%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN560-1 : 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 05:39:34 AM UTC 2025
% Result : Unsatisfiable 0.40s 0.56s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYN560-1 : TPTP v9.0.0. Released v2.5.0.
% 0.04/0.11 % 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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:38:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.40/0.56 % SZS status Unsatisfiable
% 0.40/0.56 % SZS output start Proof
% 0.40/0.56 tff(p8_type, type, (
% 0.40/0.56 p8: ( $i * $i ) > $o)).
% 0.40/0.56 tff(f6_type, type, (
% 0.40/0.56 f6: ( $i * $i ) > $i)).
% 0.40/0.56 tff(f5_type, type, (
% 0.40/0.56 f5: ( $i * $i ) > $i)).
% 0.40/0.56 tff(f3_type, type, (
% 0.40/0.56 f3: $i > $i)).
% 0.40/0.56 tff(f7_type, type, (
% 0.40/0.56 f7: $i > $i)).
% 0.40/0.56 tff(c10_type, type, (
% 0.40/0.56 c10: $i)).
% 0.40/0.56 tff(f4_type, type, (
% 0.40/0.56 f4: $i > $i)).
% 0.40/0.56 tff(c14_type, type, (
% 0.40/0.56 c14: $i)).
% 0.40/0.56 tff(c12_type, type, (
% 0.40/0.56 c12: $i)).
% 0.40/0.56 tff(c9_type, type, (
% 0.40/0.56 c9: $i)).
% 0.40/0.56 tff(p2_type, type, (
% 0.40/0.56 p2: ( $i * $i ) > $o)).
% 0.40/0.56 tff(1,plain,
% 0.40/0.56 (^[X4: $i, X3: $i] : refl((p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10)))))) <=> (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10)))))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(2,plain,
% 0.40/0.56 (![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10)))))) <=> ![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.40/0.56 tff(3,plain,
% 0.40/0.56 (![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10)))))) <=> ![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(4,axiom,(![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_15')).
% 0.40/0.56 tff(5,plain,
% 0.40/0.56 (![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.40/0.56 tff(6,plain,(
% 0.40/0.56 ![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))),
% 0.40/0.56 inference(skolemize,[status(sab)],[5])).
% 0.40/0.56 tff(7,plain,
% 0.40/0.56 (![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.40/0.56 tff(8,plain,
% 0.40/0.56 ((~p2(c9, f3(c10))) <=> (~p2(c9, f3(c10)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(9,axiom,(~p2(c9, f3(c10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_2')).
% 0.40/0.56 tff(10,plain,
% 0.40/0.56 (~p2(c9, f3(c10))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.40/0.56 tff(11,plain,
% 0.40/0.56 (((~![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))) | (p2(c9, f3(c10)) | p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))) | p2(c9, f3(c10)) | p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(12,plain,
% 0.40/0.56 ((~![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))) | (p2(c9, f3(c10)) | p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(13,plain,
% 0.40/0.56 ((~![X4: $i, X3: $i] : (p2(X3, f3(c10)) | p8(f6(X3, X4), f6(X3, f5(X4, f3(f7(c10))))))) | p2(c9, f3(c10)) | p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.40/0.56 tff(14,plain,
% 0.40/0.56 (p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.40/0.56 tff(15,plain,
% 0.40/0.56 (p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14)))) <=> p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(16,axiom,(p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_10')).
% 0.40/0.56 tff(17,plain,
% 0.40/0.56 (p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.40/0.56 tff(18,plain,
% 0.40/0.56 (![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25)) <=> ![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(19,plain,
% 0.40/0.56 (![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25)) <=> ![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(20,plain,
% 0.40/0.56 (^[X25: $i, X26: $i, X24: $i] : trans(monotonicity(rewrite((p8(X24, X25) | (~p8(X24, X26))) <=> ((~p8(X24, X26)) | p8(X24, X25))), (((p8(X24, X25) | (~p8(X24, X26))) | (~p8(X26, X25))) <=> (((~p8(X24, X26)) | p8(X24, X25)) | (~p8(X26, X25))))), rewrite((((~p8(X24, X26)) | p8(X24, X25)) | (~p8(X26, X25))) <=> ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))), (((p8(X24, X25) | (~p8(X24, X26))) | (~p8(X26, X25))) <=> ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(21,plain,
% 0.40/0.56 (![X25: $i, X26: $i, X24: $i] : ((p8(X24, X25) | (~p8(X24, X26))) | (~p8(X26, X25))) <=> ![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[20])).
