%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN484-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:39:18 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.77s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN484-1 : TPTP v9.0.0. Released v2.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:37:17 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.62/0.77 % SZS status Unsatisfiable
% 0.62/0.77 % SZS output start Proof
% 0.62/0.77 tff(c0_1_type, type, (
% 0.62/0.77 c0_1: $i > $o)).
% 0.62/0.77 tff(a2003_type, type, (
% 0.62/0.77 a2003: $i)).
% 0.62/0.77 tff(a1987_type, type, (
% 0.62/0.77 a1987: $i)).
% 0.62/0.77 tff(c2_1_type, type, (
% 0.62/0.77 c2_1: $i > $o)).
% 0.62/0.77 tff(c1_1_type, type, (
% 0.62/0.77 c1_1: $i > $o)).
% 0.62/0.77 tff(c3_1_type, type, (
% 0.62/0.77 c3_1: $i > $o)).
% 0.62/0.77 tff(ndr1_0_type, type, (
% 0.62/0.77 ndr1_0: $o)).
% 0.62/0.77 tff(a1975_type, type, (
% 0.62/0.77 a1975: $i)).
% 0.62/0.77 tff(hskp4_type, type, (
% 0.62/0.77 hskp4: $o)).
% 0.62/0.77 tff(a1977_type, type, (
% 0.62/0.77 a1977: $i)).
% 0.62/0.77 tff(a1983_type, type, (
% 0.62/0.77 a1983: $i)).
% 0.62/0.77 tff(a1991_type, type, (
% 0.62/0.77 a1991: $i)).
% 0.62/0.77 tff(a2000_type, type, (
% 0.62/0.77 a2000: $i)).
% 0.62/0.77 tff(hskp18_type, type, (
% 0.62/0.77 hskp18: $o)).
% 0.62/0.77 tff(hskp17_type, type, (
% 0.62/0.77 hskp17: $o)).
% 0.62/0.77 tff(hskp13_type, type, (
% 0.62/0.77 hskp13: $o)).
% 0.62/0.77 tff(a1970_type, type, (
% 0.62/0.77 a1970: $i)).
% 0.62/0.77 tff(hskp27_type, type, (
% 0.62/0.77 hskp27: $o)).
% 0.62/0.77 tff(a2005_type, type, (
% 0.62/0.77 a2005: $i)).
% 0.62/0.77 tff(hskp30_type, type, (
% 0.62/0.77 hskp30: $o)).
% 0.62/0.77 tff(hskp8_type, type, (
% 0.62/0.77 hskp8: $o)).
% 0.62/0.77 tff(a1971_type, type, (
% 0.62/0.77 a1971: $i)).
% 0.62/0.77 tff(hskp1_type, type, (
% 0.62/0.77 hskp1: $o)).
% 0.62/0.77 tff(a1979_type, type, (
% 0.62/0.77 a1979: $i)).
% 0.62/0.77 tff(hskp6_type, type, (
% 0.62/0.77 hskp6: $o)).
% 0.62/0.77 tff(hskp5_type, type, (
% 0.62/0.77 hskp5: $o)).
% 0.62/0.77 tff(a1993_type, type, (
% 0.62/0.77 a1993: $i)).
% 0.62/0.77 tff(hskp15_type, type, (
% 0.62/0.77 hskp15: $o)).
% 0.62/0.77 tff(hskp10_type, type, (
% 0.62/0.77 hskp10: $o)).
% 0.62/0.77 tff(a2012_type, type, (
% 0.62/0.77 a2012: $i)).
% 0.62/0.77 tff(a1998_type, type, (
% 0.62/0.77 a1998: $i)).
% 0.62/0.77 tff(hskp22_type, type, (
% 0.62/0.77 hskp22: $o)).
% 0.62/0.77 tff(hskp2_type, type, (
% 0.62/0.77 hskp2: $o)).
% 0.62/0.77 tff(hskp20_type, type, (
% 0.62/0.77 hskp20: $o)).
% 0.62/0.77 tff(a1973_type, type, (
% 0.62/0.77 a1973: $i)).
% 0.62/0.77 tff(hskp23_type, type, (
% 0.62/0.77 hskp23: $o)).
% 0.62/0.77 tff(a2014_type, type, (
% 0.62/0.77 a2014: $i)).
% 0.62/0.77 tff(a1989_type, type, (
% 0.62/0.77 a1989: $i)).
% 0.62/0.77 tff(hskp11_type, type, (
% 0.62/0.77 hskp11: $o)).
% 0.62/0.77 tff(a1996_type, type, (
% 0.62/0.77 a1996: $i)).
% 0.62/0.77 tff(hskp16_type, type, (
% 0.62/0.77 hskp16: $o)).
% 0.62/0.77 tff(a1972_type, type, (
% 0.62/0.77 a1972: $i)).
% 0.62/0.77 tff(hskp28_type, type, (
% 0.62/0.77 hskp28: $o)).
% 0.62/0.77 tff(1,plain,
% 0.62/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(2,plain,
% 0.62/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.62/0.77 tff(3,plain,
% 0.62/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(4,plain,
% 0.62/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | 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)) | (~c0_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(5,plain,
% 0.62/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[4])).
% 0.62/0.77 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.62/0.77 tff(7,plain,
% 0.62/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.62/0.77 tff(8,plain,
% 0.62/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.62/0.77 tff(9,plain,(
% 0.62/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(skolemize,[status(sab)],[8])).
% 0.62/0.77 tff(10,plain,
% 0.62/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.62/0.77 tff(11,plain,
% 0.62/0.77 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(12,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[11])).
% 0.62/0.77 tff(13,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(14,plain,
% 0.62/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(15,plain,
% 0.62/0.77 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[14])).
% 0.62/0.77 tff(16,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.62/0.77 tff(17,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.62/0.77 tff(18,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.62/0.77 tff(19,plain,(
% 0.62/0.77 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(skolemize,[status(sab)],[18])).
% 0.62/0.77 tff(20,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.62/0.77 tff(21,assumption,(~hskp4), introduced(assumption)).
% 0.62/0.77 tff(22,plain,
% 0.62/0.77 (^[U: $i] : refl((hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) <=> (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(23,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[22])).
% 0.62/0.77 tff(24,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(25,plain,
% 0.62/0.77 (^[U: $i] : 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)) | 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)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> ((hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(26,plain,
% 0.62/0.77 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[25])).
% 0.62/0.77 tff(27,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.62/0.77 tff(28,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.62/0.77 tff(29,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.62/0.77 tff(30,plain,(
% 0.62/0.77 ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(skolemize,[status(sab)],[29])).
% 0.62/0.77 tff(31,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.62/0.77 tff(32,assumption,(~hskp17), introduced(assumption)).
% 0.62/0.77 tff(33,plain,
% 0.62/0.77 (^[U: $i] : refl((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(34,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[33])).
% 0.62/0.77 tff(35,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(36,plain,
% 0.62/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(37,plain,
% 0.62/0.77 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> ![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[36])).
% 0.62/0.77 tff(38,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.62/0.77 tff(39,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.62/0.77 tff(40,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.62/0.77 tff(41,plain,(
% 0.62/0.77 ![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(skolemize,[status(sab)],[40])).
% 0.62/0.77 tff(42,plain,
% 0.62/0.77 (![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.62/0.77 tff(43,assumption,(~hskp27), introduced(assumption)).
% 0.62/0.77 tff(44,plain,
% 0.62/0.77 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(45,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[44])).
% 0.62/0.77 tff(46,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(47,plain,
% 0.62/0.77 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(48,plain,
% 0.62/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[47])).
% 0.62/0.78 tff(49,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.62/0.78 tff(50,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.62/0.78 tff(51,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.62/0.78 tff(52,plain,(
% 0.62/0.78 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.78 inference(skolemize,[status(sab)],[51])).
% 0.62/0.78 tff(53,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.62/0.78 tff(54,assumption,(~hskp30), introduced(assumption)).
% 0.62/0.78 tff(55,plain,
% 0.62/0.78 ((hskp30 | hskp27 | hskp6) <=> (hskp30 | hskp27 | hskp6)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(56,plain,
% 0.62/0.78 (((hskp30 | hskp27) | hskp6) <=> (hskp30 | hskp27 | hskp6)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(57,plain,
% 0.62/0.78 ((hskp30 | hskp27) <=> (hskp30 | hskp27)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(58,plain,
% 0.62/0.78 (((hskp30 | hskp27) | hskp6) <=> ((hskp30 | hskp27) | hskp6)),
% 0.62/0.78 inference(monotonicity,[status(thm)],[57])).
% 0.62/0.78 tff(59,plain,
% 0.62/0.78 (((hskp30 | hskp27) | hskp6) <=> (hskp30 | hskp27 | hskp6)),
% 0.62/0.78 inference(transitivity,[status(thm)],[58, 56])).
% 0.62/0.78 tff(60,axiom,((hskp30 | hskp27) | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.62/0.78 tff(61,plain,
% 0.62/0.78 (hskp30 | hskp27 | hskp6),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.62/0.78 tff(62,plain,
% 0.62/0.78 (hskp30 | hskp27 | hskp6),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[61, 55])).
% 0.62/0.78 tff(63,plain,
% 0.62/0.78 (hskp30 | hskp27 | hskp6),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.62/0.78 tff(64,plain,
% 0.62/0.78 (hskp30 | hskp27 | hskp6),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[63, 55])).
% 0.62/0.78 tff(65,plain,
% 0.62/0.78 (hskp30 | hskp27 | hskp6),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[64, 55])).
% 0.62/0.78 tff(66,plain,
% 0.62/0.78 (hskp6),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[65, 54, 43])).
% 0.62/0.78 tff(67,plain,
% 0.62/0.78 (((~hskp6) | (~c2_1(a1979))) <=> ((~hskp6) | (~c2_1(a1979)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(68,plain,
% 0.62/0.78 (((~c2_1(a1979)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1979)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(69,axiom,((~c2_1(a1979)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.62/0.78 tff(70,plain,
% 0.62/0.78 ((~hskp6) | (~c2_1(a1979))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.62/0.78 tff(71,plain,
% 0.62/0.78 ((~hskp6) | (~c2_1(a1979))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.62/0.78 tff(72,plain,
% 0.62/0.78 (~c2_1(a1979)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[71, 66])).
% 0.62/0.78 tff(73,plain,
% 0.62/0.78 (((~hskp6) | (~c0_1(a1979))) <=> ((~hskp6) | (~c0_1(a1979)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(74,plain,
% 0.62/0.78 (((~c0_1(a1979)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a1979)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(75,axiom,((~c0_1(a1979)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.62/0.78 tff(76,plain,
% 0.62/0.78 ((~hskp6) | (~c0_1(a1979))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.62/0.78 tff(77,plain,
% 0.62/0.78 ((~hskp6) | (~c0_1(a1979))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.62/0.78 tff(78,plain,
% 0.62/0.78 (~c0_1(a1979)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[77, 66])).
% 0.62/0.78 tff(79,plain,
% 0.62/0.78 (((~hskp6) | c3_1(a1979)) <=> ((~hskp6) | c3_1(a1979))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(80,axiom,((~hskp6) | c3_1(a1979)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.62/0.78 tff(81,plain,
% 0.62/0.78 ((~hskp6) | c3_1(a1979)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.62/0.78 tff(82,plain,
% 0.62/0.78 ((~hskp6) | c3_1(a1979)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.62/0.78 tff(83,plain,
% 0.62/0.78 ((~hskp6) | c3_1(a1979)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.62/0.78 tff(84,plain,
% 0.62/0.78 ((~hskp6) | c3_1(a1979)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.62/0.78 tff(85,plain,
% 0.62/0.78 ((~hskp6) | c3_1(a1979)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[84, 79])).
% 0.62/0.78 tff(86,plain,
% 0.62/0.78 (c3_1(a1979)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[85, 66])).
% 0.62/0.78 tff(87,plain,
% 0.62/0.78 (^[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) | c2_1(W) | (~c3_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) | (~c3_1(W))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(88,plain,
% 0.62/0.78 (![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) | c2_1(W) | (~c3_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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[87])).
% 0.62/0.78 tff(89,plain,
% 0.62/0.78 (![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) | c2_1(W) | (~c3_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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(90,plain,
% 0.62/0.78 (^[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))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_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)) | (~c3_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)) | (~c3_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) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_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) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_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) | (~c3_1(W))) | c2_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) | (~c3_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) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_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) | c2_1(W) | (~c3_1(W)))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(91,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[90])).
% 0.62/0.78 tff(92,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.62/0.78 tff(93,plain,
% 0.62/0.78 (![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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.62/0.78 tff(94,plain,
% 0.62/0.78 (![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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.62/0.78 tff(95,plain,(
% 0.62/0.78 ![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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(skolemize,[status(sab)],[94])).
% 0.62/0.78 tff(96,plain,
% 0.62/0.78 (![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) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.62/0.78 tff(97,assumption,(hskp4), introduced(assumption)).
% 0.62/0.78 tff(98,plain,
% 0.62/0.78 (((~hskp4) | (~c2_1(a1975))) <=> ((~hskp4) | (~c2_1(a1975)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(99,plain,
% 0.62/0.78 (((~c2_1(a1975)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1975)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(100,axiom,((~c2_1(a1975)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.62/0.78 tff(101,plain,
% 0.62/0.78 ((~hskp4) | (~c2_1(a1975))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.62/0.78 tff(102,plain,
% 0.62/0.78 ((~hskp4) | (~c2_1(a1975))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[101, 98])).
% 0.62/0.78 tff(103,plain,
% 0.62/0.78 (~c2_1(a1975)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[102, 97])).
% 0.62/0.78 tff(104,plain,
% 0.62/0.78 (((~hskp4) | (~c1_1(a1975))) <=> ((~hskp4) | (~c1_1(a1975)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(105,plain,
% 0.62/0.78 (((~c1_1(a1975)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1975)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(106,axiom,((~c1_1(a1975)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.62/0.78 tff(107,plain,
% 0.62/0.78 ((~hskp4) | (~c1_1(a1975))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.62/0.78 tff(108,plain,
% 0.62/0.78 ((~hskp4) | (~c1_1(a1975))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.62/0.78 tff(109,plain,
% 0.62/0.78 (~c1_1(a1975)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[108, 97])).
% 0.62/0.78 tff(110,plain,
% 0.62/0.78 (^[U: $i] : refl((hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(111,plain,
% 0.62/0.78 (![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[110])).
% 0.62/0.78 tff(112,plain,
% 0.62/0.78 (![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(113,plain,
% 0.62/0.78 (^[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)) | 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)) | 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) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp5) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp5) <=> (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp5) <=> (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(114,plain,
% 0.62/0.78 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp5) <=> ![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[113])).
% 0.62/0.78 tff(115,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.62/0.78 tff(116,plain,
% 0.62/0.78 (![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.62/0.78 tff(117,plain,
% 0.62/0.78 (![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.62/0.78 tff(118,plain,(
% 0.62/0.78 ![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(skolemize,[status(sab)],[117])).
% 0.62/0.78 tff(119,plain,
% 0.62/0.78 (![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.62/0.78 tff(120,plain,
% 0.62/0.78 (((~hskp4) | c0_1(a1975)) <=> ((~hskp4) | c0_1(a1975))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(121,axiom,((~hskp4) | c0_1(a1975)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.62/0.78 tff(122,plain,
% 0.62/0.78 ((~hskp4) | c0_1(a1975)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.62/0.78 tff(123,plain,
% 0.62/0.78 ((~hskp4) | c0_1(a1975)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[122, 120])).
% 0.62/0.78 tff(124,plain,
% 0.62/0.78 ((~hskp4) | c0_1(a1975)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[123, 120])).
% 0.62/0.78 tff(125,plain,
% 0.62/0.78 ((~hskp4) | c0_1(a1975)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.62/0.78 tff(126,plain,
% 0.62/0.78 ((~hskp4) | c0_1(a1975)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[125, 120])).
% 0.62/0.78 tff(127,plain,
% 0.62/0.78 (c0_1(a1975)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[126, 97])).
% 0.62/0.78 tff(128,assumption,(~ndr1_0), introduced(assumption)).
% 0.62/0.78 tff(129,plain,
% 0.62/0.78 ((ndr1_0 | (~hskp6)) <=> (ndr1_0 | (~hskp6))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(130,plain,
% 0.62/0.78 (((~hskp6) | ndr1_0) <=> (ndr1_0 | (~hskp6))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(131,axiom,((~hskp6) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 0.62/0.78 tff(132,plain,
% 0.62/0.78 (ndr1_0 | (~hskp6)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.62/0.78 tff(133,plain,
% 0.62/0.78 (ndr1_0 | (~hskp6)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[132, 129])).
% 0.62/0.78 tff(134,plain,
% 0.62/0.78 (~hskp6),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[133, 128])).
% 0.62/0.78 tff(135,plain,
% 0.62/0.78 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(136,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.62/0.78 tff(137,plain,
% 0.62/0.78 ((~hskp30) | ndr1_0),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.62/0.78 tff(138,plain,
% 0.62/0.78 ((~hskp30) | ndr1_0),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[137, 135])).
% 0.62/0.78 tff(139,plain,
% 0.62/0.78 ((~hskp30) | ndr1_0),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[138, 135])).
% 0.62/0.78 tff(140,plain,
% 0.62/0.78 ((~hskp30) | ndr1_0),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.62/0.78 tff(141,plain,
% 0.62/0.78 ((~hskp30) | ndr1_0),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[140, 135])).
% 0.62/0.78 tff(142,plain,
% 0.62/0.78 (~hskp30),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[141, 128])).
% 0.62/0.78 tff(143,plain,
% 0.62/0.78 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(144,plain,
% 0.62/0.78 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(145,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.62/0.78 tff(146,plain,
% 0.62/0.78 (ndr1_0 | (~hskp27)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.62/0.78 tff(147,plain,
% 0.62/0.78 (ndr1_0 | (~hskp27)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.62/0.78 tff(148,plain,
% 0.62/0.78 (~hskp27),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[147, 128])).
% 0.62/0.78 tff(149,plain,
% 0.62/0.78 ($false),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[65, 148, 142, 134])).
% 0.62/0.78 tff(150,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.62/0.78 tff(151,plain,
% 0.62/0.78 (((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)))) <=> ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp5 | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(152,plain,
% 0.62/0.78 ((hskp30 | hskp5 | (~ndr1_0) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975))) <=> (hskp30 | hskp5 | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(153,plain,
% 0.62/0.78 (((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | (~ndr1_0) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))) <=> ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975))))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[152])).
% 0.62/0.78 tff(154,plain,
% 0.62/0.78 (((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | (~ndr1_0) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))) <=> ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp5 | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)))),
% 0.62/0.78 inference(transitivity,[status(thm)],[153, 151])).
% 0.62/0.78 tff(155,plain,
% 0.62/0.78 ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | (~ndr1_0) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(156,plain,
% 0.62/0.78 ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp5 | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.62/0.78 tff(157,plain,
% 0.62/0.78 (hskp5),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[156, 54, 150, 127, 109, 103, 119])).
% 0.62/0.78 tff(158,plain,
% 0.62/0.78 (((~hskp5) | (~c2_1(a1977))) <=> ((~hskp5) | (~c2_1(a1977)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(159,plain,
% 0.62/0.78 (((~c2_1(a1977)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1977)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(160,axiom,((~c2_1(a1977)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.62/0.78 tff(161,plain,
% 0.62/0.78 ((~hskp5) | (~c2_1(a1977))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.62/0.78 tff(162,plain,
% 0.62/0.78 ((~hskp5) | (~c2_1(a1977))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.62/0.78 tff(163,plain,
% 0.62/0.78 (~c2_1(a1977)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[162, 157])).
% 0.62/0.78 tff(164,assumption,(~c2_1(a1979)), introduced(assumption)).
% 0.62/0.78 tff(165,assumption,(~c0_1(a1979)), introduced(assumption)).
% 0.62/0.78 tff(166,plain,
% 0.62/0.78 (((~hskp5) | c1_1(a1977)) <=> ((~hskp5) | c1_1(a1977))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(167,axiom,((~hskp5) | c1_1(a1977)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.62/0.78 tff(168,plain,
% 0.62/0.78 ((~hskp5) | c1_1(a1977)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.62/0.78 tff(169,plain,
% 0.62/0.78 ((~hskp5) | c1_1(a1977)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.62/0.78 tff(170,plain,
% 0.62/0.78 ((~hskp5) | c1_1(a1977)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.62/0.78 tff(171,plain,
% 0.62/0.78 ((~hskp5) | c1_1(a1977)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.62/0.78 tff(172,plain,
% 0.62/0.78 ((~hskp5) | c1_1(a1977)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.62/0.78 tff(173,plain,
% 0.62/0.78 (c1_1(a1977)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[172, 157])).
