,axiom,((~c2_1(a1023)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.60/0.77 tff(161,plain,
% 0.60/0.77 ((~hskp13) | (~c2_1(a1023))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.60/0.77 tff(162,plain,
% 0.60/0.77 ((~hskp13) | (~c2_1(a1023))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.60/0.77 tff(163,plain,
% 0.60/0.77 (~c2_1(a1023)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[162, 136])).
% 0.60/0.77 tff(164,plain,
% 0.60/0.77 (^[U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(165,plain,
% 0.60/0.77 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[164])).
% 0.60/0.77 tff(166,plain,
% 0.60/0.77 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(167,plain,
% 0.60/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(168,plain,
% 0.60/0.77 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[167])).
% 0.60/0.77 tff(169,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.60/0.77 tff(170,plain,
% 0.60/0.77 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.60/0.77 tff(171,plain,
% 0.60/0.77 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.60/0.77 tff(172,plain,(
% 0.60/0.77 ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[171])).
% 0.60/0.77 tff(173,plain,
% 0.60/0.77 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.60/0.77 tff(174,assumption,(hskp0), introduced(assumption)).
% 0.60/0.77 tff(175,plain,
% 0.60/0.77 (((~hskp0) | c2_1(a1000)) <=> ((~hskp0) | c2_1(a1000))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(176,axiom,((~hskp0) | c2_1(a1000)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.60/0.77 tff(177,plain,
% 0.60/0.77 ((~hskp0) | c2_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.60/0.77 tff(178,plain,
% 0.60/0.77 ((~hskp0) | c2_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.60/0.77 tff(179,plain,
% 0.60/0.77 ((~hskp0) | c2_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.60/0.77 tff(180,plain,
% 0.60/0.77 ((~hskp0) | c2_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.60/0.77 tff(181,plain,
% 0.60/0.77 ((~hskp0) | c2_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.60/0.77 tff(182,plain,
% 0.60/0.77 (c2_1(a1000)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[181, 174])).
% 0.60/0.77 tff(183,plain,
% 0.60/0.77 (((~hskp0) | c0_1(a1000)) <=> ((~hskp0) | c0_1(a1000))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(184,axiom,((~hskp0) | c0_1(a1000)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.60/0.77 tff(185,plain,
% 0.60/0.77 ((~hskp0) | c0_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.60/0.77 tff(186,plain,
% 0.60/0.77 ((~hskp0) | c0_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[185, 183])).
% 0.60/0.77 tff(187,plain,
% 0.60/0.77 ((~hskp0) | c0_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.60/0.77 tff(188,plain,
% 0.60/0.77 ((~hskp0) | c0_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.60/0.77 tff(189,plain,
% 0.60/0.77 ((~hskp0) | c0_1(a1000)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[188, 183])).
% 0.60/0.77 tff(190,plain,
% 0.60/0.77 (c0_1(a1000)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[189, 174])).
% 0.60/0.77 tff(191,assumption,(~c0_1(a1023)), introduced(assumption)).
% 0.60/0.77 tff(192,assumption,(~c2_1(a1023)), introduced(assumption)).
% 0.60/0.77 tff(193,assumption,(~c1_1(a1023)), introduced(assumption)).
% 0.60/0.77 tff(194,assumption,(c3_1(a1023)), introduced(assumption)).
% 0.60/0.77 tff(195,plain,
% 0.60/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(196,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[195])).
% 0.60/0.77 tff(197,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(198,plain,
% 0.60/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(199,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[198])).
% 0.60/0.77 tff(200,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.60/0.77 tff(201,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.60/0.77 tff(202,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.60/0.77 tff(203,plain,(
% 0.60/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[202])).
% 0.60/0.77 tff(204,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.60/0.77 tff(205,assumption,(hskp7), introduced(assumption)).
% 0.60/0.77 tff(206,plain,
% 0.60/0.77 (((~hskp7) | (~c3_1(a1008))) <=> ((~hskp7) | (~c3_1(a1008)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(207,plain,
% 0.60/0.77 (((~c3_1(a1008)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1008)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(208,axiom,((~c3_1(a1008)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.60/0.77 tff(209,plain,
% 0.60/0.77 ((~hskp7) | (~c3_1(a1008))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.60/0.77 tff(210,plain,
% 0.60/0.77 ((~hskp7) | (~c3_1(a1008))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[209, 206])).
% 0.60/0.77 tff(211,plain,
% 0.60/0.77 (~c3_1(a1008)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[210, 205])).
% 0.60/0.77 tff(212,plain,
% 0.60/0.77 (((~hskp7) | (~c1_1(a1008))) <=> ((~hskp7) | (~c1_1(a1008)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(213,plain,
% 0.60/0.77 (((~c1_1(a1008)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1008)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(214,axiom,((~c1_1(a1008)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.60/0.77 tff(215,plain,
% 0.60/0.77 ((~hskp7) | (~c1_1(a1008))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.60/0.77 tff(216,plain,
% 0.60/0.77 ((~hskp7) | (~c1_1(a1008))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.60/0.77 tff(217,plain,
% 0.60/0.77 (~c1_1(a1008)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[216, 205])).
% 0.60/0.77 tff(218,plain,
% 0.60/0.77 (((~hskp7) | c2_1(a1008)) <=> ((~hskp7) | c2_1(a1008))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(219,axiom,((~hskp7) | c2_1(a1008)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.60/0.77 tff(220,plain,
% 0.60/0.77 ((~hskp7) | c2_1(a1008)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.60/0.77 tff(221,plain,
% 0.60/0.77 ((~hskp7) | c2_1(a1008)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[220, 218])).
% 0.60/0.77 tff(222,plain,
% 0.60/0.77 ((~hskp7) | c2_1(a1008)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[221, 218])).
% 0.60/0.77 tff(223,plain,
% 0.60/0.77 ((~hskp7) | c2_1(a1008)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.60/0.77 tff(224,plain,
% 0.60/0.77 ((~hskp7) | c2_1(a1008)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[223, 218])).
% 0.60/0.77 tff(225,plain,
% 0.60/0.77 (c2_1(a1008)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[224, 205])).
% 0.60/0.77 tff(226,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(227,plain,
% 0.60/0.77 (((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023))) <=> (c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(228,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[227])).
% 0.60/0.78 tff(229,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[228, 226])).
% 0.60/0.78 tff(230,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(231,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.60/0.78 tff(232,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[231, 81, 194, 225, 193, 192, 217, 211, 204, 191])).
% 0.60/0.78 tff(233,plain,((~hskp7) | (~c3_1(a1023)) | c1_1(a1023) | c2_1(a1023) | c0_1(a1023)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(234,plain,
% 0.60/0.78 (~hskp7),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[233, 194, 193, 192, 191])).
% 0.60/0.78 tff(235,plain,
% 0.60/0.78 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(236,plain,
% 0.60/0.78 ((hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(237,plain,
% 0.60/0.78 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[236])).
% 0.60/0.78 tff(238,plain,
% 0.60/0.78 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[237, 235])).
% 0.60/0.78 tff(239,plain,
% 0.60/0.78 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(240,plain,
% 0.60/0.78 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.60/0.78 tff(241,plain,
% 0.60/0.78 (~c1_1(a1000)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[240, 81, 234, 190, 182, 173])).
% 0.60/0.78 tff(242,plain,
% 0.60/0.78 (((~hskp0) | (~c3_1(a1000))) <=> ((~hskp0) | (~c3_1(a1000)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(243,plain,
% 0.60/0.78 (((~c3_1(a1000)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1000)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(244,axiom,((~c3_1(a1000)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.60/0.78 tff(245,plain,
% 0.60/0.78 ((~hskp0) | (~c3_1(a1000))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.60/0.78 tff(246,plain,
% 0.60/0.78 ((~hskp0) | (~c3_1(a1000))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[245, 242])).
% 0.60/0.78 tff(247,plain,
% 0.60/0.78 (~c3_1(a1000)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[246, 174])).
% 0.60/0.78 tff(248,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(249,plain,
% 0.60/0.78 (((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023))) <=> (c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(250,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[249])).
% 0.60/0.78 tff(251,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[250, 248])).
% 0.60/0.78 tff(252,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(253,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.60/0.78 tff(254,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[253, 81, 194, 182, 193, 192, 247, 204, 191, 241])).
% 0.60/0.78 tff(255,plain,((~hskp0) | (~c3_1(a1023)) | c1_1(a1023) | c2_1(a1023) | c0_1(a1023)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(256,plain,
% 0.60/0.78 (~hskp0),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[255, 150, 142, 163, 157])).
% 0.60/0.78 tff(257,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(258,plain,
% 0.60/0.78 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[257])).
% 0.60/0.78 tff(259,plain,
% 0.60/0.78 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(260,plain,
% 0.60/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(261,plain,
% 0.60/0.78 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[260])).
% 0.60/0.78 tff(262,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.60/0.78 tff(263,plain,
% 0.60/0.78 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.60/0.78 tff(264,plain,
% 0.60/0.78 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.60/0.78 tff(265,plain,(
% 0.60/0.78 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(skolemize,[status(sab)],[264])).
% 0.60/0.78 tff(266,plain,
% 0.60/0.78 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.60/0.78 tff(267,plain,
% 0.60/0.78 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(268,plain,
% 0.60/0.78 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023)) <=> (hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(269,plain,
% 0.60/0.78 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[268])).
% 0.60/0.78 tff(270,plain,
% 0.60/0.78 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))),
% 0.60/0.78 inference(transitivity,[status(thm)],[269, 267])).
% 0.60/0.78 tff(271,plain,
% 0.60/0.78 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(272,plain,
% 0.60/0.78 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.60/0.78 tff(273,plain,
% 0.60/0.78 (hskp1 | hskp0),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[272, 81, 142, 163, 266, 157])).
% 0.60/0.78 tff(274,plain,
% 0.60/0.78 (hskp1),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[273, 256])).
% 0.60/0.78 tff(275,plain,
% 0.60/0.78 (((~hskp1) | (~c1_1(a1001))) <=> ((~hskp1) | (~c1_1(a1001)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(276,plain,
% 0.60/0.78 (((~c1_1(a1001)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1001)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(277,axiom,((~c1_1(a1001)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.60/0.78 tff(278,plain,
% 0.60/0.78 ((~hskp1) | (~c1_1(a1001))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.60/0.78 tff(279,plain,
% 0.60/0.78 ((~hskp1) | (~c1_1(a1001))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[278, 275])).
% 0.60/0.78 tff(280,plain,
% 0.60/0.78 (~c1_1(a1001)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[279, 274])).
% 0.60/0.78 tff(281,plain,
% 0.60/0.78 (((~hskp1) | c3_1(a1001)) <=> ((~hskp1) | c3_1(a1001))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(282,axiom,((~hskp1) | c3_1(a1001)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.60/0.78 tff(283,plain,
% 0.60/0.78 ((~hskp1) | c3_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.60/0.78 tff(284,plain,
% 0.60/0.78 ((~hskp1) | c3_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[283, 281])).
% 0.60/0.78 tff(285,plain,
% 0.60/0.78 ((~hskp1) | c3_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[284, 281])).
% 0.60/0.78 tff(286,plain,
% 0.60/0.78 ((~hskp1) | c3_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.60/0.78 tff(287,plain,
% 0.60/0.78 ((~hskp1) | c3_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[286, 281])).
% 0.60/0.78 tff(288,plain,
% 0.60/0.78 (c3_1(a1001)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[287, 274])).
% 0.60/0.78 tff(289,plain,
% 0.60/0.78 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(290,plain,
% 0.60/0.78 ((hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001))) <=> (hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(291,plain,
% 0.60/0.78 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[290])).
% 0.60/0.78 tff(292,plain,
% 0.60/0.78 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[291, 289])).
% 0.60/0.78 tff(293,plain,
% 0.60/0.78 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(294,plain,
% 0.60/0.78 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.60/0.78 tff(295,plain,
% 0.60/0.78 (~c0_1(a1001)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[294, 81, 22, 288, 280, 32])).
% 0.60/0.78 tff(296,plain,
% 0.60/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(297,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[296])).
% 0.60/0.78 tff(298,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(299,plain,
% 0.60/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(300,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[299])).
% 0.60/0.78 tff(301,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.60/0.78 tff(302,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.60/0.78 tff(303,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.60/0.78 tff(304,plain,(
% 0.60/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(skolemize,[status(sab)],[303])).
% 0.60/0.78 tff(305,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.60/0.78 tff(306,plain,
% 0.60/0.78 (((~hskp1) | c2_1(a1001)) <=> ((~hskp1) | c2_1(a1001))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(307,axiom,((~hskp1) | c2_1(a1001)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.60/0.78 tff(308,plain,
% 0.60/0.78 ((~hskp1) | c2_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.60/0.78 tff(309,plain,
% 0.60/0.78 ((~hskp1) | c2_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[308, 306])).
% 0.60/0.78 tff(310,plain,
% 0.60/0.78 ((~hskp1) | c2_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[309, 306])).
% 0.60/0.78 tff(311,plain,
% 0.60/0.78 ((~hskp1) | c2_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.60/0.78 tff(312,plain,
% 0.60/0.78 ((~hskp1) | c2_1(a1001)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[311, 306])).
% 0.60/0.78 tff(313,plain,
% 0.60/0.78 (c2_1(a1001)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[312, 274])).
% 0.60/0.78 tff(314,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(315,plain,
% 0.60/0.78 (((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023)) <=> (c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(316,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[315])).
% 0.60/0.79 tff(317,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[316, 314])).
% 0.60/0.79 tff(318,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(319,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.60/0.79 tff(320,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[319, 81, 150, 313, 142, 163, 280, 305, 157, 295])).
% 0.60/0.79 tff(321,plain,((~hskp13) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(322,plain,
% 0.60/0.79 (~hskp13),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[321, 22])).
% 0.60/0.79 tff(323,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(324,plain,
% 0.60/0.79 ((hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037)) <=> (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(325,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[324])).
% 0.60/0.79 tff(326,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))),
% 0.60/0.79 inference(transitivity,[status(thm)],[325, 323])).
% 0.60/0.79 tff(327,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(328,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.60/0.79 tff(329,plain,
% 0.60/0.79 (c2_1(a1037)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[328, 81, 322, 47, 135, 129, 39, 98, 88])).
% 0.60/0.79 tff(330,assumption,(~hskp3), introduced(assumption)).
% 0.60/0.79 tff(331,plain,
% 0.60/0.79 (^[U: $i] : refl((hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(332,plain,
% 0.60/0.79 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[331])).
% 0.60/0.79 tff(333,plain,
% 0.60/0.79 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(334,plain,
% 0.60/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3) <=> ((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(335,plain,
% 0.60/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3) <=> ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[334])).
% 0.60/0.79 tff(336,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.60/0.79 tff(337,plain,
% 0.60/0.79 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.60/0.79 tff(338,plain,
% 0.60/0.79 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.60/0.79 tff(339,plain,(
% 0.60/0.79 ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[338])).
% 0.60/0.79 tff(340,plain,
% 0.60/0.79 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.60/0.79 tff(341,plain,
% 0.60/0.79 (hskp29),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[79, 322, 22])).
% 0.60/0.79 tff(342,plain,
% 0.60/0.79 (((~hskp29) | c3_1(a1040)) <=> ((~hskp29) | c3_1(a1040))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(343,axiom,((~hskp29) | c3_1(a1040)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.60/0.79 tff(344,plain,
% 0.60/0.79 ((~hskp29) | c3_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.60/0.79 tff(345,plain,
% 0.60/0.79 ((~hskp29) | c3_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[344, 342])).
% 0.60/0.79 tff(346,plain,
% 0.60/0.79 ((~hskp29) | c3_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[345, 342])).
% 0.60/0.79 tff(347,plain,
% 0.60/0.79 ((~hskp29) | c3_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[346, 342])).
% 0.60/0.79 tff(348,plain,
% 0.60/0.79 ((~hskp29) | c3_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[347, 342])).
% 0.60/0.79 tff(349,plain,
% 0.60/0.79 (c3_1(a1040)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[348, 341])).
% 0.60/0.79 tff(350,plain,
% 0.60/0.79 (((~hskp29) | c0_1(a1040)) <=> ((~hskp29) | c0_1(a1040))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(351,axiom,((~hskp29) | c0_1(a1040)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.60/0.79 tff(352,plain,
% 0.60/0.79 ((~hskp29) | c0_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.60/0.79 tff(353,plain,
% 0.60/0.79 ((~hskp29) | c0_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[352, 350])).