% 0.40/0.56 tff(22,axiom,(![X25: $i, X26: $i, X24: $i] : ((p8(X24, X25) | (~p8(X24, X26))) | (~p8(X26, X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_9')).
% 0.40/0.56 tff(23,plain,
% 0.40/0.56 (![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.40/0.56 tff(24,plain,
% 0.40/0.56 (![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.40/0.56 tff(25,plain,(
% 0.40/0.56 ![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(skolemize,[status(sab)],[24])).
% 0.40/0.56 tff(26,plain,
% 0.40/0.56 (![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.40/0.56 tff(27,plain,
% 0.40/0.56 (((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | ((~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | (~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | (~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(28,plain,
% 0.40/0.56 (((~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) <=> ((~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | (~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(29,plain,
% 0.40/0.56 (((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | ((~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | ((~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | (~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[28])).
% 0.40/0.56 tff(30,plain,
% 0.40/0.56 (((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | ((~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | (~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.56 inference(transitivity,[status(thm)],[29, 27])).
% 0.40/0.56 tff(31,plain,
% 0.40/0.56 ((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | ((~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(32,plain,
% 0.40/0.57 ((~![X25: $i, X26: $i, X24: $i] : ((~p8(X26, X25)) | (~p8(X24, X26)) | p8(X24, X25))) | (~p8(f6(c9, f4(c12)), f6(c9, f4(f5(c12, c14))))) | (~p8(f6(c9, f4(f5(c12, c14))), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.40/0.57 tff(33,plain,
% 0.40/0.57 (p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[32, 26, 17, 14])).
% 0.40/0.57 tff(34,assumption,(~p2(f4(f5(c12, c14)), f4(f5(c12, c14)))), introduced(assumption)).
% 0.40/0.57 tff(35,plain,
% 0.40/0.57 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(36,plain,
% 0.40/0.57 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.40/0.57 inference(quant_intro,[status(thm)],[35])).
% 0.40/0.57 tff(37,plain,
% 0.40/0.57 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(38,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.40/0.57 tff(39,plain,
% 0.40/0.57 (![X0: $i] : p2(X0, X0)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.40/0.57 tff(40,plain,(
% 0.40/0.57 ![X0: $i] : p2(X0, X0)),
% 0.40/0.57 inference(skolemize,[status(sab)],[39])).
% 0.40/0.57 tff(41,plain,
% 0.40/0.57 (![X0: $i] : p2(X0, X0)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.40/0.57 tff(42,plain,
% 0.40/0.57 ((~![X0: $i] : p2(X0, X0)) | p2(f4(f5(c12, c14)), f4(f5(c12, c14)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(43,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[42, 41, 34])).
% 0.40/0.57 tff(44,plain,(p2(f4(f5(c12, c14)), f4(f5(c12, c14)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(45,plain,
% 0.40/0.57 (^[X7: $i, X8: $i] : refl(((~p2(X7, X8)) | p2(f4(X7), f4(X8))) <=> ((~p2(X7, X8)) | p2(f4(X7), f4(X8))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(46,plain,
% 0.40/0.57 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[45])).
% 0.40/0.57 tff(47,plain,
% 0.40/0.57 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(48,plain,
% 0.40/0.57 (^[X7: $i, X8: $i] : rewrite((p2(f4(X7), f4(X8)) | (~p2(X7, X8))) <=> ((~p2(X7, X8)) | p2(f4(X7), f4(X8))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(49,plain,
% 0.40/0.57 (![X7: $i, X8: $i] : (p2(f4(X7), f4(X8)) | (~p2(X7, X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[48])).