% 0.62/0.78 tff(174,assumption,(c3_1(a1979)), introduced(assumption)).
% 0.62/0.78 tff(175,plain,
% 0.62/0.78 (((~![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) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(176,plain,
% 0.62/0.78 (((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(177,plain,
% 0.62/0.78 (((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979))))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[176])).
% 0.62/0.78 tff(178,plain,
% 0.62/0.78 (((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)))),
% 0.62/0.78 inference(transitivity,[status(thm)],[177, 175])).
% 0.62/0.78 tff(179,plain,
% 0.62/0.78 ((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(180,plain,
% 0.62/0.78 ((~![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) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.62/0.78 tff(181,plain,
% 0.62/0.78 (~c0_1(a1977)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[180, 150, 174, 173, 127, 165, 164, 163, 109, 103, 96])).
% 0.62/0.78 tff(182,plain,
% 0.62/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(183,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_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)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[182])).
% 0.62/0.78 tff(184,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_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)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(185,plain,
% 0.62/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(186,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[185])).
% 0.62/0.79 tff(187,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.62/0.79 tff(188,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.62/0.79 tff(189,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.62/0.79 tff(190,plain,(
% 0.62/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(skolemize,[status(sab)],[189])).
% 0.62/0.79 tff(191,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.62/0.79 tff(192,plain,
% 0.62/0.79 (((~hskp5) | (~c3_1(a1977))) <=> ((~hskp5) | (~c3_1(a1977)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(193,plain,
% 0.62/0.79 (((~c3_1(a1977)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1977)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(194,axiom,((~c3_1(a1977)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.62/0.79 tff(195,plain,
% 0.62/0.79 ((~hskp5) | (~c3_1(a1977))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.62/0.79 tff(196,plain,
% 0.62/0.79 ((~hskp5) | (~c3_1(a1977))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[195, 192])).
% 0.62/0.79 tff(197,plain,
% 0.62/0.79 (~c3_1(a1977)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[196, 157])).
% 0.62/0.79 tff(198,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1979) | c2_1(a1979) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c0_1(a1977) | (~c3_1(a1979)) | (~c1_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c0_1(a1977) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(199,plain,
% 0.62/0.79 (((~ndr1_0) | c2_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)) | c3_1(a1977) | c0_1(a1977) | (~c1_1(a1977)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (c0_1(a1979) | c2_1(a1979) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c0_1(a1977) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(200,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)) | c3_1(a1977) | c0_1(a1977) | (~c1_1(a1977)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1979) | c2_1(a1979) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c0_1(a1977) | (~c3_1(a1979)) | (~c1_1(a1979))))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[199])).
% 0.62/0.79 tff(201,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)) | c3_1(a1977) | c0_1(a1977) | (~c1_1(a1977)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c0_1(a1977) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.79 inference(transitivity,[status(thm)],[200, 198])).
% 0.62/0.79 tff(202,plain,
% 0.62/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)) | c3_1(a1977) | c0_1(a1977) | (~c1_1(a1977)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(203,plain,
% 0.62/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c0_1(a1977) | (~c3_1(a1979)) | (~c1_1(a1979))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.62/0.79 tff(204,plain,
% 0.62/0.79 (~c1_1(a1979)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[203, 150, 174, 173, 165, 164, 197, 191, 181])).
% 0.62/0.79 tff(205,plain,
% 0.62/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(206,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_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) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[205])).
% 0.62/0.79 tff(207,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_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) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(208,plain,
% 0.62/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(209,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[208])).
% 0.62/0.79 tff(210,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.62/0.79 tff(211,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.62/0.79 tff(212,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.62/0.79 tff(213,plain,(
% 0.62/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(skolemize,[status(sab)],[212])).
% 0.62/0.79 tff(214,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.62/0.79 tff(215,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c3_1(a1979)) | c1_1(a1979))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(216,plain,
% 0.62/0.79 (((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(217,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c3_1(a1979)) | c1_1(a1979)))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[216])).
% 0.62/0.79 tff(218,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.79 inference(transitivity,[status(thm)],[217, 215])).
% 0.62/0.79 tff(219,plain,
% 0.62/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(220,plain,
% 0.62/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c3_1(a1979)) | c1_1(a1979)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.62/0.79 tff(221,plain,
% 0.62/0.79 ($false),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[220, 150, 174, 173, 165, 164, 163, 197, 214, 204])).
% 0.62/0.79 tff(222,plain,((~hskp4) | (~c3_1(a1979)) | c0_1(a1979) | c2_1(a1979) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.62/0.79 tff(223,plain,
% 0.62/0.79 (~hskp4),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[222, 86, 78, 72, 54])).
% 0.62/0.79 tff(224,assumption,(hskp18), introduced(assumption)).
% 0.62/0.79 tff(225,plain,
% 0.62/0.79 (((~hskp18) | (~c0_1(a2000))) <=> ((~hskp18) | (~c0_1(a2000)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(226,plain,
% 0.62/0.79 (((~c0_1(a2000)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a2000)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(227,axiom,((~c0_1(a2000)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.62/0.79 tff(228,plain,
% 0.62/0.79 ((~hskp18) | (~c0_1(a2000))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.62/0.79 tff(229,plain,
% 0.62/0.79 ((~hskp18) | (~c0_1(a2000))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[228, 225])).
% 0.62/0.79 tff(230,plain,
% 0.62/0.79 (~c0_1(a2000)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[229, 224])).
% 0.62/0.79 tff(231,plain,
% 0.62/0.79 (((~hskp18) | (~c1_1(a2000))) <=> ((~hskp18) | (~c1_1(a2000)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(232,plain,
% 0.62/0.79 (((~c1_1(a2000)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a2000)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(233,axiom,((~c1_1(a2000)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.62/0.79 tff(234,plain,
% 0.62/0.79 ((~hskp18) | (~c1_1(a2000))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.62/0.79 tff(235,plain,
% 0.62/0.79 ((~hskp18) | (~c1_1(a2000))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[234, 231])).
% 0.62/0.79 tff(236,plain,
% 0.62/0.79 (~c1_1(a2000)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[235, 224])).
% 0.62/0.79 tff(237,plain,
% 0.62/0.79 (((~hskp18) | (~c3_1(a2000))) <=> ((~hskp18) | (~c3_1(a2000)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(238,plain,
% 0.62/0.79 (((~c3_1(a2000)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a2000)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(239,axiom,((~c3_1(a2000)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.62/0.79 tff(240,plain,
% 0.62/0.79 ((~hskp18) | (~c3_1(a2000))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.62/0.79 tff(241,plain,
% 0.62/0.79 ((~hskp18) | (~c3_1(a2000))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[240, 237])).
% 0.62/0.79 tff(242,plain,
% 0.62/0.79 (~c3_1(a2000)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[241, 224])).
% 0.62/0.79 tff(243,plain,
% 0.62/0.79 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(244,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[243])).
% 0.62/0.79 tff(245,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(246,plain,
% 0.62/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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) | c2_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(247,plain,
% 0.62/0.79 (![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[246])).
% 0.62/0.79 tff(248,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.62/0.79 tff(249,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.62/0.79 tff(250,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.62/0.79 tff(251,plain,(
% 0.62/0.79 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(skolemize,[status(sab)],[250])).
% 0.62/0.79 tff(252,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.62/0.79 tff(253,assumption,(~c3_1(a2000)), introduced(assumption)).
% 0.62/0.79 tff(254,assumption,(~c1_1(a2000)), introduced(assumption)).
% 0.62/0.79 tff(255,assumption,(~c0_1(a2000)), introduced(assumption)).
% 0.62/0.79 tff(256,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | c2_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | c2_1(a2000))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(257,plain,
% 0.62/0.79 ((hskp27 | (~ndr1_0) | c0_1(a2000) | c2_1(a2000) | c3_1(a2000) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000)) <=> (hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | c2_1(a2000))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(258,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a2000) | c2_1(a2000) | c3_1(a2000) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | c2_1(a2000)))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[257])).
% 0.62/0.79 tff(259,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a2000) | c2_1(a2000) | c3_1(a2000) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | c2_1(a2000))),
% 0.62/0.79 inference(transitivity,[status(thm)],[258, 256])).
% 0.62/0.79 tff(260,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a2000) | c2_1(a2000) | c3_1(a2000) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(261,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | c2_1(a2000)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.62/0.79 tff(262,plain,
% 0.62/0.79 (c2_1(a2000)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[261, 150, 43, 255, 254, 253, 252])).
% 0.62/0.79 tff(263,plain,
% 0.62/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(264,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[263])).
% 0.62/0.79 tff(265,plain,
% 0.62/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(266,plain,
% 0.62/0.80 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_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)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(267,plain,
% 0.62/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[266])).
% 0.62/0.80 tff(268,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.62/0.80 tff(269,plain,
% 0.62/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.62/0.80 tff(270,plain,
% 0.62/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.62/0.80 tff(271,plain,(
% 0.62/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.80 inference(skolemize,[status(sab)],[270])).
% 0.62/0.80 tff(272,plain,
% 0.62/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.62/0.80 tff(273,plain,
% 0.62/0.80 (^[U: $i] : refl((hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(274,plain,
% 0.62/0.80 (![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[273])).
% 0.62/0.80 tff(275,plain,
% 0.62/0.80 (![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(276,plain,
% 0.62/0.80 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp27) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp27))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp27) <=> (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp27) <=> (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(277,plain,
% 0.62/0.80 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp27) <=> ![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[276])).
% 0.62/0.80 tff(278,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.62/0.80 tff(279,plain,
% 0.62/0.80 (![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.62/0.80 tff(280,plain,
% 0.62/0.80 (![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.62/0.80 tff(281,plain,(
% 0.62/0.80 ![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(skolemize,[status(sab)],[280])).
% 0.62/0.80 tff(282,plain,
% 0.62/0.80 (![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.62/0.80 tff(283,plain,
% 0.62/0.80 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c0_1(a2000) | c1_1(a2000) | (~ndr1_0) | (~c2_1(a2000)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a2000) | c1_1(a2000) | (~ndr1_0) | (~c2_1(a2000)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(284,plain,
% 0.62/0.80 ((hskp27 | hskp4 | (~ndr1_0) | c1_1(a2000) | c0_1(a2000) | (~c2_1(a2000))) <=> (hskp27 | hskp4 | c0_1(a2000) | c1_1(a2000) | (~ndr1_0) | (~c2_1(a2000)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(285,plain,
% 0.62/0.80 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a2000) | c0_1(a2000) | (~c2_1(a2000)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c0_1(a2000) | c1_1(a2000) | (~ndr1_0) | (~c2_1(a2000))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[284])).
% 0.62/0.80 tff(286,plain,
% 0.62/0.80 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a2000) | c0_1(a2000) | (~c2_1(a2000)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a2000) | c1_1(a2000) | (~ndr1_0) | (~c2_1(a2000)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[285, 283])).
% 0.62/0.80 tff(287,plain,
% 0.62/0.80 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a2000) | c0_1(a2000) | (~c2_1(a2000)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(288,plain,
% 0.62/0.80 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a2000) | c1_1(a2000) | (~ndr1_0) | (~c2_1(a2000))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.62/0.80 tff(289,plain,
% 0.62/0.80 (hskp4 | c1_1(a2000) | (~c2_1(a2000))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[288, 150, 43, 255, 282])).
% 0.62/0.80 tff(290,plain,
% 0.62/0.80 (hskp4),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[289, 262, 254])).
% 0.62/0.80 tff(291,plain,
% 0.62/0.80 (~c2_1(a1975)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[102, 290])).
% 0.62/0.80 tff(292,plain,
% 0.62/0.80 (~c1_1(a1975)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[108, 290])).
% 0.62/0.80 tff(293,plain,
% 0.62/0.80 (c0_1(a1975)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[126, 290])).
% 0.62/0.80 tff(294,plain,
% 0.62/0.80 (hskp5),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[156, 54, 150, 293, 292, 291, 119])).
% 0.62/0.80 tff(295,plain,
% 0.62/0.80 (~c2_1(a1977)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[162, 294])).
% 0.62/0.80 tff(296,plain,
% 0.62/0.80 (c1_1(a1977)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[172, 294])).
% 0.62/0.80 tff(297,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2000) | c3_1(a2000) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)) | (~c2_1(a2000)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2000) | c3_1(a2000) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)) | (~c2_1(a2000)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(298,plain,
% 0.62/0.80 (((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c3_1(a2000) | c1_1(a2000) | (~c2_1(a2000)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (c1_1(a2000) | c3_1(a2000) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)) | (~c2_1(a2000)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(299,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c3_1(a2000) | c1_1(a2000) | (~c2_1(a2000)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2000) | c3_1(a2000) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)) | (~c2_1(a2000))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[298])).
% 0.62/0.80 tff(300,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c3_1(a2000) | c1_1(a2000) | (~c2_1(a2000)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2000) | c3_1(a2000) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)) | (~c2_1(a2000)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[299, 297])).
% 0.62/0.80 tff(301,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c3_1(a2000) | c1_1(a2000) | (~c2_1(a2000)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(302,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2000) | c3_1(a2000) | c0_1(a1979) | c2_1(a1979) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1979)) | (~c2_1(a2000))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.62/0.80 tff(303,plain,
% 0.62/0.80 (~c0_1(a1977)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[302, 150, 86, 296, 254, 253, 78, 72, 295, 272, 262])).
% 0.62/0.80 tff(304,plain,
% 0.62/0.80 (~c3_1(a1977)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[196, 294])).
% 0.62/0.80 tff(305,plain,
% 0.62/0.80 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | c0_1(a1977))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | c0_1(a1977))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(306,plain,
% 0.62/0.80 ((hskp27 | (~ndr1_0) | c0_1(a1977) | c2_1(a1977) | c3_1(a1977) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000)) <=> (hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | c0_1(a1977))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(307,plain,
% 0.62/0.80 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a1977) | c2_1(a1977) | c3_1(a1977) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | c0_1(a1977)))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[306])).
% 0.62/0.80 tff(308,plain,
% 0.62/0.80 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a1977) | c2_1(a1977) | c3_1(a1977) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | c0_1(a1977))),
% 0.62/0.80 inference(transitivity,[status(thm)],[307, 305])).
% 0.62/0.80 tff(309,plain,
% 0.62/0.80 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a1977) | c2_1(a1977) | c3_1(a1977) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(310,plain,
% 0.62/0.80 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | c0_1(a1977)),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.62/0.80 tff(311,plain,
% 0.62/0.80 ($false),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[310, 150, 43, 255, 254, 253, 295, 304, 252, 303])).
% 0.62/0.80 tff(312,plain,(c3_1(a2000) | hskp27 | c0_1(a2000) | c1_1(a2000) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.62/0.80 tff(313,plain,
% 0.62/0.80 ($false),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[312, 242, 236, 230, 43, 54])).
% 0.62/0.80 tff(314,plain,((~hskp18) | hskp27 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.62/0.80 tff(315,plain,
% 0.62/0.80 (~hskp18),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[314, 54, 43])).
% 0.62/0.80 tff(316,assumption,(~hskp1), introduced(assumption)).
% 0.62/0.80 tff(317,assumption,(~hskp18), introduced(assumption)).
% 0.62/0.80 tff(318,plain,
% 0.62/0.80 (^[U: $i] : refl((hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(319,plain,
% 0.62/0.80 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[318])).
% 0.62/0.80 tff(320,plain,
% 0.62/0.80 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(321,plain,
% 0.62/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp18) <=> ((hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp18) <=> (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(322,plain,
% 0.62/0.80 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp18) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[321])).
% 0.62/0.80 tff(323,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.62/0.80 tff(324,plain,
% 0.62/0.80 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.62/0.80 tff(325,plain,
% 0.62/0.80 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.62/0.80 tff(326,plain,(
% 0.62/0.80 ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(skolemize,[status(sab)],[325])).
% 0.62/0.80 tff(327,plain,
% 0.62/0.80 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.62/0.80 tff(328,plain,
% 0.62/0.80 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | c0_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | (~c1_1(a1979)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | c0_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(329,plain,
% 0.62/0.80 ((hskp18 | hskp4 | (~ndr1_0) | c0_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979))) <=> (hskp18 | hskp4 | c0_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(330,plain,
% 0.62/0.80 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | c0_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | (~c1_1(a1979))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[329])).
% 0.62/0.80 tff(331,plain,
% 0.62/0.80 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | c0_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[330, 328])).
% 0.62/0.80 tff(332,plain,
% 0.62/0.80 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1979) | (~c3_1(a1979)) | (~c1_1(a1979)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(333,plain,
% 0.62/0.80 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | c0_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | (~c1_1(a1979))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.62/0.80 tff(334,plain,
% 0.62/0.80 (hskp18 | hskp4 | (~c1_1(a1979))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[333, 150, 86, 78, 327])).
% 0.62/0.80 tff(335,plain,
% 0.62/0.80 (~c1_1(a1979)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[334, 21, 317])).
% 0.62/0.80 tff(336,plain,
% 0.62/0.80 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(337,plain,
% 0.62/0.80 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[336])).
% 0.62/0.80 tff(338,plain,
% 0.62/0.80 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(339,plain,
% 0.62/0.80 (^[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) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp10))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(340,plain,
% 0.62/0.81 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[339])).
% 0.62/0.81 tff(341,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.62/0.81 tff(342,plain,
% 0.62/0.81 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.62/0.81 tff(343,plain,
% 0.62/0.81 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.62/0.81 tff(344,plain,(
% 0.62/0.81 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[343])).
% 0.62/0.81 tff(345,plain,
% 0.62/0.81 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[344, 337])).
% 0.62/0.81 tff(346,plain,
% 0.62/0.81 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(347,plain,
% 0.62/0.81 ((hskp10 | hskp1 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (hskp10 | hskp1 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(348,plain,
% 0.62/0.81 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979)))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[347])).
% 0.62/0.81 tff(349,plain,
% 0.62/0.81 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.81 inference(transitivity,[status(thm)],[348, 346])).
% 0.62/0.81 tff(350,plain,
% 0.62/0.81 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(351,plain,
% 0.62/0.81 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.62/0.81 tff(352,plain,
% 0.62/0.81 (hskp10 | hskp1 | c1_1(a1979)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[351, 150, 86, 72, 345])).
% 0.62/0.81 tff(353,plain,
% 0.62/0.81 (hskp10),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[352, 335, 316])).
% 0.62/0.81 tff(354,plain,
% 0.62/0.81 (((~hskp10) | (~c1_1(a1987))) <=> ((~hskp10) | (~c1_1(a1987)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(355,plain,
% 0.62/0.81 (((~c1_1(a1987)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1987)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(356,axiom,((~c1_1(a1987)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.62/0.81 tff(357,plain,
% 0.62/0.81 ((~hskp10) | (~c1_1(a1987))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.62/0.81 tff(358,plain,
% 0.62/0.81 ((~hskp10) | (~c1_1(a1987))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[357, 354])).
% 0.62/0.81 tff(359,plain,
% 0.62/0.81 (~c1_1(a1987)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[358, 353])).
% 0.62/0.81 tff(360,plain,
% 0.62/0.81 (((~hskp10) | c2_1(a1987)) <=> ((~hskp10) | c2_1(a1987))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(361,axiom,((~hskp10) | c2_1(a1987)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.62/0.81 tff(362,plain,
% 0.62/0.81 ((~hskp10) | c2_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.62/0.81 tff(363,plain,
% 0.62/0.81 ((~hskp10) | c2_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[362, 360])).
% 0.62/0.81 tff(364,plain,
% 0.62/0.81 ((~hskp10) | c2_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[363, 360])).
% 0.62/0.81 tff(365,plain,
% 0.62/0.81 ((~hskp10) | c2_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[364, 360])).
% 0.62/0.81 tff(366,plain,
% 0.62/0.81 ((~hskp10) | c2_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[365, 360])).
% 0.62/0.81 tff(367,plain,
% 0.62/0.81 (c2_1(a1987)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[366, 353])).
% 0.62/0.81 tff(368,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | c0_1(a1987))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | c0_1(a1987))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(369,plain,
% 0.62/0.81 ((hskp27 | hskp4 | (~ndr1_0) | c1_1(a1987) | c0_1(a1987) | (~c2_1(a1987))) <=> (hskp27 | hskp4 | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | c0_1(a1987))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(370,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1987) | c0_1(a1987) | (~c2_1(a1987)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | c0_1(a1987)))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[369])).
% 0.62/0.81 tff(371,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1987) | c0_1(a1987) | (~c2_1(a1987)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | c0_1(a1987))),
% 0.62/0.81 inference(transitivity,[status(thm)],[370, 368])).
% 0.62/0.81 tff(372,plain,
% 0.62/0.81 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1987) | c0_1(a1987) | (~c2_1(a1987)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(373,plain,
% 0.62/0.81 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | c0_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.62/0.81 tff(374,plain,
% 0.62/0.81 (c0_1(a1987)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[373, 150, 43, 21, 367, 359, 282])).