% 0.60/0.79 tff(354,plain,
% 0.60/0.79 ((~hskp29) | c0_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[353, 350])).
% 0.60/0.79 tff(355,plain,
% 0.60/0.79 ((~hskp29) | c0_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[354, 350])).
% 0.60/0.79 tff(356,plain,
% 0.60/0.79 ((~hskp29) | c0_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[355, 350])).
% 0.60/0.79 tff(357,plain,
% 0.60/0.79 (c0_1(a1040)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[356, 341])).
% 0.60/0.79 tff(358,plain,
% 0.60/0.79 (((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))) <=> ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(359,plain,
% 0.60/0.79 ((hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040))) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(360,plain,
% 0.60/0.79 (((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[359])).
% 0.60/0.79 tff(361,plain,
% 0.60/0.79 (((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[360, 358])).
% 0.60/0.79 tff(362,plain,
% 0.60/0.79 ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(363,plain,
% 0.60/0.79 ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.60/0.79 tff(364,plain,
% 0.60/0.79 (hskp3 | c2_1(a1040)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[363, 81, 22, 357, 349, 340])).
% 0.60/0.79 tff(365,plain,
% 0.60/0.79 (c2_1(a1040)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[364, 330])).
% 0.60/0.79 tff(366,plain,
% 0.60/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(367,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[366])).
% 0.60/0.79 tff(368,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(369,plain,
% 0.60/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(370,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[369])).
% 0.60/0.79 tff(371,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.60/0.79 tff(372,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.60/0.79 tff(373,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[372, 368])).
% 0.60/0.79 tff(374,plain,(
% 0.60/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[373])).
% 0.60/0.79 tff(375,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[374, 367])).
% 0.60/0.79 tff(376,assumption,(~c3_1(a1002)), introduced(assumption)).
% 0.60/0.79 tff(377,assumption,(c2_1(a1002)), introduced(assumption)).
% 0.60/0.79 tff(378,assumption,(c0_1(a1002)), introduced(assumption)).
% 0.60/0.79 tff(379,plain,
% 0.60/0.79 (((~hskp29) | c1_1(a1040)) <=> ((~hskp29) | c1_1(a1040))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(380,axiom,((~hskp29) | c1_1(a1040)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.60/0.79 tff(381,plain,
% 0.60/0.79 ((~hskp29) | c1_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.60/0.79 tff(382,plain,
% 0.60/0.79 ((~hskp29) | c1_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[381, 379])).
% 0.60/0.79 tff(383,plain,
% 0.60/0.79 ((~hskp29) | c1_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[382, 379])).
% 0.60/0.79 tff(384,plain,
% 0.60/0.79 ((~hskp29) | c1_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.60/0.79 tff(385,plain,
% 0.60/0.79 ((~hskp29) | c1_1(a1040)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[384, 379])).
% 0.60/0.79 tff(386,plain,
% 0.60/0.79 (c1_1(a1040)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[385, 341])).
% 0.60/0.79 tff(387,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(388,plain,
% 0.60/0.79 ((hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002))) <=> (hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(389,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[388])).
% 0.60/0.79 tff(390,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[389, 387])).
% 0.60/0.79 tff(391,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(392,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.60/0.79 tff(393,plain,
% 0.60/0.79 (hskp17 | (~c2_1(a1040))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[392, 81, 357, 386, 378, 377, 11, 376])).
% 0.60/0.79 tff(394,plain,
% 0.60/0.79 (hskp17),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[393, 365])).
% 0.60/0.79 tff(395,plain,
% 0.60/0.79 (((~hskp17) | (~c0_1(a1032))) <=> ((~hskp17) | (~c0_1(a1032)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(396,plain,
% 0.60/0.79 (((~c0_1(a1032)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1032)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(397,axiom,((~c0_1(a1032)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.60/0.79 tff(398,plain,
% 0.60/0.79 ((~hskp17) | (~c0_1(a1032))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.60/0.79 tff(399,plain,
% 0.60/0.79 ((~hskp17) | (~c0_1(a1032))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[398, 395])).
% 0.60/0.79 tff(400,plain,
% 0.60/0.79 (~c0_1(a1032)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[399, 394])).
% 0.60/0.79 tff(401,plain,
% 0.60/0.79 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(402,plain,
% 0.60/0.79 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[401])).
% 0.60/0.79 tff(403,plain,
% 0.60/0.79 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(404,plain,
% 0.60/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3) <=> ((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(405,plain,
% 0.60/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[404])).
% 0.60/0.79 tff(406,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.60/0.79 tff(407,plain,
% 0.60/0.79 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.60/0.79 tff(408,plain,
% 0.60/0.79 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.60/0.79 tff(409,plain,(
% 0.60/0.79 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[408])).
% 0.60/0.79 tff(410,plain,
% 0.60/0.79 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[409, 402])).
% 0.60/0.79 tff(411,plain,
% 0.60/0.79 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(412,plain,
% 0.60/0.79 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(413,plain,
% 0.60/0.79 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[412])).
% 0.60/0.79 tff(414,plain,
% 0.60/0.79 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[413, 411])).
% 0.60/0.79 tff(415,plain,
% 0.60/0.79 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(416,plain,
% 0.60/0.79 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.60/0.79 tff(417,plain,
% 0.60/0.79 (hskp24 | hskp3 | (~c2_1(a1040))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[416, 81, 357, 349, 410])).
% 0.60/0.79 tff(418,plain,
% 0.60/0.79 (hskp24),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[417, 365, 330])).
% 0.60/0.79 tff(419,plain,
% 0.60/0.79 (((~hskp24) | (~c0_1(a1045))) <=> ((~hskp24) | (~c0_1(a1045)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(420,plain,
% 0.60/0.80 (((~c0_1(a1045)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a1045)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(421,axiom,((~c0_1(a1045)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.60/0.80 tff(422,plain,
% 0.60/0.80 ((~hskp24) | (~c0_1(a1045))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.60/0.80 tff(423,plain,
% 0.60/0.80 ((~hskp24) | (~c0_1(a1045))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[422, 419])).
% 0.60/0.80 tff(424,plain,
% 0.60/0.80 (~c0_1(a1045)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[423, 418])).
% 0.60/0.80 tff(425,plain,
% 0.60/0.80 (((~hskp17) | c3_1(a1032)) <=> ((~hskp17) | c3_1(a1032))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(426,axiom,((~hskp17) | c3_1(a1032)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.60/0.80 tff(427,plain,
% 0.60/0.80 ((~hskp17) | c3_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.60/0.80 tff(428,plain,
% 0.60/0.80 ((~hskp17) | c3_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[427, 425])).
% 0.60/0.80 tff(429,plain,
% 0.60/0.80 ((~hskp17) | c3_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[428, 425])).
% 0.60/0.80 tff(430,plain,
% 0.60/0.80 ((~hskp17) | c3_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[429, 425])).
% 0.60/0.80 tff(431,plain,
% 0.60/0.80 ((~hskp17) | c3_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[430, 425])).
% 0.60/0.80 tff(432,plain,
% 0.60/0.80 (c3_1(a1032)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[431, 394])).
% 0.60/0.80 tff(433,plain,
% 0.60/0.80 (((~hskp17) | c2_1(a1032)) <=> ((~hskp17) | c2_1(a1032))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(434,axiom,((~hskp17) | c2_1(a1032)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.60/0.80 tff(435,plain,
% 0.60/0.80 ((~hskp17) | c2_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.60/0.80 tff(436,plain,
% 0.60/0.80 ((~hskp17) | c2_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[435, 433])).
% 0.60/0.80 tff(437,plain,
% 0.60/0.80 ((~hskp17) | c2_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[436, 433])).
% 0.60/0.80 tff(438,plain,
% 0.60/0.80 ((~hskp17) | c2_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[437, 433])).
% 0.60/0.80 tff(439,plain,
% 0.60/0.80 ((~hskp17) | c2_1(a1032)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[438, 433])).
% 0.60/0.80 tff(440,plain,
% 0.60/0.80 (c2_1(a1032)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[439, 394])).
% 0.60/0.80 tff(441,plain,
% 0.60/0.80 (((~hskp24) | c3_1(a1045)) <=> ((~hskp24) | c3_1(a1045))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(442,axiom,((~hskp24) | c3_1(a1045)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.60/0.80 tff(443,plain,
% 0.60/0.80 ((~hskp24) | c3_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.60/0.80 tff(444,plain,
% 0.60/0.80 ((~hskp24) | c3_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[443, 441])).
% 0.60/0.80 tff(445,plain,
% 0.60/0.80 ((~hskp24) | c3_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[444, 441])).
% 0.60/0.80 tff(446,plain,
% 0.60/0.80 ((~hskp24) | c3_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[445, 441])).
% 0.60/0.80 tff(447,plain,
% 0.60/0.80 ((~hskp24) | c3_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[446, 441])).
% 0.60/0.80 tff(448,plain,
% 0.60/0.80 (c3_1(a1045)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[447, 418])).
% 0.60/0.80 tff(449,plain,
% 0.60/0.80 (((~hskp24) | c1_1(a1045)) <=> ((~hskp24) | c1_1(a1045))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(450,axiom,((~hskp24) | c1_1(a1045)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.60/0.80 tff(451,plain,
% 0.60/0.80 ((~hskp24) | c1_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.60/0.80 tff(452,plain,
% 0.60/0.80 ((~hskp24) | c1_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[451, 449])).
% 0.60/0.80 tff(453,plain,
% 0.60/0.80 ((~hskp24) | c1_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[452, 449])).
% 0.60/0.80 tff(454,plain,
% 0.60/0.80 ((~hskp24) | c1_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[453, 449])).
% 0.60/0.80 tff(455,plain,
% 0.60/0.80 ((~hskp24) | c1_1(a1045)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[454, 449])).
% 0.60/0.80 tff(456,plain,
% 0.60/0.80 (c1_1(a1045)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[455, 418])).
% 0.60/0.80 tff(457,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(458,plain,
% 0.60/0.80 (((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045))) <=> (c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(459,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[458])).
% 0.60/0.80 tff(460,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[459, 457])).
% 0.60/0.80 tff(461,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(462,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.60/0.80 tff(463,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[462, 81, 386, 349, 456, 448, 440, 432, 424, 400, 375, 365])).
% 0.60/0.80 tff(464,plain,(hskp3 | (~c0_1(a1002)) | (~c2_1(a1002)) | c3_1(a1002) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(465,plain,
% 0.60/0.80 (hskp3),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[464, 47, 116, 88, 22])).
% 0.60/0.80 tff(466,plain,
% 0.60/0.80 (((~hskp3) | (~c2_1(a1003))) <=> ((~hskp3) | (~c2_1(a1003)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(467,plain,
% 0.60/0.80 (((~c2_1(a1003)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1003)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(468,axiom,((~c2_1(a1003)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.60/0.80 tff(469,plain,
% 0.60/0.80 ((~hskp3) | (~c2_1(a1003))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.60/0.80 tff(470,plain,
% 0.60/0.80 ((~hskp3) | (~c2_1(a1003))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[469, 466])).
% 0.60/0.80 tff(471,plain,
% 0.60/0.80 (~c2_1(a1003)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[470, 465])).
% 0.60/0.80 tff(472,plain,
% 0.60/0.80 (((~hskp3) | (~c0_1(a1003))) <=> ((~hskp3) | (~c0_1(a1003)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(473,plain,
% 0.60/0.80 (((~c0_1(a1003)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1003)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(474,axiom,((~c0_1(a1003)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.60/0.80 tff(475,plain,
% 0.60/0.80 ((~hskp3) | (~c0_1(a1003))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.60/0.80 tff(476,plain,
% 0.60/0.80 ((~hskp3) | (~c0_1(a1003))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[475, 472])).
% 0.60/0.80 tff(477,plain,
% 0.60/0.80 (~c0_1(a1003)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[476, 465])).
% 0.60/0.80 tff(478,plain,
% 0.60/0.80 (((~hskp3) | c1_1(a1003)) <=> ((~hskp3) | c1_1(a1003))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(479,axiom,((~hskp3) | c1_1(a1003)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.60/0.80 tff(480,plain,
% 0.60/0.80 ((~hskp3) | c1_1(a1003)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.60/0.80 tff(481,plain,
% 0.60/0.80 ((~hskp3) | c1_1(a1003)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[480, 478])).
% 0.60/0.80 tff(482,plain,
% 0.60/0.80 ((~hskp3) | c1_1(a1003)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[481, 478])).
% 0.60/0.80 tff(483,plain,
% 0.60/0.80 ((~hskp3) | c1_1(a1003)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[482, 478])).
% 0.60/0.80 tff(484,plain,
% 0.60/0.80 ((~hskp3) | c1_1(a1003)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[483, 478])).
% 0.60/0.80 tff(485,plain,
% 0.60/0.80 (c1_1(a1003)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[484, 465])).
% 0.60/0.80 tff(486,assumption,(hskp8), introduced(assumption)).
% 0.60/0.80 tff(487,plain,
% 0.60/0.80 (((~hskp8) | (~c1_1(a1010))) <=> ((~hskp8) | (~c1_1(a1010)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(488,plain,
% 0.60/0.80 (((~c1_1(a1010)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1010)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(489,axiom,((~c1_1(a1010)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.60/0.80 tff(490,plain,
% 0.60/0.80 ((~hskp8) | (~c1_1(a1010))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.60/0.80 tff(491,plain,
% 0.60/0.80 ((~hskp8) | (~c1_1(a1010))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[490, 487])).
% 0.60/0.80 tff(492,plain,
% 0.60/0.80 (~c1_1(a1010)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[491, 486])).
% 0.60/0.80 tff(493,plain,
% 0.60/0.80 (((~hskp8) | c3_1(a1010)) <=> ((~hskp8) | c3_1(a1010))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(494,axiom,((~hskp8) | c3_1(a1010)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.60/0.80 tff(495,plain,
% 0.60/0.80 ((~hskp8) | c3_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.60/0.80 tff(496,plain,
% 0.60/0.80 ((~hskp8) | c3_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[495, 493])).
% 0.60/0.80 tff(497,plain,
% 0.60/0.80 ((~hskp8) | c3_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[496, 493])).
% 0.60/0.80 tff(498,plain,
% 0.60/0.80 ((~hskp8) | c3_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[497, 493])).
% 0.60/0.80 tff(499,plain,
% 0.60/0.80 ((~hskp8) | c3_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[498, 493])).
% 0.60/0.80 tff(500,plain,
% 0.60/0.80 (c3_1(a1010)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[499, 486])).
% 0.60/0.80 tff(501,plain,
% 0.60/0.80 (((~hskp8) | c0_1(a1010)) <=> ((~hskp8) | c0_1(a1010))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(502,axiom,((~hskp8) | c0_1(a1010)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.60/0.80 tff(503,plain,
% 0.60/0.80 ((~hskp8) | c0_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.60/0.80 tff(504,plain,
% 0.60/0.80 ((~hskp8) | c0_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[503, 501])).
% 0.60/0.80 tff(505,plain,
% 0.60/0.80 ((~hskp8) | c0_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[504, 501])).
% 0.60/0.80 tff(506,plain,
% 0.60/0.80 ((~hskp8) | c0_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[505, 501])).
% 0.60/0.80 tff(507,plain,
% 0.60/0.80 ((~hskp8) | c0_1(a1010)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[506, 501])).
% 0.60/0.80 tff(508,plain,
% 0.60/0.80 (c0_1(a1010)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[507, 486])).
% 0.60/0.80 tff(509,plain,
% 0.60/0.80 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(510,plain,
% 0.60/0.80 ((hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010))) <=> (hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(511,plain,
% 0.60/0.80 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[510])).
% 0.60/0.80 tff(512,plain,
% 0.60/0.80 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[511, 509])).
% 0.60/0.80 tff(513,plain,
% 0.60/0.80 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(514,plain,
% 0.60/0.80 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.60/0.80 tff(515,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[514, 81, 22, 508, 500, 492, 32])).
% 0.60/0.80 tff(516,plain,((~hskp8) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(517,plain,
% 0.60/0.80 (~hskp8),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[516, 22])).
