%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN576-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:39:36 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN576-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:38:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(p2_type, type, (
% 0.20/0.41 p2: ( $i * $i ) > $o)).
% 0.20/0.41 tff(f7_type, type, (
% 0.20/0.41 f7: ( $i * $i ) > $i)).
% 0.20/0.41 tff(f3_type, type, (
% 0.20/0.41 f3: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c16_type, type, (
% 0.20/0.41 c16: $i)).
% 0.20/0.41 tff(c15_type, type, (
% 0.20/0.41 c15: $i)).
% 0.20/0.41 tff(f9_type, type, (
% 0.20/0.41 f9: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(c14_type, type, (
% 0.20/0.41 c14: $i)).
% 0.20/0.41 tff(c13_type, type, (
% 0.20/0.41 c13: $i)).
% 0.20/0.41 tff(p4_type, type, (
% 0.20/0.41 p4: ( $i * $i ) > $o)).
% 0.20/0.41 tff(p8_type, type, (
% 0.20/0.41 p8: ( $i * $i ) > $o)).
% 0.20/0.41 tff(p12_type, type, (
% 0.20/0.41 p12: ( $i * $i ) > $o)).
% 0.20/0.41 tff(f6_type, type, (
% 0.20/0.41 f6: $i > $i)).
% 0.20/0.41 tff(p11_type, type, (
% 0.20/0.41 p11: ( $i * $i ) > $o)).
% 0.20/0.41 tff(f10_type, type, (
% 0.20/0.41 f10: $i > $i)).
% 0.20/0.41 tff(p5_type, type, (
% 0.20/0.41 p5: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(~p4(c13, c13)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X34: $i] : refl(p4(X34, X34) <=> p4(X34, X34))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X34: $i] : p4(X34, X34) <=> ![X34: $i] : p4(X34, X34)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X34: $i] : p4(X34, X34) <=> ![X34: $i] : p4(X34, X34)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X34: $i] : p4(X34, X34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_3')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X34: $i] : p4(X34, X34)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X34: $i] : p4(X34, X34)),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X34: $i] : p4(X34, X34)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X34: $i] : p4(X34, X34)) | p4(c13, c13)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(p4(c13, c13)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,assumption,(~p8(c14, c14)), introduced(assumption)).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[X42: $i] : refl(p8(X42, X42) <=> p8(X42, X42))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![X42: $i] : p8(X42, X42) <=> ![X42: $i] : p8(X42, X42)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![X42: $i] : p8(X42, X42) <=> ![X42: $i] : p8(X42, X42)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,axiom,(![X42: $i] : p8(X42, X42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p8_1')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![X42: $i] : p8(X42, X42)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,(
% 0.20/0.41 ![X42: $i] : p8(X42, X42)),
% 0.20/0.41 inference(skolemize,[status(sab)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![X42: $i] : p8(X42, X42)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~![X42: $i] : p8(X42, X42)) | p8(c14, c14)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.20/0.41 tff(22,plain,(p8(c14, c14)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (^[X22: $i, X23: $i] : refl(p2(f3(X22, X23), f3(X23, X22)) <=> p2(f3(X22, X23), f3(X23, X22)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22)) <=> ![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22)) <=> ![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,axiom,(![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_8')).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,(
% 0.20/0.41 ![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))),
% 0.20/0.41 inference(skolemize,[status(sab)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~![X22: $i, X23: $i] : p2(f3(X22, X23), f3(X23, X22))) | p2(f3(c16, c15), f3(c15, c16))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (p2(f3(c16, c15), f3(c15, c16))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (^[X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : refl(((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) <=> ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) <=> ![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) <=> ![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : trans(monotonicity(trans(monotonicity(rewrite((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) <=> ((~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))), (((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) | (~p8(X29, X32))) <=> (((~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) | (~p8(X29, X32))))), rewrite((((~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) | (~p8(X29, X32))) <=> ((~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))), (((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) | (~p8(X29, X32))) <=> ((~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))))), ((((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) | (~p8(X29, X32))) | (~p2(X30, X33))) <=> (((~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) | (~p2(X30, X33))))), rewrite((((~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33))) | (~p2(X30, X33))) <=> ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))), ((((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) | (~p8(X29, X32))) | (~p2(X30, X33))) <=> ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : (((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) | (~p8(X29, X32))) | (~p2(X30, X33))) <=> ![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,axiom,(![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : (((p2(f9(X28, X29, X30), f9(X31, X32, X33)) | (~p4(X28, X31))) | (~p8(X29, X32))) | (~p2(X30, X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_20')).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.42 tff(40,plain,(