% 0.62/0.81 tff(375,plain,
% 0.62/0.81 (^[U: $i] : refl((hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(376,plain,
% 0.62/0.81 (![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[375])).
% 0.62/0.81 tff(377,plain,
% 0.62/0.81 (![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(378,plain,
% 0.62/0.81 (^[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)) | 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)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp30) | hskp15) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp30) | hskp15) <=> (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(379,plain,
% 0.62/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp30) | hskp15) <=> ![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[378])).
% 0.62/0.81 tff(380,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp30) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.62/0.81 tff(381,plain,
% 0.62/0.81 (![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.62/0.81 tff(382,plain,
% 0.62/0.81 (![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.62/0.81 tff(383,plain,(
% 0.62/0.81 ![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[382])).
% 0.62/0.81 tff(384,plain,
% 0.62/0.81 (![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[383, 376])).
% 0.62/0.81 tff(385,plain,
% 0.62/0.81 (((~hskp10) | c3_1(a1987)) <=> ((~hskp10) | c3_1(a1987))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(386,axiom,((~hskp10) | c3_1(a1987)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.62/0.81 tff(387,plain,
% 0.62/0.81 ((~hskp10) | c3_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.62/0.81 tff(388,plain,
% 0.62/0.81 ((~hskp10) | c3_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[387, 385])).
% 0.62/0.81 tff(389,plain,
% 0.62/0.81 ((~hskp10) | c3_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[388, 385])).
% 0.62/0.81 tff(390,plain,
% 0.62/0.81 ((~hskp10) | c3_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[389, 385])).
% 0.62/0.81 tff(391,plain,
% 0.62/0.81 ((~hskp10) | c3_1(a1987)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[390, 385])).
% 0.62/0.81 tff(392,plain,
% 0.62/0.81 (c3_1(a1987)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[391, 353])).
% 0.62/0.81 tff(393,plain,
% 0.62/0.81 (((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | (~c0_1(a1987)))) <=> ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp15 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(394,plain,
% 0.62/0.81 ((hskp30 | hskp15 | (~ndr1_0) | c1_1(a1987) | (~c3_1(a1987)) | (~c0_1(a1987))) <=> (hskp30 | hskp15 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(395,plain,
% 0.62/0.81 (((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | (~ndr1_0) | c1_1(a1987) | (~c3_1(a1987)) | (~c0_1(a1987)))) <=> ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | (~c0_1(a1987))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[394])).
% 0.62/0.81 tff(396,plain,
% 0.62/0.81 (((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | (~ndr1_0) | c1_1(a1987) | (~c3_1(a1987)) | (~c0_1(a1987)))) <=> ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp15 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[395, 393])).
% 0.62/0.81 tff(397,plain,
% 0.62/0.81 ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | (~ndr1_0) | c1_1(a1987) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(398,plain,
% 0.62/0.81 ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp15 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | (~c0_1(a1987))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.62/0.81 tff(399,plain,
% 0.62/0.81 (hskp15),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[398, 54, 150, 392, 359, 384, 374])).
% 0.62/0.81 tff(400,plain,
% 0.62/0.81 (((~hskp15) | (~c1_1(a1993))) <=> ((~hskp15) | (~c1_1(a1993)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(401,plain,
% 0.62/0.81 (((~c1_1(a1993)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1993)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(402,axiom,((~c1_1(a1993)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.62/0.81 tff(403,plain,
% 0.62/0.81 ((~hskp15) | (~c1_1(a1993))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.62/0.81 tff(404,plain,
% 0.62/0.81 ((~hskp15) | (~c1_1(a1993))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[403, 400])).
% 0.62/0.81 tff(405,plain,
% 0.62/0.81 (~c1_1(a1993)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[404, 399])).
% 0.62/0.81 tff(406,plain,
% 0.62/0.81 (((~hskp15) | (~c0_1(a1993))) <=> ((~hskp15) | (~c0_1(a1993)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(407,plain,
% 0.62/0.81 (((~c0_1(a1993)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1993)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(408,axiom,((~c0_1(a1993)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.62/0.81 tff(409,plain,
% 0.62/0.81 ((~hskp15) | (~c0_1(a1993))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.62/0.81 tff(410,plain,
% 0.62/0.81 ((~hskp15) | (~c0_1(a1993))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[409, 406])).
% 0.62/0.81 tff(411,plain,
% 0.62/0.81 (~c0_1(a1993)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[410, 399])).
% 0.62/0.81 tff(412,plain,
% 0.62/0.81 (((~hskp15) | c2_1(a1993)) <=> ((~hskp15) | c2_1(a1993))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(413,axiom,((~hskp15) | c2_1(a1993)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.62/0.81 tff(414,plain,
% 0.62/0.81 ((~hskp15) | c2_1(a1993)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.62/0.81 tff(415,plain,
% 0.62/0.81 ((~hskp15) | c2_1(a1993)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[414, 412])).
% 0.62/0.81 tff(416,plain,
% 0.62/0.81 ((~hskp15) | c2_1(a1993)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[415, 412])).
% 0.62/0.81 tff(417,plain,
% 0.62/0.81 ((~hskp15) | c2_1(a1993)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[416, 412])).
% 0.62/0.81 tff(418,plain,
% 0.62/0.81 ((~hskp15) | c2_1(a1993)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[417, 412])).
% 0.62/0.81 tff(419,plain,
% 0.62/0.81 (c2_1(a1993)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[418, 399])).
% 0.62/0.81 tff(420,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c0_1(a1993) | c1_1(a1993) | (~ndr1_0) | (~c2_1(a1993)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a1993) | c1_1(a1993) | (~ndr1_0) | (~c2_1(a1993)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(421,plain,
% 0.62/0.81 ((hskp27 | hskp4 | (~ndr1_0) | c1_1(a1993) | c0_1(a1993) | (~c2_1(a1993))) <=> (hskp27 | hskp4 | c0_1(a1993) | c1_1(a1993) | (~ndr1_0) | (~c2_1(a1993)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(422,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1993) | c0_1(a1993) | (~c2_1(a1993)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c0_1(a1993) | c1_1(a1993) | (~ndr1_0) | (~c2_1(a1993))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[421])).
% 0.62/0.81 tff(423,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1993) | c0_1(a1993) | (~c2_1(a1993)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a1993) | c1_1(a1993) | (~ndr1_0) | (~c2_1(a1993)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[422, 420])).
% 0.62/0.81 tff(424,plain,
% 0.62/0.81 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1993) | c0_1(a1993) | (~c2_1(a1993)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(425,plain,
% 0.62/0.81 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a1993) | c1_1(a1993) | (~ndr1_0) | (~c2_1(a1993))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.62/0.81 tff(426,plain,
% 0.62/0.81 ($false),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[425, 150, 43, 21, 419, 411, 405, 282])).
% 0.62/0.81 tff(427,plain,(hskp4 | hskp27 | hskp30 | hskp1 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.62/0.81 tff(428,plain,
% 0.62/0.81 (hskp1),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[427, 315, 54, 223, 43])).
% 0.62/0.81 tff(429,plain,
% 0.62/0.81 (((~hskp1) | (~c1_1(a1971))) <=> ((~hskp1) | (~c1_1(a1971)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(430,plain,
% 0.62/0.81 (((~c1_1(a1971)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1971)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(431,axiom,((~c1_1(a1971)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.62/0.81 tff(432,plain,
% 0.62/0.81 ((~hskp1) | (~c1_1(a1971))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.62/0.81 tff(433,plain,
% 0.62/0.81 ((~hskp1) | (~c1_1(a1971))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[432, 429])).
% 0.62/0.81 tff(434,plain,
% 0.62/0.81 (~c1_1(a1971)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[433, 428])).
% 0.62/0.81 tff(435,plain,
% 0.62/0.81 (((~hskp1) | c2_1(a1971)) <=> ((~hskp1) | c2_1(a1971))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(436,axiom,((~hskp1) | c2_1(a1971)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.62/0.81 tff(437,plain,
% 0.62/0.81 ((~hskp1) | c2_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.62/0.81 tff(438,plain,
% 0.62/0.81 ((~hskp1) | c2_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[437, 435])).
% 0.62/0.81 tff(439,plain,
% 0.62/0.81 ((~hskp1) | c2_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[438, 435])).
% 0.62/0.81 tff(440,plain,
% 0.62/0.81 ((~hskp1) | c2_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[439, 435])).
% 0.62/0.81 tff(441,plain,
% 0.62/0.81 ((~hskp1) | c2_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[440, 435])).
% 0.62/0.81 tff(442,plain,
% 0.62/0.81 (c2_1(a1971)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[441, 428])).
% 0.62/0.81 tff(443,plain,
% 0.62/0.81 (((~hskp1) | c0_1(a1971)) <=> ((~hskp1) | c0_1(a1971))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(444,axiom,((~hskp1) | c0_1(a1971)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.62/0.81 tff(445,plain,
% 0.62/0.81 ((~hskp1) | c0_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.62/0.81 tff(446,plain,
% 0.62/0.81 ((~hskp1) | c0_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[445, 443])).
% 0.62/0.81 tff(447,plain,
% 0.62/0.81 ((~hskp1) | c0_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[446, 443])).
% 0.62/0.81 tff(448,plain,
% 0.62/0.81 ((~hskp1) | c0_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[447, 443])).
% 0.62/0.81 tff(449,plain,
% 0.62/0.81 ((~hskp1) | c0_1(a1971)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[448, 443])).
% 0.62/0.81 tff(450,plain,
% 0.62/0.81 (c0_1(a1971)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[449, 428])).
% 0.62/0.81 tff(451,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1979) | c2_1(a1979) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1979) | c2_1(a1979) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | (~c3_1(a1979)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(452,plain,
% 0.62/0.81 ((hskp8 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (hskp8 | c0_1(a1979) | c2_1(a1979) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | (~c3_1(a1979)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(453,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1979) | c2_1(a1979) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | (~c3_1(a1979))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[452])).
% 0.62/0.81 tff(454,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1979) | c2_1(a1979) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | (~c3_1(a1979)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[453, 451])).
% 0.62/0.81 tff(455,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(456,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1979) | c2_1(a1979) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | (~c3_1(a1979))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.62/0.81 tff(457,plain,
% 0.62/0.81 (hskp8),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[456, 150, 86, 450, 442, 78, 72, 434, 53])).
% 0.62/0.81 tff(458,plain,
% 0.62/0.81 (((~hskp8) | (~c0_1(a1983))) <=> ((~hskp8) | (~c0_1(a1983)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(459,plain,
% 0.62/0.81 (((~c0_1(a1983)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1983)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(460,axiom,((~c0_1(a1983)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.62/0.81 tff(461,plain,
% 0.62/0.81 ((~hskp8) | (~c0_1(a1983))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.62/0.81 tff(462,plain,
% 0.62/0.81 ((~hskp8) | (~c0_1(a1983))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[461, 458])).
% 0.62/0.81 tff(463,plain,
% 0.62/0.81 (~c0_1(a1983)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[462, 457])).
% 0.62/0.81 tff(464,plain,
% 0.62/0.81 (((~hskp8) | c3_1(a1983)) <=> ((~hskp8) | c3_1(a1983))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(465,axiom,((~hskp8) | c3_1(a1983)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.62/0.81 tff(466,plain,
% 0.62/0.81 ((~hskp8) | c3_1(a1983)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.62/0.81 tff(467,plain,
% 0.62/0.81 ((~hskp8) | c3_1(a1983)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[466, 464])).
% 0.62/0.81 tff(468,plain,
% 0.62/0.81 ((~hskp8) | c3_1(a1983)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[467, 464])).
% 0.62/0.81 tff(469,plain,
% 0.62/0.81 ((~hskp8) | c3_1(a1983)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[468, 464])).
% 0.62/0.81 tff(470,plain,
% 0.62/0.81 ((~hskp8) | c3_1(a1983)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[469, 464])).
% 0.62/0.81 tff(471,plain,
% 0.62/0.81 (c3_1(a1983)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[470, 457])).
% 0.62/0.81 tff(472,plain,
% 0.62/0.81 (((~hskp8) | (~c1_1(a1983))) <=> ((~hskp8) | (~c1_1(a1983)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(473,plain,
% 0.62/0.81 (((~c1_1(a1983)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1983)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(474,axiom,((~c1_1(a1983)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.62/0.81 tff(475,plain,
% 0.62/0.81 ((~hskp8) | (~c1_1(a1983))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.62/0.81 tff(476,plain,
% 0.62/0.81 ((~hskp8) | (~c1_1(a1983))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[475, 472])).
% 0.62/0.81 tff(477,plain,
% 0.62/0.81 (~c1_1(a1983)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[476, 457])).
% 0.62/0.81 tff(478,plain,
% 0.62/0.81 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(479,plain,
% 0.62/0.82 ((hskp27 | hskp4 | (~ndr1_0) | c1_1(a1983) | c0_1(a1983) | (~c2_1(a1983))) <=> (hskp27 | hskp4 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(480,plain,
% 0.62/0.82 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1983) | c0_1(a1983) | (~c2_1(a1983)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[479])).
% 0.62/0.82 tff(481,plain,
% 0.62/0.82 (((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1983) | c0_1(a1983) | (~c2_1(a1983)))) <=> ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[480, 478])).
% 0.62/0.82 tff(482,plain,
% 0.62/0.82 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp27 | hskp4 | (~ndr1_0) | c1_1(a1983) | c0_1(a1983) | (~c2_1(a1983)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(483,plain,
% 0.62/0.82 ((~![U: $i] : (hskp27 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp27 | hskp4 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.62/0.82 tff(484,plain,
% 0.62/0.82 (~c2_1(a1983)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[483, 150, 43, 223, 463, 477, 282])).
% 0.62/0.82 tff(485,assumption,(hskp15), introduced(assumption)).
% 0.62/0.82 tff(486,plain,
% 0.62/0.82 (~c1_1(a1993)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[404, 485])).
% 0.62/0.82 tff(487,plain,
% 0.62/0.82 (~c0_1(a1993)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[410, 485])).
% 0.62/0.82 tff(488,plain,
% 0.62/0.82 (c2_1(a1993)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[418, 485])).
% 0.62/0.82 tff(489,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[425, 150, 43, 21, 488, 487, 486, 282])).
% 0.62/0.82 tff(490,plain,((~hskp15) | hskp27 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(491,plain,
% 0.62/0.82 (~hskp15),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[490, 223, 43])).
% 0.62/0.82 tff(492,plain,
% 0.62/0.82 (((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | c1_1(a1971) | (~ndr1_0) | (~c3_1(a1971)) | (~c0_1(a1971)))) <=> ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp15 | c1_1(a1971) | (~ndr1_0) | (~c3_1(a1971)) | (~c0_1(a1971)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(493,plain,
% 0.62/0.82 ((hskp30 | hskp15 | (~ndr1_0) | c1_1(a1971) | (~c3_1(a1971)) | (~c0_1(a1971))) <=> (hskp30 | hskp15 | c1_1(a1971) | (~ndr1_0) | (~c3_1(a1971)) | (~c0_1(a1971)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(494,plain,
% 0.62/0.82 (((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | (~ndr1_0) | c1_1(a1971) | (~c3_1(a1971)) | (~c0_1(a1971)))) <=> ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | c1_1(a1971) | (~ndr1_0) | (~c3_1(a1971)) | (~c0_1(a1971))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[493])).
% 0.62/0.82 tff(495,plain,
% 0.62/0.82 (((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | (~ndr1_0) | c1_1(a1971) | (~c3_1(a1971)) | (~c0_1(a1971)))) <=> ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp15 | c1_1(a1971) | (~ndr1_0) | (~c3_1(a1971)) | (~c0_1(a1971)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[494, 492])).
% 0.62/0.82 tff(496,plain,
% 0.62/0.82 ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp15 | (~ndr1_0) | c1_1(a1971) | (~c3_1(a1971)) | (~c0_1(a1971)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(497,plain,
% 0.62/0.82 ((~![U: $i] : (hskp30 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp15 | c1_1(a1971) | (~ndr1_0) | (~c3_1(a1971)) | (~c0_1(a1971))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.62/0.82 tff(498,plain,
% 0.62/0.82 (hskp15 | (~c3_1(a1971))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[497, 54, 150, 450, 434, 384])).
% 0.62/0.82 tff(499,plain,
% 0.62/0.82 (~c3_1(a1971)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[498, 491])).
% 0.62/0.82 tff(500,plain,
% 0.62/0.82 (~c1_1(a1979)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[334, 315, 223])).
% 0.62/0.82 tff(501,plain,
% 0.62/0.82 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(502,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[501])).
% 0.62/0.82 tff(503,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(504,plain,
% 0.62/0.82 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_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) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(505,plain,
% 0.62/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[504])).
% 0.62/0.82 tff(506,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.62/0.82 tff(507,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.62/0.82 tff(508,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[507, 503])).
% 0.62/0.82 tff(509,plain,(
% 0.62/0.82 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[508])).
% 0.62/0.82 tff(510,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[509, 502])).
% 0.62/0.82 tff(511,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1979) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1979)) | c1_1(a1979))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1979) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(512,plain,
% 0.62/0.82 ((hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1979) | c0_1(a1979) | (~c3_1(a1979))) <=> (hskp5 | c0_1(a1979) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(513,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1979) | c0_1(a1979) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1979) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1979)) | c1_1(a1979)))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[512])).
% 0.62/0.82 tff(514,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1979) | c0_1(a1979) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1979) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.82 inference(transitivity,[status(thm)],[513, 511])).
% 0.62/0.82 tff(515,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1979) | c0_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(516,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1979) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1979)) | c1_1(a1979)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.62/0.82 tff(517,plain,
% 0.62/0.82 (hskp5 | c3_1(a1971)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[516, 150, 86, 450, 442, 78, 510, 500])).
% 0.62/0.82 tff(518,plain,
% 0.62/0.82 (hskp5),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[517, 499])).
% 0.62/0.82 tff(519,plain,
% 0.62/0.82 (~c2_1(a1977)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[162, 518])).
% 0.62/0.82 tff(520,plain,
% 0.62/0.82 (~c3_1(a1977)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[196, 518])).
% 0.62/0.82 tff(521,assumption,(~c3_1(a1977)), introduced(assumption)).
% 0.62/0.82 tff(522,assumption,(~c2_1(a1983)), introduced(assumption)).
% 0.62/0.82 tff(523,assumption,(~c2_1(a1977)), introduced(assumption)).
% 0.62/0.82 tff(524,assumption,(~c1_1(a1983)), introduced(assumption)).
% 0.62/0.82 tff(525,assumption,(~c0_1(a1983)), introduced(assumption)).
% 0.62/0.82 tff(526,assumption,(c3_1(a1983)), introduced(assumption)).
% 0.62/0.82 tff(527,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1983) | c1_1(a1983) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1983) | c1_1(a1983) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(528,plain,
% 0.62/0.82 (((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983))) <=> (c0_1(a1983) | c1_1(a1983) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(529,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1983) | c1_1(a1983) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c2_1(a1983) | (~c3_1(a1983))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[528])).
% 0.62/0.82 tff(530,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1983) | c1_1(a1983) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[529, 527])).
% 0.62/0.82 tff(531,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | c3_1(a1977) | (~c1_1(a1977)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(532,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1983) | c1_1(a1983) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | c2_1(a1983) | (~c3_1(a1983))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.62/0.82 tff(533,plain,
% 0.62/0.82 (c3_1(a1977) | (~c1_1(a1977))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[532, 150, 526, 525, 524, 523, 214, 522])).
% 0.62/0.82 tff(534,plain,
% 0.62/0.82 (~c1_1(a1977)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[533, 521])).
% 0.62/0.82 tff(535,plain,
% 0.62/0.82 (~hskp5),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[172, 534])).
% 0.62/0.82 tff(536,plain,
% 0.62/0.82 (((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | c1_1(a1977) | c2_1(a1977) | (~ndr1_0) | (~c0_1(a1977)))) <=> ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp5 | c1_1(a1977) | c2_1(a1977) | (~ndr1_0) | (~c0_1(a1977)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(537,plain,
% 0.62/0.82 ((hskp30 | hskp5 | (~ndr1_0) | c1_1(a1977) | c2_1(a1977) | (~c0_1(a1977))) <=> (hskp30 | hskp5 | c1_1(a1977) | c2_1(a1977) | (~ndr1_0) | (~c0_1(a1977)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(538,plain,
% 0.62/0.82 (((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | (~ndr1_0) | c1_1(a1977) | c2_1(a1977) | (~c0_1(a1977)))) <=> ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | c1_1(a1977) | c2_1(a1977) | (~ndr1_0) | (~c0_1(a1977))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[537])).