% 0.60/0.80 tff(518,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(519,plain,
% 0.60/0.80 ((hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(520,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[519])).
% 0.60/0.80 tff(521,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[520, 518])).
% 0.60/0.80 tff(522,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(523,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.60/0.80 tff(524,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[523, 81, 517, 485, 135, 129, 477, 471, 21, 329])).
% 0.60/0.80 tff(525,plain,((~hskp2) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(526,plain,
% 0.60/0.80 (~hskp2),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[525, 22])).
% 0.60/0.80 tff(527,plain,
% 0.60/0.80 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(528,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[527])).
% 0.60/0.80 tff(529,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(530,plain,
% 0.60/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(531,plain,
% 0.60/0.80 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[530])).
% 0.60/0.80 tff(532,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.60/0.80 tff(533,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.60/0.80 tff(534,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[533, 529])).
% 0.60/0.80 tff(535,plain,(
% 0.60/0.80 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(skolemize,[status(sab)],[534])).
% 0.60/0.80 tff(536,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[535, 528])).
% 0.60/0.80 tff(537,assumption,(hskp5), introduced(assumption)).
% 0.60/0.80 tff(538,plain,
% 0.60/0.80 (((~hskp5) | (~c3_1(a1005))) <=> ((~hskp5) | (~c3_1(a1005)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(539,plain,
% 0.60/0.80 (((~c3_1(a1005)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1005)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(540,axiom,((~c3_1(a1005)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.60/0.80 tff(541,plain,
% 0.60/0.80 ((~hskp5) | (~c3_1(a1005))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.60/0.80 tff(542,plain,
% 0.60/0.80 ((~hskp5) | (~c3_1(a1005))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[541, 538])).
% 0.60/0.80 tff(543,plain,
% 0.60/0.80 (~c3_1(a1005)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[542, 537])).
% 0.60/0.80 tff(544,plain,
% 0.60/0.80 (((~hskp5) | (~c2_1(a1005))) <=> ((~hskp5) | (~c2_1(a1005)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(545,plain,
% 0.60/0.80 (((~c2_1(a1005)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1005)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(546,axiom,((~c2_1(a1005)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.60/0.80 tff(547,plain,
% 0.60/0.80 ((~hskp5) | (~c2_1(a1005))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.60/0.80 tff(548,plain,
% 0.60/0.80 ((~hskp5) | (~c2_1(a1005))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[547, 544])).
% 0.60/0.80 tff(549,plain,
% 0.60/0.80 (~c2_1(a1005)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[548, 537])).
% 0.60/0.80 tff(550,plain,
% 0.60/0.80 (((~hskp5) | (~c1_1(a1005))) <=> ((~hskp5) | (~c1_1(a1005)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(551,plain,
% 0.60/0.80 (((~c1_1(a1005)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a1005)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(552,axiom,((~c1_1(a1005)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.60/0.80 tff(553,plain,
% 0.60/0.80 ((~hskp5) | (~c1_1(a1005))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.60/0.80 tff(554,plain,
% 0.60/0.80 ((~hskp5) | (~c1_1(a1005))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[553, 550])).
% 0.60/0.80 tff(555,plain,
% 0.60/0.80 (~c1_1(a1005)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[554, 537])).
% 0.60/0.80 tff(556,assumption,(~hskp2), introduced(assumption)).
% 0.60/0.80 tff(557,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(558,plain,
% 0.60/0.80 ((hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005)) <=> (hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(559,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[558])).
% 0.60/0.80 tff(560,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))),
% 0.60/0.81 inference(transitivity,[status(thm)],[559, 557])).
% 0.60/0.81 tff(561,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(562,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.60/0.81 tff(563,plain,
% 0.60/0.81 (c0_1(a1005)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[562, 81, 556, 555, 549, 543, 536])).
% 0.60/0.81 tff(564,assumption,(~hskp13), introduced(assumption)).
% 0.60/0.81 tff(565,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(566,plain,
% 0.60/0.81 ((hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005)) <=> (hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(567,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[566])).
% 0.60/0.81 tff(568,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[567, 565])).
% 0.60/0.81 tff(569,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(570,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.60/0.81 tff(571,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[570, 81, 564, 555, 549, 543, 98, 563])).
% 0.60/0.81 tff(572,plain,((~hskp5) | hskp13 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(573,plain,
% 0.60/0.81 (~hskp5),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[572, 322, 526])).
% 0.60/0.81 tff(574,plain,
% 0.60/0.81 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(575,plain,
% 0.60/0.81 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[574])).
% 0.60/0.81 tff(576,plain,
% 0.60/0.81 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(577,plain,
% 0.60/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(578,plain,
% 0.60/0.81 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[577])).
% 0.60/0.81 tff(579,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.60/0.81 tff(580,plain,
% 0.60/0.81 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.60/0.81 tff(581,plain,
% 0.60/0.81 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[580, 576])).
% 0.60/0.81 tff(582,plain,(
% 0.60/0.81 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[581])).
% 0.60/0.81 tff(583,plain,
% 0.60/0.81 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[582, 575])).
% 0.60/0.81 tff(584,assumption,(~hskp7), introduced(assumption)).
% 0.60/0.81 tff(585,plain,
% 0.60/0.81 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(586,plain,
% 0.60/0.81 ((hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(587,plain,
% 0.60/0.81 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[586])).
% 0.60/0.81 tff(588,plain,
% 0.60/0.81 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[587, 585])).
% 0.60/0.81 tff(589,plain,
% 0.60/0.81 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(590,plain,
% 0.60/0.81 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.60/0.81 tff(591,plain,
% 0.60/0.81 (hskp7 | (~c2_1(a1040))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[590, 81, 357, 386, 173])).
% 0.60/0.81 tff(592,plain,
% 0.60/0.81 (~c2_1(a1040)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[591, 584])).
% 0.60/0.81 tff(593,plain,
% 0.60/0.81 (hskp3),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[364, 592])).
% 0.60/0.81 tff(594,plain,
% 0.60/0.81 (~c2_1(a1003)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[470, 593])).
% 0.60/0.81 tff(595,plain,
% 0.60/0.81 (~c0_1(a1003)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[476, 593])).
% 0.60/0.81 tff(596,plain,
% 0.60/0.81 (c1_1(a1003)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[484, 593])).
% 0.60/0.81 tff(597,plain,
% 0.60/0.81 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(598,plain,
% 0.60/0.81 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003))) <=> (hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(599,plain,
% 0.60/0.81 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[598])).
% 0.60/0.81 tff(600,plain,
% 0.60/0.81 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[599, 597])).
% 0.60/0.81 tff(601,plain,
% 0.60/0.81 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(602,plain,
% 0.60/0.81 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.60/0.81 tff(603,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[602, 81, 517, 584, 596, 595, 594, 583])).
% 0.60/0.81 tff(604,plain,(hskp7 | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(605,plain,
% 0.60/0.81 (hskp7),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[604, 22])).
% 0.60/0.81 tff(606,plain,
% 0.60/0.81 (c2_1(a1008)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[224, 605])).
% 0.60/0.81 tff(607,plain,
% 0.60/0.81 (~c3_1(a1008)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[210, 605])).
% 0.60/0.81 tff(608,plain,
% 0.60/0.81 (~c1_1(a1008)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[216, 605])).
% 0.60/0.81 tff(609,plain,
% 0.60/0.81 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(610,plain,
% 0.60/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[609])).
% 0.60/0.81 tff(611,plain,
% 0.60/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(612,plain,
% 0.60/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(613,plain,
% 0.60/0.81 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[612])).
% 0.60/0.81 tff(614,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.60/0.81 tff(615,plain,
% 0.60/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.60/0.81 tff(616,plain,
% 0.60/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[615, 611])).
% 0.60/0.81 tff(617,plain,(
% 0.60/0.81 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[616])).
% 0.60/0.81 tff(618,plain,
% 0.60/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[617, 610])).
% 0.60/0.81 tff(619,assumption,(~hskp1), introduced(assumption)).
% 0.60/0.81 tff(620,assumption,(~c3_1(a1008)), introduced(assumption)).
% 0.60/0.81 tff(621,assumption,(c2_1(a1008)), introduced(assumption)).
% 0.60/0.81 tff(622,plain,
% 0.60/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(623,plain,
% 0.60/0.81 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008))) <=> (hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(624,plain,
% 0.60/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[623])).
% 0.60/0.81 tff(625,plain,
% 0.60/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.60/0.81 inference(transitivity,[status(thm)],[624, 622])).
% 0.60/0.81 tff(626,plain,
% 0.60/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(627,plain,
% 0.60/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.60/0.81 tff(628,plain,
% 0.60/0.81 (hskp2 | hskp1 | c0_1(a1008)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[627, 81, 621, 620, 618])).
% 0.60/0.81 tff(629,plain,
% 0.60/0.81 (c0_1(a1008)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[628, 556, 619])).
% 0.60/0.81 tff(630,assumption,(~c1_1(a1008)), introduced(assumption)).
% 0.60/0.81 tff(631,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(632,plain,
% 0.60/0.81 ((hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008))) <=> (hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(633,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[632])).
% 0.60/0.81 tff(634,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[633, 631])).
% 0.60/0.81 tff(635,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(636,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.60/0.81 tff(637,plain,
% 0.60/0.81 (hskp19 | (~c0_1(a1008))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[636, 81, 621, 630, 620, 108])).
% 0.60/0.81 tff(638,plain,
% 0.60/0.81 (hskp19),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[637, 629])).
% 0.60/0.81 tff(639,plain,
% 0.60/0.81 (~c3_1(a1037)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[128, 638])).
% 0.60/0.81 tff(640,plain,
% 0.60/0.81 (((~hskp19) | (~c0_1(a1037))) <=> ((~hskp19) | (~c0_1(a1037)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(641,plain,
% 0.60/0.81 (((~c0_1(a1037)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1037)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(642,axiom,((~c0_1(a1037)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.60/0.81 tff(643,plain,
% 0.60/0.81 ((~hskp19) | (~c0_1(a1037))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[642, 641])).
% 0.60/0.81 tff(644,plain,
% 0.60/0.81 ((~hskp19) | (~c0_1(a1037))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[643, 640])).
% 0.60/0.81 tff(645,plain,
% 0.60/0.81 (~c0_1(a1037)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[644, 638])).
% 0.60/0.81 tff(646,plain,
% 0.60/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(647,plain,
% 0.60/0.81 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037))) <=> (hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(648,plain,
% 0.60/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[647])).
% 0.60/0.81 tff(649,plain,
% 0.60/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[648, 646])).
% 0.60/0.81 tff(650,plain,
% 0.60/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(651,plain,
% 0.60/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.60/0.81 tff(652,plain,
% 0.60/0.81 (~c2_1(a1037)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[651, 81, 556, 619, 645, 639, 618])).
% 0.60/0.81 tff(653,plain,
% 0.60/0.81 (~c1_1(a1037)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[134, 638])).
% 0.60/0.81 tff(654,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(655,plain,
% 0.60/0.81 ((hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037)) <=> (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(656,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[655])).
% 0.60/0.81 tff(657,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))),
% 0.60/0.81 inference(transitivity,[status(thm)],[656, 654])).
% 0.60/0.81 tff(658,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(659,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.60/0.81 tff(660,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[659, 81, 564, 653, 639, 630, 620, 98, 629, 652])).
% 0.60/0.82 tff(661,plain,(hskp2 | hskp13 | c1_1(a1008) | c3_1(a1008) | hskp1 | (~c2_1(a1008))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(662,plain,
% 0.60/0.82 (hskp1),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[661, 526, 608, 607, 322, 606])).
% 0.60/0.82 tff(663,plain,
% 0.60/0.82 (~c1_1(a1001)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[279, 662])).
% 0.60/0.82 tff(664,plain,
% 0.60/0.82 (c3_1(a1001)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[287, 662])).
% 0.60/0.82 tff(665,plain,
% 0.60/0.82 (~c0_1(a1001)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[294, 81, 22, 664, 663, 32])).
% 0.60/0.82 tff(666,plain,
% 0.60/0.82 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(667,plain,
% 0.60/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[666])).
% 0.60/0.82 tff(668,plain,
% 0.60/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(669,plain,
% 0.60/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(670,plain,
% 0.60/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[669])).
% 0.60/0.82 tff(671,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.60/0.82 tff(672,plain,
% 0.60/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.60/0.82 tff(673,plain,
% 0.60/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[672, 668])).
% 0.60/0.82 tff(674,plain,(
% 0.60/0.82 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[673])).
% 0.60/0.82 tff(675,plain,
% 0.60/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[674, 667])).
% 0.60/0.82 tff(676,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(677,plain,
% 0.60/0.82 ((hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001))) <=> (hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(678,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[677])).
% 0.60/0.82 tff(679,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[678, 676])).
% 0.60/0.82 tff(680,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(681,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.60/0.82 tff(682,plain,
% 0.60/0.82 (hskp5 | (~c2_1(a1040))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[681, 81, 357, 386, 664, 663, 675, 665])).
% 0.60/0.82 tff(683,plain,
% 0.60/0.82 (~c2_1(a1040)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[682, 573])).
% 0.60/0.82 tff(684,plain,
% 0.60/0.82 (hskp3),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[364, 683])).
% 0.60/0.82 tff(685,plain,
% 0.60/0.82 (~c2_1(a1003)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[470, 684])).
% 0.60/0.82 tff(686,plain,
% 0.60/0.82 (~c0_1(a1003)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[476, 684])).
% 0.60/0.82 tff(687,plain,
% 0.60/0.82 (c1_1(a1003)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[484, 684])).
% 0.60/0.82 tff(688,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(689,plain,
% 0.60/0.82 ((hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(690,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[689])).
% 0.60/0.82 tff(691,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[690, 688])).
% 0.60/0.82 tff(692,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(693,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.60/0.82 tff(694,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[693, 81, 517, 606, 687, 608, 607, 686, 685, 21])).
% 0.60/0.82 tff(695,plain,(hskp23), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(696,plain,
% 0.60/0.82 (((~hskp23) | (~c3_1(a1044))) <=> ((~hskp23) | (~c3_1(a1044)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(697,plain,
% 0.60/0.82 (((~c3_1(a1044)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1044)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(698,axiom,((~c3_1(a1044)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.60/0.82 tff(699,plain,
% 0.60/0.82 ((~hskp23) | (~c3_1(a1044))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.60/0.82 tff(700,plain,
% 0.60/0.82 ((~hskp23) | (~c3_1(a1044))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[699, 696])).
% 0.60/0.82 tff(701,plain,
% 0.60/0.82 (~c3_1(a1044)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[700, 695])).
% 0.60/0.82 tff(702,plain,
% 0.60/0.82 (((~hskp23) | c1_1(a1044)) <=> ((~hskp23) | c1_1(a1044))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(703,axiom,((~hskp23) | c1_1(a1044)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.60/0.82 tff(704,plain,
% 0.60/0.82 ((~hskp23) | c1_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.60/0.82 tff(705,plain,
% 0.60/0.82 ((~hskp23) | c1_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[704, 702])).
% 0.60/0.82 tff(706,plain,
% 0.60/0.82 ((~hskp23) | c1_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[705, 702])).
% 0.60/0.82 tff(707,plain,
% 0.60/0.82 ((~hskp23) | c1_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[706, 702])).
% 0.60/0.82 tff(708,plain,
% 0.60/0.82 ((~hskp23) | c1_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[707, 702])).
% 0.60/0.82 tff(709,plain,
% 0.60/0.82 (c1_1(a1044)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[708, 695])).
% 0.60/0.82 tff(710,plain,
% 0.60/0.82 (((~hskp23) | c0_1(a1044)) <=> ((~hskp23) | c0_1(a1044))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(711,axiom,((~hskp23) | c0_1(a1044)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.60/0.82 tff(712,plain,
% 0.60/0.82 ((~hskp23) | c0_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.60/0.82 tff(713,plain,
% 0.60/0.82 ((~hskp23) | c0_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[712, 710])).
% 0.60/0.82 tff(714,plain,
% 0.60/0.82 ((~hskp23) | c0_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[713, 710])).
% 0.60/0.82 tff(715,plain,
% 0.60/0.82 ((~hskp23) | c0_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[714, 710])).
% 0.60/0.82 tff(716,plain,
% 0.60/0.82 ((~hskp23) | c0_1(a1044)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[715, 710])).