% 0.20/0.42 ![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | ((~p8(c14, c14)) | (~p4(c13, c13)) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))) <=> ((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | (~p8(c14, c14)) | (~p4(c13, c13)) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~p2(f3(c16, c15), f3(c15, c16))) | (~p8(c14, c14)) | (~p4(c13, c13)) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) <=> ((~p8(c14, c14)) | (~p4(c13, c13)) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | ((~p2(f3(c16, c15), f3(c15, c16))) | (~p8(c14, c14)) | (~p4(c13, c13)) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))) <=> ((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | ((~p8(c14, c14)) | (~p4(c13, c13)) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | ((~p2(f3(c16, c15), f3(c15, c16))) | (~p8(c14, c14)) | (~p4(c13, c13)) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))) <=> ((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | (~p8(c14, c14)) | (~p4(c13, c13)) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | ((~p2(f3(c16, c15), f3(c15, c16))) | (~p8(c14, c14)) | (~p4(c13, c13)) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 ((~![X31: $i, X32: $i, X30: $i, X29: $i, X28: $i, X33: $i] : ((~p2(X30, X33)) | (~p8(X29, X32)) | (~p4(X28, X31)) | p2(f9(X28, X29, X30), f9(X31, X32, X33)))) | (~p8(c14, c14)) | (~p4(c13, c13)) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[47, 41, 31, 22, 11])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (^[X25: $i, X27: $i, X26: $i, X24: $i] : refl(((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27))) <=> ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (^[X25: $i, X27: $i, X26: $i, X24: $i] : trans(monotonicity(rewrite((p2(f7(X24, X25), f7(X26, X27)) | (~p2(X24, X26))) <=> ((~p2(X24, X26)) | p2(f7(X24, X25), f7(X26, X27)))), (((p2(f7(X24, X25), f7(X26, X27)) | (~p2(X24, X26))) | (~p2(X25, X27))) <=> (((~p2(X24, X26)) | p2(f7(X24, X25), f7(X26, X27))) | (~p2(X25, X27))))), rewrite((((~p2(X24, X26)) | p2(f7(X24, X25), f7(X26, X27))) | (~p2(X25, X27))) <=> ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))), (((p2(f7(X24, X25), f7(X26, X27)) | (~p2(X24, X26))) | (~p2(X25, X27))) <=> ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((p2(f7(X24, X25), f7(X26, X27)) | (~p2(X24, X26))) | (~p2(X25, X27))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.42 tff(54,axiom,(![X25: $i, X27: $i, X26: $i, X24: $i] : ((p2(f7(X24, X25), f7(X26, X27)) | (~p2(X24, X26))) | (~p2(X25, X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_19')).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.42 tff(57,plain,(
% 0.20/0.42 ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | ((~p2(f3(c16, c15), f3(c15, c16))) | (~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | (~p2(f3(c16, c15), f3(c15, c16))) | (~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) <=> ((~p2(f3(c16, c15), f3(c15, c16))) | (~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | ((~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | ((~p2(f3(c16, c15), f3(c15, c16))) | (~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | ((~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | (~p2(f3(c16, c15), f3(c15, c16))) | (~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | ((~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | (~p2(f3(c16, c15), f3(c15, c16))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X25, X27)) | p2(f7(X24, X25), f7(X26, X27)))) | (~p2(f3(c16, c15), f3(c15, c16))) | (~p2(f9(c13, c14, f3(c16, c15)), f9(c13, c14, f3(c15, c16)))) | p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[64, 58, 31, 48])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (^[X12: $i, X11: $i, X10: $i] : refl(((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) <=> ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) <=> ![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) <=> ![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (^[X12: $i, X11: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) <=> ((~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))), (((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) | (~p12(X11, f6(X10)))) <=> (((~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) | (~p12(X11, f6(X10)))))), rewrite((((~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) | (~p12(X11, f6(X10)))) <=> ((~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))), (((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) | (~p12(X11, f6(X10)))) <=> ((~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))))), ((((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) | (~p12(X11, f6(X10)))) | (~p11(f10(X11), f10(X12)))) <=> (((~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) | (~p11(f10(X11), f10(X12)))))), rewrite((((~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10))) | (~p11(f10(X11), f10(X12)))) <=> ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))), ((((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) | (~p12(X11, f6(X10)))) | (~p11(f10(X11), f10(X12)))) <=> ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![X12: $i, X11: $i, X10: $i] : (((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) | (~p12(X11, f6(X10)))) | (~p11(f10(X11), f10(X12)))) <=> ![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.43 tff(71,axiom,(![X12: $i, X11: $i, X10: $i] : (((p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)) | (~p12(X12, f6(X10)))) | (~p12(X11, f6(X10)))) | (~p11(f10(X11), f10(X12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_22')).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.43 tff(74,plain,(
% 0.20/0.43 ![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 ((~p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13))) <=> (~p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,axiom,(~p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p12_17')).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (~p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (p12(c16, f6(c13)) <=> p12(c16, f6(c13))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,axiom,(p12(c16, f6(c13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_6')).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (p12(c16, f6(c13))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (p12(c15, f6(c13)) <=> p12(c15, f6(c13))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(83,axiom,(p12(c15, f6(c13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_5')).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (p12(c15, f6(c13))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p11(f10(c15), f10(c16))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))) <=> ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | (~p11(f10(c15), f10(c16))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p11(f10(c15), f10(c16))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | (~p11(f10(c15), f10(c16))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (~p11(f10(c15), f10(c16))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 84, 81, 78, 75])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (^[X4: $i, X5: $i] : refl((p11(X5, X4) | p11(X4, X5)) <=> (p11(X5, X4) | p11(X4, X5)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5)) <=> ![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5)) <=> ![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (^[X4: $i, X5: $i] : rewrite((p11(X4, X5) | p11(X5, X4)) <=> (p11(X5, X4) | p11(X4, X5)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![X4: $i, X5: $i] : (p11(X4, X5) | p11(X5, X4)) <=> ![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.43 tff(94,axiom,(![X4: $i, X5: $i] : (p11(X4, X5) | p11(X5, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_7')).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.43 tff(97,plain,(
% 0.20/0.43 ![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(skolemize,[status(sab)],[96])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (((~![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))) | (p11(f10(c15), f10(c16)) | p11(f10(c16), f10(c15)))) <=> ((~![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))) | p11(f10(c15), f10(c16)) | p11(f10(c16), f10(c15)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))) | (p11(f10(c15), f10(c16)) | p11(f10(c16), f10(c15)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((~![X4: $i, X5: $i] : (p11(X5, X4) | p11(X4, X5))) | p11(f10(c15), f10(c16)) | p11(f10(c16), f10(c15))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (p11(f10(c16), f10(c15))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | (~p11(f10(c16), f10(c15))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))) <=> ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | (~p11(f10(c16), f10(c15))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~p11(f10(c16), f10(c15))) | (~p12(c16, f6(c13))) | (~p12(c15, f6(c13))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))) <=> ((~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | (~p11(f10(c16), f10(c15))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p11(f10(c16), f10(c15))) | (~p12(c16, f6(c13))) | (~p12(c15, f6(c13))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))) <=> ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | (~p11(f10(c16), f10(c15))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p11(f10(c16), f10(c15))) | (~p12(c16, f6(c13))) | (~p12(c15, f6(c13))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))) <=> ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | (~p11(f10(c16), f10(c15))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | ((~p11(f10(c16), f10(c15))) | (~p12(c16, f6(c13))) | (~p12(c15, f6(c13))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 ((~![X12: $i, X11: $i, X10: $i] : ((~p11(f10(X11), f10(X12))) | (~p12(X11, f6(X10))) | (~p12(X12, f6(X10))) | p12(f7(f9(X10, c14, f3(X11, X12)), f3(X11, X12)), f6(X10)))) | (~p12(c15, f6(c13))) | (~p12(c16, f6(c13))) | (~p11(f10(c16), f10(c15))) | p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[108, 84, 81, 75, 102])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (^[X41: $i, X40: $i] : refl(((~p4(X40, X41)) | p5(f6(X40), f6(X41))) <=> ((~p4(X40, X41)) | p5(f6(X40), f6(X41))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41))) <=> ![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41))) <=> ![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (^[X41: $i, X40: $i] : rewrite((p5(f6(X40), f6(X41)) | (~p4(X40, X41))) <=> ((~p4(X40, X41)) | p5(f6(X40), f6(X41))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (![X41: $i, X40: $i] : (p5(f6(X40), f6(X41)) | (~p4(X40, X41))) <=> ![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.44 tff(115,axiom,(![X41: $i, X40: $i] : (p5(f6(X40), f6(X41)) | (~p4(X40, X41)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_9')).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.44 tff(118,plain,(
% 0.20/0.44 ![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[117])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (((~![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))) | ((~p4(c13, c13)) | p5(f6(c13), f6(c13)))) <=> ((~![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))) | (~p4(c13, c13)) | p5(f6(c13), f6(c13)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))) | ((~p4(c13, c13)) | p5(f6(c13), f6(c13)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((~![X41: $i, X40: $i] : ((~p4(X40, X41)) | p5(f6(X40), f6(X41)))) | (~p4(c13, c13)) | p5(f6(c13), f6(c13))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (p5(f6(c13), f6(c13))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[122, 119, 11])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (^[X9: $i, X6: $i, X7: $i, X8: $i] : refl(((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)) <=> ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)) <=> ![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)) <=> ![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (^[X9: $i, X6: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p12(X6, X7) | (~p2(X8, X6))) <=> ((~p2(X8, X6)) | p12(X6, X7))), (((p12(X6, X7) | (~p2(X8, X6))) | (~p5(X9, X7))) <=> (((~p2(X8, X6)) | p12(X6, X7)) | (~p5(X9, X7))))), rewrite((((~p2(X8, X6)) | p12(X6, X7)) | (~p5(X9, X7))) <=> ((~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))), (((p12(X6, X7) | (~p2(X8, X6))) | (~p5(X9, X7))) <=> ((~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)))), ((((p12(X6, X7) | (~p2(X8, X6))) | (~p5(X9, X7))) | (~p12(X8, X9))) <=> (((~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)) | (~p12(X8, X9))))), rewrite((((~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7)) | (~p12(X8, X9))) <=> ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))), ((((p12(X6, X7) | (~p2(X8, X6))) | (~p5(X9, X7))) | (~p12(X8, X9))) <=> ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![X9: $i, X6: $i, X7: $i, X8: $i] : (((p12(X6, X7) | (~p2(X8, X6))) | (~p5(X9, X7))) | (~p12(X8, X9))) <=> ![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.44 tff(129,axiom,(![X9: $i, X6: $i, X7: $i, X8: $i] : (((p12(X6, X7) | (~p2(X8, X6))) | (~p5(X9, X7))) | (~p12(X8, X9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_16')).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.44 tff(132,plain,(
% 0.20/0.44 ![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(skolemize,[status(sab)],[131])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | (p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | (~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))))) <=> ((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | (~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (((~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13))) <=> (p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | (~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | ((~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))) <=> ((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | (p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | (~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | ((~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))) <=> ((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | (~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | ((~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13))) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~![X9: $i, X6: $i, X7: $i, X8: $i] : ((~p12(X8, X9)) | (~p5(X9, X7)) | (~p2(X8, X6)) | p12(X6, X7))) | p12(f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)), f6(c13)) | (~p5(f6(c13), f6(c13))) | (~p2(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f7(f9(c13, c14, f3(c15, c16)), f3(c15, c16)))) | (~p12(f7(f9(c13, c14, f3(c16, c15)), f3(c16, c15)), f6(c13)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 133, 78, 123, 109, 65])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------