% 0.62/0.82 tff(539,plain,
% 0.62/0.82 (((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | (~ndr1_0) | c1_1(a1977) | c2_1(a1977) | (~c0_1(a1977)))) <=> ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp5 | c1_1(a1977) | c2_1(a1977) | (~ndr1_0) | (~c0_1(a1977)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[538, 536])).
% 0.62/0.82 tff(540,plain,
% 0.62/0.82 ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp5 | (~ndr1_0) | c1_1(a1977) | c2_1(a1977) | (~c0_1(a1977)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(541,plain,
% 0.62/0.82 ((~![U: $i] : (hskp30 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp5 | c1_1(a1977) | c2_1(a1977) | (~ndr1_0) | (~c0_1(a1977))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.62/0.82 tff(542,plain,
% 0.62/0.82 (hskp5 | c1_1(a1977) | (~c0_1(a1977))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[541, 54, 150, 523, 119])).
% 0.62/0.82 tff(543,plain,
% 0.62/0.82 (~c0_1(a1977)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[542, 535, 534])).
% 0.62/0.82 tff(544,plain,
% 0.62/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_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)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(545,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[544])).
% 0.62/0.82 tff(546,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(547,plain,
% 0.62/0.82 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(548,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[547])).
% 0.62/0.82 tff(549,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.62/0.82 tff(550,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.62/0.82 tff(551,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[550, 546])).
% 0.62/0.82 tff(552,plain,(
% 0.62/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(skolemize,[status(sab)],[551])).
% 0.62/0.82 tff(553,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[552, 545])).
% 0.62/0.82 tff(554,assumption,(~c1_1(a1971)), introduced(assumption)).
% 0.62/0.82 tff(555,assumption,(c2_1(a1971)), introduced(assumption)).
% 0.62/0.82 tff(556,assumption,(c0_1(a1971)), introduced(assumption)).
% 0.62/0.82 tff(557,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1977) | c1_1(a1983) | c3_1(a1977) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1977) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1977) | c1_1(a1983) | c3_1(a1977) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1977) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(558,plain,
% 0.62/0.83 (((~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a1977) | c1_1(a1977) | c0_1(a1977)) <=> (c1_1(a1977) | c1_1(a1983) | c3_1(a1977) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1977) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(559,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a1977) | c1_1(a1977) | c0_1(a1977))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1977) | c1_1(a1983) | c3_1(a1977) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1977) | c2_1(a1983) | (~c3_1(a1983))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[558])).
% 0.62/0.83 tff(560,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a1977) | c1_1(a1977) | c0_1(a1977))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1977) | c1_1(a1983) | c3_1(a1977) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1977) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[559, 557])).
% 0.62/0.83 tff(561,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c0_1(a1971)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a1977) | c1_1(a1977) | c0_1(a1977))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(562,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1977) | c1_1(a1983) | c3_1(a1977) | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c0_1(a1971)) | c0_1(a1977) | c2_1(a1983) | (~c3_1(a1983))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.62/0.83 tff(563,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[562, 150, 526, 534, 556, 555, 524, 521, 554, 553, 522, 543])).
% 0.62/0.83 tff(564,plain,(c3_1(a1977) | (~c3_1(a1983)) | (~c0_1(a1971)) | (~c2_1(a1971)) | c1_1(a1983) | c1_1(a1971) | c2_1(a1983) | hskp30 | c2_1(a1977) | c0_1(a1983)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(565,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[564, 520, 519, 450, 442, 477, 434, 484, 54, 471, 463])).
% 0.62/0.83 tff(566,plain,(hskp30 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(567,plain,
% 0.62/0.83 (hskp30),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[566, 43])).
% 0.62/0.83 tff(568,plain,
% 0.62/0.83 (((~hskp30) | c3_1(a2005)) <=> ((~hskp30) | c3_1(a2005))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(569,axiom,((~hskp30) | c3_1(a2005)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.62/0.83 tff(570,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.62/0.83 tff(571,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[570, 568])).
% 0.62/0.83 tff(572,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[571, 568])).
% 0.62/0.83 tff(573,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[572, 568])).
% 0.62/0.83 tff(574,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[573, 568])).
% 0.62/0.83 tff(575,plain,
% 0.62/0.83 (c3_1(a2005)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[574, 567])).
% 0.62/0.83 tff(576,plain,
% 0.62/0.83 (~c2_1(a2000)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[288, 150, 43, 21, 230, 236, 282])).
% 0.62/0.83 tff(577,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[261, 150, 43, 230, 236, 242, 252, 576])).
% 0.62/0.83 tff(578,plain,((~hskp18) | hskp27 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(579,plain,
% 0.62/0.83 (~hskp18),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[578, 21, 43])).
% 0.62/0.83 tff(580,assumption,(hskp17), introduced(assumption)).
% 0.62/0.83 tff(581,plain,
% 0.62/0.83 (((~hskp17) | (~c0_1(a1998))) <=> ((~hskp17) | (~c0_1(a1998)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(582,plain,
% 0.62/0.83 (((~c0_1(a1998)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1998)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(583,axiom,((~c0_1(a1998)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.62/0.83 tff(584,plain,
% 0.62/0.83 ((~hskp17) | (~c0_1(a1998))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.62/0.83 tff(585,plain,
% 0.62/0.83 ((~hskp17) | (~c0_1(a1998))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[584, 581])).
% 0.62/0.83 tff(586,plain,
% 0.62/0.83 (~c0_1(a1998)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[585, 580])).
% 0.62/0.83 tff(587,plain,
% 0.62/0.83 (((~hskp17) | c3_1(a1998)) <=> ((~hskp17) | c3_1(a1998))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(588,axiom,((~hskp17) | c3_1(a1998)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.62/0.83 tff(589,plain,
% 0.62/0.83 ((~hskp17) | c3_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.62/0.83 tff(590,plain,
% 0.62/0.83 ((~hskp17) | c3_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[589, 587])).
% 0.62/0.83 tff(591,plain,
% 0.62/0.83 ((~hskp17) | c3_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[590, 587])).
% 0.62/0.83 tff(592,plain,
% 0.62/0.83 ((~hskp17) | c3_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[591, 587])).
% 0.62/0.83 tff(593,plain,
% 0.62/0.83 ((~hskp17) | c3_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[592, 587])).
% 0.62/0.83 tff(594,plain,
% 0.62/0.83 (c3_1(a1998)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[593, 580])).
% 0.62/0.83 tff(595,plain,
% 0.62/0.83 (((~hskp17) | c1_1(a1998)) <=> ((~hskp17) | c1_1(a1998))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(596,axiom,((~hskp17) | c1_1(a1998)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.62/0.83 tff(597,plain,
% 0.62/0.83 ((~hskp17) | c1_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.62/0.83 tff(598,plain,
% 0.62/0.83 ((~hskp17) | c1_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[597, 595])).
% 0.62/0.83 tff(599,plain,
% 0.62/0.83 ((~hskp17) | c1_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[598, 595])).
% 0.62/0.83 tff(600,plain,
% 0.62/0.83 ((~hskp17) | c1_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[599, 595])).
% 0.62/0.83 tff(601,plain,
% 0.62/0.83 ((~hskp17) | c1_1(a1998)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[600, 595])).
% 0.62/0.83 tff(602,plain,
% 0.62/0.83 (c1_1(a1998)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[601, 580])).
% 0.62/0.83 tff(603,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(604,plain,
% 0.62/0.83 ((hskp18 | hskp4 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998))) <=> (hskp18 | hskp4 | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(605,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[604])).
% 0.62/0.83 tff(606,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[605, 603])).
% 0.62/0.83 tff(607,plain,
% 0.62/0.83 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(608,plain,
% 0.62/0.83 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.62/0.83 tff(609,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[608, 150, 317, 21, 602, 594, 586, 327])).
% 0.62/0.83 tff(610,plain,((~hskp17) | hskp18 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(611,plain,
% 0.62/0.83 (~hskp17),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[610, 579, 21])).
% 0.62/0.83 tff(612,plain,
% 0.62/0.83 (((~hskp30) | c2_1(a2005)) <=> ((~hskp30) | c2_1(a2005))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(613,axiom,((~hskp30) | c2_1(a2005)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.62/0.83 tff(614,plain,
% 0.62/0.83 ((~hskp30) | c2_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.62/0.83 tff(615,plain,
% 0.62/0.83 ((~hskp30) | c2_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[614, 612])).
% 0.62/0.83 tff(616,plain,
% 0.62/0.83 ((~hskp30) | c2_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[615, 612])).
% 0.62/0.83 tff(617,plain,
% 0.62/0.83 ((~hskp30) | c2_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[616, 612])).
% 0.62/0.83 tff(618,plain,
% 0.62/0.83 ((~hskp30) | c2_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[617, 612])).
% 0.62/0.83 tff(619,plain,
% 0.62/0.83 (c2_1(a2005)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[618, 567])).
% 0.62/0.83 tff(620,plain,
% 0.62/0.83 (((~hskp30) | c0_1(a2005)) <=> ((~hskp30) | c0_1(a2005))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(621,axiom,((~hskp30) | c0_1(a2005)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.62/0.83 tff(622,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.62/0.83 tff(623,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[622, 620])).
% 0.62/0.83 tff(624,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[623, 620])).
% 0.62/0.83 tff(625,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[624, 620])).
% 0.62/0.83 tff(626,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a2005)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[625, 620])).
% 0.62/0.83 tff(627,plain,
% 0.62/0.83 (c0_1(a2005)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[626, 567])).
% 0.62/0.83 tff(628,plain,
% 0.62/0.83 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c0_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c0_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(629,plain,
% 0.62/0.83 ((hskp17 | (~ndr1_0) | (~c2_1(a2005)) | (~c1_1(a2005)) | (~c0_1(a2005))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(630,plain,
% 0.62/0.83 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a2005)) | (~c1_1(a2005)) | (~c0_1(a2005)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c0_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[629])).
% 0.62/0.83 tff(631,plain,
% 0.62/0.83 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a2005)) | (~c1_1(a2005)) | (~c0_1(a2005)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c0_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[630, 628])).
% 0.62/0.83 tff(632,plain,
% 0.62/0.83 ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a2005)) | (~c1_1(a2005)) | (~c0_1(a2005)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(633,plain,
% 0.62/0.83 ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c0_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.62/0.83 tff(634,plain,
% 0.62/0.83 (hskp17 | (~c1_1(a2005))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[633, 150, 627, 619, 42])).
% 0.62/0.83 tff(635,plain,
% 0.62/0.83 (~c1_1(a2005)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[634, 611])).
% 0.62/0.83 tff(636,plain,
% 0.62/0.83 (^[U: $i] : refl((hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(637,plain,
% 0.62/0.83 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[636])).
% 0.62/0.83 tff(638,plain,
% 0.62/0.83 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(639,plain,
% 0.62/0.83 (^[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)) | 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)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp6) | hskp18) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp6) | hskp18) <=> (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(640,plain,
% 0.62/0.83 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp6) | hskp18) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[639])).
% 0.62/0.83 tff(641,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp6) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.62/0.83 tff(642,plain,
% 0.62/0.83 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.62/0.83 tff(643,plain,
% 0.62/0.83 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[642, 638])).
% 0.62/0.83 tff(644,plain,(
% 0.62/0.83 ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[643])).
% 0.62/0.83 tff(645,plain,
% 0.62/0.83 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[644, 637])).
% 0.62/0.83 tff(646,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c0_1(a2005)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c0_1(a2005)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(647,plain,
% 0.62/0.83 ((hskp18 | hskp6 | (~ndr1_0) | c1_1(a2005) | (~c3_1(a2005)) | (~c0_1(a2005))) <=> (hskp18 | hskp6 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c0_1(a2005)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(648,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c1_1(a2005) | (~c3_1(a2005)) | (~c0_1(a2005)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c0_1(a2005))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[647])).
% 0.62/0.83 tff(649,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c1_1(a2005) | (~c3_1(a2005)) | (~c0_1(a2005)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c0_1(a2005)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[648, 646])).
% 0.62/0.83 tff(650,plain,
% 0.62/0.83 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c1_1(a2005) | (~c3_1(a2005)) | (~c0_1(a2005)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(651,plain,
% 0.62/0.83 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c0_1(a2005))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.62/0.83 tff(652,plain,
% 0.62/0.83 (hskp18 | hskp6 | c1_1(a2005)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[651, 150, 627, 575, 645])).
% 0.62/0.83 tff(653,plain,
% 0.62/0.83 (hskp6),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[652, 635, 579])).
% 0.62/0.83 tff(654,plain,
% 0.62/0.83 (~c2_1(a1979)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[71, 653])).
% 0.62/0.83 tff(655,plain,
% 0.62/0.83 (~c0_1(a1979)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[77, 653])).
% 0.62/0.83 tff(656,plain,
% 0.62/0.83 (c3_1(a1979)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[85, 653])).
% 0.62/0.83 tff(657,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1979) | c2_1(a1979) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1979) | c2_1(a1979) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c3_1(a1979)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(658,plain,
% 0.62/0.83 ((hskp8 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (hskp8 | c0_1(a1979) | c2_1(a1979) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c3_1(a1979)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(659,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1979) | c2_1(a1979) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c3_1(a1979))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[658])).
% 0.62/0.83 tff(660,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1979) | c2_1(a1979) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c3_1(a1979)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[659, 657])).
% 0.62/0.83 tff(661,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c0_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(662,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1979) | c2_1(a1979) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c3_1(a1979))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.62/0.83 tff(663,plain,
% 0.62/0.83 (hskp8),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[662, 150, 627, 619, 656, 655, 654, 53, 635])).
% 0.62/0.83 tff(664,plain,
% 0.62/0.83 (~c1_1(a1983)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[476, 663])).
% 0.62/0.83 tff(665,plain,
% 0.62/0.83 (~c0_1(a1983)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[462, 663])).
% 0.62/0.83 tff(666,plain,
% 0.62/0.83 (~c2_1(a1983)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[483, 150, 43, 21, 665, 664, 282])).
% 0.62/0.83 tff(667,plain,
% 0.62/0.83 (~c1_1(a1979)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[333, 150, 579, 21, 656, 655, 327])).
% 0.62/0.83 tff(668,plain,
% 0.62/0.83 (c3_1(a1983)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[470, 663])).
% 0.62/0.83 tff(669,assumption,(hskp2), introduced(assumption)).
% 0.62/0.83 tff(670,plain,
% 0.62/0.83 (((~hskp2) | c3_1(a1973)) <=> ((~hskp2) | c3_1(a1973))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(671,axiom,((~hskp2) | c3_1(a1973)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.62/0.83 tff(672,plain,
% 0.62/0.83 ((~hskp2) | c3_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.62/0.83 tff(673,plain,
% 0.62/0.83 ((~hskp2) | c3_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[672, 670])).
% 0.62/0.83 tff(674,plain,
% 0.62/0.83 ((~hskp2) | c3_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[673, 670])).
% 0.62/0.83 tff(675,plain,
% 0.62/0.83 ((~hskp2) | c3_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[674, 670])).
% 0.62/0.83 tff(676,plain,
% 0.62/0.83 ((~hskp2) | c3_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[675, 670])).
% 0.62/0.83 tff(677,plain,
% 0.62/0.83 (c3_1(a1973)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[676, 669])).
% 0.62/0.83 tff(678,plain,
% 0.62/0.83 (((~hskp2) | c1_1(a1973)) <=> ((~hskp2) | c1_1(a1973))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(679,axiom,((~hskp2) | c1_1(a1973)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.62/0.83 tff(680,plain,
% 0.62/0.83 ((~hskp2) | c1_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.62/0.83 tff(681,plain,
% 0.62/0.83 ((~hskp2) | c1_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[680, 678])).
% 0.62/0.83 tff(682,plain,
% 0.62/0.83 ((~hskp2) | c1_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[681, 678])).
% 0.62/0.83 tff(683,plain,
% 0.62/0.83 ((~hskp2) | c1_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[682, 678])).
% 0.62/0.83 tff(684,plain,
% 0.62/0.83 ((~hskp2) | c1_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[683, 678])).
% 0.62/0.83 tff(685,plain,
% 0.62/0.83 (c1_1(a1973)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[684, 669])).
% 0.62/0.83 tff(686,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c0_1(a1973))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c0_1(a1973))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(687,plain,
% 0.62/0.83 ((hskp18 | hskp4 | (~ndr1_0) | c0_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973))) <=> (hskp18 | hskp4 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c0_1(a1973))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(688,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c0_1(a1973)))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[687])).
% 0.62/0.83 tff(689,plain,
% 0.62/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c0_1(a1973))),
% 0.62/0.83 inference(transitivity,[status(thm)],[688, 686])).
% 0.62/0.83 tff(690,plain,
% 0.62/0.83 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c0_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(691,plain,
% 0.62/0.83 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp4 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c0_1(a1973)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.62/0.83 tff(692,plain,
% 0.62/0.83 (c0_1(a1973)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[691, 150, 317, 21, 685, 677, 327])).
% 0.62/0.83 tff(693,plain,
% 0.62/0.83 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(694,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[693])).
% 0.62/0.83 tff(695,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(696,plain,
% 0.62/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(697,plain,
% 0.62/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[696])).
% 0.62/0.84 tff(698,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.62/0.84 tff(699,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.62/0.84 tff(700,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[699, 695])).
% 0.62/0.84 tff(701,plain,(
% 0.62/0.84 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[700])).
% 0.62/0.84 tff(702,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[701, 694])).
% 0.62/0.84 tff(703,plain,
% 0.62/0.84 (((~hskp2) | (~c2_1(a1973))) <=> ((~hskp2) | (~c2_1(a1973)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(704,plain,
% 0.62/0.84 (((~c2_1(a1973)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1973)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(705,axiom,((~c2_1(a1973)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.62/0.84 tff(706,plain,
% 0.62/0.84 ((~hskp2) | (~c2_1(a1973))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.62/0.84 tff(707,plain,
% 0.62/0.84 ((~hskp2) | (~c2_1(a1973))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[706, 703])).
% 0.62/0.84 tff(708,plain,
% 0.62/0.84 (~c2_1(a1973)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[707, 669])).
% 0.62/0.84 tff(709,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(710,plain,
% 0.62/0.84 ((hskp20 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973))) <=> (hskp20 | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(711,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[710])).
% 0.62/0.84 tff(712,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[711, 709])).
% 0.62/0.84 tff(713,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973)) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(714,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | (~c0_1(a1973))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.62/0.84 tff(715,plain,
% 0.62/0.84 (hskp20),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[714, 150, 685, 677, 708, 702, 692])).
% 0.62/0.84 tff(716,plain,
% 0.62/0.84 (((~hskp20) | c2_1(a2003)) <=> ((~hskp20) | c2_1(a2003))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(717,axiom,((~hskp20) | c2_1(a2003)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.62/0.84 tff(718,plain,
% 0.62/0.84 ((~hskp20) | c2_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.62/0.84 tff(719,plain,
% 0.62/0.84 ((~hskp20) | c2_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[718, 716])).
% 0.62/0.84 tff(720,plain,
% 0.62/0.84 ((~hskp20) | c2_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[719, 716])).
% 0.62/0.84 tff(721,plain,
% 0.62/0.84 ((~hskp20) | c2_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[720, 716])).
% 0.62/0.84 tff(722,plain,
% 0.62/0.84 ((~hskp20) | c2_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[721, 716])).
% 0.62/0.84 tff(723,plain,
% 0.62/0.84 (c2_1(a2003)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[722, 715])).
% 0.62/0.84 tff(724,plain,
% 0.62/0.84 (((~hskp20) | c1_1(a2003)) <=> ((~hskp20) | c1_1(a2003))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(725,axiom,((~hskp20) | c1_1(a2003)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.62/0.84 tff(726,plain,
% 0.62/0.84 ((~hskp20) | c1_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.62/0.84 tff(727,plain,
% 0.62/0.84 ((~hskp20) | c1_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[726, 724])).
% 0.62/0.84 tff(728,plain,
% 0.62/0.84 ((~hskp20) | c1_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[727, 724])).
% 0.62/0.84 tff(729,plain,
% 0.62/0.84 ((~hskp20) | c1_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[728, 724])).
% 0.62/0.84 tff(730,plain,
% 0.62/0.84 ((~hskp20) | c1_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[729, 724])).
% 0.62/0.84 tff(731,plain,
% 0.62/0.84 (c1_1(a2003)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[730, 715])).
% 0.62/0.84 tff(732,plain,
% 0.62/0.84 (~hskp17),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[610, 317, 21])).