% 0.60/0.82 tff(717,plain,
% 0.60/0.82 (c0_1(a1044)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[716, 695])).
% 0.60/0.82 tff(718,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(719,plain,
% 0.60/0.82 ((hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044))) <=> (hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(720,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[719])).
% 0.60/0.82 tff(721,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[720, 718])).
% 0.60/0.82 tff(722,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(723,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.60/0.82 tff(724,plain,
% 0.60/0.82 (hskp17 | (~c2_1(a1044))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[723, 81, 717, 709, 701, 11])).
% 0.60/0.82 tff(725,plain,
% 0.60/0.82 (hskp17),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[724, 1])).
% 0.60/0.82 tff(726,plain,
% 0.60/0.82 (~c0_1(a1032)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[399, 725])).
% 0.60/0.82 tff(727,plain,
% 0.60/0.82 (c3_1(a1032)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[431, 725])).
% 0.60/0.82 tff(728,plain,
% 0.60/0.82 (c2_1(a1032)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[439, 725])).
% 0.60/0.82 tff(729,assumption,(c1_1(a1032)), introduced(assumption)).
% 0.60/0.82 tff(730,assumption,(~c0_1(a1032)), introduced(assumption)).
% 0.60/0.82 tff(731,assumption,(c3_1(a1032)), introduced(assumption)).
% 0.60/0.82 tff(732,assumption,(c2_1(a1032)), introduced(assumption)).
% 0.60/0.82 tff(733,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(734,plain,
% 0.60/0.82 (((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032))) <=> (c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(735,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[734])).
% 0.60/0.82 tff(736,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[735, 733])).
% 0.60/0.82 tff(737,plain,
% 0.60/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(738,plain,
% 0.60/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.60/0.82 tff(739,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[738, 81, 732, 731, 730, 375, 729])).
% 0.60/0.82 tff(740,plain,((~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(741,plain,
% 0.60/0.82 (~c1_1(a1032)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[740, 728, 727, 726])).
% 0.60/0.82 tff(742,plain,
% 0.60/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(743,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[742])).
% 0.60/0.82 tff(744,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(745,plain,
% 0.60/0.82 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(746,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[745])).
% 0.60/0.82 tff(747,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.60/0.83 tff(748,plain,
% 0.60/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.60/0.83 tff(749,plain,
% 0.60/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[748, 744])).
% 0.60/0.83 tff(750,plain,(
% 0.60/0.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[749])).
% 0.60/0.83 tff(751,plain,
% 0.60/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[750, 743])).
% 0.60/0.83 tff(752,plain,
% 0.60/0.83 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(753,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[752])).
% 0.60/0.83 tff(754,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(755,plain,
% 0.60/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.67/0.83 inference(bind,[status(th)],[])).
% 0.67/0.83 tff(756,plain,
% 0.67/0.83 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.67/0.83 inference(quant_intro,[status(thm)],[755])).
% 0.67/0.83 tff(757,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.67/0.83 tff(758,plain,
% 0.67/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.67/0.83 tff(759,plain,
% 0.67/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[758, 754])).
% 0.67/0.83 tff(760,plain,(
% 0.67/0.83 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.67/0.83 inference(skolemize,[status(sab)],[759])).
% 0.67/0.83 tff(761,plain,
% 0.67/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[760, 753])).
% 0.67/0.83 tff(762,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[661, 211, 217, 556, 619, 564, 225])).
% 0.67/0.83 tff(763,plain,((~hskp7) | hskp2 | hskp1 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.67/0.83 tff(764,plain,
% 0.67/0.83 (~hskp7),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[763, 619, 556, 564])).
% 0.67/0.83 tff(765,assumption,(hskp4), introduced(assumption)).
% 0.67/0.83 tff(766,plain,
% 0.67/0.83 (((~hskp4) | c2_1(a1004)) <=> ((~hskp4) | c2_1(a1004))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(767,axiom,((~hskp4) | c2_1(a1004)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.67/0.83 tff(768,plain,
% 0.67/0.83 ((~hskp4) | c2_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.67/0.83 tff(769,plain,
% 0.67/0.83 ((~hskp4) | c2_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[768, 766])).
% 0.67/0.83 tff(770,plain,
% 0.67/0.83 ((~hskp4) | c2_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[769, 766])).
% 0.67/0.83 tff(771,plain,
% 0.67/0.83 ((~hskp4) | c2_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[770, 766])).
% 0.67/0.83 tff(772,plain,
% 0.67/0.83 ((~hskp4) | c2_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[771, 766])).
% 0.67/0.83 tff(773,plain,
% 0.67/0.83 (c2_1(a1004)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[772, 765])).
% 0.67/0.83 tff(774,plain,
% 0.67/0.83 (((~hskp4) | c1_1(a1004)) <=> ((~hskp4) | c1_1(a1004))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(775,axiom,((~hskp4) | c1_1(a1004)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.67/0.83 tff(776,plain,
% 0.67/0.83 ((~hskp4) | c1_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.67/0.83 tff(777,plain,
% 0.67/0.83 ((~hskp4) | c1_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[776, 774])).
% 0.67/0.83 tff(778,plain,
% 0.67/0.83 ((~hskp4) | c1_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[777, 774])).
% 0.67/0.83 tff(779,plain,
% 0.67/0.83 ((~hskp4) | c1_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[778, 774])).
% 0.67/0.83 tff(780,plain,
% 0.67/0.83 ((~hskp4) | c1_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[779, 774])).
% 0.67/0.83 tff(781,plain,
% 0.67/0.83 (c1_1(a1004)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[780, 765])).
% 0.67/0.83 tff(782,plain,
% 0.67/0.83 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(783,plain,
% 0.67/0.83 ((hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(784,plain,
% 0.67/0.83 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004))))),
% 0.67/0.83 inference(monotonicity,[status(thm)],[783])).
% 0.67/0.83 tff(785,plain,
% 0.67/0.83 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))),
% 0.67/0.83 inference(transitivity,[status(thm)],[784, 782])).
% 0.67/0.83 tff(786,plain,
% 0.67/0.83 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004)))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(787,plain,
% 0.67/0.83 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.67/0.83 tff(788,plain,
% 0.67/0.83 (~c0_1(a1004)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[787, 81, 584, 781, 773, 173])).
% 0.67/0.83 tff(789,plain,
% 0.67/0.83 (((~hskp4) | (~c3_1(a1004))) <=> ((~hskp4) | (~c3_1(a1004)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(790,plain,
% 0.67/0.83 (((~c3_1(a1004)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1004)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(791,axiom,((~c3_1(a1004)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.67/0.83 tff(792,plain,
% 0.67/0.83 ((~hskp4) | (~c3_1(a1004))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.67/0.83 tff(793,plain,
% 0.67/0.83 ((~hskp4) | (~c3_1(a1004))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[792, 789])).
% 0.67/0.83 tff(794,plain,
% 0.67/0.83 (~c3_1(a1004)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[793, 765])).
% 0.67/0.83 tff(795,plain,
% 0.67/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(796,plain,
% 0.67/0.83 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004))) <=> (hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(797,plain,
% 0.67/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004)))),
% 0.67/0.83 inference(monotonicity,[status(thm)],[796])).
% 0.67/0.83 tff(798,plain,
% 0.67/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))),
% 0.67/0.83 inference(transitivity,[status(thm)],[797, 795])).
% 0.67/0.83 tff(799,plain,
% 0.67/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004)))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(800,plain,
% 0.67/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.67/0.83 tff(801,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[800, 81, 556, 619, 773, 794, 618, 788])).
% 0.67/0.83 tff(802,plain,((~hskp4) | hskp2 | hskp1 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.67/0.83 tff(803,plain,
% 0.67/0.83 (~hskp4),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[802, 619, 556, 764])).
% 0.67/0.83 tff(804,plain,
% 0.67/0.83 ((hskp21 | hskp7 | hskp4) <=> (hskp21 | hskp7 | hskp4)),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(805,plain,
% 0.67/0.83 (((hskp21 | hskp4) | hskp7) <=> (hskp21 | hskp7 | hskp4)),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(806,plain,
% 0.67/0.83 ((hskp4 | hskp21) <=> (hskp21 | hskp4)),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(807,plain,
% 0.67/0.83 (((hskp4 | hskp21) | hskp7) <=> ((hskp21 | hskp4) | hskp7)),
% 0.67/0.83 inference(monotonicity,[status(thm)],[806])).
% 0.67/0.83 tff(808,plain,
% 0.67/0.83 (((hskp4 | hskp21) | hskp7) <=> (hskp21 | hskp7 | hskp4)),
% 0.67/0.83 inference(transitivity,[status(thm)],[807, 805])).
% 0.67/0.83 tff(809,axiom,((hskp4 | hskp21) | hskp7), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.67/0.83 tff(810,plain,
% 0.67/0.83 (hskp21 | hskp7 | hskp4),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.67/0.83 tff(811,plain,
% 0.67/0.83 (hskp21 | hskp7 | hskp4),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[810, 804])).
% 0.67/0.83 tff(812,plain,
% 0.67/0.83 (hskp21 | hskp7 | hskp4),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[811, 804])).
% 0.67/0.83 tff(813,plain,
% 0.67/0.83 (hskp21 | hskp7 | hskp4),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[812, 804])).
% 0.67/0.83 tff(814,plain,
% 0.67/0.83 (hskp21 | hskp7 | hskp4),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[813, 804])).
% 0.67/0.83 tff(815,plain,
% 0.67/0.83 (hskp21),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[814, 803, 764])).
% 0.67/0.83 tff(816,plain,
% 0.67/0.83 (((~hskp21) | (~c3_1(a1041))) <=> ((~hskp21) | (~c3_1(a1041)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(817,plain,
% 0.67/0.83 (((~c3_1(a1041)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1041)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(818,axiom,((~c3_1(a1041)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.67/0.83 tff(819,plain,
% 0.67/0.83 ((~hskp21) | (~c3_1(a1041))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.67/0.83 tff(820,plain,
% 0.67/0.83 ((~hskp21) | (~c3_1(a1041))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[819, 816])).
% 0.67/0.83 tff(821,plain,
% 0.67/0.83 (~c3_1(a1041)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[820, 815])).
% 0.67/0.83 tff(822,plain,
% 0.67/0.83 (((~hskp21) | (~c0_1(a1041))) <=> ((~hskp21) | (~c0_1(a1041)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(823,plain,
% 0.67/0.83 (((~c0_1(a1041)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1041)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(824,axiom,((~c0_1(a1041)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.67/0.83 tff(825,plain,
% 0.67/0.83 ((~hskp21) | (~c0_1(a1041))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.67/0.83 tff(826,plain,
% 0.67/0.83 ((~hskp21) | (~c0_1(a1041))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[825, 822])).
% 0.67/0.83 tff(827,plain,
% 0.67/0.83 (~c0_1(a1041)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[826, 815])).
% 0.67/0.83 tff(828,plain,
% 0.67/0.83 (((~hskp21) | c2_1(a1041)) <=> ((~hskp21) | c2_1(a1041))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(829,axiom,((~hskp21) | c2_1(a1041)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.67/0.83 tff(830,plain,
% 0.67/0.83 ((~hskp21) | c2_1(a1041)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.67/0.83 tff(831,plain,
% 0.67/0.83 ((~hskp21) | c2_1(a1041)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[830, 828])).
% 0.67/0.83 tff(832,plain,
% 0.67/0.83 ((~hskp21) | c2_1(a1041)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[831, 828])).
% 0.67/0.83 tff(833,plain,
% 0.67/0.83 ((~hskp21) | c2_1(a1041)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.67/0.83 tff(834,plain,
% 0.67/0.83 ((~hskp21) | c2_1(a1041)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[833, 828])).
% 0.67/0.83 tff(835,plain,
% 0.67/0.83 (c2_1(a1041)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[834, 815])).
% 0.67/0.83 tff(836,plain,
% 0.67/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(837,plain,
% 0.67/0.83 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041))) <=> (hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(838,plain,
% 0.67/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041))))),
% 0.67/0.83 inference(monotonicity,[status(thm)],[837])).
% 0.67/0.83 tff(839,plain,
% 0.67/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))),
% 0.67/0.83 inference(transitivity,[status(thm)],[838, 836])).
% 0.67/0.83 tff(840,plain,
% 0.67/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041)))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(841,plain,
% 0.67/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.67/0.83 tff(842,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[841, 81, 556, 619, 835, 827, 821, 618])).
% 0.67/0.83 tff(843,plain,(hskp1 | hskp2 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.67/0.83 tff(844,plain,
% 0.67/0.83 (hskp1),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[843, 564, 556])).
% 0.67/0.83 tff(845,plain,
% 0.67/0.83 (~c1_1(a1001)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[279, 844])).
% 0.67/0.83 tff(846,plain,
% 0.67/0.83 (~hskp5),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[572, 564, 556])).
% 0.67/0.83 tff(847,plain,
% 0.67/0.83 (c3_1(a1001)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[287, 844])).
% 0.67/0.83 tff(848,plain,
% 0.67/0.83 (c2_1(a1001)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[312, 844])).
% 0.67/0.83 tff(849,assumption,(~c1_1(a1001)), introduced(assumption)).
% 0.67/0.83 tff(850,assumption,(c3_1(a1001)), introduced(assumption)).
% 0.67/0.83 tff(851,assumption,(~hskp5), introduced(assumption)).
% 0.67/0.83 tff(852,plain,
% 0.67/0.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(853,plain,
% 0.67/0.83 ((hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001))) <=> (hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(854,plain,
% 0.67/0.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.67/0.83 inference(monotonicity,[status(thm)],[853])).
% 0.67/0.83 tff(855,plain,
% 0.67/0.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.83 inference(transitivity,[status(thm)],[854, 852])).
% 0.67/0.83 tff(856,plain,
% 0.67/0.83 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(857,plain,
% 0.67/0.83 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.67/0.83 tff(858,plain,
% 0.67/0.83 (c0_1(a1001) | (~c2_1(a1044))),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[857, 81, 851, 717, 709, 850, 849, 675])).
% 0.67/0.83 tff(859,plain,
% 0.67/0.83 (c0_1(a1001)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[858, 1])).
% 0.67/0.83 tff(860,assumption,(c2_1(a1001)), introduced(assumption)).
% 0.67/0.83 tff(861,plain,
% 0.67/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(862,plain,
% 0.67/0.83 ((hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001))) <=> (hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(863,plain,
% 0.67/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))))),
% 0.67/0.83 inference(monotonicity,[status(thm)],[862])).
% 0.67/0.83 tff(864,plain,
% 0.67/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.83 inference(transitivity,[status(thm)],[863, 861])).
% 0.67/0.83 tff(865,plain,
% 0.67/0.83 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(866,plain,
% 0.67/0.83 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.67/0.83 tff(867,plain,
% 0.67/0.83 (hskp6 | (~c0_1(a1001))),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[866, 81, 860, 850, 849, 761])).
% 0.67/0.83 tff(868,plain,
% 0.67/0.83 (hskp6),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[867, 859])).
% 0.67/0.83 tff(869,plain,
% 0.67/0.83 (((~hskp6) | (~c2_1(a1006))) <=> ((~hskp6) | (~c2_1(a1006)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(870,plain,
% 0.67/0.83 (((~c2_1(a1006)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1006)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(871,axiom,((~c2_1(a1006)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.67/0.83 tff(872,plain,
% 0.67/0.83 ((~hskp6) | (~c2_1(a1006))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.67/0.83 tff(873,plain,
% 0.67/0.83 ((~hskp6) | (~c2_1(a1006))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[872, 869])).
% 0.67/0.83 tff(874,plain,
% 0.67/0.83 (~c2_1(a1006)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[873, 868])).
% 0.67/0.83 tff(875,plain,
% 0.67/0.83 (((~hskp6) | c3_1(a1006)) <=> ((~hskp6) | c3_1(a1006))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(876,axiom,((~hskp6) | c3_1(a1006)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.67/0.83 tff(877,plain,
% 0.67/0.83 ((~hskp6) | c3_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.67/0.83 tff(878,plain,
% 0.67/0.83 ((~hskp6) | c3_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[877, 875])).
% 0.67/0.83 tff(879,plain,
% 0.67/0.83 ((~hskp6) | c3_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[878, 875])).
% 0.67/0.83 tff(880,plain,
% 0.67/0.83 ((~hskp6) | c3_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[879, 875])).
