%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN554-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:39:34 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN554-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.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 12:38:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(p4_type, type, (
% 0.11/0.36 p4: ( $i * $i ) > $o)).
% 0.11/0.36 tff(f3_type, type, (
% 0.11/0.36 f3: ( $i * $i ) > $i)).
% 0.11/0.36 tff(c7_type, type, (
% 0.11/0.36 c7: $i)).
% 0.11/0.36 tff(c5_type, type, (
% 0.11/0.36 c5: $i)).
% 0.11/0.36 tff(c6_type, type, (
% 0.11/0.36 c6: $i)).
% 0.11/0.36 tff(p2_type, type, (
% 0.11/0.36 p2: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,assumption,(p4(f3(c5, c7), f3(c5, c7))), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[X15: $i] : refl((~p4(X15, X15)) <=> (~p4(X15, X15)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X15: $i] : (~p4(X15, X15)) <=> ![X15: $i] : (~p4(X15, X15))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![X15: $i] : (~p4(X15, X15)) <=> ![X15: $i] : (~p4(X15, X15))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(![X15: $i] : (~p4(X15, X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p4_2')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![X15: $i] : (~p4(X15, X15))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,(
% 0.11/0.36 ![X15: $i] : (~p4(X15, X15))),
% 0.11/0.36 inference(skolemize,[status(sab)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![X15: $i] : (~p4(X15, X15))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~![X15: $i] : (~p4(X15, X15))) | (~p4(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.36 tff(11,plain,(~p4(f3(c5, c7), f3(c5, c7))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(12,assumption,(p4(f3(c5, c6), f3(c5, c7))), introduced(assumption)).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[X4: $i, X3: $i, X2: $i] : refl(((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4)) <=> ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4)) <=> ![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4)) <=> ![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (^[X4: $i, X3: $i, X2: $i] : trans(monotonicity(rewrite((p2(X3, X4) | (~p2(X2, X4))) <=> ((~p2(X2, X4)) | p2(X3, X4))), (((p2(X3, X4) | (~p2(X2, X4))) | (~p2(X2, X3))) <=> (((~p2(X2, X4)) | p2(X3, X4)) | (~p2(X2, X3))))), rewrite((((~p2(X2, X4)) | p2(X3, X4)) | (~p2(X2, X3))) <=> ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))), (((p2(X3, X4) | (~p2(X2, X4))) | (~p2(X2, X3))) <=> ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X4: $i, X3: $i, X2: $i] : ((p2(X3, X4) | (~p2(X2, X4))) | (~p2(X2, X3))) <=> ![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.36 tff(18,axiom,(![X4: $i, X3: $i, X2: $i] : ((p2(X3, X4) | (~p2(X2, X4))) | (~p2(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_6')).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.36 tff(21,plain,(
% 0.11/0.36 ![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(skolemize,[status(sab)],[20])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (p2(f3(c5, c6), f3(c5, c7)) <=> p2(f3(c5, c6), f3(c5, c7))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,axiom,(p2(f3(c5, c6), f3(c5, c7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (p2(f3(c5, c6), f3(c5, c7))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | ((~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((~p2(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7))) <=> ((~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | ((~p2(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | ((~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | ((~p2(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[28, 26])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | ((~p2(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![X4: $i, X3: $i, X2: $i] : ((~p2(X2, X3)) | (~p2(X2, X4)) | p2(X3, X4))) | (~p2(f3(c5, c6), f3(c5, c7))) | p2(f3(c5, c7), f3(c5, c7))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (p2(f3(c5, c7), f3(c5, c7))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 25, 22])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (^[X9: $i, X12: $i, X11: $i, X10: $i] : refl(((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)) <=> ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (^[X9: $i, X12: $i, X11: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((p4(X9, X10) | (~p2(X12, X10))) <=> ((~p2(X12, X10)) | p4(X9, X10))), (((p4(X9, X10) | (~p2(X12, X10))) | (~p4(X11, X12))) <=> (((~p2(X12, X10)) | p4(X9, X10)) | (~p4(X11, X12))))), rewrite((((~p2(X12, X10)) | p4(X9, X10)) | (~p4(X11, X12))) <=> ((~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))), (((p4(X9, X10) | (~p2(X12, X10))) | (~p4(X11, X12))) <=> ((~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)))), ((((p4(X9, X10) | (~p2(X12, X10))) | (~p4(X11, X12))) | (~p2(X11, X9))) <=> (((~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)) | (~p2(X11, X9))))), rewrite((((~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10)) | (~p2(X11, X9))) <=> ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))), ((((p4(X9, X10) | (~p2(X12, X10))) | (~p4(X11, X12))) | (~p2(X11, X9))) <=> ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![X9: $i, X12: $i, X11: $i, X10: $i] : (((p4(X9, X10) | (~p2(X12, X10))) | (~p4(X11, X12))) | (~p2(X11, X9))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.37 tff(38,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i] : (((p4(X9, X10) | (~p2(X12, X10))) | (~p4(X11, X12))) | (~p2(X11, X9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_8')).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.11/0.37 tff(41,plain,(
% 0.11/0.37 ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(skolemize,[status(sab)],[40])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (((~p2(f3(c5, c6), f3(c5, c7))) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7))) <=> ((~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[45, 43])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p4(f3(c5, c6), f3(c5, c7))) | (~p2(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[48, 25, 42, 32, 12, 11])).