% 0.62/0.84 tff(733,plain,
% 0.62/0.84 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c1_1(a2003)) | (~c0_1(a2003)) | (~c2_1(a2003)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c1_1(a2003)) | (~c0_1(a2003)) | (~c2_1(a2003)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(734,plain,
% 0.62/0.84 ((hskp17 | (~ndr1_0) | (~c2_1(a2003)) | (~c1_1(a2003)) | (~c0_1(a2003))) <=> (hskp17 | (~ndr1_0) | (~c1_1(a2003)) | (~c0_1(a2003)) | (~c2_1(a2003)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(735,plain,
% 0.62/0.84 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a2003)) | (~c1_1(a2003)) | (~c0_1(a2003)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c1_1(a2003)) | (~c0_1(a2003)) | (~c2_1(a2003))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[734])).
% 0.62/0.84 tff(736,plain,
% 0.62/0.84 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a2003)) | (~c1_1(a2003)) | (~c0_1(a2003)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c1_1(a2003)) | (~c0_1(a2003)) | (~c2_1(a2003)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[735, 733])).
% 0.62/0.84 tff(737,plain,
% 0.62/0.84 ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a2003)) | (~c1_1(a2003)) | (~c0_1(a2003)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(738,plain,
% 0.62/0.84 ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c1_1(a2003)) | (~c0_1(a2003)) | (~c2_1(a2003))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.62/0.84 tff(739,plain,
% 0.62/0.84 (~c0_1(a2003)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[738, 150, 732, 731, 723, 42])).
% 0.62/0.84 tff(740,plain,
% 0.62/0.84 (((~hskp20) | (~c3_1(a2003))) <=> ((~hskp20) | (~c3_1(a2003)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(741,plain,
% 0.62/0.84 (((~c3_1(a2003)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a2003)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(742,axiom,((~c3_1(a2003)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.62/0.84 tff(743,plain,
% 0.62/0.84 ((~hskp20) | (~c3_1(a2003))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.62/0.84 tff(744,plain,
% 0.62/0.84 ((~hskp20) | (~c3_1(a2003))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[743, 740])).
% 0.62/0.84 tff(745,plain,
% 0.62/0.84 (~c3_1(a2003)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[744, 715])).
% 0.62/0.84 tff(746,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a2003) | c0_1(a1983) | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2003)) | c0_1(a2003))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2003) | c0_1(a1983) | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2003)) | c0_1(a2003))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(747,plain,
% 0.62/0.84 (((~ndr1_0) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)) | c3_1(a2003) | c0_1(a2003) | (~c1_1(a2003)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983))) <=> (c3_1(a2003) | c0_1(a1983) | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2003)) | c0_1(a2003))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(748,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)) | c3_1(a2003) | c0_1(a2003) | (~c1_1(a2003)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a2003) | c0_1(a1983) | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2003)) | c0_1(a2003)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[747])).
% 0.62/0.84 tff(749,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)) | c3_1(a2003) | c0_1(a2003) | (~c1_1(a2003)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2003) | c0_1(a1983) | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2003)) | c0_1(a2003))),
% 0.62/0.84 inference(transitivity,[status(thm)],[748, 746])).
% 0.62/0.84 tff(750,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1973) | (~c3_1(a1973)) | (~c1_1(a1973)) | c3_1(a2003) | c0_1(a2003) | (~c1_1(a2003)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(751,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2003) | c0_1(a1983) | c2_1(a1973) | (~ndr1_0) | (~c3_1(a1973)) | (~c1_1(a1973)) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2003)) | c0_1(a2003)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.62/0.84 tff(752,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[751, 150, 731, 526, 685, 677, 745, 525, 708, 191, 522, 739])).
% 0.62/0.84 tff(753,plain,((~hskp2) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | hskp18 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(754,plain,
% 0.62/0.84 (~hskp2),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[753, 668, 665, 666, 579, 21])).
% 0.62/0.84 tff(755,plain,
% 0.62/0.84 (^[U: $i] : refl((hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(756,plain,
% 0.62/0.84 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[755])).
% 0.62/0.84 tff(757,plain,
% 0.62/0.84 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(758,plain,
% 0.62/0.84 (^[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) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp2) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp2))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp2) <=> (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp2) <=> (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(759,plain,
% 0.62/0.84 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp2) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[758])).
% 0.62/0.84 tff(760,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.62/0.84 tff(761,plain,
% 0.62/0.84 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.62/0.84 tff(762,plain,
% 0.62/0.84 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[761, 757])).
% 0.62/0.84 tff(763,plain,(
% 0.62/0.84 ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[762])).
% 0.62/0.84 tff(764,plain,
% 0.62/0.84 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[763, 756])).
% 0.62/0.84 tff(765,plain,
% 0.62/0.84 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp2 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp2 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(766,plain,
% 0.62/0.84 ((hskp22 | hskp2 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979))) <=> (hskp22 | hskp2 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(767,plain,
% 0.62/0.84 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp2 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[766])).
% 0.62/0.84 tff(768,plain,
% 0.62/0.84 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp2 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979))),
% 0.62/0.84 inference(transitivity,[status(thm)],[767, 765])).
% 0.62/0.84 tff(769,plain,
% 0.62/0.84 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | c1_1(a1979) | c2_1(a1979) | (~c3_1(a1979)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(770,plain,
% 0.62/0.84 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp2 | c2_1(a1979) | (~ndr1_0) | (~c3_1(a1979)) | c1_1(a1979)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.62/0.84 tff(771,plain,
% 0.62/0.84 (hskp22 | hskp2 | c1_1(a1979)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[770, 150, 656, 654, 764])).
% 0.62/0.84 tff(772,plain,
% 0.62/0.84 (hskp22),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[771, 754, 667])).
% 0.62/0.84 tff(773,plain,
% 0.62/0.84 (((~hskp22) | (~c3_1(a2012))) <=> ((~hskp22) | (~c3_1(a2012)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(774,plain,
% 0.62/0.84 (((~c3_1(a2012)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a2012)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(775,axiom,((~c3_1(a2012)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.62/0.84 tff(776,plain,
% 0.62/0.84 ((~hskp22) | (~c3_1(a2012))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.62/0.84 tff(777,plain,
% 0.62/0.84 ((~hskp22) | (~c3_1(a2012))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[776, 773])).
% 0.62/0.84 tff(778,plain,
% 0.62/0.84 (~c3_1(a2012)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[777, 772])).
% 0.62/0.84 tff(779,plain,
% 0.62/0.84 (((~hskp22) | (~c2_1(a2012))) <=> ((~hskp22) | (~c2_1(a2012)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(780,plain,
% 0.62/0.84 (((~c2_1(a2012)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a2012)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(781,axiom,((~c2_1(a2012)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.62/0.84 tff(782,plain,
% 0.62/0.84 ((~hskp22) | (~c2_1(a2012))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.62/0.84 tff(783,plain,
% 0.62/0.84 ((~hskp22) | (~c2_1(a2012))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[782, 779])).
% 0.62/0.84 tff(784,plain,
% 0.62/0.84 (~c2_1(a2012)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[783, 772])).
% 0.62/0.84 tff(785,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2012) | c3_1(a2012) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2012)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2012) | c3_1(a2012) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2012)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(786,plain,
% 0.62/0.84 (((~ndr1_0) | c2_1(a2012) | c3_1(a2012) | (~c1_1(a2012)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983))) <=> (c2_1(a2012) | c3_1(a2012) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2012)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(787,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2012) | c3_1(a2012) | (~c1_1(a2012)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2012) | c3_1(a2012) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2012))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[786])).
% 0.62/0.84 tff(788,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2012) | c3_1(a2012) | (~c1_1(a2012)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2012) | c3_1(a2012) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2012)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[787, 785])).
% 0.62/0.85 tff(789,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2012) | c3_1(a2012) | (~c1_1(a2012)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c0_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(790,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2012) | c3_1(a2012) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | (~c1_1(a2012))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.62/0.85 tff(791,plain,
% 0.62/0.85 (~c1_1(a2012)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[790, 150, 668, 784, 778, 665, 664, 214, 666])).
% 0.62/0.85 tff(792,plain,
% 0.62/0.85 (^[U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(793,plain,
% 0.62/0.85 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[792])).
% 0.62/0.85 tff(794,plain,
% 0.62/0.85 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(795,plain,
% 0.62/0.85 (^[U: $i] : 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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(796,plain,
% 0.62/0.85 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[795])).
% 0.62/0.85 tff(797,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.62/0.85 tff(798,plain,
% 0.62/0.85 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.62/0.85 tff(799,plain,
% 0.62/0.85 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[798, 794])).
% 0.62/0.85 tff(800,plain,(
% 0.62/0.85 ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(skolemize,[status(sab)],[799])).
% 0.62/0.85 tff(801,plain,
% 0.62/0.85 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[800, 793])).
% 0.62/0.85 tff(802,plain,
% 0.62/0.85 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c2_1(a2005)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c2_1(a2005)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(803,plain,
% 0.62/0.85 ((hskp10 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c3_1(a2005))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c2_1(a2005)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(804,plain,
% 0.62/0.85 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c3_1(a2005)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c2_1(a2005))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[803])).
% 0.62/0.85 tff(805,plain,
% 0.62/0.85 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c3_1(a2005)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c2_1(a2005)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[804, 802])).
% 0.62/0.85 tff(806,plain,
% 0.62/0.85 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a2005) | (~c2_1(a2005)) | (~c3_1(a2005)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(807,plain,
% 0.62/0.85 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a2005)) | c1_1(a2005) | (~c2_1(a2005))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.62/0.85 tff(808,plain,
% 0.62/0.85 (hskp10 | c1_1(a2005)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[807, 150, 619, 575, 801])).
% 0.62/0.85 tff(809,plain,
% 0.62/0.85 (hskp10),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[808, 635])).
% 0.62/0.85 tff(810,plain,
% 0.62/0.85 (~c1_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[358, 809])).
% 0.62/0.85 tff(811,plain,
% 0.62/0.85 (c2_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[366, 809])).
% 0.62/0.85 tff(812,plain,
% 0.62/0.85 (c0_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[373, 150, 43, 21, 811, 810, 282])).
% 0.62/0.85 tff(813,plain,
% 0.62/0.85 (c3_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[391, 809])).
% 0.62/0.85 tff(814,plain,
% 0.62/0.85 (((~hskp22) | c0_1(a2012)) <=> ((~hskp22) | c0_1(a2012))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(815,axiom,((~hskp22) | c0_1(a2012)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.62/0.85 tff(816,plain,
% 0.62/0.85 ((~hskp22) | c0_1(a2012)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.62/0.85 tff(817,plain,
% 0.62/0.85 ((~hskp22) | c0_1(a2012)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[816, 814])).
% 0.62/0.85 tff(818,plain,
% 0.62/0.85 ((~hskp22) | c0_1(a2012)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[817, 814])).
% 0.62/0.85 tff(819,plain,
% 0.62/0.85 ((~hskp22) | c0_1(a2012)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[818, 814])).
% 0.62/0.85 tff(820,plain,
% 0.62/0.85 ((~hskp22) | c0_1(a2012)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[819, 814])).
% 0.62/0.85 tff(821,plain,
% 0.62/0.85 (c0_1(a2012)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[820, 772])).
% 0.62/0.85 tff(822,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a2012) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | (~c0_1(a2012)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a2012) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | (~c0_1(a2012)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(823,plain,
% 0.62/0.85 (((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | c2_1(a2012) | (~c0_1(a2012))) <=> (c2_1(a2012) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | (~c0_1(a2012)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(824,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | c2_1(a2012) | (~c0_1(a2012)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a2012) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | (~c0_1(a2012))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[823])).
% 0.62/0.85 tff(825,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | c2_1(a2012) | (~c0_1(a2012)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a2012) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | (~c0_1(a2012)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[824, 822])).
% 0.62/0.85 tff(826,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | c2_1(a2012) | (~c0_1(a2012)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(827,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a2012) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)) | c1_1(a2012) | (~c0_1(a2012))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.62/0.85 tff(828,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[827, 150, 821, 811, 813, 784, 810, 10, 812, 791])).
% 0.62/0.85 tff(829,plain,(hskp4 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(830,plain,
% 0.62/0.85 (hskp4),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[829, 43])).
% 0.62/0.85 tff(831,plain,
% 0.62/0.85 (~c2_1(a1975)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[102, 830])).
% 0.62/0.85 tff(832,plain,
% 0.62/0.85 (~c1_1(a1975)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[108, 830])).
% 0.62/0.85 tff(833,plain,
% 0.62/0.85 (c0_1(a1975)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[126, 830])).
% 0.62/0.85 tff(834,assumption,(~c1_1(a2005)), introduced(assumption)).
% 0.62/0.85 tff(835,assumption,(~c2_1(a1975)), introduced(assumption)).
% 0.62/0.85 tff(836,assumption,(~c1_1(a1975)), introduced(assumption)).
% 0.62/0.85 tff(837,assumption,(c3_1(a2005)), introduced(assumption)).
% 0.62/0.85 tff(838,assumption,(c2_1(a2005)), introduced(assumption)).
% 0.62/0.85 tff(839,plain,
% 0.62/0.85 (hskp10 | c1_1(a2005)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[807, 150, 838, 837, 801])).
% 0.62/0.85 tff(840,plain,
% 0.62/0.85 (hskp10),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[839, 834])).
% 0.62/0.85 tff(841,plain,
% 0.62/0.85 (~c1_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[358, 840])).
% 0.62/0.85 tff(842,assumption,(c0_1(a1975)), introduced(assumption)).
% 0.62/0.85 tff(843,plain,
% 0.62/0.85 (c3_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[391, 840])).
% 0.62/0.85 tff(844,plain,
% 0.62/0.85 (c2_1(a1987)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[366, 840])).
% 0.62/0.85 tff(845,assumption,(c0_1(a2005)), introduced(assumption)).
% 0.62/0.85 tff(846,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(847,plain,
% 0.62/0.85 (((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975))) <=> (c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(848,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[847])).
% 0.62/0.85 tff(849,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[848, 846])).
% 0.62/0.85 tff(850,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a2005) | (~c2_1(a2005)) | (~c0_1(a2005)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(851,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.62/0.85 tff(852,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[851, 150, 845, 838, 844, 843, 842, 841, 836, 835, 10, 834])).
% 0.62/0.85 tff(853,plain,(c1_1(a2005) | (~c0_1(a2005)) | (~c2_1(a2005)) | (~c0_1(a1975)) | c1_1(a1975) | c2_1(a1975) | (~c3_1(a2005))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(854,plain,
% 0.62/0.85 (c1_1(a2005)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[853, 627, 619, 833, 832, 831, 575])).
% 0.62/0.85 tff(855,plain,
% 0.62/0.85 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(856,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[855])).
% 0.62/0.85 tff(857,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(858,plain,
% 0.62/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~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(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~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(V)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~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(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(859,plain,
% 0.62/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[858])).
% 0.62/0.85 tff(860,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.62/0.85 tff(861,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.62/0.85 tff(862,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[861, 857])).
% 0.62/0.85 tff(863,plain,(
% 0.62/0.85 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(skolemize,[status(sab)],[862])).
% 0.62/0.85 tff(864,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[863, 856])).
% 0.62/0.85 tff(865,plain,
% 0.62/0.85 (hskp17),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[634, 854])).
% 0.62/0.85 tff(866,plain,
% 0.62/0.85 (~c0_1(a1998)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[585, 865])).
% 0.62/0.85 tff(867,plain,
% 0.62/0.85 (c3_1(a1998)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[593, 865])).
% 0.62/0.85 tff(868,assumption,(c1_1(a2005)), introduced(assumption)).
% 0.62/0.85 tff(869,assumption,(hskp5), introduced(assumption)).
% 0.62/0.85 tff(870,plain,
% 0.62/0.85 (~c3_1(a1977)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[196, 869])).
% 0.62/0.85 tff(871,plain,
% 0.62/0.85 (~c2_1(a1977)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[162, 869])).
% 0.62/0.85 tff(872,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | c0_1(a1977))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | c0_1(a1977))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(873,plain,
% 0.62/0.85 (((~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977)) <=> (c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | c0_1(a1977))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(874,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | c0_1(a1977)))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[873])).
% 0.71/0.85 tff(875,plain,
% 0.71/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | c0_1(a1977))),
% 0.71/0.85 inference(transitivity,[status(thm)],[874, 872])).
% 0.71/0.85 tff(876,plain,
% 0.71/0.85 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977))),
% 0.71/0.85 inference(quant_inst,[status(thm)],[])).
% 0.71/0.85 tff(877,plain,
% 0.71/0.85 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | c0_1(a1977)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.71/0.85 tff(878,plain,
% 0.71/0.85 (c0_1(a1977)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[877, 150, 838, 837, 871, 870, 20, 868])).
% 0.71/0.85 tff(879,assumption,(~c0_1(a1998)), introduced(assumption)).
% 0.71/0.85 tff(880,plain,
% 0.71/0.85 (c1_1(a1977)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[172, 869])).
% 0.71/0.85 tff(881,assumption,(c3_1(a1998)), introduced(assumption)).
% 0.71/0.85 tff(882,plain,
% 0.71/0.85 (((~![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) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1998) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | c0_1(a1998) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(883,plain,
% 0.71/0.85 (((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998))) <=> (c0_1(a1998) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(884,plain,
% 0.71/0.85 (((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1998) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | c2_1(a1998) | (~c3_1(a1998))))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[883])).
% 0.71/0.85 tff(885,plain,
% 0.71/0.85 (((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | c0_1(a1998) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.71/0.85 inference(transitivity,[status(thm)],[884, 882])).
% 0.71/0.85 tff(886,plain,
% 0.71/0.85 ((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.71/0.85 inference(quant_inst,[status(thm)],[])).
% 0.71/0.85 tff(887,plain,
% 0.71/0.85 ((~![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) | c2_1(W) | (~c3_1(W)))) | c0_1(a1998) | c2_1(a1977) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c1_1(a1977)) | (~c0_1(a1977)) | c2_1(a1998) | (~c3_1(a1998))),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.71/0.85 tff(888,plain,
% 0.71/0.85 ((~c0_1(a1977)) | c2_1(a1998)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[887, 150, 881, 880, 842, 879, 871, 836, 835, 96])).
% 0.71/0.85 tff(889,plain,
% 0.71/0.85 (c2_1(a1998)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[888, 878])).
% 0.71/0.85 tff(890,plain,
% 0.71/0.85 (^[V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.71/0.85 inference(bind,[status(th)],[])).
% 0.71/0.85 tff(891,plain,
% 0.71/0.85 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.85 inference(quant_intro,[status(thm)],[890])).
% 0.71/0.85 tff(892,plain,
% 0.71/0.85 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(893,plain,
% 0.71/0.85 (^[V: $i, U: $i] : 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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(894,plain,
% 0.71/0.86 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[893])).
% 0.71/0.86 tff(895,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.71/0.86 tff(896,plain,
% 0.71/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.71/0.86 tff(897,plain,
% 0.71/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[896, 892])).
% 0.71/0.86 tff(898,plain,(
% 0.71/0.86 ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[897])).
% 0.71/0.86 tff(899,plain,
% 0.71/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[898, 891])).
% 0.71/0.86 tff(900,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c0_1(a1998) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1998)) | (~c2_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1998) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1998)) | (~c2_1(a1998)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(901,plain,
% 0.71/0.86 (((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998))) <=> (c0_1(a1998) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1998)) | (~c2_1(a1998)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(902,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c0_1(a1998) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1998)) | (~c2_1(a1998))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[901])).
% 0.71/0.86 tff(903,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1998) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1998)) | (~c2_1(a1998)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[902, 900])).
% 0.71/0.86 tff(904,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(905,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1998) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c3_1(a1998)) | (~c2_1(a1998))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.71/0.86 tff(906,plain,
% 0.71/0.86 ((~c0_1(a1977)) | (~c2_1(a1998))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[905, 150, 881, 880, 879, 871, 899])).
% 0.71/0.86 tff(907,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[906, 889, 878])).
% 0.71/0.86 tff(908,plain,((~hskp5) | (~c3_1(a1998)) | c0_1(a1998) | (~c0_1(a1975)) | c1_1(a1975) | c2_1(a1975) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(909,plain,
% 0.71/0.86 (~hskp5),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[908, 867, 866, 833, 832, 831, 619, 575, 854])).
% 0.71/0.86 tff(910,assumption,(hskp23), introduced(assumption)).
% 0.71/0.86 tff(911,plain,
% 0.71/0.86 (((~hskp23) | (~c2_1(a2014))) <=> ((~hskp23) | (~c2_1(a2014)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(912,plain,
% 0.71/0.86 (((~c2_1(a2014)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a2014)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(913,axiom,((~c2_1(a2014)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.71/0.86 tff(914,plain,
% 0.71/0.86 ((~hskp23) | (~c2_1(a2014))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.71/0.86 tff(915,plain,
% 0.71/0.86 ((~hskp23) | (~c2_1(a2014))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[914, 911])).
% 0.71/0.86 tff(916,plain,
% 0.71/0.86 (~c2_1(a2014)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[915, 910])).