% 0.67/0.83 tff(881,plain,
% 0.67/0.83 ((~hskp6) | c3_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[880, 875])).
% 0.67/0.83 tff(882,plain,
% 0.67/0.83 (c3_1(a1006)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[881, 868])).
% 0.67/0.83 tff(883,plain,
% 0.67/0.83 (((~hskp6) | c0_1(a1006)) <=> ((~hskp6) | c0_1(a1006))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(884,axiom,((~hskp6) | c0_1(a1006)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.67/0.83 tff(885,plain,
% 0.67/0.83 ((~hskp6) | c0_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.67/0.83 tff(886,plain,
% 0.67/0.83 ((~hskp6) | c0_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[885, 883])).
% 0.67/0.83 tff(887,plain,
% 0.67/0.83 ((~hskp6) | c0_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[886, 883])).
% 0.67/0.83 tff(888,plain,
% 0.67/0.83 ((~hskp6) | c0_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[887, 883])).
% 0.67/0.83 tff(889,plain,
% 0.67/0.83 ((~hskp6) | c0_1(a1006)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[888, 883])).
% 0.67/0.83 tff(890,plain,
% 0.67/0.83 (c0_1(a1006)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[889, 868])).
% 0.67/0.83 tff(891,plain,
% 0.67/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(892,plain,
% 0.67/0.83 (((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(893,plain,
% 0.67/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[892])).
% 0.67/0.84 tff(894,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[893, 891])).
% 0.67/0.84 tff(895,plain,
% 0.67/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(896,plain,
% 0.67/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.67/0.84 tff(897,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[896, 81, 709, 890, 882, 860, 850, 701, 874, 849, 751, 1])).
% 0.67/0.84 tff(898,plain,((~c2_1(a1044)) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(899,plain,
% 0.67/0.84 (~c2_1(a1044)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[898, 848, 847, 845, 846])).
% 0.67/0.84 tff(900,plain,
% 0.67/0.84 (^[U: $i] : refl((hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(901,plain,
% 0.67/0.84 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[900])).
% 0.67/0.84 tff(902,plain,
% 0.67/0.84 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(903,plain,
% 0.67/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(904,plain,
% 0.67/0.84 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[903])).
% 0.67/0.84 tff(905,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.67/0.84 tff(906,plain,
% 0.67/0.84 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.67/0.84 tff(907,plain,
% 0.67/0.84 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[906, 902])).
% 0.67/0.84 tff(908,plain,(
% 0.67/0.84 ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(skolemize,[status(sab)],[907])).
% 0.67/0.84 tff(909,plain,
% 0.67/0.84 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[908, 901])).
% 0.67/0.84 tff(910,plain,
% 0.67/0.84 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(911,plain,
% 0.67/0.84 ((hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044))) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(912,plain,
% 0.67/0.84 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[911])).
% 0.67/0.84 tff(913,plain,
% 0.67/0.84 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[912, 910])).
% 0.67/0.84 tff(914,plain,
% 0.67/0.84 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(915,plain,
% 0.67/0.84 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.67/0.84 tff(916,plain,
% 0.67/0.84 (hskp13 | hskp6 | c2_1(a1044)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[915, 81, 717, 709, 909])).
% 0.67/0.84 tff(917,plain,
% 0.67/0.84 (hskp6),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[916, 899, 564])).
% 0.67/0.84 tff(918,plain,
% 0.67/0.84 (~c2_1(a1006)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[873, 917])).
% 0.67/0.84 tff(919,plain,
% 0.67/0.84 (c3_1(a1006)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[881, 917])).
% 0.67/0.84 tff(920,plain,
% 0.67/0.84 (c0_1(a1006)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[889, 917])).
% 0.67/0.84 tff(921,plain,
% 0.67/0.84 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(922,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[921])).
% 0.67/0.84 tff(923,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(924,plain,
% 0.67/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(925,plain,
% 0.67/0.84 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[924])).
% 0.67/0.84 tff(926,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.67/0.84 tff(927,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.67/0.84 tff(928,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[927, 923])).
% 0.67/0.84 tff(929,plain,(
% 0.67/0.84 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(skolemize,[status(sab)],[928])).
% 0.67/0.84 tff(930,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[929, 922])).
% 0.67/0.84 tff(931,plain,
% 0.67/0.84 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(932,plain,
% 0.67/0.84 ((hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(933,plain,
% 0.67/0.84 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[932])).
% 0.67/0.84 tff(934,plain,
% 0.67/0.84 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[933, 931])).
% 0.67/0.84 tff(935,plain,
% 0.67/0.84 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(936,plain,
% 0.67/0.84 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.67/0.84 tff(937,plain,
% 0.67/0.84 (hskp7 | (~c2_1(a1044))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[936, 81, 717, 709, 173])).
% 0.67/0.84 tff(938,plain,
% 0.67/0.84 (~c2_1(a1044)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[937, 584])).
% 0.67/0.84 tff(939,assumption,(~hskp8), introduced(assumption)).
% 0.67/0.84 tff(940,plain,
% 0.67/0.84 (^[U: $i] : refl((hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(941,plain,
% 0.67/0.84 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[940])).
% 0.67/0.84 tff(942,plain,
% 0.67/0.84 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(943,plain,
% 0.67/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(944,plain,
% 0.67/0.84 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26) <=> ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[943])).
% 0.67/0.84 tff(945,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.67/0.84 tff(946,plain,
% 0.67/0.84 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.67/0.84 tff(947,plain,
% 0.67/0.84 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[946, 942])).
% 0.67/0.84 tff(948,plain,(
% 0.67/0.84 ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(skolemize,[status(sab)],[947])).
% 0.67/0.84 tff(949,plain,
% 0.67/0.84 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[948, 941])).
% 0.67/0.84 tff(950,plain,
% 0.67/0.84 (((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(951,plain,
% 0.67/0.84 ((hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044))) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(952,plain,
% 0.67/0.84 (((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[951])).
% 0.67/0.84 tff(953,plain,
% 0.67/0.84 (((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[952, 950])).
% 0.67/0.84 tff(954,plain,
% 0.67/0.84 ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(955,plain,
% 0.67/0.84 ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.67/0.84 tff(956,plain,
% 0.67/0.84 (hskp26 | hskp8 | c2_1(a1044)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[955, 81, 717, 709, 949])).
% 0.67/0.84 tff(957,plain,
% 0.67/0.84 (hskp26),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[956, 938, 939])).
% 0.67/0.84 tff(958,plain,
% 0.67/0.84 (((~hskp26) | (~c2_1(a1052))) <=> ((~hskp26) | (~c2_1(a1052)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(959,plain,
% 0.67/0.84 (((~c2_1(a1052)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1052)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(960,axiom,((~c2_1(a1052)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.67/0.84 tff(961,plain,
% 0.67/0.84 ((~hskp26) | (~c2_1(a1052))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.67/0.84 tff(962,plain,
% 0.67/0.84 ((~hskp26) | (~c2_1(a1052))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[961, 958])).
% 0.67/0.84 tff(963,plain,
% 0.67/0.84 (~c2_1(a1052)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[962, 957])).
% 0.67/0.84 tff(964,plain,
% 0.67/0.84 (((~hskp26) | (~c0_1(a1052))) <=> ((~hskp26) | (~c0_1(a1052)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(965,plain,
% 0.67/0.84 (((~c0_1(a1052)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1052)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(966,axiom,((~c0_1(a1052)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.67/0.84 tff(967,plain,
% 0.67/0.84 ((~hskp26) | (~c0_1(a1052))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.67/0.84 tff(968,plain,
% 0.67/0.84 ((~hskp26) | (~c0_1(a1052))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[967, 964])).
% 0.67/0.84 tff(969,plain,
% 0.67/0.84 (~c0_1(a1052)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[968, 957])).
% 0.67/0.84 tff(970,plain,
% 0.67/0.84 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(971,plain,
% 0.67/0.84 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052))) <=> (hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(972,plain,
% 0.67/0.84 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[971])).
% 0.67/0.84 tff(973,plain,
% 0.67/0.84 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[972, 970])).
% 0.67/0.84 tff(974,plain,
% 0.67/0.84 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(975,plain,
% 0.67/0.84 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.67/0.84 tff(976,plain,
% 0.67/0.84 (~c1_1(a1052)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[975, 81, 939, 584, 969, 963, 583])).
% 0.67/0.84 tff(977,plain,
% 0.67/0.84 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(978,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[977])).
% 0.67/0.84 tff(979,plain,
% 0.67/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(980,plain,
% 0.67/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(981,plain,
% 0.67/0.85 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[980])).
% 0.67/0.85 tff(982,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.67/0.85 tff(983,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[982, 981])).
% 0.67/0.85 tff(984,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[983, 979])).
% 0.67/0.85 tff(985,plain,(
% 0.67/0.85 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.85 inference(skolemize,[status(sab)],[984])).
% 0.67/0.85 tff(986,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[985, 978])).
% 0.67/0.85 tff(987,plain,
% 0.67/0.85 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(988,plain,
% 0.67/0.85 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[987])).
% 0.67/0.85 tff(989,plain,
% 0.67/0.85 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(990,plain,
% 0.67/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(991,plain,
% 0.67/0.85 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[990])).
% 0.67/0.85 tff(992,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.67/0.85 tff(993,plain,
% 0.67/0.85 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.67/0.85 tff(994,plain,
% 0.67/0.85 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[993, 989])).
% 0.67/0.85 tff(995,plain,(
% 0.67/0.85 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(skolemize,[status(sab)],[994])).
% 0.67/0.85 tff(996,plain,
% 0.67/0.85 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[995, 988])).
% 0.67/0.85 tff(997,plain,
% 0.67/0.85 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(998,plain,
% 0.67/0.85 ((hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044))) <=> (hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(999,plain,
% 0.67/0.85 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[998])).
% 0.67/0.85 tff(1000,plain,
% 0.67/0.85 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[999, 997])).
% 0.67/0.85 tff(1001,plain,
% 0.67/0.85 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1002,plain,
% 0.67/0.85 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.67/0.85 tff(1003,plain,
% 0.67/0.85 (hskp25 | hskp3 | c2_1(a1044)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1002, 81, 717, 701, 996])).
% 0.67/0.85 tff(1004,plain,
% 0.67/0.85 (hskp25),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1003, 938, 330])).
% 0.67/0.85 tff(1005,plain,
% 0.67/0.85 (((~hskp25) | (~c0_1(a1048))) <=> ((~hskp25) | (~c0_1(a1048)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1006,plain,
% 0.67/0.85 (((~c0_1(a1048)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1048)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1007,axiom,((~c0_1(a1048)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.67/0.85 tff(1008,plain,
% 0.67/0.85 ((~hskp25) | (~c0_1(a1048))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.67/0.85 tff(1009,plain,
% 0.67/0.85 ((~hskp25) | (~c0_1(a1048))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1008, 1005])).
% 0.67/0.85 tff(1010,plain,
% 0.67/0.85 (~c0_1(a1048)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1009, 1004])).
% 0.67/0.85 tff(1011,plain,
% 0.67/0.85 (((~hskp25) | c1_1(a1048)) <=> ((~hskp25) | c1_1(a1048))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1012,axiom,((~hskp25) | c1_1(a1048)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.67/0.85 tff(1013,plain,
% 0.67/0.85 ((~hskp25) | c1_1(a1048)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.67/0.85 tff(1014,plain,
% 0.67/0.85 ((~hskp25) | c1_1(a1048)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1013, 1011])).
% 0.67/0.85 tff(1015,plain,
% 0.67/0.85 ((~hskp25) | c1_1(a1048)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1014, 1011])).
% 0.67/0.85 tff(1016,plain,
% 0.67/0.85 ((~hskp25) | c1_1(a1048)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1015, 1011])).
% 0.67/0.85 tff(1017,plain,
% 0.67/0.85 ((~hskp25) | c1_1(a1048)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1016, 1011])).
% 0.67/0.85 tff(1018,plain,
% 0.67/0.85 (c1_1(a1048)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1017, 1004])).
% 0.67/0.85 tff(1019,plain,
% 0.67/0.85 (((~hskp26) | c3_1(a1052)) <=> ((~hskp26) | c3_1(a1052))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1020,axiom,((~hskp26) | c3_1(a1052)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.67/0.85 tff(1021,plain,
% 0.67/0.85 ((~hskp26) | c3_1(a1052)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.67/0.85 tff(1022,plain,
% 0.67/0.85 ((~hskp26) | c3_1(a1052)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1021, 1019])).
% 0.67/0.85 tff(1023,plain,
% 0.67/0.85 ((~hskp26) | c3_1(a1052)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1022, 1019])).
% 0.67/0.85 tff(1024,plain,
% 0.67/0.85 ((~hskp26) | c3_1(a1052)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 0.67/0.85 tff(1025,plain,
% 0.67/0.85 ((~hskp26) | c3_1(a1052)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1024, 1019])).
% 0.67/0.85 tff(1026,plain,
% 0.67/0.85 (c3_1(a1052)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1025, 957])).
% 0.67/0.85 tff(1027,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1028,plain,
% 0.67/0.85 ((hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048))) <=> (hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1029,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1028])).
% 0.67/0.85 tff(1030,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.67/0.85 tff(1031,plain,
% 0.67/0.85 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1032,plain,
% 0.67/0.85 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.67/0.85 tff(1033,plain,
% 0.67/0.85 (~c2_1(a1048)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1032, 81, 564, 1026, 1018, 963, 1010, 986, 976])).
% 0.67/0.85 tff(1034,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1035,plain,
% 0.67/0.85 ((hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048))) <=> (hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1036,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1035])).
% 0.67/0.85 tff(1037,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.67/0.85 tff(1038,plain,
% 0.67/0.85 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1039,plain,
% 0.67/0.85 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.67/0.85 tff(1040,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1039, 81, 584, 1026, 1018, 963, 1010, 930, 1033, 976])).
% 0.67/0.85 tff(1041,plain,(hskp7 | hskp13 | hskp8 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(1042,plain,
% 0.67/0.85 (hskp3),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1041, 939, 584, 564])).
% 0.67/0.85 tff(1043,plain,
% 0.67/0.85 (~c2_1(a1003)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[470, 1042])).
% 0.67/0.85 tff(1044,plain,
% 0.67/0.85 (~c0_1(a1003)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[476, 1042])).
% 0.67/0.85 tff(1045,plain,
% 0.67/0.85 (c1_1(a1003)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[484, 1042])).
% 0.67/0.85 tff(1046,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[602, 81, 939, 584, 1045, 1044, 1043, 583])).
% 0.67/0.85 tff(1047,plain,(hskp8 | hskp7 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(1048,plain,
% 0.67/0.85 (hskp8),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1047, 584, 564])).
% 0.67/0.85 tff(1049,plain,
% 0.67/0.85 (~c1_1(a1010)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[491, 1048])).
% 0.67/0.85 tff(1050,plain,
% 0.67/0.85 (c3_1(a1010)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[499, 1048])).
% 0.67/0.85 tff(1051,plain,
% 0.67/0.85 (c0_1(a1010)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[507, 1048])).
% 0.67/0.85 tff(1052,plain,
% 0.67/0.85 (hskp6),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[916, 938, 564])).
% 0.67/0.85 tff(1053,plain,
% 0.67/0.85 (~c2_1(a1006)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[873, 1052])).
% 0.67/0.85 tff(1054,plain,
% 0.67/0.85 (c3_1(a1006)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[881, 1052])).
% 0.67/0.85 tff(1055,plain,
% 0.67/0.85 (c0_1(a1006)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[889, 1052])).
% 0.67/0.85 tff(1056,assumption,(~c2_1(a1006)), introduced(assumption)).
% 0.67/0.85 tff(1057,assumption,(~c2_1(a1044)), introduced(assumption)).
% 0.67/0.85 tff(1058,plain,
% 0.67/0.85 (hskp25),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1003, 330, 1057])).
% 0.67/0.85 tff(1059,plain,
% 0.67/0.85 (((~hskp25) | (~c3_1(a1048))) <=> ((~hskp25) | (~c3_1(a1048)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1060,plain,
% 0.67/0.85 (((~c3_1(a1048)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a1048)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1061,axiom,((~c3_1(a1048)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.67/0.85 tff(1062,plain,
% 0.67/0.85 ((~hskp25) | (~c3_1(a1048))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 0.67/0.85 tff(1063,plain,
% 0.67/0.85 ((~hskp25) | (~c3_1(a1048))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1062, 1059])).