% 0.40/0.57 tff(50,axiom,(![X7: $i, X8: $i] : (p2(f4(X7), f4(X8)) | (~p2(X7, X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 0.40/0.57 tff(51,plain,
% 0.40/0.57 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.40/0.57 tff(52,plain,
% 0.40/0.57 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.40/0.57 tff(53,plain,(
% 0.40/0.57 ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(skolemize,[status(sab)],[52])).
% 0.40/0.57 tff(54,plain,
% 0.40/0.57 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.40/0.57 tff(55,plain,
% 0.40/0.57 (((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | ((~p2(f4(f5(c12, c14)), f4(f5(c12, c14)))) | p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14)))))) <=> ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | (~p2(f4(f5(c12, c14)), f4(f5(c12, c14)))) | p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14)))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(56,plain,
% 0.40/0.57 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | ((~p2(f4(f5(c12, c14)), f4(f5(c12, c14)))) | p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14)))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(57,plain,
% 0.40/0.57 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | (~p2(f4(f5(c12, c14)), f4(f5(c12, c14)))) | p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.40/0.57 tff(58,plain,
% 0.40/0.57 ((~p2(f4(f5(c12, c14)), f4(f5(c12, c14)))) | p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.40/0.57 tff(59,plain,
% 0.40/0.57 (p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[58, 44])).
% 0.40/0.57 tff(60,plain,
% 0.40/0.57 (^[X9: $i] : refl(p2(f4(X9), f5(X9, f3(f7(c10)))) <=> p2(f4(X9), f5(X9, f3(f7(c10)))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(61,plain,
% 0.40/0.57 (![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10)))) <=> ![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[60])).
% 0.40/0.57 tff(62,plain,
% 0.40/0.57 (![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10)))) <=> ![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(63,axiom,(![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.40/0.57 tff(64,plain,
% 0.40/0.57 (![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.40/0.57 tff(65,plain,(
% 0.40/0.57 ![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))),
% 0.40/0.57 inference(skolemize,[status(sab)],[64])).
% 0.40/0.57 tff(66,plain,
% 0.40/0.57 (![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.40/0.57 tff(67,plain,
% 0.40/0.57 ((~![X9: $i] : p2(f4(X9), f5(X9, f3(f7(c10))))) | p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(68,plain,
% 0.40/0.57 (p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.40/0.57 tff(69,plain,
% 0.40/0.57 (^[X0: $i, X2: $i, X1: $i] : refl((p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1))) <=> (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(70,plain,
% 0.40/0.57 (![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[69])).
% 0.40/0.57 tff(71,plain,
% 0.40/0.57 (![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(72,plain,
% 0.40/0.57 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p2(X1, X2) | (~p2(X0, X1))) <=> (p2(X1, X2) | (~p2(X0, X1)))), (((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))))), rewrite(((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))), (((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(73,plain,
% 0.40/0.57 (![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[72])).
% 0.40/0.57 tff(74,axiom,(![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_8')).
% 0.40/0.57 tff(75,plain,
% 0.40/0.57 (![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.40/0.57 tff(76,plain,
% 0.40/0.57 (![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.40/0.57 tff(77,plain,(
% 0.40/0.57 ![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(skolemize,[status(sab)],[76])).
% 0.40/0.57 tff(78,plain,
% 0.40/0.57 (![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.40/0.57 tff(79,plain,
% 0.40/0.57 (((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | ((~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(80,plain,
% 0.40/0.57 ((p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10)))))) <=> ((~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(81,plain,
% 0.40/0.57 (((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | (p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | ((~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10)))))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[80])).
% 0.40/0.57 tff(82,plain,
% 0.40/0.57 (((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | (p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.57 inference(transitivity,[status(thm)],[81, 79])).