% 0.71/0.86 tff(917,plain,
% 0.71/0.86 (((~hskp23) | c1_1(a2014)) <=> ((~hskp23) | c1_1(a2014))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(918,axiom,((~hskp23) | c1_1(a2014)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.71/0.86 tff(919,plain,
% 0.71/0.86 ((~hskp23) | c1_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.71/0.86 tff(920,plain,
% 0.71/0.86 ((~hskp23) | c1_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[919, 917])).
% 0.71/0.86 tff(921,plain,
% 0.71/0.86 ((~hskp23) | c1_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[920, 917])).
% 0.71/0.86 tff(922,plain,
% 0.71/0.86 ((~hskp23) | c1_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[921, 917])).
% 0.71/0.86 tff(923,plain,
% 0.71/0.86 ((~hskp23) | c1_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[922, 917])).
% 0.71/0.86 tff(924,plain,
% 0.71/0.86 (c1_1(a2014)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[923, 910])).
% 0.71/0.86 tff(925,plain,
% 0.71/0.86 (((~hskp23) | c0_1(a2014)) <=> ((~hskp23) | c0_1(a2014))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(926,axiom,((~hskp23) | c0_1(a2014)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.71/0.86 tff(927,plain,
% 0.71/0.86 ((~hskp23) | c0_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.71/0.86 tff(928,plain,
% 0.71/0.86 ((~hskp23) | c0_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[927, 925])).
% 0.71/0.86 tff(929,plain,
% 0.71/0.86 ((~hskp23) | c0_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[928, 925])).
% 0.71/0.86 tff(930,plain,
% 0.71/0.86 ((~hskp23) | c0_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[929, 925])).
% 0.71/0.86 tff(931,plain,
% 0.71/0.86 ((~hskp23) | c0_1(a2014)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[930, 925])).
% 0.71/0.86 tff(932,plain,
% 0.71/0.86 (c0_1(a2014)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[931, 910])).
% 0.71/0.86 tff(933,plain,
% 0.71/0.86 (((~![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) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2014) | c0_1(a1998) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | c2_1(a1998) | (~c3_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | c2_1(a2014) | c0_1(a1998) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | c2_1(a1998) | (~c3_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(934,plain,
% 0.71/0.86 (((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998))) <=> (c2_1(a2014) | c0_1(a1998) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | c2_1(a1998) | (~c3_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(935,plain,
% 0.71/0.86 (((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2014) | c0_1(a1998) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | c2_1(a1998) | (~c3_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[934])).
% 0.71/0.86 tff(936,plain,
% 0.71/0.86 (((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![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) | c2_1(W) | (~c3_1(W)))) | c2_1(a2014) | c0_1(a1998) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | c2_1(a1998) | (~c3_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[935, 933])).
% 0.71/0.86 tff(937,plain,
% 0.71/0.86 ((~![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) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(938,plain,
% 0.71/0.86 ((~![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) | c2_1(W) | (~c3_1(W)))) | c2_1(a2014) | c0_1(a1998) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | c2_1(a1998) | (~c3_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.71/0.86 tff(939,plain,
% 0.71/0.86 (c2_1(a1998)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[938, 150, 932, 924, 881, 842, 916, 879, 836, 835, 96])).
% 0.71/0.86 tff(940,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c2_1(a2014) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c2_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c2_1(a2014) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c2_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(941,plain,
% 0.71/0.86 (((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998))) <=> (c2_1(a2014) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c2_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(942,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c2_1(a2014) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c2_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[941])).
% 0.71/0.86 tff(943,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c2_1(a2014) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c2_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[942, 940])).
% 0.71/0.86 tff(944,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a2014) | (~c1_1(a2014)) | (~c0_1(a2014)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(945,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c2_1(a2014) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c2_1(a1998)) | (~c1_1(a2014)) | (~c0_1(a2014))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[944, 943])).
% 0.71/0.86 tff(946,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[945, 150, 932, 924, 881, 916, 879, 899, 939])).
% 0.71/0.86 tff(947,plain,((~hskp23) | (~c3_1(a1998)) | c0_1(a1998) | (~c0_1(a1975)) | c1_1(a1975) | c2_1(a1975)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(948,plain,
% 0.71/0.86 (~hskp23),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[947, 867, 866, 833, 832, 831])).
% 0.71/0.86 tff(949,plain,
% 0.71/0.86 ((hskp23 | hskp8 | hskp5) <=> (hskp23 | hskp8 | hskp5)),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(950,plain,
% 0.71/0.86 (((hskp23 | hskp5) | hskp8) <=> (hskp23 | hskp8 | hskp5)),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(951,axiom,((hskp23 | hskp5) | hskp8), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.71/0.86 tff(952,plain,
% 0.71/0.86 (hskp23 | hskp8 | hskp5),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[951, 950])).
% 0.71/0.86 tff(953,plain,
% 0.71/0.86 (hskp23 | hskp8 | hskp5),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[952, 949])).
% 0.71/0.86 tff(954,plain,
% 0.71/0.86 (hskp23 | hskp8 | hskp5),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[953, 949])).
% 0.71/0.86 tff(955,plain,
% 0.71/0.86 (hskp23 | hskp8 | hskp5),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[954, 949])).
% 0.71/0.86 tff(956,plain,
% 0.71/0.86 (hskp23 | hskp8 | hskp5),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[955, 949])).
% 0.71/0.86 tff(957,plain,
% 0.71/0.86 (hskp8),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[956, 948, 909])).
% 0.71/0.86 tff(958,plain,
% 0.71/0.86 (~c0_1(a1983)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[462, 957])).
% 0.71/0.86 tff(959,plain,
% 0.71/0.86 (c3_1(a1983)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[470, 957])).
% 0.71/0.86 tff(960,plain,
% 0.71/0.86 (~c1_1(a1983)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[476, 957])).
% 0.71/0.86 tff(961,assumption,(~hskp10), introduced(assumption)).
% 0.71/0.86 tff(962,plain,
% 0.71/0.86 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)) | (~c3_1(a1983)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(963,plain,
% 0.71/0.86 ((hskp10 | (~ndr1_0) | c1_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983))) <=> (hskp10 | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(964,plain,
% 0.71/0.86 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)) | (~c3_1(a1983))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[963])).
% 0.71/0.86 tff(965,plain,
% 0.71/0.86 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[964, 962])).
% 0.71/0.86 tff(966,plain,
% 0.71/0.86 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(967,plain,
% 0.71/0.86 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1983)) | (~c3_1(a1983))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.71/0.86 tff(968,plain,
% 0.71/0.86 (hskp10 | c1_1(a1983) | (~c2_1(a1983))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[967, 150, 526, 801])).
% 0.71/0.86 tff(969,plain,
% 0.71/0.86 (~c2_1(a1983)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[968, 524, 961])).
% 0.71/0.86 tff(970,plain,
% 0.71/0.86 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(971,plain,
% 0.71/0.86 ((hskp10 | hskp1 | (~ndr1_0) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983))) <=> (hskp10 | hskp1 | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(972,plain,
% 0.71/0.86 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[971])).
% 0.71/0.86 tff(973,plain,
% 0.71/0.86 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[972, 970])).
% 0.71/0.86 tff(974,plain,
% 0.71/0.86 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(975,plain,
% 0.71/0.86 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.71/0.86 tff(976,plain,
% 0.71/0.86 (hskp10 | hskp1 | c1_1(a1983) | c2_1(a1983)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[975, 150, 526, 345])).
% 0.71/0.86 tff(977,plain,
% 0.71/0.86 (hskp1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[976, 524, 961, 969])).
% 0.71/0.86 tff(978,plain,
% 0.71/0.86 (c2_1(a1971)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[441, 977])).
% 0.71/0.86 tff(979,plain,
% 0.71/0.86 (c0_1(a1971)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[449, 977])).
% 0.71/0.86 tff(980,assumption,(~hskp5), introduced(assumption)).
% 0.71/0.86 tff(981,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(982,plain,
% 0.71/0.86 ((hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983))) <=> (hskp5 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(983,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1983))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[982])).
% 0.71/0.86 tff(984,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1983)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[983, 981])).
% 0.71/0.86 tff(985,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(986,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c2_1(a1971)) | c3_1(a1971) | (~c0_1(a1971)) | (~c3_1(a1983))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.71/0.87 tff(987,plain,
% 0.71/0.87 (c3_1(a1971)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[986, 150, 980, 526, 979, 978, 525, 524, 510])).
% 0.71/0.87 tff(988,plain,
% 0.71/0.87 (~c1_1(a1971)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[433, 977])).
% 0.71/0.87 tff(989,plain,
% 0.71/0.87 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c3_1(a1971)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c3_1(a1971)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(990,plain,
% 0.71/0.87 ((hskp10 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c3_1(a1971))) <=> (hskp10 | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c3_1(a1971)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(991,plain,
% 0.71/0.87 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c3_1(a1971)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c3_1(a1971))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[990])).
% 0.71/0.87 tff(992,plain,
% 0.71/0.87 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c3_1(a1971)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c3_1(a1971)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[991, 989])).
% 0.71/0.87 tff(993,plain,
% 0.71/0.87 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a1971) | (~c2_1(a1971)) | (~c3_1(a1971)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(994,plain,
% 0.71/0.87 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | c1_1(a1971) | (~ndr1_0) | (~c2_1(a1971)) | (~c3_1(a1971))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.71/0.87 tff(995,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[994, 150, 961, 978, 988, 801, 987])).
% 0.71/0.87 tff(996,plain,(c1_1(a1983) | hskp10 | hskp5 | (~c3_1(a1983)) | c0_1(a1983)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(997,plain,
% 0.71/0.87 (hskp10),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[996, 960, 909, 959, 958])).
% 0.71/0.87 tff(998,plain,
% 0.71/0.87 (~c1_1(a1987)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[358, 997])).
% 0.71/0.87 tff(999,plain,
% 0.71/0.87 (c3_1(a1987)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[391, 997])).
% 0.71/0.87 tff(1000,plain,
% 0.71/0.87 (c2_1(a1987)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[366, 997])).
% 0.71/0.87 tff(1001,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | (~c2_1(a1987)) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1002,plain,
% 0.71/0.87 ((hskp27 | (~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987))) <=> (hskp27 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1003,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | (~c2_1(a1987)) | (~c3_1(a1987))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1002])).
% 0.71/0.87 tff(1004,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1003, 1001])).
% 0.71/0.87 tff(1005,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a2005)) | (~c3_1(a2005)) | (~c1_1(a2005)) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1006,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c1_1(a1987) | (~ndr1_0) | (~c3_1(a2005)) | (~c1_1(a2005)) | (~c2_1(a2005)) | (~c2_1(a1987)) | (~c3_1(a1987))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.71/0.87 tff(1007,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1006, 150, 43, 619, 575, 1000, 999, 998, 864, 854])).
% 0.71/0.87 tff(1008,plain,(hskp27), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1009,plain,
% 0.71/0.87 (((~hskp27) | c2_1(a1970)) <=> ((~hskp27) | c2_1(a1970))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1010,axiom,((~hskp27) | c2_1(a1970)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.71/0.87 tff(1011,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.71/0.87 tff(1012,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1011, 1009])).
% 0.71/0.87 tff(1013,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1012, 1009])).
% 0.71/0.87 tff(1014,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1013, 1009])).
% 0.71/0.87 tff(1015,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1014, 1009])).
% 0.71/0.87 tff(1016,plain,
% 0.71/0.87 (c2_1(a1970)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1015, 1008])).
% 0.71/0.87 tff(1017,plain,
% 0.71/0.87 (((~hskp27) | c1_1(a1970)) <=> ((~hskp27) | c1_1(a1970))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1018,axiom,((~hskp27) | c1_1(a1970)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.71/0.87 tff(1019,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.71/0.87 tff(1020,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1019, 1017])).
% 0.71/0.87 tff(1021,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1020, 1017])).
% 0.71/0.87 tff(1022,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1021, 1017])).
% 0.71/0.87 tff(1023,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1022, 1017])).
% 0.71/0.87 tff(1024,plain,
% 0.71/0.87 (c1_1(a1970)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1023, 1008])).
% 0.71/0.87 tff(1025,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c0_1(a1970)) | (~c1_1(a1970)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c0_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1026,plain,
% 0.71/0.87 ((hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c1_1(a1970)) | (~c0_1(a1970))) <=> (hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c0_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1027,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c1_1(a1970)) | (~c0_1(a1970)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c0_1(a1970)) | (~c1_1(a1970))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1026])).
% 0.71/0.87 tff(1028,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c1_1(a1970)) | (~c0_1(a1970)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c0_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1027, 1025])).
% 0.71/0.87 tff(1029,plain,
% 0.71/0.87 ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c1_1(a1970)) | (~c0_1(a1970)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1030,plain,
% 0.71/0.87 ((~![U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | (~ndr1_0) | (~c2_1(a1970)) | (~c0_1(a1970)) | (~c1_1(a1970))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.71/0.87 tff(1031,plain,
% 0.71/0.87 (hskp17 | (~c0_1(a1970))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1030, 150, 1024, 1016, 42])).
% 0.71/0.87 tff(1032,plain,
% 0.71/0.87 (~c0_1(a1970)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1031, 32])).
% 0.71/0.87 tff(1033,plain,
% 0.71/0.87 (^[U: $i] : refl((hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1034,plain,
% 0.71/0.87 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1033])).
% 0.71/0.87 tff(1035,plain,
% 0.71/0.87 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1036,plain,
% 0.71/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp17) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp17) <=> (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1037,plain,
% 0.71/0.87 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp17) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1036])).
% 0.71/0.87 tff(1038,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.71/0.87 tff(1039,plain,
% 0.71/0.87 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.71/0.87 tff(1040,plain,
% 0.71/0.87 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 0.71/0.87 tff(1041,plain,(
% 0.71/0.87 ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(skolemize,[status(sab)],[1040])).
% 0.71/0.87 tff(1042,plain,
% 0.71/0.87 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1041, 1034])).
% 0.71/0.87 tff(1043,plain,
% 0.71/0.87 (((~hskp27) | c3_1(a1970)) <=> ((~hskp27) | c3_1(a1970))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1044,axiom,((~hskp27) | c3_1(a1970)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.71/0.87 tff(1045,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.71/0.87 tff(1046,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1045, 1043])).
% 0.71/0.87 tff(1047,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1046, 1043])).
% 0.71/0.87 tff(1048,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 0.71/0.87 tff(1049,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a1970)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1048, 1043])).
% 0.71/0.87 tff(1050,plain,
% 0.71/0.87 (c3_1(a1970)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1049, 1008])).
% 0.71/0.87 tff(1051,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1970)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1052,plain,
% 0.71/0.87 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1053,plain,
% 0.71/0.87 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1970))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 0.71/0.87 tff(1054,plain,
% 0.71/0.87 (hskp17 | hskp13 | c0_1(a1970)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1053, 150, 1024, 1050, 1042])).
% 0.71/0.87 tff(1055,plain,
% 0.71/0.87 (hskp13),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1054, 32, 1032])).
% 0.71/0.87 tff(1056,plain,
% 0.71/0.87 (((~hskp13) | (~c3_1(a1991))) <=> ((~hskp13) | (~c3_1(a1991)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1057,plain,
% 0.71/0.87 (((~c3_1(a1991)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1991)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1058,axiom,((~c3_1(a1991)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.71/0.87 tff(1059,plain,
% 0.71/0.87 ((~hskp13) | (~c3_1(a1991))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.71/0.87 tff(1060,plain,
% 0.71/0.87 ((~hskp13) | (~c3_1(a1991))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1059, 1056])).
% 0.71/0.87 tff(1061,plain,
% 0.71/0.87 (~c3_1(a1991)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1060, 1055])).
% 0.71/0.87 tff(1062,plain,
% 0.71/0.87 (((~hskp13) | c2_1(a1991)) <=> ((~hskp13) | c2_1(a1991))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1063,axiom,((~hskp13) | c2_1(a1991)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.71/0.87 tff(1064,plain,
% 0.71/0.87 ((~hskp13) | c2_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.71/0.87 tff(1065,plain,
% 0.71/0.87 ((~hskp13) | c2_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1064, 1062])).
% 0.71/0.87 tff(1066,plain,
% 0.71/0.87 ((~hskp13) | c2_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1065, 1062])).
% 0.71/0.87 tff(1067,plain,
% 0.71/0.87 ((~hskp13) | c2_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1066, 1062])).
% 0.71/0.87 tff(1068,plain,
% 0.71/0.87 ((~hskp13) | c2_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1067, 1062])).
% 0.71/0.87 tff(1069,plain,
% 0.71/0.87 (c2_1(a1991)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1068, 1055])).
% 0.71/0.87 tff(1070,plain,
% 0.71/0.87 (((~hskp13) | c0_1(a1991)) <=> ((~hskp13) | c0_1(a1991))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1071,axiom,((~hskp13) | c0_1(a1991)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.71/0.87 tff(1072,plain,
% 0.71/0.87 ((~hskp13) | c0_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.71/0.87 tff(1073,plain,
% 0.71/0.87 ((~hskp13) | c0_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1072, 1070])).
% 0.71/0.87 tff(1074,plain,
% 0.71/0.87 ((~hskp13) | c0_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 0.71/0.87 tff(1075,plain,
% 0.71/0.87 ((~hskp13) | c0_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1074, 1070])).
% 0.71/0.87 tff(1076,plain,
% 0.71/0.87 ((~hskp13) | c0_1(a1991)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1075, 1070])).
% 0.71/0.87 tff(1077,plain,
% 0.71/0.87 (c0_1(a1991)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1076, 1055])).
% 0.71/0.87 tff(1078,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a1991) | (~ndr1_0) | (~c0_1(a1991)) | (~c2_1(a1991)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a1991) | (~ndr1_0) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1079,plain,
% 0.71/0.87 ((hskp17 | hskp4 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991))) <=> (hskp17 | hskp4 | c3_1(a1991) | (~ndr1_0) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1080,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a1991) | (~ndr1_0) | (~c0_1(a1991)) | (~c2_1(a1991))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1079])).
% 0.71/0.87 tff(1081,plain,
% 0.71/0.87 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a1991) | (~ndr1_0) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1080, 1078])).
% 0.71/0.87 tff(1082,plain,
% 0.71/0.87 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1083,plain,
% 0.71/0.87 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a1991) | (~ndr1_0) | (~c0_1(a1991)) | (~c2_1(a1991))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.71/0.87 tff(1084,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1083, 150, 32, 21, 1077, 1069, 1061, 31])).
% 0.71/0.87 tff(1085,plain,(hskp17 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1086,plain,
% 0.71/0.87 (hskp17),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1085, 21])).
% 0.71/0.87 tff(1087,plain,
% 0.71/0.87 (hskp18),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[610, 21, 1086])).
% 0.71/0.87 tff(1088,plain,
% 0.71/0.87 (~c3_1(a2000)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[241, 1087])).
% 0.71/0.87 tff(1089,plain,
% 0.71/0.87 (~c0_1(a2000)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[229, 1087])).
% 0.71/0.87 tff(1090,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (c0_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c2_1(a2000))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c0_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c2_1(a2000))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1091,plain,
% 0.71/0.87 (((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c0_1(a2000) | c2_1(a2000)) <=> (c0_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c2_1(a2000))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1092,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c0_1(a2000) | c2_1(a2000))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (c0_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c2_1(a2000)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1091])).
% 0.71/0.87 tff(1093,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c0_1(a2000) | c2_1(a2000))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c0_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c2_1(a2000))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1092, 1090])).
% 0.71/0.87 tff(1094,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c0_1(a2000) | c2_1(a2000))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1095,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c0_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c2_1(a2000)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 0.71/0.87 tff(1096,plain,
% 0.71/0.87 (c2_1(a2000)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1095, 150, 1024, 1016, 1050, 1089, 1088, 20])).
% 0.71/0.87 tff(1097,plain,
% 0.71/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1098,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1097])).
% 0.71/0.87 tff(1099,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1100,plain,
% 0.71/0.87 (^[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) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | 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)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1101,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1100])).
% 0.71/0.87 tff(1102,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.71/0.87 tff(1103,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.71/0.87 tff(1104,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1103, 1099])).
% 0.71/0.87 tff(1105,plain,(
% 0.71/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(skolemize,[status(sab)],[1104])).
% 0.71/0.87 tff(1106,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1105, 1098])).
% 0.71/0.87 tff(1107,plain,
% 0.71/0.87 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1108,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1107])).
% 0.71/0.88 tff(1109,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1110,plain,
% 0.71/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1111,plain,
% 0.71/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1110])).
% 0.71/0.88 tff(1112,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.71/0.88 tff(1113,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.71/0.88 tff(1114,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1113, 1109])).
% 0.71/0.88 tff(1115,plain,(
% 0.71/0.88 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[1114])).