% 0.67/0.85 tff(1064,plain,
% 0.67/0.85 (~c3_1(a1048)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1063, 1058])).
% 0.67/0.85 tff(1065,assumption,(c3_1(a1006)), introduced(assumption)).
% 0.67/0.85 tff(1066,assumption,(c0_1(a1006)), introduced(assumption)).
% 0.67/0.85 tff(1067,plain,
% 0.67/0.85 (c1_1(a1048)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1017, 1058])).
% 0.67/0.85 tff(1068,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1069,plain,
% 0.67/0.85 (((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1070,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1069])).
% 0.67/0.85 tff(1071,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1070, 1068])).
% 0.67/0.85 tff(1072,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1073,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.67/0.85 tff(1074,plain,
% 0.67/0.85 (~c2_1(a1048)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1073, 81, 1067, 1066, 1065, 860, 850, 1064, 1056, 849, 751])).
% 0.67/0.85 tff(1075,plain,
% 0.67/0.85 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(1076,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1075])).
% 0.67/0.85 tff(1077,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1078,plain,
% 0.67/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(1079,plain,
% 0.67/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1078])).
% 0.67/0.85 tff(1080,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.67/0.85 tff(1081,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.67/0.85 tff(1082,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1081, 1077])).
% 0.67/0.85 tff(1083,plain,(
% 0.67/0.85 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(skolemize,[status(sab)],[1082])).
% 0.67/0.85 tff(1084,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1083, 1076])).
% 0.67/0.85 tff(1085,plain,
% 0.67/0.85 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(1086,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1085])).
% 0.67/0.85 tff(1087,plain,
% 0.67/0.85 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1088,plain,
% 0.67/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(1089,plain,
% 0.67/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[1088])).
% 0.67/0.86 tff(1090,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.67/0.86 tff(1091,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.67/0.86 tff(1092,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1091, 1087])).
% 0.67/0.86 tff(1093,plain,(
% 0.67/0.86 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.86 inference(skolemize,[status(sab)],[1092])).
% 0.67/0.86 tff(1094,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1093, 1086])).
% 0.67/0.86 tff(1095,assumption,(~c1_1(a1010)), introduced(assumption)).
% 0.67/0.86 tff(1096,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1097,plain,
% 0.67/0.86 ((hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001))) <=> (hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1098,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1097])).
% 0.67/0.86 tff(1099,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1098, 1096])).
% 0.67/0.86 tff(1100,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1101,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 0.67/0.86 tff(1102,plain,
% 0.67/0.86 (hskp3 | c0_1(a1001)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1101, 81, 709, 860, 701, 849, 1084, 1057])).
% 0.67/0.86 tff(1103,plain,
% 0.67/0.86 (c0_1(a1001)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1102, 330])).
% 0.67/0.86 tff(1104,plain,
% 0.67/0.86 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1105,plain,
% 0.67/0.86 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1106,plain,
% 0.67/0.86 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1105])).
% 0.67/0.86 tff(1107,plain,
% 0.67/0.86 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1106, 1104])).
% 0.67/0.86 tff(1108,plain,
% 0.67/0.86 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1109,plain,
% 0.67/0.86 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.67/0.86 tff(1110,plain,
% 0.67/0.86 (hskp24 | hskp3 | (~c0_1(a1001))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1109, 81, 860, 850, 410])).
% 0.67/0.86 tff(1111,plain,
% 0.67/0.86 (hskp24),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1110, 1103, 330])).
% 0.67/0.86 tff(1112,plain,
% 0.67/0.86 (~c0_1(a1045)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[423, 1111])).
% 0.67/0.86 tff(1113,assumption,(c3_1(a1010)), introduced(assumption)).
% 0.67/0.86 tff(1114,assumption,(c0_1(a1010)), introduced(assumption)).
% 0.67/0.86 tff(1115,plain,
% 0.67/0.86 (c3_1(a1045)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[447, 1111])).
% 0.67/0.86 tff(1116,plain,
% 0.67/0.86 (c1_1(a1045)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[455, 1111])).
% 0.67/0.86 tff(1117,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1118,plain,
% 0.67/0.86 ((hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045))) <=> (hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1119,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1118])).
% 0.67/0.86 tff(1120,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.67/0.86 tff(1121,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1122,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.67/0.86 tff(1123,plain,
% 0.67/0.86 (hskp15),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1122, 81, 1116, 1115, 1114, 1113, 1112, 1095, 1094])).
% 0.67/0.86 tff(1124,plain,
% 0.67/0.86 (((~hskp15) | (~c1_1(a1026))) <=> ((~hskp15) | (~c1_1(a1026)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1125,plain,
% 0.67/0.86 (((~c1_1(a1026)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1026)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1126,axiom,((~c1_1(a1026)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.67/0.86 tff(1127,plain,
% 0.67/0.86 ((~hskp15) | (~c1_1(a1026))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.67/0.86 tff(1128,plain,
% 0.67/0.86 ((~hskp15) | (~c1_1(a1026))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1127, 1124])).
% 0.67/0.86 tff(1129,plain,
% 0.67/0.86 (~c1_1(a1026)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1128, 1123])).
% 0.67/0.86 tff(1130,plain,
% 0.67/0.86 (((~hskp15) | (~c0_1(a1026))) <=> ((~hskp15) | (~c0_1(a1026)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1131,plain,
% 0.67/0.86 (((~c0_1(a1026)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1026)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1132,axiom,((~c0_1(a1026)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.67/0.86 tff(1133,plain,
% 0.67/0.86 ((~hskp15) | (~c0_1(a1026))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.67/0.86 tff(1134,plain,
% 0.67/0.86 ((~hskp15) | (~c0_1(a1026))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1133, 1130])).
% 0.67/0.86 tff(1135,plain,
% 0.67/0.86 (~c0_1(a1026)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1134, 1123])).
% 0.67/0.86 tff(1136,plain,
% 0.67/0.86 (((~hskp15) | c2_1(a1026)) <=> ((~hskp15) | c2_1(a1026))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1137,axiom,((~hskp15) | c2_1(a1026)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.67/0.86 tff(1138,plain,
% 0.67/0.86 ((~hskp15) | c2_1(a1026)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.67/0.86 tff(1139,plain,
% 0.67/0.86 ((~hskp15) | c2_1(a1026)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1138, 1136])).
% 0.67/0.86 tff(1140,plain,
% 0.67/0.86 ((~hskp15) | c2_1(a1026)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1139, 1136])).
% 0.67/0.86 tff(1141,plain,
% 0.67/0.86 ((~hskp15) | c2_1(a1026)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1140, 1136])).
% 0.67/0.86 tff(1142,plain,
% 0.67/0.86 ((~hskp15) | c2_1(a1026)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1141, 1136])).
% 0.67/0.86 tff(1143,plain,
% 0.67/0.86 (c2_1(a1026)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1142, 1123])).
% 0.67/0.86 tff(1144,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1145,plain,
% 0.67/0.86 ((hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026))) <=> (hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1146,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1145])).
% 0.67/0.86 tff(1147,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1146, 1144])).
% 0.67/0.86 tff(1148,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1149,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.67/0.86 tff(1150,plain,
% 0.67/0.86 ($false),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1149, 81, 330, 1067, 1143, 1064, 1135, 1129, 1084, 1074])).
% 0.67/0.86 tff(1151,plain,(hskp3 | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1001)) | (~c3_1(a1001)) | c2_1(a1006) | c1_1(a1001) | (~c0_1(a1010)) | (~c3_1(a1010)) | c1_1(a1010) | c2_1(a1044)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.86 tff(1152,plain,
% 0.67/0.86 (hskp3),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1151, 1055, 1054, 860, 850, 1053, 849, 1051, 1050, 1049, 938])).
% 0.67/0.86 tff(1153,plain,
% 0.67/0.86 (~c2_1(a1003)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[470, 1152])).
% 0.67/0.86 tff(1154,plain,
% 0.67/0.86 (~c0_1(a1003)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[476, 1152])).
% 0.67/0.86 tff(1155,plain,
% 0.67/0.86 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(1156,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[1155])).
% 0.70/0.86 tff(1157,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1158,plain,
% 0.70/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(1159,plain,
% 0.70/0.86 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[1158])).
% 0.70/0.86 tff(1160,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.70/0.86 tff(1161,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.70/0.86 tff(1162,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1161, 1157])).
% 0.70/0.86 tff(1163,plain,(
% 0.70/0.86 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(skolemize,[status(sab)],[1162])).
% 0.70/0.86 tff(1164,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1163, 1156])).
% 0.70/0.86 tff(1165,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1166,plain,
% 0.70/0.86 ((hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010))) <=> (hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1167,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1166])).
% 0.70/0.86 tff(1168,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.70/0.86 inference(transitivity,[status(thm)],[1167, 1165])).
% 0.70/0.86 tff(1169,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(1170,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.70/0.86 tff(1171,plain,
% 0.70/0.86 (hskp22),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1170, 81, 709, 1051, 1050, 701, 1049, 1164, 938])).
% 0.70/0.86 tff(1172,plain,
% 0.70/0.86 (((~hskp22) | (~c2_1(a1043))) <=> ((~hskp22) | (~c2_1(a1043)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1173,plain,
% 0.70/0.86 (((~c2_1(a1043)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1043)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1174,axiom,((~c2_1(a1043)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.70/0.86 tff(1175,plain,
% 0.70/0.86 ((~hskp22) | (~c2_1(a1043))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 0.70/0.86 tff(1176,plain,
% 0.70/0.86 ((~hskp22) | (~c2_1(a1043))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1175, 1172])).
% 0.70/0.86 tff(1177,plain,
% 0.70/0.86 (~c2_1(a1043)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1176, 1171])).
% 0.70/0.86 tff(1178,plain,
% 0.70/0.86 (((~hskp22) | (~c1_1(a1043))) <=> ((~hskp22) | (~c1_1(a1043)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1179,plain,
% 0.70/0.86 (((~c1_1(a1043)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1043)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1180,axiom,((~c1_1(a1043)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.70/0.86 tff(1181,plain,
% 0.70/0.86 ((~hskp22) | (~c1_1(a1043))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.70/0.86 tff(1182,plain,
% 0.70/0.86 ((~hskp22) | (~c1_1(a1043))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1181, 1178])).
% 0.70/0.86 tff(1183,plain,
% 0.70/0.86 (~c1_1(a1043)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1182, 1171])).
% 0.70/0.86 tff(1184,plain,
% 0.70/0.86 (c1_1(a1003)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[484, 1152])).
% 0.70/0.86 tff(1185,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1186,plain,
% 0.70/0.86 ((hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1187,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1186])).
% 0.70/0.86 tff(1188,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))),
% 0.70/0.86 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.70/0.86 tff(1189,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(1190,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.70/0.86 tff(1191,plain,
% 0.70/0.86 (~c3_1(a1043)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1190, 81, 584, 1184, 1183, 1177, 1154, 1153, 930])).
% 0.70/0.86 tff(1192,plain,
% 0.70/0.86 (((~hskp22) | c0_1(a1043)) <=> ((~hskp22) | c0_1(a1043))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1193,axiom,((~hskp22) | c0_1(a1043)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.70/0.86 tff(1194,plain,
% 0.70/0.86 ((~hskp22) | c0_1(a1043)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.70/0.86 tff(1195,plain,
% 0.70/0.86 ((~hskp22) | c0_1(a1043)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1194, 1192])).
% 0.70/0.86 tff(1196,plain,
% 0.70/0.86 ((~hskp22) | c0_1(a1043)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1195, 1192])).
% 0.70/0.86 tff(1197,plain,
% 0.70/0.86 ((~hskp22) | c0_1(a1043)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1196, 1192])).
% 0.70/0.86 tff(1198,plain,
% 0.70/0.86 ((~hskp22) | c0_1(a1043)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1197, 1192])).
% 0.70/0.86 tff(1199,plain,
% 0.70/0.86 (c0_1(a1043)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1198, 1171])).
% 0.70/0.86 tff(1200,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1201,plain,
% 0.70/0.86 ((hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043)) <=> (hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1202,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043)))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1201])).
% 0.70/0.86 tff(1203,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.70/0.86 inference(transitivity,[status(thm)],[1202, 1200])).
% 0.70/0.86 tff(1204,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(1205,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.70/0.86 tff(1206,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1205, 81, 564, 1199, 1183, 1177, 98, 1191])).
% 0.70/0.86 tff(1207,plain,(hskp7 | hskp13 | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(1208,plain,
% 0.70/0.86 (hskp7),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1207, 564, 848, 847, 845])).
% 0.70/0.86 tff(1209,plain,
% 0.70/0.86 (c2_1(a1008)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[224, 1208])).
% 0.70/0.86 tff(1210,plain,
% 0.70/0.86 (~c3_1(a1008)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[210, 1208])).
% 0.70/0.86 tff(1211,plain,
% 0.70/0.86 (~c1_1(a1008)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[216, 1208])).
% 0.70/0.86 tff(1212,plain,
% 0.70/0.86 (hskp26),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[956, 939, 1057])).
% 0.70/0.86 tff(1213,plain,
% 0.70/0.86 (~c2_1(a1052)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[962, 1212])).
% 0.70/0.86 tff(1214,plain,
% 0.70/0.86 (~c0_1(a1052)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[968, 1212])).
% 0.70/0.86 tff(1215,plain,
% 0.70/0.86 (c3_1(a1052)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1025, 1212])).
% 0.70/0.86 tff(1216,plain,
% 0.70/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1217,plain,
% 0.70/0.86 (((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052))) <=> (c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(1218,plain,
% 0.70/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1217])).
% 0.70/0.87 tff(1219,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[1218, 1216])).
% 0.70/0.87 tff(1220,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(1221,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 0.70/0.87 tff(1222,plain,
% 0.70/0.87 (c1_1(a1052)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1221, 81, 1215, 621, 1214, 1213, 630, 620, 204])).
% 0.70/0.87 tff(1223,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1224,plain,
% 0.70/0.87 ((hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052))) <=> (hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1225,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1224])).
% 0.70/0.87 tff(1226,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[1225, 1223])).
% 0.70/0.87 tff(1227,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(1228,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.70/0.87 tff(1229,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1228, 81, 939, 621, 1214, 1213, 630, 620, 21, 1222])).
% 0.70/0.87 tff(1230,plain,(hskp8 | (~c2_1(a1008)) | c1_1(a1008) | c3_1(a1008) | c2_1(a1044)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(1231,plain,
% 0.70/0.87 (hskp8),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1230, 1209, 1211, 1210, 899])).
% 0.70/0.87 tff(1232,plain,
% 0.70/0.87 (~c1_1(a1010)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[491, 1231])).
% 0.70/0.87 tff(1233,plain,
% 0.70/0.87 (c0_1(a1010)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[507, 1231])).
% 0.70/0.87 tff(1234,plain,
% 0.70/0.87 (c3_1(a1010)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[499, 1231])).
% 0.70/0.87 tff(1235,plain,
% 0.70/0.87 (hskp3),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1151, 1234, 1233, 848, 847, 918, 845, 920, 919, 1232, 899])).
% 0.70/0.87 tff(1236,plain,
% 0.70/0.87 (~c2_1(a1003)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[470, 1235])).
% 0.70/0.87 tff(1237,plain,
% 0.70/0.87 (~c0_1(a1003)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[476, 1235])).
% 0.70/0.87 tff(1238,plain,
% 0.70/0.87 (c1_1(a1003)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[484, 1235])).
% 0.70/0.87 tff(1239,assumption,(~hskp4), introduced(assumption)).
% 0.70/0.87 tff(1240,plain,
% 0.70/0.87 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(1241,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1240])).
% 0.70/0.87 tff(1242,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1243,plain,
% 0.70/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(1244,plain,
% 0.70/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1243])).
% 0.70/0.87 tff(1245,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.70/0.87 tff(1246,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.70/0.87 tff(1247,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1246, 1242])).
% 0.70/0.87 tff(1248,plain,(
% 0.70/0.87 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[1247])).
% 0.70/0.87 tff(1249,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1248, 1241])).
% 0.70/0.87 tff(1250,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1251,plain,
% 0.70/0.87 ((hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008))) <=> (hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1252,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008)))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1251])).