% 0.40/0.57 tff(83,plain,
% 0.40/0.57 ((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | (p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(84,plain,
% 0.40/0.57 ((~![X0: $i, X2: $i, X1: $i] : (p2(X1, X2) | (~p2(X0, X2)) | (~p2(X0, X1)))) | (~p2(f4(f4(f5(c12, c14))), f4(f4(f5(c12, c14))))) | p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14)))) | (~p2(f4(f4(f5(c12, c14))), f5(f4(f5(c12, c14)), f3(f7(c10)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.40/0.57 tff(85,plain,
% 0.40/0.57 (p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[84, 78, 68, 59])).
% 0.40/0.57 tff(86,assumption,(~p2(c9, c9)), introduced(assumption)).
% 0.40/0.57 tff(87,plain,
% 0.40/0.57 ((~![X0: $i] : p2(X0, X0)) | p2(c9, c9)),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(88,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[87, 41, 86])).
% 0.40/0.57 tff(89,plain,(p2(c9, c9)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(90,plain,
% 0.40/0.57 (^[X14: $i, X17: $i, X16: $i, X15: $i] : refl(((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17))) <=> ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(91,plain,
% 0.40/0.57 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[90])).
% 0.40/0.57 tff(92,plain,
% 0.40/0.57 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(93,plain,
% 0.40/0.57 (^[X14: $i, X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p2(f6(X14, X15), f6(X16, X17)) | (~p2(X15, X17))) <=> ((~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))), (((p2(f6(X14, X15), f6(X16, X17)) | (~p2(X15, X17))) | (~p2(X14, X16))) <=> (((~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17))) | (~p2(X14, X16))))), rewrite((((~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17))) | (~p2(X14, X16))) <=> ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))), (((p2(f6(X14, X15), f6(X16, X17)) | (~p2(X15, X17))) | (~p2(X14, X16))) <=> ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(94,plain,
% 0.40/0.57 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((p2(f6(X14, X15), f6(X16, X17)) | (~p2(X15, X17))) | (~p2(X14, X16))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[93])).
% 0.40/0.57 tff(95,axiom,(![X14: $i, X17: $i, X16: $i, X15: $i] : ((p2(f6(X14, X15), f6(X16, X17)) | (~p2(X15, X17))) | (~p2(X14, X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 0.40/0.57 tff(96,plain,
% 0.40/0.57 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.40/0.57 tff(97,plain,
% 0.40/0.57 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.40/0.57 tff(98,plain,(
% 0.40/0.57 ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(skolemize,[status(sab)],[97])).
% 0.40/0.57 tff(99,plain,
% 0.40/0.57 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.40/0.57 tff(100,plain,
% 0.40/0.57 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | ((~p2(c9, c9)) | (~p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14))))) | p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14))))))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | (~p2(c9, c9)) | (~p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14))))) | p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(101,plain,
% 0.40/0.57 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | ((~p2(c9, c9)) | (~p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14))))) | p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(102,plain,
% 0.40/0.57 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | (~p2(c9, c9)) | (~p2(f5(f4(f5(c12, c14)), f3(f7(c10))), f4(f4(f5(c12, c14))))) | p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.40/0.57 tff(103,plain,
% 0.40/0.57 (p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14)))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[102, 99, 89, 85])).
% 0.40/0.57 tff(104,assumption,(~p2(c12, c12)), introduced(assumption)).
% 0.40/0.57 tff(105,plain,
% 0.40/0.57 ((~![X0: $i] : p2(X0, X0)) | p2(c12, c12)),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(106,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[105, 41, 104])).
% 0.40/0.57 tff(107,plain,(p2(c12, c12)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(108,plain,
% 0.40/0.57 (((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | ((~p2(c12, c12)) | p2(f4(c12), f4(c12)))) <=> ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | (~p2(c12, c12)) | p2(f4(c12), f4(c12)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(109,plain,
% 0.40/0.57 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | ((~p2(c12, c12)) | p2(f4(c12), f4(c12)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(110,plain,
% 0.40/0.57 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | (~p2(c12, c12)) | p2(f4(c12), f4(c12))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.40/0.57 tff(111,plain,
% 0.40/0.57 ((~p2(c12, c12)) | p2(f4(c12), f4(c12))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[110, 54])).