% 0.71/0.88 tff(1116,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1115, 1108])).
% 0.71/0.88 tff(1117,plain,
% 0.71/0.88 (^[U: $i] : refl((hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1118,plain,
% 0.71/0.88 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1117])).
% 0.71/0.88 tff(1119,plain,
% 0.71/0.88 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1120,plain,
% 0.71/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) | hskp11) <=> ((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) | hskp11) <=> (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1121,plain,
% 0.71/0.88 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) | hskp11) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1120])).
% 0.71/0.88 tff(1122,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.71/0.88 tff(1123,plain,
% 0.71/0.88 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.71/0.88 tff(1124,plain,
% 0.71/0.88 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1123, 1119])).
% 0.71/0.88 tff(1125,plain,(
% 0.71/0.88 ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[1124])).
% 0.71/0.88 tff(1126,plain,
% 0.71/0.88 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1125, 1118])).
% 0.71/0.88 tff(1127,plain,
% 0.71/0.88 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1128,plain,
% 0.71/0.88 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1129,plain,
% 0.71/0.88 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.71/0.88 tff(1130,plain,
% 0.71/0.88 (hskp11 | hskp4),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1129, 150, 1024, 1016, 1050, 1126])).
% 0.71/0.88 tff(1131,plain,
% 0.71/0.88 (hskp11),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1130, 21])).
% 0.71/0.88 tff(1132,plain,
% 0.71/0.88 (((~hskp11) | (~c3_1(a1989))) <=> ((~hskp11) | (~c3_1(a1989)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1133,plain,
% 0.71/0.88 (((~c3_1(a1989)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1989)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1134,axiom,((~c3_1(a1989)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.71/0.88 tff(1135,plain,
% 0.71/0.88 ((~hskp11) | (~c3_1(a1989))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.71/0.88 tff(1136,plain,
% 0.71/0.88 ((~hskp11) | (~c3_1(a1989))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1135, 1132])).
% 0.71/0.88 tff(1137,plain,
% 0.71/0.88 (~c3_1(a1989)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1136, 1131])).
% 0.71/0.88 tff(1138,plain,
% 0.71/0.88 (((~hskp11) | (~c0_1(a1989))) <=> ((~hskp11) | (~c0_1(a1989)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1139,plain,
% 0.71/0.88 (((~c0_1(a1989)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a1989)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1140,axiom,((~c0_1(a1989)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.71/0.88 tff(1141,plain,
% 0.71/0.88 ((~hskp11) | (~c0_1(a1989))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.71/0.88 tff(1142,plain,
% 0.71/0.88 ((~hskp11) | (~c0_1(a1989))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1141, 1138])).
% 0.71/0.88 tff(1143,plain,
% 0.71/0.88 (~c0_1(a1989)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1142, 1131])).
% 0.71/0.88 tff(1144,plain,
% 0.71/0.88 (~c0_1(a1998)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[585, 1086])).
% 0.71/0.88 tff(1145,plain,
% 0.71/0.88 (((~hskp11) | c2_1(a1989)) <=> ((~hskp11) | c2_1(a1989))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1146,axiom,((~hskp11) | c2_1(a1989)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.71/0.88 tff(1147,plain,
% 0.71/0.88 ((~hskp11) | c2_1(a1989)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.71/0.88 tff(1148,plain,
% 0.71/0.88 ((~hskp11) | c2_1(a1989)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1147, 1145])).
% 0.71/0.88 tff(1149,plain,
% 0.71/0.88 ((~hskp11) | c2_1(a1989)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1148, 1145])).
% 0.71/0.88 tff(1150,plain,
% 0.71/0.88 ((~hskp11) | c2_1(a1989)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1149, 1145])).
% 0.71/0.88 tff(1151,plain,
% 0.71/0.88 ((~hskp11) | c2_1(a1989)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1150, 1145])).
% 0.71/0.88 tff(1152,plain,
% 0.71/0.88 (c2_1(a1989)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1151, 1131])).
% 0.71/0.88 tff(1153,plain,
% 0.71/0.88 (c3_1(a1998)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[593, 1086])).
% 0.71/0.88 tff(1154,plain,
% 0.71/0.88 (c1_1(a1998)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[601, 1086])).
% 0.71/0.88 tff(1155,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a1998) | c0_1(a1989) | c3_1(a1989) | (~ndr1_0) | (~c2_1(a1989)) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a1998) | c0_1(a1989) | c3_1(a1989) | (~ndr1_0) | (~c2_1(a1989)) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1156,plain,
% 0.71/0.88 ((hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a1989) | c0_1(a1989) | (~c2_1(a1989))) <=> (hskp13 | c0_1(a1998) | c0_1(a1989) | c3_1(a1989) | (~ndr1_0) | (~c2_1(a1989)) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1157,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a1989) | c0_1(a1989) | (~c2_1(a1989)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a1998) | c0_1(a1989) | c3_1(a1989) | (~ndr1_0) | (~c2_1(a1989)) | (~c3_1(a1998)) | (~c1_1(a1998))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1156])).
% 0.71/0.88 tff(1158,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a1989) | c0_1(a1989) | (~c2_1(a1989)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a1998) | c0_1(a1989) | c3_1(a1989) | (~ndr1_0) | (~c2_1(a1989)) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1157, 1155])).
% 0.71/0.88 tff(1159,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a1989) | c0_1(a1989) | (~c2_1(a1989)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1160,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a1998) | c0_1(a1989) | c3_1(a1989) | (~ndr1_0) | (~c2_1(a1989)) | (~c3_1(a1998)) | (~c1_1(a1998))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.71/0.88 tff(1161,plain,
% 0.71/0.88 (hskp13),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1160, 150, 1154, 1153, 1152, 1144, 1143, 1137, 1116])).
% 0.71/0.88 tff(1162,plain,
% 0.71/0.88 (~c3_1(a1991)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1060, 1161])).
% 0.71/0.88 tff(1163,plain,
% 0.71/0.88 (~c1_1(a2000)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[235, 1087])).
% 0.71/0.88 tff(1164,plain,
% 0.71/0.88 (c2_1(a1991)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1068, 1161])).
% 0.71/0.88 tff(1165,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1991)) | (~c2_1(a1991)) | (~c2_1(a2000)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1991)) | (~c2_1(a1991)) | (~c2_1(a2000)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1166,plain,
% 0.73/0.88 (((~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c1_1(a1991)) | c3_1(a2000) | c0_1(a2000) | (~c2_1(a2000)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000)) <=> (c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1991)) | (~c2_1(a1991)) | (~c2_1(a2000)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1167,plain,
% 0.73/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c1_1(a1991)) | c3_1(a2000) | c0_1(a2000) | (~c2_1(a2000)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1991)) | (~c2_1(a1991)) | (~c2_1(a2000))))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[1166])).
% 0.73/0.88 tff(1168,plain,
% 0.73/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c1_1(a1991)) | c3_1(a2000) | c0_1(a2000) | (~c2_1(a2000)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1991)) | (~c2_1(a1991)) | (~c2_1(a2000)))),
% 0.73/0.88 inference(transitivity,[status(thm)],[1167, 1165])).
% 0.73/0.88 tff(1169,plain,
% 0.73/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c1_1(a1991)) | c3_1(a2000) | c0_1(a2000) | (~c2_1(a2000)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))),
% 0.73/0.88 inference(quant_inst,[status(thm)],[])).
% 0.73/0.88 tff(1170,plain,
% 0.73/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1991)) | (~c2_1(a1991)) | (~c2_1(a2000))),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.73/0.88 tff(1171,plain,
% 0.73/0.88 (~c1_1(a1991)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1170, 150, 1164, 1089, 1163, 1088, 1162, 1106, 1096])).
% 0.73/0.88 tff(1172,assumption,(~hskp8), introduced(assumption)).
% 0.73/0.88 tff(1173,plain,
% 0.73/0.88 (hskp18),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[610, 1086, 21])).
% 0.73/0.88 tff(1174,plain,
% 0.73/0.88 (~c3_1(a2000)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[241, 1173])).
% 0.73/0.88 tff(1175,plain,
% 0.73/0.88 (~c0_1(a2000)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[229, 1173])).
% 0.73/0.88 tff(1176,plain,
% 0.73/0.88 (c2_1(a2000)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1095, 150, 1024, 1016, 1050, 1175, 1174, 20])).
% 0.73/0.88 tff(1177,plain,
% 0.73/0.88 (~c1_1(a2000)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[235, 1173])).
% 0.73/0.88 tff(1178,plain,
% 0.73/0.88 (~c1_1(a1991)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1170, 150, 1164, 1175, 1177, 1174, 1162, 1106, 1176])).
% 0.73/0.88 tff(1179,plain,
% 0.73/0.88 (c0_1(a1991)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1076, 1161])).
% 0.73/0.88 tff(1180,plain,
% 0.73/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1998) | (~ndr1_0) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1998) | (~ndr1_0) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1181,plain,
% 0.73/0.88 ((hskp8 | (~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998))) <=> (hskp8 | c0_1(a1998) | (~ndr1_0) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1182,plain,
% 0.73/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1998) | (~ndr1_0) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c2_1(a1998) | (~c3_1(a1998))))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[1181])).
% 0.73/0.88 tff(1183,plain,
% 0.73/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1998) | (~ndr1_0) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.73/0.88 inference(transitivity,[status(thm)],[1182, 1180])).
% 0.73/0.88 tff(1184,plain,
% 0.73/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c0_1(a1998) | c2_1(a1998) | (~c3_1(a1998)))),
% 0.73/0.88 inference(quant_inst,[status(thm)],[])).
% 0.73/0.88 tff(1185,plain,
% 0.73/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1998) | (~ndr1_0) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c2_1(a1998) | (~c3_1(a1998))),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 0.73/0.88 tff(1186,plain,
% 0.73/0.88 (c2_1(a1998)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1185, 150, 1172, 1153, 1179, 1164, 1144, 53, 1178])).
% 0.73/0.88 tff(1187,plain,
% 0.73/0.88 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.73/0.88 inference(bind,[status(th)],[])).
% 0.73/0.88 tff(1188,plain,
% 0.73/0.88 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.88 inference(quant_intro,[status(thm)],[1187])).
% 0.73/0.88 tff(1189,plain,
% 0.73/0.88 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1190,plain,
% 0.73/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.73/0.88 inference(bind,[status(th)],[])).
% 0.73/0.88 tff(1191,plain,
% 0.73/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.88 inference(quant_intro,[status(thm)],[1190])).
% 0.73/0.88 tff(1192,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.73/0.89 tff(1193,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.73/0.89 tff(1194,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1193, 1189])).
% 0.73/0.89 tff(1195,plain,(
% 0.73/0.89 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.89 inference(skolemize,[status(sab)],[1194])).
% 0.73/0.89 tff(1196,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1195, 1188])).
% 0.73/0.89 tff(1197,plain,
% 0.73/0.89 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.73/0.89 inference(bind,[status(th)],[])).
% 0.73/0.89 tff(1198,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(quant_intro,[status(thm)],[1197])).
% 0.73/0.89 tff(1199,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1200,plain,
% 0.73/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.73/0.89 inference(bind,[status(th)],[])).
% 0.73/0.89 tff(1201,plain,
% 0.73/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(quant_intro,[status(thm)],[1200])).
% 0.73/0.89 tff(1202,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.73/0.89 tff(1203,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.73/0.89 tff(1204,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1203, 1199])).
% 0.73/0.89 tff(1205,plain,(
% 0.73/0.89 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(skolemize,[status(sab)],[1204])).
% 0.73/0.89 tff(1206,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1205, 1198])).
% 0.73/0.89 tff(1207,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1208,plain,
% 0.73/0.89 ((hskp28 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000)) <=> (hskp28 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1209,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970))))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1208])).
% 0.73/0.89 tff(1210,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)))),
% 0.73/0.89 inference(transitivity,[status(thm)],[1209, 1207])).
% 0.73/0.89 tff(1211,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))),
% 0.73/0.89 inference(quant_inst,[status(thm)],[])).
% 0.73/0.89 tff(1212,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.73/0.89 tff(1213,plain,
% 0.73/0.89 (hskp28),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1212, 150, 1024, 1016, 1050, 1175, 1177, 1174, 1206])).
% 0.73/0.89 tff(1214,plain,
% 0.73/0.89 (((~hskp28) | c3_1(a1972)) <=> ((~hskp28) | c3_1(a1972))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1215,axiom,((~hskp28) | c3_1(a1972)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.73/0.89 tff(1216,plain,
% 0.73/0.89 ((~hskp28) | c3_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.73/0.89 tff(1217,plain,
% 0.73/0.89 ((~hskp28) | c3_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1216, 1214])).
% 0.73/0.89 tff(1218,plain,
% 0.73/0.89 ((~hskp28) | c3_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1217, 1214])).
% 0.73/0.89 tff(1219,plain,
% 0.73/0.89 ((~hskp28) | c3_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1218, 1214])).
% 0.73/0.89 tff(1220,plain,
% 0.73/0.89 ((~hskp28) | c3_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1219, 1214])).
% 0.73/0.89 tff(1221,plain,
% 0.73/0.89 (c3_1(a1972)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1220, 1213])).
% 0.73/0.89 tff(1222,plain,
% 0.73/0.89 (((~hskp28) | c1_1(a1972)) <=> ((~hskp28) | c1_1(a1972))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1223,axiom,((~hskp28) | c1_1(a1972)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.73/0.89 tff(1224,plain,
% 0.73/0.89 ((~hskp28) | c1_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 0.73/0.89 tff(1225,plain,
% 0.73/0.89 ((~hskp28) | c1_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1224, 1222])).
% 0.73/0.89 tff(1226,plain,
% 0.73/0.89 ((~hskp28) | c1_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1225, 1222])).
% 0.73/0.89 tff(1227,plain,
% 0.73/0.89 ((~hskp28) | c1_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 0.73/0.89 tff(1228,plain,
% 0.73/0.89 ((~hskp28) | c1_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1227, 1222])).
% 0.73/0.89 tff(1229,plain,
% 0.73/0.89 (c1_1(a1972)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1228, 1213])).
% 0.73/0.89 tff(1230,plain,
% 0.73/0.89 (((~hskp28) | c0_1(a1972)) <=> ((~hskp28) | c0_1(a1972))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1231,axiom,((~hskp28) | c0_1(a1972)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.73/0.89 tff(1232,plain,
% 0.73/0.89 ((~hskp28) | c0_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.73/0.89 tff(1233,plain,
% 0.73/0.89 ((~hskp28) | c0_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1232, 1230])).
% 0.73/0.89 tff(1234,plain,
% 0.73/0.89 ((~hskp28) | c0_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1233, 1230])).
% 0.73/0.89 tff(1235,plain,
% 0.73/0.89 ((~hskp28) | c0_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1234, 1230])).
% 0.73/0.89 tff(1236,plain,
% 0.73/0.89 ((~hskp28) | c0_1(a1972)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1235, 1230])).
% 0.73/0.89 tff(1237,plain,
% 0.73/0.89 (c0_1(a1972)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1236, 1213])).
% 0.73/0.89 tff(1238,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a1998) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a1998) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1239,plain,
% 0.73/0.89 ((hskp16 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998))) <=> (hskp16 | c0_1(a1998) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1240,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a1998) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c3_1(a1998)) | (~c1_1(a1998))))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1239])).
% 0.73/0.89 tff(1241,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a1998) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.73/0.89 inference(transitivity,[status(thm)],[1240, 1238])).
% 0.73/0.89 tff(1242,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)))),
% 0.73/0.89 inference(quant_inst,[status(thm)],[])).
% 0.73/0.89 tff(1243,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a1998) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c3_1(a1998)) | (~c1_1(a1998))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.73/0.89 tff(1244,plain,
% 0.73/0.89 (hskp16),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1243, 150, 1237, 1229, 1221, 1154, 1153, 1144, 1196])).
% 0.73/0.89 tff(1245,plain,
% 0.73/0.89 (((~hskp16) | (~c2_1(a1996))) <=> ((~hskp16) | (~c2_1(a1996)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1246,plain,
% 0.73/0.89 (((~c2_1(a1996)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1996)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1247,axiom,((~c2_1(a1996)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.73/0.89 tff(1248,plain,
% 0.73/0.89 ((~hskp16) | (~c2_1(a1996))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.73/0.89 tff(1249,plain,
% 0.73/0.89 ((~hskp16) | (~c2_1(a1996))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1248, 1245])).
% 0.73/0.89 tff(1250,plain,
% 0.73/0.89 (~c2_1(a1996)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1249, 1244])).
% 0.73/0.89 tff(1251,plain,
% 0.73/0.89 (((~hskp16) | c0_1(a1996)) <=> ((~hskp16) | c0_1(a1996))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1252,axiom,((~hskp16) | c0_1(a1996)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.73/0.89 tff(1253,plain,
% 0.73/0.89 ((~hskp16) | c0_1(a1996)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.73/0.89 tff(1254,plain,
% 0.73/0.89 ((~hskp16) | c0_1(a1996)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1253, 1251])).
% 0.73/0.89 tff(1255,plain,
% 0.73/0.89 ((~hskp16) | c0_1(a1996)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1254, 1251])).
% 0.73/0.89 tff(1256,plain,
% 0.73/0.89 ((~hskp16) | c0_1(a1996)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1255, 1251])).
% 0.73/0.89 tff(1257,plain,
% 0.73/0.89 ((~hskp16) | c0_1(a1996)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1256, 1251])).
% 0.73/0.89 tff(1258,plain,
% 0.73/0.89 (c0_1(a1996)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1257, 1244])).
% 0.73/0.89 tff(1259,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c0_1(a1998) | c2_1(a1996) | (~ndr1_0) | (~c1_1(a1996)) | (~c0_1(a1996)) | (~c3_1(a1998)) | (~c2_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1998) | c2_1(a1996) | (~ndr1_0) | (~c1_1(a1996)) | (~c0_1(a1996)) | (~c3_1(a1998)) | (~c2_1(a1998)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1260,plain,
% 0.73/0.89 (((~ndr1_0) | c2_1(a1996) | (~c1_1(a1996)) | (~c0_1(a1996)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998))) <=> (c0_1(a1998) | c2_1(a1996) | (~ndr1_0) | (~c1_1(a1996)) | (~c0_1(a1996)) | (~c3_1(a1998)) | (~c2_1(a1998)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1261,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1996) | (~c1_1(a1996)) | (~c0_1(a1996)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c0_1(a1998) | c2_1(a1996) | (~ndr1_0) | (~c1_1(a1996)) | (~c0_1(a1996)) | (~c3_1(a1998)) | (~c2_1(a1998))))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1260])).
% 0.73/0.89 tff(1262,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1996) | (~c1_1(a1996)) | (~c0_1(a1996)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1998) | c2_1(a1996) | (~ndr1_0) | (~c1_1(a1996)) | (~c0_1(a1996)) | (~c3_1(a1998)) | (~c2_1(a1998)))),
% 0.73/0.89 inference(transitivity,[status(thm)],[1261, 1259])).
% 0.73/0.89 tff(1263,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1996) | (~c1_1(a1996)) | (~c0_1(a1996)) | c0_1(a1998) | (~c2_1(a1998)) | (~c3_1(a1998)))),
% 0.73/0.89 inference(quant_inst,[status(thm)],[])).
% 0.73/0.89 tff(1264,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1998) | c2_1(a1996) | (~ndr1_0) | (~c1_1(a1996)) | (~c0_1(a1996)) | (~c3_1(a1998)) | (~c2_1(a1998))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.73/0.89 tff(1265,plain,
% 0.73/0.89 (~c1_1(a1996)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1264, 150, 1153, 1258, 1144, 1250, 899, 1186])).
% 0.73/0.89 tff(1266,plain,
% 0.73/0.89 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.73/0.89 inference(bind,[status(th)],[])).
% 0.73/0.89 tff(1267,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(quant_intro,[status(thm)],[1266])).
% 0.73/0.89 tff(1268,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1269,plain,
% 0.73/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.73/0.89 inference(bind,[status(th)],[])).
% 0.73/0.89 tff(1270,plain,
% 0.73/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(quant_intro,[status(thm)],[1269])).
% 0.73/0.89 tff(1271,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.73/0.89 tff(1272,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.73/0.89 tff(1273,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 0.73/0.89 tff(1274,plain,(
% 0.73/0.89 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(skolemize,[status(sab)],[1273])).
% 0.73/0.89 tff(1275,plain,
% 0.73/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1274, 1267])).
% 0.73/0.89 tff(1276,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c0_1(a1991)) | (~c2_1(a1991)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1277,plain,
% 0.73/0.89 ((hskp10 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c3_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991))) <=> (hskp10 | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(1278,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c3_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c0_1(a1991)) | (~c2_1(a1991))))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1277])).