% 0.11/0.37 tff(50,plain,(~p4(f3(c5, c6), f3(c5, c7))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (^[X14: $i, X13: $i] : refl(((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14))) <=> ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14))) <=> ![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[51])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14))) <=> ![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 (^[X14: $i, X13: $i] : rewrite((p4(f3(c5, X13), f3(c5, X14)) | (~p4(X13, X14))) <=> ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (![X14: $i, X13: $i] : (p4(f3(c5, X13), f3(c5, X14)) | (~p4(X13, X14))) <=> ![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.11/0.37 tff(56,axiom,(![X14: $i, X13: $i] : (p4(f3(c5, X13), f3(c5, X14)) | (~p4(X13, X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_7')).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.11/0.37 tff(59,plain,(
% 0.11/0.37 ![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[58])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 (((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | ((~p4(c6, c7)) | p4(f3(c5, c6), f3(c5, c7)))) <=> ((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | (~p4(c6, c7)) | p4(f3(c5, c6), f3(c5, c7)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 ((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | ((~p4(c6, c7)) | p4(f3(c5, c6), f3(c5, c7)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 ((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | (~p4(c6, c7)) | p4(f3(c5, c6), f3(c5, c7))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 ((~p4(c6, c7)) | p4(f3(c5, c6), f3(c5, c7))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 (~p4(c6, c7)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[64, 50])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 (^[X0: $i, X1: $i] : refl((p4(X1, X0) | p4(X0, X1) | p2(X0, X1)) <=> (p4(X1, X0) | p4(X0, X1) | p2(X0, X1)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1)) <=> ![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[66])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1)) <=> ![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (^[X0: $i, X1: $i] : rewrite(((p2(X0, X1) | p4(X0, X1)) | p4(X1, X0)) <=> (p4(X1, X0) | p4(X0, X1) | p2(X0, X1)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : ((p2(X0, X1) | p4(X0, X1)) | p4(X1, X0)) <=> ![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[69])).
% 0.11/0.38 tff(71,axiom,(![X0: $i, X1: $i] : ((p2(X0, X1) | p4(X0, X1)) | p4(X1, X0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.11/0.38 tff(74,plain,(
% 0.11/0.38 ![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(skolemize,[status(sab)],[73])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 ((~p2(c6, c7)) <=> (~p2(c6, c7))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(77,axiom,(~p2(c6, c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_3')).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (~p2(c6, c7)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | (p2(c6, c7) | p4(c7, c6) | p4(c6, c7))) <=> ((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | p2(c6, c7) | p4(c7, c6) | p4(c6, c7))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 ((p4(c7, c6) | p4(c6, c7) | p2(c6, c7)) <=> (p2(c6, c7) | p4(c7, c6) | p4(c6, c7))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | (p4(c7, c6) | p4(c6, c7) | p2(c6, c7))) <=> ((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | (p2(c6, c7) | p4(c7, c6) | p4(c6, c7)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[80])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 (((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | (p4(c7, c6) | p4(c6, c7) | p2(c6, c7))) <=> ((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | p2(c6, c7) | p4(c7, c6) | p4(c6, c7))),
% 0.11/0.38 inference(transitivity,[status(thm)],[81, 79])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 ((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | (p4(c7, c6) | p4(c6, c7) | p2(c6, c7))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 ((~![X0: $i, X1: $i] : (p4(X1, X0) | p4(X0, X1) | p2(X0, X1))) | p2(c6, c7) | p4(c7, c6) | p4(c6, c7)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.11/0.38 tff(85,plain,
% 0.11/0.38 (p4(c7, c6) | p4(c6, c7)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[84, 78, 75])).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (p4(c7, c6)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[85, 65])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | ((~p4(c7, c6)) | p4(f3(c5, c7), f3(c5, c6)))) <=> ((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | (~p4(c7, c6)) | p4(f3(c5, c7), f3(c5, c6)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(88,plain,
% 0.11/0.38 ((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | ((~p4(c7, c6)) | p4(f3(c5, c7), f3(c5, c6)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 ((~![X14: $i, X13: $i] : ((~p4(X13, X14)) | p4(f3(c5, X13), f3(c5, X14)))) | (~p4(c7, c6)) | p4(f3(c5, c7), f3(c5, c6))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 ((~p4(c7, c6)) | p4(f3(c5, c7), f3(c5, c6))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[89, 60])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (p4(f3(c5, c7), f3(c5, c6))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[90, 86])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 (((~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7))) <=> ((~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(94,plain,
% 0.11/0.38 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[93])).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[94, 92])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | ((~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(97,plain,
% 0.11/0.38 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X11, X9)) | (~p4(X11, X12)) | (~p2(X12, X10)) | p4(X9, X10))) | (~p2(f3(c5, c6), f3(c5, c7))) | p4(f3(c5, c7), f3(c5, c7)) | (~p2(f3(c5, c7), f3(c5, c7))) | (~p4(f3(c5, c7), f3(c5, c6)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[97, 25, 42, 32, 91, 11])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------