% 0.70/0.87 tff(1253,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.70/0.87 inference(transitivity,[status(thm)],[1252, 1250])).
% 0.70/0.87 tff(1254,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(1255,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.70/0.87 tff(1256,plain,
% 0.70/0.87 (hskp4 | c0_1(a1008)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1255, 81, 621, 1066, 1065, 630, 1056, 1249])).
% 0.70/0.87 tff(1257,plain,
% 0.70/0.87 (c0_1(a1008)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1256, 1239])).
% 0.70/0.87 tff(1258,plain,
% 0.70/0.87 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(1259,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1258])).
% 0.70/0.87 tff(1260,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1261,plain,
% 0.70/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(1262,plain,
% 0.70/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1261])).
% 0.70/0.87 tff(1263,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.70/0.87 tff(1264,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.70/0.87 tff(1265,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1264, 1260])).
% 0.70/0.87 tff(1266,plain,(
% 0.70/0.87 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[1265])).
% 0.70/0.87 tff(1267,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1266, 1259])).
% 0.70/0.87 tff(1268,assumption,(~c2_1(a1003)), introduced(assumption)).
% 0.70/0.87 tff(1269,assumption,(~c0_1(a1003)), introduced(assumption)).
% 0.70/0.87 tff(1270,assumption,(c1_1(a1003)), introduced(assumption)).
% 0.70/0.87 tff(1271,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1272,plain,
% 0.70/0.87 ((hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1273,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1272])).
% 0.70/0.87 tff(1274,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[1273, 1271])).
% 0.70/0.87 tff(1275,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(1276,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 0.70/0.87 tff(1277,plain,
% 0.70/0.87 (hskp4 | (~c0_1(a1008))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1276, 81, 1270, 630, 620, 1269, 1268, 1267])).
% 0.70/0.87 tff(1278,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1277, 1257, 1239])).
% 0.70/0.87 tff(1279,plain,(hskp4 | (~c1_1(a1003)) | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~c2_1(a1008)) | (~c0_1(a1006)) | (~c3_1(a1006)) | c2_1(a1006)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(1280,plain,
% 0.70/0.87 (hskp4),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1279, 1238, 1211, 1210, 1237, 1236, 1209, 920, 919, 918])).
% 0.70/0.87 tff(1281,plain,
% 0.70/0.87 (~c3_1(a1004)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[793, 1280])).
% 0.70/0.87 tff(1282,plain,
% 0.70/0.87 (c2_1(a1004)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[772, 1280])).
% 0.70/0.87 tff(1283,plain,
% 0.70/0.87 (c1_1(a1004)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[780, 1280])).
% 0.70/0.87 tff(1284,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1285,plain,
% 0.70/0.87 (((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1286,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1285])).
% 0.70/0.87 tff(1287,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[1286, 1284])).
% 0.70/0.87 tff(1288,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(1289,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 0.70/0.87 tff(1290,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1289, 81, 920, 919, 1283, 1282, 848, 847, 918, 1281, 845, 751])).
% 0.70/0.87 tff(1291,plain,(hskp13 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(1292,plain,
% 0.70/0.87 (hskp13),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1291, 556])).
% 0.70/0.87 tff(1293,plain,
% 0.70/0.87 (c3_1(a1023)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[149, 1292])).
% 0.70/0.87 tff(1294,plain,
% 0.70/0.87 (~c2_1(a1023)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[162, 1292])).
% 0.70/0.87 tff(1295,plain,
% 0.70/0.87 (~c1_1(a1023)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[141, 1292])).
% 0.70/0.87 tff(1296,plain,
% 0.70/0.87 (~hskp4),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[802, 619, 556, 584])).
% 0.70/0.87 tff(1297,plain,
% 0.70/0.87 (hskp21),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[814, 1296, 584])).
% 0.70/0.87 tff(1298,plain,
% 0.70/0.87 (~c3_1(a1041)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[820, 1297])).
% 0.70/0.87 tff(1299,plain,
% 0.70/0.87 (~c0_1(a1041)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[826, 1297])).
% 0.70/0.87 tff(1300,plain,
% 0.70/0.87 (c2_1(a1041)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[834, 1297])).
% 0.70/0.87 tff(1301,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[841, 81, 556, 619, 1300, 1299, 1298, 618])).
% 0.70/0.87 tff(1302,plain,(hskp1 | hskp2 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(1303,plain,
% 0.70/0.87 (hskp1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1302, 584, 556])).
% 0.70/0.87 tff(1304,plain,
% 0.70/0.87 (~c1_1(a1001)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[279, 1303])).
% 0.70/0.87 tff(1305,plain,
% 0.70/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(1306,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1305])).
% 0.70/0.87 tff(1307,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(1308,plain,
% 0.70/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(1309,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1308])).
% 0.70/0.87 tff(1310,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.70/0.87 tff(1311,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.70/0.87 tff(1312,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1311, 1307])).
% 0.70/0.87 tff(1313,plain,(
% 0.70/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[1312])).
% 0.70/0.87 tff(1314,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1313, 1306])).
% 0.70/0.88 tff(1315,plain,
% 0.70/0.88 (hskp21),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[814, 1239, 584])).
% 0.70/0.88 tff(1316,plain,
% 0.70/0.88 (~c3_1(a1041)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[820, 1315])).
% 0.70/0.88 tff(1317,plain,
% 0.70/0.88 (~c0_1(a1041)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[826, 1315])).
% 0.70/0.88 tff(1318,plain,
% 0.70/0.88 (c2_1(a1001)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[312, 1303])).
% 0.70/0.88 tff(1319,plain,
% 0.70/0.88 (c2_1(a1041)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[834, 1315])).
% 0.70/0.88 tff(1320,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1321,plain,
% 0.70/0.88 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041))) <=> (c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1322,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1321])).
% 0.70/0.88 tff(1323,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1322, 1320])).
% 0.70/0.88 tff(1324,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1325,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.70/0.88 tff(1326,plain,
% 0.70/0.88 (~c0_1(a1001)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1325, 81, 717, 1319, 1318, 701, 1317, 1316, 1304, 1314, 938])).
% 0.70/0.88 tff(1327,plain,
% 0.70/0.88 (^[U: $i] : refl((hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(1328,plain,
% 0.70/0.88 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[1327])).
% 0.70/0.88 tff(1329,plain,
% 0.70/0.88 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1330,plain,
% 0.70/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19) <=> ((hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(1331,plain,
% 0.70/0.88 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[1330])).
% 0.70/0.88 tff(1332,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.70/0.88 tff(1333,plain,
% 0.70/0.88 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.70/0.88 tff(1334,plain,
% 0.70/0.88 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1333, 1329])).
% 0.70/0.88 tff(1335,plain,(
% 0.70/0.88 ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[1334])).
% 0.70/0.88 tff(1336,plain,
% 0.70/0.88 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1335, 1328])).
% 0.70/0.88 tff(1337,plain,
% 0.70/0.88 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1338,plain,
% 0.70/0.88 ((hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044))) <=> (hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1339,plain,
% 0.70/0.88 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1338])).
% 0.70/0.88 tff(1340,plain,
% 0.70/0.88 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1339, 1337])).
% 0.70/0.88 tff(1341,plain,
% 0.70/0.88 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1342,plain,
% 0.70/0.88 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.70/0.88 tff(1343,plain,
% 0.70/0.88 (hskp19 | hskp4),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1342, 81, 717, 709, 701, 1336])).
% 0.70/0.88 tff(1344,plain,
% 0.70/0.88 (hskp19),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1343, 1239])).
% 0.70/0.88 tff(1345,plain,
% 0.70/0.88 (~c3_1(a1037)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[128, 1344])).
% 0.70/0.88 tff(1346,plain,
% 0.70/0.88 (~c1_1(a1037)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[134, 1344])).
% 0.70/0.88 tff(1347,plain,
% 0.70/0.88 (~c0_1(a1037)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[644, 1344])).
% 0.70/0.88 tff(1348,assumption,(hskp28), introduced(assumption)).
% 0.70/0.88 tff(1349,plain,
% 0.70/0.88 (((~hskp28) | c2_1(a1033)) <=> ((~hskp28) | c2_1(a1033))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1350,axiom,((~hskp28) | c2_1(a1033)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.70/0.88 tff(1351,plain,
% 0.70/0.88 ((~hskp28) | c2_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.70/0.88 tff(1352,plain,
% 0.70/0.88 ((~hskp28) | c2_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1351, 1349])).
% 0.70/0.88 tff(1353,plain,
% 0.70/0.88 ((~hskp28) | c2_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1352, 1349])).
% 0.70/0.88 tff(1354,plain,
% 0.70/0.88 ((~hskp28) | c2_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1353, 1349])).
% 0.70/0.88 tff(1355,plain,
% 0.70/0.88 ((~hskp28) | c2_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1354, 1349])).
% 0.70/0.88 tff(1356,plain,
% 0.70/0.88 (c2_1(a1033)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1355, 1348])).
% 0.70/0.88 tff(1357,plain,
% 0.70/0.88 (((~hskp28) | c1_1(a1033)) <=> ((~hskp28) | c1_1(a1033))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1358,axiom,((~hskp28) | c1_1(a1033)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.70/0.88 tff(1359,plain,
% 0.70/0.88 ((~hskp28) | c1_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.70/0.88 tff(1360,plain,
% 0.70/0.88 ((~hskp28) | c1_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1359, 1357])).
% 0.70/0.88 tff(1361,plain,
% 0.70/0.88 ((~hskp28) | c1_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1360, 1357])).
% 0.70/0.88 tff(1362,plain,
% 0.70/0.88 ((~hskp28) | c1_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1361, 1357])).
% 0.70/0.88 tff(1363,plain,
% 0.70/0.88 ((~hskp28) | c1_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1362, 1357])).
% 0.70/0.88 tff(1364,plain,
% 0.70/0.88 (c1_1(a1033)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1363, 1348])).
% 0.70/0.88 tff(1365,plain,
% 0.70/0.88 (((~hskp28) | c0_1(a1033)) <=> ((~hskp28) | c0_1(a1033))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1366,axiom,((~hskp28) | c0_1(a1033)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.70/0.88 tff(1367,plain,
% 0.70/0.88 ((~hskp28) | c0_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.70/0.88 tff(1368,plain,
% 0.70/0.88 ((~hskp28) | c0_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1367, 1365])).
% 0.70/0.88 tff(1369,plain,
% 0.70/0.88 ((~hskp28) | c0_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1368, 1365])).
% 0.70/0.88 tff(1370,plain,
% 0.70/0.88 ((~hskp28) | c0_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1369, 1365])).
% 0.70/0.88 tff(1371,plain,
% 0.70/0.88 ((~hskp28) | c0_1(a1033)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1370, 1365])).
% 0.70/0.88 tff(1372,plain,
% 0.70/0.88 (c0_1(a1033)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1371, 1348])).
% 0.70/0.88 tff(1373,plain,
% 0.70/0.88 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1374,plain,
% 0.70/0.88 ((hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1375,plain,
% 0.70/0.88 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1374])).
% 0.70/0.88 tff(1376,plain,
% 0.70/0.88 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1375, 1373])).
% 0.70/0.88 tff(1377,plain,
% 0.70/0.88 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1378,plain,
% 0.70/0.88 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 0.70/0.88 tff(1379,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1378, 81, 584, 1372, 1364, 1356, 173])).
% 0.70/0.88 tff(1380,plain,((~hskp28) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(1381,plain,
% 0.70/0.88 (~hskp28),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1380, 584])).
% 0.70/0.88 tff(1382,plain,
% 0.70/0.88 (^[U: $i] : refl((hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(1383,plain,
% 0.70/0.88 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[1382])).
% 0.70/0.88 tff(1384,plain,
% 0.70/0.88 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1385,plain,
% 0.70/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp8))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(1386,plain,
% 0.70/0.88 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[1385])).
% 0.70/0.88 tff(1387,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.70/0.88 tff(1388,plain,
% 0.70/0.88 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 0.70/0.88 tff(1389,plain,
% 0.70/0.88 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1388, 1384])).
% 0.70/0.88 tff(1390,plain,(
% 0.70/0.88 ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[1389])).
% 0.70/0.88 tff(1391,plain,
% 0.70/0.88 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1390, 1383])).
% 0.70/0.88 tff(1392,plain,
% 0.70/0.88 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1393,plain,
% 0.70/0.88 ((hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023))) <=> (hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1394,plain,
% 0.70/0.88 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1393])).
% 0.70/0.88 tff(1395,plain,
% 0.70/0.88 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.70/0.88 tff(1396,plain,
% 0.70/0.88 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1397,plain,
% 0.70/0.88 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.70/0.88 tff(1398,plain,
% 0.70/0.88 (hskp28 | hskp8),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1397, 81, 1293, 1295, 1294, 1391])).
% 0.70/0.88 tff(1399,plain,
% 0.70/0.88 (hskp8),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1398, 1381])).
% 0.70/0.88 tff(1400,plain,
% 0.70/0.88 (~c1_1(a1010)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[491, 1399])).
% 0.70/0.88 tff(1401,plain,
% 0.70/0.88 (c3_1(a1010)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[499, 1399])).
% 0.70/0.88 tff(1402,plain,
% 0.70/0.88 (c0_1(a1010)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[507, 1399])).
% 0.70/0.88 tff(1403,plain,
% 0.70/0.88 (hskp22),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1170, 81, 709, 1402, 1401, 701, 1400, 1164, 938])).
% 0.70/0.88 tff(1404,plain,
% 0.70/0.88 (~c2_1(a1043)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1176, 1403])).
% 0.70/0.88 tff(1405,plain,
% 0.70/0.88 (~c1_1(a1043)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1182, 1403])).
% 0.70/0.88 tff(1406,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1407,plain,
% 0.70/0.88 ((hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037)) <=> (hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1408,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1407])).
% 0.70/0.88 tff(1409,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1408, 1406])).
% 0.70/0.88 tff(1410,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1411,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 0.70/0.88 tff(1412,plain,
% 0.70/0.88 (c3_1(a1043)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1411, 81, 556, 1405, 1404, 1347, 1346, 1345, 536])).
% 0.70/0.88 tff(1413,plain,
% 0.70/0.88 (c0_1(a1043)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1198, 1403])).
% 0.70/0.88 tff(1414,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1415,plain,
% 0.70/0.88 ((hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001))) <=> (hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1416,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1415])).
% 0.70/0.88 tff(1417,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1416, 1414])).
% 0.70/0.88 tff(1418,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1419,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 0.70/0.88 tff(1420,plain,
% 0.70/0.88 (hskp4 | c0_1(a1001) | (~c3_1(a1043))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1419, 81, 1413, 1318, 1404, 1304, 1249])).
% 0.70/0.88 tff(1421,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1420, 1412, 1326, 1239])).
% 0.70/0.88 tff(1422,plain,(hskp4 | hskp2 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(1423,plain,
% 0.70/0.88 (hskp4),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1422, 584, 556])).
% 0.70/0.88 tff(1424,plain,
% 0.70/0.88 (~c3_1(a1004)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[793, 1423])).
% 0.70/0.88 tff(1425,plain,
% 0.70/0.88 (c3_1(a1001)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[287, 1303])).
% 0.70/0.88 tff(1426,plain,
% 0.70/0.88 (c2_1(a1004)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[772, 1423])).
% 0.70/0.88 tff(1427,plain,
% 0.70/0.88 (c1_1(a1004)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[780, 1423])).
% 0.70/0.88 tff(1428,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1429,plain,
% 0.70/0.88 (((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(1430,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[1429])).
% 0.70/0.88 tff(1431,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.70/0.88 tff(1432,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(1433,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.70/0.89 tff(1434,plain,
% 0.70/0.89 (~c0_1(a1023)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1433, 81, 1293, 1427, 1426, 1318, 1425, 1294, 1424, 1304, 751])).
% 0.70/0.89 tff(1435,plain,
% 0.70/0.89 (~c0_1(a1004)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[787, 81, 584, 1427, 1426, 173])).
% 0.70/0.89 tff(1436,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1437,plain,
% 0.70/0.89 (((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1438,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1437])).
% 0.70/0.89 tff(1439,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.70/0.89 tff(1440,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1441,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.70/0.89 tff(1442,plain,
% 0.70/0.89 (~c3_1(a1043)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1441, 81, 1413, 1427, 1426, 1318, 1425, 1404, 1424, 1304, 751])).