% 0.73/0.89 tff(1279,plain,
% 0.73/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c3_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.89 inference(transitivity,[status(thm)],[1278, 1276])).
% 0.73/0.89 tff(1280,plain,
% 0.73/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1972)) | (~c1_1(a1972)) | (~c0_1(a1972)) | c3_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1281,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a1991) | (~ndr1_0) | (~c1_1(a1972)) | (~c0_1(a1972)) | (~c3_1(a1972)) | (~c0_1(a1991)) | (~c2_1(a1991))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.73/0.90 tff(1282,plain,
% 0.73/0.90 (hskp10),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1281, 150, 1237, 1229, 1221, 1179, 1164, 1162, 1275])).
% 0.73/0.90 tff(1283,plain,
% 0.73/0.90 (~c1_1(a1987)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[358, 1282])).
% 0.73/0.90 tff(1284,plain,
% 0.73/0.90 (c3_1(a1987)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[391, 1282])).
% 0.73/0.90 tff(1285,plain,
% 0.73/0.90 (c2_1(a1987)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[366, 1282])).
% 0.73/0.90 tff(1286,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1996) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c1_1(a1996) | (~c0_1(a1996)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1996) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c1_1(a1996) | (~c0_1(a1996)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1287,plain,
% 0.73/0.90 (((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1996) | c2_1(a1996) | (~c0_1(a1996))) <=> (c2_1(a1996) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c1_1(a1996) | (~c0_1(a1996)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1288,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1996) | c2_1(a1996) | (~c0_1(a1996)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1996) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c1_1(a1996) | (~c0_1(a1996))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1287])).
% 0.73/0.90 tff(1289,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1996) | c2_1(a1996) | (~c0_1(a1996)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1996) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c1_1(a1996) | (~c0_1(a1996)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.73/0.90 tff(1290,plain,
% 0.73/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1996) | c2_1(a1996) | (~c0_1(a1996)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1291,plain,
% 0.73/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1996) | c1_1(a1987) | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)) | c1_1(a1996) | (~c0_1(a1996))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.73/0.90 tff(1292,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1291, 150, 1258, 1179, 1164, 1285, 1284, 1250, 1283, 10, 1178, 1265])).
% 0.73/0.90 tff(1293,plain,(hskp4 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(1294,plain,
% 0.73/0.90 (hskp4),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1293, 1172])).
% 0.73/0.90 tff(1295,plain,
% 0.73/0.90 (~c2_1(a1975)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[102, 1294])).
% 0.73/0.90 tff(1296,plain,
% 0.73/0.90 (~c1_1(a1975)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[108, 1294])).
% 0.73/0.90 tff(1297,plain,
% 0.73/0.90 (c0_1(a1975)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[126, 1294])).
% 0.73/0.90 tff(1298,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c0_1(a1977))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c0_1(a1977))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1299,plain,
% 0.73/0.90 (((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977)) <=> (c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c0_1(a1977))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1300,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c0_1(a1977)))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1299])).
% 0.73/0.90 tff(1301,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c0_1(a1977))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1300, 1298])).
% 0.73/0.90 tff(1302,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | ((~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c3_1(a1977) | c0_1(a1977) | c2_1(a1977))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1303,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | c2_1(a1977) | c3_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | (~c3_1(a1970)) | (~c1_1(a1970)) | c0_1(a1977)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.73/0.90 tff(1304,plain,
% 0.73/0.90 (c0_1(a1977)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1303, 150, 1024, 1016, 1050, 871, 870, 20])).
% 0.73/0.90 tff(1305,assumption,(~c0_1(a1970)), introduced(assumption)).
% 0.73/0.90 tff(1306,assumption,(c0_1(a1977)), introduced(assumption)).
% 0.73/0.90 tff(1307,assumption,(c1_1(a1977)), introduced(assumption)).
% 0.73/0.90 tff(1308,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c2_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1977)) | (~c0_1(a1977)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c2_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1977)) | (~c0_1(a1977)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1309,plain,
% 0.73/0.90 (((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1970) | (~c2_1(a1970)) | (~c3_1(a1970))) <=> (c2_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1977)) | (~c0_1(a1977)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1310,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1970) | (~c2_1(a1970)) | (~c3_1(a1970)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c2_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1977)) | (~c0_1(a1977))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1309])).
% 0.73/0.90 tff(1311,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1970) | (~c2_1(a1970)) | (~c3_1(a1970)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c2_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1977)) | (~c0_1(a1977)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1310, 1308])).
% 0.73/0.90 tff(1312,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1970) | (~c2_1(a1970)) | (~c3_1(a1970)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1313,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c2_1(a1977) | (~ndr1_0) | (~c2_1(a1970)) | c0_1(a1970) | (~c3_1(a1970)) | (~c1_1(a1977)) | (~c0_1(a1977))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 0.73/0.90 tff(1314,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1313, 150, 1016, 1050, 1307, 523, 899, 1306, 1305])).
% 0.73/0.90 tff(1315,plain,(c0_1(a1970) | (~c1_1(a1977)) | c2_1(a1977) | (~c0_1(a1977))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(1316,plain,
% 0.73/0.90 (c0_1(a1970)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1315, 880, 871, 1304])).
% 0.73/0.90 tff(1317,plain,
% 0.73/0.90 (hskp17),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1031, 1316])).
% 0.73/0.90 tff(1318,plain,
% 0.73/0.90 (~c0_1(a1998)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[585, 1317])).
% 0.73/0.90 tff(1319,plain,
% 0.73/0.90 (c3_1(a1998)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[593, 1317])).
% 0.73/0.90 tff(1320,plain,
% 0.73/0.90 (c2_1(a1998)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[887, 150, 1319, 880, 842, 1318, 871, 836, 835, 96, 1304])).
% 0.73/0.90 tff(1321,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[905, 150, 1319, 880, 1318, 871, 899, 1304, 1320])).
% 0.73/0.90 tff(1322,plain,((~hskp5) | (~c0_1(a1975)) | c1_1(a1975) | c2_1(a1975)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(1323,plain,
% 0.73/0.90 (~hskp5),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1322, 1297, 1296, 1295])).
% 0.73/0.90 tff(1324,plain,
% 0.73/0.90 (hskp23),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[956, 1323, 1172])).
% 0.73/0.90 tff(1325,plain,
% 0.73/0.90 (hskp30 | hskp5),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[156, 150, 1297, 1296, 1295, 119])).
% 0.73/0.90 tff(1326,plain,
% 0.73/0.90 (hskp30),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1325, 1323])).
% 0.73/0.90 tff(1327,plain,
% 0.73/0.90 (c0_1(a2005)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[626, 1326])).
% 0.73/0.90 tff(1328,plain,
% 0.73/0.90 (c2_1(a2005)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[618, 1326])).
% 0.73/0.90 tff(1329,plain,
% 0.73/0.90 (c3_1(a2005)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[574, 1326])).
% 0.73/0.90 tff(1330,plain,
% 0.73/0.90 (c1_1(a2005)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[853, 1329, 1328, 1297, 1296, 1295, 1327])).
% 0.73/0.90 tff(1331,plain,
% 0.73/0.90 (hskp17),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[633, 150, 1327, 1328, 42, 1330])).
% 0.73/0.90 tff(1332,plain,
% 0.73/0.90 (c3_1(a1998)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[593, 1331])).
% 0.73/0.90 tff(1333,plain,
% 0.73/0.90 (~c0_1(a1998)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[585, 1331])).
% 0.73/0.90 tff(1334,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[947, 1333, 1332, 1297, 1324, 1296, 1295])).
% 0.73/0.90 tff(1335,plain,(hskp8), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(1336,plain,
% 0.73/0.90 (~c1_1(a1983)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[476, 1335])).
% 0.73/0.90 tff(1337,plain,
% 0.73/0.90 (c3_1(a1983)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[470, 1335])).
% 0.73/0.90 tff(1338,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1339,plain,
% 0.73/0.90 (((~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000)) <=> (c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1340,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1339])).
% 0.73/0.90 tff(1341,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1340, 1338])).
% 0.73/0.90 tff(1342,plain,
% 0.73/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1991) | (~c2_1(a1991)) | (~c0_1(a1991)) | c1_1(a1983) | c2_1(a1983) | (~c3_1(a1983)) | c3_1(a2000) | c1_1(a2000) | c0_1(a2000))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1343,plain,
% 0.73/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2000) | c1_1(a2000) | c3_1(a2000) | c1_1(a1983) | (~ndr1_0) | c2_1(a1983) | (~c3_1(a1983)) | c1_1(a1991) | (~c0_1(a1991)) | (~c2_1(a1991))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.73/0.90 tff(1344,plain,
% 0.73/0.90 (c2_1(a1983)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1343, 150, 1179, 1164, 1337, 1089, 1163, 1088, 1336, 553, 1171])).
% 0.73/0.90 tff(1345,plain,
% 0.73/0.90 (~c0_1(a1983)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[462, 1335])).
% 0.73/0.90 tff(1346,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1991) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c3_1(a1983)) | (~c0_1(a1991)) | (~c2_1(a1991)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1991) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c3_1(a1983)) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1347,plain,
% 0.73/0.90 ((hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983))) <=> (hskp5 | c3_1(a1991) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c3_1(a1983)) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1348,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1991) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c3_1(a1983)) | (~c0_1(a1991)) | (~c2_1(a1991))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1347])).
% 0.73/0.90 tff(1349,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1991) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c3_1(a1983)) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.73/0.90 tff(1350,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1983) | c0_1(a1983) | (~c3_1(a1983)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1351,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1991) | c0_1(a1983) | c1_1(a1983) | (~ndr1_0) | (~c3_1(a1983)) | (~c0_1(a1991)) | (~c2_1(a1991))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.73/0.90 tff(1352,plain,
% 0.73/0.90 (hskp5),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1351, 150, 1179, 1164, 1337, 1162, 1345, 1336, 510])).
% 0.73/0.90 tff(1353,plain,
% 0.73/0.90 (~c2_1(a1977)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[162, 1352])).
% 0.73/0.90 tff(1354,plain,
% 0.73/0.90 (c1_1(a1977)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[172, 1352])).
% 0.73/0.90 tff(1355,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c0_1(a1983) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c2_1(a1983)) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1983) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1356,plain,
% 0.73/0.90 (((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983))) <=> (c0_1(a1983) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1357,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (c0_1(a1983) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c2_1(a1983)) | (~c3_1(a1983))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1356])).
% 0.73/0.90 tff(1358,plain,
% 0.73/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1983) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1357, 1355])).
% 0.73/0.90 tff(1359,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | c2_1(a1977) | (~c1_1(a1977)) | (~c0_1(a1977)) | c0_1(a1983) | (~c2_1(a1983)) | (~c3_1(a1983)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1360,plain,
% 0.73/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | c0_1(a1983) | c2_1(a1977) | (~ndr1_0) | (~c1_1(a1977)) | (~c0_1(a1977)) | (~c2_1(a1983)) | (~c3_1(a1983))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.73/0.90 tff(1361,plain,
% 0.73/0.90 (~c0_1(a1977)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1360, 150, 1337, 1354, 1345, 1353, 899, 1344])).
% 0.73/0.90 tff(1362,plain,
% 0.73/0.90 (~c3_1(a1977)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[196, 1352])).
% 0.73/0.90 tff(1363,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1303, 150, 1024, 1016, 1050, 1353, 1362, 20, 1361])).
% 0.73/0.90 tff(1364,plain,(hskp4), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(1365,plain,
% 0.73/0.90 (~c2_1(a1975)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[102, 1364])).
% 0.73/0.90 tff(1366,plain,
% 0.73/0.90 (~c1_1(a1975)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[108, 1364])).
% 0.73/0.90 tff(1367,plain,
% 0.73/0.90 (c0_1(a1975)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[126, 1364])).
% 0.73/0.90 tff(1368,plain,
% 0.73/0.90 (~hskp5),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1322, 1366, 1367, 1365])).
% 0.73/0.90 tff(1369,plain,
% 0.73/0.90 (hskp10),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[996, 1368, 1337, 1336, 1345])).
% 0.73/0.90 tff(1370,plain,
% 0.73/0.90 (~c1_1(a1987)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[358, 1369])).
% 0.73/0.90 tff(1371,plain,
% 0.73/0.90 (c3_1(a1987)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[391, 1369])).
% 0.73/0.90 tff(1372,plain,
% 0.73/0.90 (c2_1(a1987)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[366, 1369])).
% 0.73/0.90 tff(1373,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1374,plain,
% 0.73/0.90 (((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975))) <=> (c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(1375,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[1374])).
% 0.73/0.90 tff(1376,plain,
% 0.73/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[1375, 1373])).
% 0.73/0.90 tff(1377,plain,
% 0.73/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)) | c1_1(a1987) | (~c2_1(a1987)) | (~c0_1(a1987)) | c1_1(a1975) | c2_1(a1975) | (~c0_1(a1975)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(1378,plain,
% 0.73/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a1987) | c1_1(a1975) | c2_1(a1975) | (~ndr1_0) | (~c0_1(a1975)) | (~c2_1(a1987)) | (~c3_1(a1987)) | (~c0_1(a1987))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 0.73/0.91 tff(1379,plain,
% 0.73/0.91 (~c0_1(a1987)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1378, 150, 1372, 1371, 1367, 1370, 1366, 1365, 10])).
% 0.73/0.91 tff(1380,assumption,(hskp13), introduced(assumption)).
% 0.73/0.91 tff(1381,plain,
% 0.73/0.91 (~c3_1(a1991)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1060, 1380])).
% 0.73/0.91 tff(1382,plain,
% 0.73/0.91 (c2_1(a1991)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1068, 1380])).
% 0.73/0.91 tff(1383,plain,
% 0.73/0.91 (c0_1(a1991)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1076, 1380])).
% 0.73/0.91 tff(1384,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1991) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a1991)) | (~c2_1(a1991)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1991) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1385,plain,
% 0.73/0.91 ((hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987))) <=> (hskp5 | c3_1(a1991) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1386,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1991) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a1991)) | (~c2_1(a1991))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[1385])).
% 0.73/0.91 tff(1387,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1991) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a1991)) | (~c2_1(a1991)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[1386, 1384])).
% 0.73/0.91 tff(1388,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a1991)) | c3_1(a1991) | (~c0_1(a1991)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(1389,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1991) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a1991)) | (~c2_1(a1991))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 0.73/0.91 tff(1390,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1389, 150, 1368, 1383, 1382, 1371, 1381, 1370, 510, 1379])).
% 0.73/0.91 tff(1391,plain,(~hskp13), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(1392,plain,
% 0.73/0.91 (^[U: $i] : refl((hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(1393,plain,
% 0.73/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[1392])).
% 0.73/0.91 tff(1394,plain,
% 0.73/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1395,plain,
% 0.73/0.91 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp20) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp20))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp20) <=> (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp20) <=> (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(1396,plain,
% 0.73/0.91 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp20) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[1395])).
% 0.73/0.91 tff(1397,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.73/0.91 tff(1398,plain,
% 0.73/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 0.73/0.91 tff(1399,plain,
% 0.73/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1398, 1394])).
% 0.73/0.91 tff(1400,plain,(
% 0.73/0.91 ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(skolemize,[status(sab)],[1399])).
% 0.73/0.91 tff(1401,plain,
% 0.73/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1400, 1393])).
% 0.73/0.91 tff(1402,plain,
% 0.73/0.91 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c0_1(a1987))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c0_1(a1987))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1403,plain,
% 0.73/0.91 ((hskp20 | hskp13 | (~ndr1_0) | c0_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987))) <=> (hskp20 | hskp13 | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c0_1(a1987))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1404,plain,
% 0.73/0.91 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c0_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c0_1(a1987)))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[1403])).
% 0.73/0.91 tff(1405,plain,
% 0.73/0.91 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c0_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c0_1(a1987))),
% 0.73/0.91 inference(transitivity,[status(thm)],[1404, 1402])).
% 0.73/0.91 tff(1406,plain,
% 0.73/0.91 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c0_1(a1987) | (~c2_1(a1987)) | (~c3_1(a1987)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(1407,plain,
% 0.73/0.91 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | (~ndr1_0) | (~c2_1(a1987)) | (~c3_1(a1987)) | c0_1(a1987)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.73/0.91 tff(1408,plain,
% 0.73/0.91 (hskp20 | hskp13 | c0_1(a1987)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1407, 150, 1372, 1371, 1401])).
% 0.73/0.91 tff(1409,plain,
% 0.73/0.91 (hskp20),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1408, 1391, 1379])).
% 0.73/0.91 tff(1410,plain,
% 0.73/0.91 (~c3_1(a2003)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[744, 1409])).
% 0.73/0.91 tff(1411,plain,
% 0.73/0.91 (c2_1(a2003)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[722, 1409])).
% 0.73/0.91 tff(1412,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a2003) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a2003)) | (~c2_1(a2003)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a2003) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a2003)) | (~c2_1(a2003)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1413,plain,
% 0.73/0.91 ((hskp5 | (~ndr1_0) | (~c2_1(a2003)) | c3_1(a2003) | (~c0_1(a2003)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987))) <=> (hskp5 | c3_1(a2003) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a2003)) | (~c2_1(a2003)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(1414,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a2003)) | c3_1(a2003) | (~c0_1(a2003)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a2003) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a2003)) | (~c2_1(a2003))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[1413])).
% 0.73/0.91 tff(1415,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a2003)) | c3_1(a2003) | (~c0_1(a2003)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a2003) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a2003)) | (~c2_1(a2003)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[1414, 1412])).
% 0.73/0.91 tff(1416,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a2003)) | c3_1(a2003) | (~c0_1(a2003)) | c1_1(a1987) | c0_1(a1987) | (~c3_1(a1987)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(1417,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a2003) | c1_1(a1987) | (~ndr1_0) | (~c3_1(a1987)) | c0_1(a1987) | (~c0_1(a2003)) | (~c2_1(a2003))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.73/0.91 tff(1418,plain,
% 0.73/0.91 (~c0_1(a2003)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1417, 150, 1368, 1411, 1371, 1410, 1370, 510, 1379])).
% 0.73/0.91 tff(1419,plain,
% 0.73/0.91 (hskp30),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[156, 150, 1368, 1367, 1366, 1365, 119])).
% 0.73/0.91 tff(1420,plain,
% 0.73/0.91 (c0_1(a2005)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[626, 1419])).
% 0.73/0.91 tff(1421,plain,
% 0.73/0.91 (c2_1(a2005)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[618, 1419])).
% 0.73/0.91 tff(1422,plain,
% 0.73/0.91 (c3_1(a2005)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[574, 1419])).
% 0.73/0.91 tff(1423,plain,
% 0.73/0.91 (c1_1(a2005)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[853, 1422, 1421, 1367, 1366, 1365, 1420])).
% 0.73/0.91 tff(1424,plain,
% 0.73/0.91 (hskp17),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[633, 150, 1420, 1421, 42, 1423])).
% 0.73/0.91 tff(1425,plain,
% 0.73/0.91 (~c0_1(a1998)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[585, 1424])).
% 0.73/0.91 tff(1426,plain,
% 0.73/0.91 (c3_1(a1998)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[593, 1424])).
% 0.73/0.92 tff(1427,plain,
% 0.73/0.92 (c1_1(a1998)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[601, 1424])).
% 0.73/0.92 tff(1428,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c3_1(a2003) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)) | c0_1(a2003) | (~c2_1(a2003)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c3_1(a2003) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)) | c0_1(a2003) | (~c2_1(a2003)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(1429,plain,
% 0.73/0.92 ((hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a2003) | c0_1(a2003) | (~c2_1(a2003))) <=> (hskp13 | c3_1(a2003) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)) | c0_1(a2003) | (~c2_1(a2003)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(1430,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a2003) | c0_1(a2003) | (~c2_1(a2003)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c3_1(a2003) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)) | c0_1(a2003) | (~c2_1(a2003))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[1429])).
% 0.73/0.92 tff(1431,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a2003) | c0_1(a2003) | (~c2_1(a2003)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c3_1(a2003) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)) | c0_1(a2003) | (~c2_1(a2003)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.73/0.92 tff(1432,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c0_1(a1998) | (~c3_1(a1998)) | (~c1_1(a1998)) | c3_1(a2003) | c0_1(a2003) | (~c2_1(a2003)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(1433,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c3_1(a2003) | c0_1(a1998) | (~ndr1_0) | (~c3_1(a1998)) | (~c1_1(a1998)) | c0_1(a2003) | (~c2_1(a2003))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.73/0.92 tff(1434,plain,
% 0.73/0.92 ($false),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[1433, 150, 1391, 1411, 1427, 1426, 1410, 1425, 1116, 1418])).
% 0.73/0.92 % SZS output end Proof
% 0.73/0.92 % E exiting
%------------------------------------------------------------------------------