% 0.70/0.89 tff(1443,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1444,plain,
% 0.70/0.89 (((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004))) <=> (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1445,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1444])).
% 0.70/0.89 tff(1446,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1445, 1443])).
% 0.70/0.89 tff(1447,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1448,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 0.70/0.89 tff(1449,plain,
% 0.70/0.89 (~c0_1(a1001)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1448, 81, 1413, 1426, 1318, 1404, 1424, 1304, 1314, 1442, 1435])).
% 0.70/0.89 tff(1450,plain,
% 0.70/0.89 (c0_1(a1001) | c0_1(a1023)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[319, 81, 1293, 1318, 1295, 1294, 1304, 305])).
% 0.70/0.89 tff(1451,plain,
% 0.70/0.89 ($false),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1450, 1449, 1434])).
% 0.70/0.89 tff(1452,plain,(hskp7 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.70/0.89 tff(1453,plain,
% 0.70/0.89 (hskp7),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1452, 556])).
% 0.70/0.89 tff(1454,plain,
% 0.70/0.89 (c0_1(a1023)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[233, 1453, 1295, 1294, 1293])).
% 0.70/0.89 tff(1455,plain,
% 0.70/0.89 (~c3_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[210, 1453])).
% 0.70/0.89 tff(1456,plain,
% 0.70/0.89 (c2_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[224, 1453])).
% 0.70/0.89 tff(1457,plain,
% 0.70/0.89 (hskp1 | c0_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[627, 81, 556, 1456, 1455, 618])).
% 0.70/0.89 tff(1458,plain,
% 0.70/0.89 (c0_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1457, 619])).
% 0.70/0.89 tff(1459,plain,
% 0.70/0.89 (~c1_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[216, 1453])).
% 0.70/0.89 tff(1460,plain,
% 0.70/0.89 (hskp19 | (~c0_1(a1008))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[636, 81, 1456, 1459, 1455, 108])).
% 0.70/0.89 tff(1461,plain,
% 0.70/0.89 (hskp19),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1460, 1458])).
% 0.70/0.89 tff(1462,plain,
% 0.70/0.89 (~c3_1(a1037)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[128, 1461])).
% 0.70/0.89 tff(1463,plain,
% 0.70/0.89 (~c0_1(a1037)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[644, 1461])).
% 0.70/0.89 tff(1464,plain,
% 0.70/0.89 (~c2_1(a1037)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[651, 81, 556, 619, 1463, 1462, 618])).
% 0.70/0.89 tff(1465,plain,
% 0.70/0.89 (~c1_1(a1037)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[134, 1461])).
% 0.70/0.89 tff(1466,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1467,plain,
% 0.70/0.89 ((hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037)) <=> (hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1468,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1467])).
% 0.70/0.89 tff(1469,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1468, 1466])).
% 0.70/0.89 tff(1470,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1471,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 0.70/0.89 tff(1472,plain,
% 0.70/0.89 ($false),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1471, 81, 556, 1463, 1465, 1462, 536, 1464])).
% 0.70/0.89 tff(1473,plain,(hskp1 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.70/0.89 tff(1474,plain,
% 0.70/0.89 (hskp1),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1473, 556])).
% 0.70/0.89 tff(1475,plain,
% 0.70/0.89 (~c1_1(a1001)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[279, 1474])).
% 0.70/0.89 tff(1476,plain,
% 0.70/0.89 (c2_1(a1001)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[312, 1474])).
% 0.70/0.89 tff(1477,plain,
% 0.70/0.89 (c3_1(a1001)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[287, 1474])).
% 0.70/0.89 tff(1478,assumption,(c0_1(a1023)), introduced(assumption)).
% 0.70/0.89 tff(1479,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1480,plain,
% 0.70/0.89 ((hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008))) <=> (hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1481,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1480])).
% 0.70/0.89 tff(1482,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1481, 1479])).
% 0.70/0.89 tff(1483,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1484,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 0.70/0.89 tff(1485,plain,
% 0.70/0.89 (hskp4 | c0_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1484, 81, 194, 621, 192, 630, 1249, 1478])).
% 0.70/0.89 tff(1486,plain,
% 0.70/0.89 (c0_1(a1008)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1485, 1239])).
% 0.70/0.89 tff(1487,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1488,plain,
% 0.70/0.89 ((hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008))) <=> (hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1489,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1488])).
% 0.70/0.89 tff(1490,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1489, 1487])).
% 0.70/0.89 tff(1491,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1492,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 0.70/0.89 tff(1493,plain,
% 0.70/0.89 (hskp6 | (~c0_1(a1008))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1492, 81, 621, 860, 850, 630, 849, 761])).
% 0.70/0.89 tff(1494,plain,
% 0.70/0.89 (hskp6),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1493, 1486])).
% 0.70/0.89 tff(1495,plain,
% 0.70/0.89 (~c2_1(a1006)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[873, 1494])).
% 0.70/0.89 tff(1496,plain,
% 0.70/0.89 (c3_1(a1006)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[881, 1494])).
% 0.70/0.89 tff(1497,plain,
% 0.70/0.89 (c0_1(a1006)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[889, 1494])).
% 0.70/0.89 tff(1498,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1499,plain,
% 0.70/0.89 (((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1500,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1499])).
% 0.70/0.89 tff(1501,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1500, 1498])).
% 0.70/0.89 tff(1502,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1503,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 0.70/0.89 tff(1504,plain,
% 0.70/0.89 (~c2_1(a1044)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1503, 81, 709, 194, 860, 850, 701, 192, 849, 751, 1478])).
% 0.70/0.89 tff(1505,plain,
% 0.70/0.89 (hskp8),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1230, 1504, 630, 620, 621])).
% 0.70/0.89 tff(1506,plain,
% 0.70/0.89 (~c1_1(a1010)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[491, 1505])).
% 0.70/0.89 tff(1507,plain,
% 0.70/0.89 (c3_1(a1010)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[499, 1505])).
% 0.70/0.89 tff(1508,plain,
% 0.70/0.89 (c0_1(a1010)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[507, 1505])).
% 0.70/0.89 tff(1509,plain,
% 0.70/0.89 (hskp3),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1151, 1495, 1508, 1507, 850, 860, 849, 1497, 1496, 1506, 1504])).
% 0.70/0.89 tff(1510,plain,
% 0.70/0.89 (~c2_1(a1003)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[470, 1509])).
% 0.70/0.89 tff(1511,plain,
% 0.70/0.89 (c1_1(a1003)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[484, 1509])).
% 0.70/0.89 tff(1512,plain,
% 0.70/0.89 (~c0_1(a1003)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[476, 1509])).
% 0.70/0.89 tff(1513,plain,
% 0.70/0.89 ($false),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1279, 1512, 1511, 630, 620, 1239, 1510, 621, 1497, 1496, 1495])).
% 0.70/0.89 tff(1514,plain,(hskp4 | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | (~c3_1(a1001)) | (~c2_1(a1001)) | c1_1(a1001) | (~c3_1(a1023)) | c2_1(a1023) | (~c0_1(a1023))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.89 tff(1515,plain,
% 0.70/0.89 (hskp4),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1514, 1459, 1455, 1456, 1477, 1476, 1475, 1293, 1294, 1454])).
% 0.70/0.89 tff(1516,plain,
% 0.70/0.89 (~c3_1(a1004)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[793, 1515])).
% 0.70/0.89 tff(1517,plain,
% 0.70/0.89 (c2_1(a1004)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[772, 1515])).
% 0.70/0.89 tff(1518,plain,
% 0.70/0.89 (c1_1(a1004)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[780, 1515])).
% 0.70/0.89 tff(1519,plain,
% 0.70/0.89 ($false),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1433, 81, 1293, 1518, 1517, 1476, 1477, 1294, 1516, 1475, 751, 1454])).
% 0.70/0.89 tff(1520,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 0.70/0.89 tff(1521,plain,
% 0.70/0.89 (~c1_1(a1002)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[38, 1520])).
% 0.70/0.89 tff(1522,plain,
% 0.70/0.89 (c2_1(a1002)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[115, 1520])).
% 0.70/0.89 tff(1523,plain,
% 0.70/0.89 (c0_1(a1002)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[46, 1520])).
% 0.70/0.89 tff(1524,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1525,plain,
% 0.70/0.89 ((hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002))) <=> (hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1526,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1525])).
% 0.70/0.89 tff(1527,plain,
% 0.70/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1526, 1524])).
% 0.70/0.89 tff(1528,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1529,plain,
% 0.70/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 0.70/0.89 tff(1530,plain,
% 0.70/0.89 (hskp6),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1529, 81, 728, 727, 1523, 1522, 1521, 761, 741])).
% 0.70/0.89 tff(1531,plain,
% 0.70/0.89 (~c2_1(a1006)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[873, 1530])).
% 0.70/0.89 tff(1532,plain,
% 0.70/0.89 (c3_1(a1006)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[881, 1530])).
% 0.70/0.89 tff(1533,plain,
% 0.70/0.89 (c0_1(a1006)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[889, 1530])).
% 0.70/0.89 tff(1534,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1535,plain,
% 0.70/0.89 (((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032))) <=> (c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1536,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[1535])).
% 0.70/0.89 tff(1537,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[1536, 1534])).
% 0.70/0.89 tff(1538,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(1539,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.70/0.89 tff(1540,plain,
% 0.70/0.89 ($false),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[1539, 81, 709, 728, 727, 1533, 1532, 701, 1531, 751, 1, 741])).
% 0.70/0.89 tff(1541,plain,(~c2_1(a1044)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.89 tff(1542,plain,
% 0.70/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(1543,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[1542])).
% 0.70/0.89 tff(1544,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(1545,plain,
% 0.70/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(1546,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[1545])).
% 0.70/0.89 tff(1547,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.70/0.89 tff(1548,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 0.70/0.89 tff(1549,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1548, 1544])).
% 0.70/0.89 tff(1550,plain,(
% 0.70/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(skolemize,[status(sab)],[1549])).
% 0.70/0.89 tff(1551,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[1550, 1543])).
% 0.70/0.90 tff(1552,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1553,plain,
% 0.70/0.90 (((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041))) <=> (c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1554,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[1553])).
% 0.70/0.90 tff(1555,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[1554, 1552])).
% 0.70/0.90 tff(1556,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(1557,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 0.70/0.90 tff(1558,plain,
% 0.70/0.90 (c1_1(a1041)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1557, 81, 717, 709, 1319, 1523, 1522, 1317, 1521, 1551, 938])).
% 0.70/0.90 tff(1559,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1560,plain,
% 0.70/0.90 (((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037))) <=> (c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1561,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[1560])).
% 0.70/0.90 tff(1562,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[1561, 1559])).
% 0.70/0.90 tff(1563,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(1564,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 0.70/0.90 tff(1565,plain,
% 0.70/0.90 (~c2_1(a1037)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1564, 81, 717, 709, 1523, 1522, 1347, 1346, 1521, 1551, 938])).
% 0.70/0.90 tff(1566,plain,
% 0.70/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(1567,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[1566])).
% 0.70/0.90 tff(1568,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1569,plain,
% 0.70/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(1570,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[1569])).
% 0.70/0.90 tff(1571,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.70/0.90 tff(1572,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 0.70/0.90 tff(1573,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1572, 1568])).
% 0.70/0.90 tff(1574,plain,(
% 0.70/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(skolemize,[status(sab)],[1573])).
% 0.70/0.90 tff(1575,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1574, 1567])).
% 0.70/0.90 tff(1576,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1577,plain,
% 0.70/0.90 (((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037)) <=> (c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1578,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[1577])).
% 0.70/0.90 tff(1579,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[1578, 1576])).
% 0.70/0.90 tff(1580,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(1581,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 0.70/0.90 tff(1582,plain,
% 0.70/0.90 ($false),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1581, 81, 1317, 1316, 1347, 1346, 1345, 1575, 1565, 1558])).
% 0.70/0.90 tff(1583,plain,(hskp4 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.90 tff(1584,plain,
% 0.70/0.90 (hskp4),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1583, 584])).
% 0.70/0.90 tff(1585,plain,
% 0.70/0.90 (c2_1(a1004)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[772, 1584])).
% 0.70/0.90 tff(1586,plain,
% 0.70/0.90 (c1_1(a1004)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[780, 1584])).
% 0.70/0.90 tff(1587,plain,
% 0.70/0.90 (~c0_1(a1004)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[787, 81, 584, 1586, 1585, 173])).
% 0.70/0.90 tff(1588,plain,
% 0.70/0.90 (~c3_1(a1004)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[793, 1584])).
% 0.70/0.90 tff(1589,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1590,plain,
% 0.70/0.90 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004))) <=> (c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1591,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[1590])).
% 0.70/0.90 tff(1592,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[1591, 1589])).
% 0.70/0.90 tff(1593,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(1594,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 0.70/0.90 tff(1595,plain,
% 0.70/0.90 ($false),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1594, 81, 717, 1585, 1523, 1522, 701, 1588, 1521, 1314, 938, 1587])).
% 0.70/0.90 tff(1596,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.90 tff(1597,plain,
% 0.70/0.90 (~c3_1(a1008)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[210, 1596])).
% 0.70/0.90 tff(1598,plain,
% 0.70/0.90 (c2_1(a1008)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[224, 1596])).
% 0.70/0.90 tff(1599,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1600,plain,
% 0.70/0.90 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008))) <=> (c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1601,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[1600])).
% 0.70/0.90 tff(1602,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[1601, 1599])).
% 0.70/0.90 tff(1603,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(1604,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.70/0.90 tff(1605,plain,
% 0.70/0.90 (c0_1(a1008)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1604, 81, 717, 1598, 1523, 1522, 701, 1597, 1521, 1314, 1541])).
% 0.70/0.90 tff(1606,plain,
% 0.70/0.90 (~c1_1(a1008)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[216, 1596])).
% 0.70/0.90 tff(1607,plain,
% 0.70/0.90 (hskp19 | (~c0_1(a1008))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[636, 81, 1598, 1606, 1597, 108])).
% 0.70/0.90 tff(1608,plain,
% 0.70/0.90 (hskp19),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1607, 1605])).
% 0.70/0.90 tff(1609,plain,
% 0.70/0.90 (~c1_1(a1037)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[134, 1608])).
% 0.70/0.90 tff(1610,plain,
% 0.70/0.90 (~c0_1(a1037)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[644, 1608])).
% 0.70/0.90 tff(1611,plain,
% 0.70/0.90 (~c3_1(a1037)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[128, 1608])).
% 0.70/0.90 tff(1612,assumption,(~c1_1(a1037)), introduced(assumption)).
% 0.70/0.90 tff(1613,assumption,(~c0_1(a1037)), introduced(assumption)).
% 0.70/0.90 tff(1614,plain,
% 0.70/0.90 (~c2_1(a1037)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1564, 81, 717, 709, 1523, 1522, 1613, 1612, 1521, 1551, 1057])).
% 0.70/0.90 tff(1615,plain,
% 0.70/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(1616,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[1615])).
% 0.70/0.90 tff(1617,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1618,plain,
% 0.70/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(1619,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[1618])).
% 0.70/0.90 tff(1620,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.70/0.90 tff(1621,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 0.70/0.90 tff(1622,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1621, 1617])).
% 0.70/0.90 tff(1623,plain,(
% 0.70/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(skolemize,[status(sab)],[1622])).
% 0.70/0.90 tff(1624,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1623, 1616])).
% 0.70/0.90 tff(1625,assumption,(~c3_1(a1037)), introduced(assumption)).
% 0.70/0.90 tff(1626,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1627,plain,
% 0.70/0.90 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037)) <=> (c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(1628,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[1627])).
% 0.70/0.90 tff(1629,plain,
% 0.70/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[1628, 1626])).
% 0.70/0.90 tff(1630,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(1631,plain,
% 0.70/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.70/0.90 tff(1632,plain,
% 0.70/0.90 ($false),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1631, 81, 717, 1598, 701, 1613, 1625, 1606, 1597, 1624, 1057, 1614])).
% 0.70/0.91 tff(1633,plain,(c2_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1037)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(1634,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1633, 1611, 1610, 1541, 1609])).
% 0.70/0.91 % SZS output end Proof
% 0.70/0.91 % E exiting
%------------------------------------------------------------------------------