% 0.40/0.57 tff(112,plain,
% 0.40/0.57 (p2(f4(c12), f4(c12))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.40/0.57 tff(113,plain,
% 0.40/0.57 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | ((~p2(c9, c9)) | (~p2(f4(c12), f4(c12))) | p2(f6(c9, f4(c12)), f6(c9, f4(c12))))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | (~p2(c9, c9)) | (~p2(f4(c12), f4(c12))) | p2(f6(c9, f4(c12)), f6(c9, f4(c12))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(114,plain,
% 0.40/0.57 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | ((~p2(c9, c9)) | (~p2(f4(c12), f4(c12))) | p2(f6(c9, f4(c12)), f6(c9, f4(c12))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(115,plain,
% 0.40/0.57 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f6(X14, X15), f6(X16, X17)))) | (~p2(c9, c9)) | (~p2(f4(c12), f4(c12))) | p2(f6(c9, f4(c12)), f6(c9, f4(c12)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.40/0.57 tff(116,plain,
% 0.40/0.57 ((~p2(c9, c9)) | (~p2(f4(c12), f4(c12))) | p2(f6(c9, f4(c12)), f6(c9, f4(c12)))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[115, 99])).
% 0.40/0.57 tff(117,plain,
% 0.40/0.57 (p2(f6(c9, f4(c12)), f6(c9, f4(c12)))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[116, 89, 112])).
% 0.40/0.57 tff(118,plain,
% 0.40/0.57 (^[X22: $i, X21: $i, X20: $i, X23: $i] : refl((p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21))) <=> (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(119,plain,
% 0.40/0.57 (![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21))) <=> ![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[118])).
% 0.40/0.57 tff(120,plain,
% 0.40/0.57 (![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21))) <=> ![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(121,plain,
% 0.40/0.57 (^[X22: $i, X21: $i, X20: $i, X23: $i] : trans(monotonicity(trans(monotonicity(rewrite((p8(X20, X21) | (~p2(X23, X21))) <=> (p8(X20, X21) | (~p2(X23, X21)))), (((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) <=> ((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))))), rewrite(((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) <=> (p8(X20, X21) | (~p8(X22, X23)) | (~p2(X23, X21)))), (((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) <=> (p8(X20, X21) | (~p8(X22, X23)) | (~p2(X23, X21))))), ((((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) | (~p2(X22, X20))) <=> ((p8(X20, X21) | (~p8(X22, X23)) | (~p2(X23, X21))) | (~p2(X22, X20))))), rewrite(((p8(X20, X21) | (~p8(X22, X23)) | (~p2(X23, X21))) | (~p2(X22, X20))) <=> (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))), ((((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) | (~p2(X22, X20))) <=> (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(122,plain,
% 0.40/0.57 (![X22: $i, X21: $i, X20: $i, X23: $i] : (((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) | (~p2(X22, X20))) <=> ![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[121])).
% 0.40/0.57 tff(123,axiom,(![X22: $i, X21: $i, X20: $i, X23: $i] : (((p8(X20, X21) | (~p2(X23, X21))) | (~p8(X22, X23))) | (~p2(X22, X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_12')).
% 0.40/0.57 tff(124,plain,
% 0.40/0.57 (![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.40/0.57 tff(125,plain,
% 0.40/0.57 (![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.40/0.57 tff(126,plain,(
% 0.40/0.57 ![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(skolemize,[status(sab)],[125])).
% 0.40/0.57 tff(127,plain,
% 0.40/0.57 (![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.40/0.57 tff(128,plain,
% 0.40/0.57 ((~p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14)))))) <=> (~p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(129,axiom,(~p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p8_11')).
% 0.40/0.57 tff(130,plain,
% 0.40/0.57 (~p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.40/0.57 tff(131,plain,
% 0.40/0.57 (((~![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))) | (p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14))))) | (~p2(f6(c9, f4(c12)), f6(c9, f4(c12)))) | (~p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14)))))))) <=> ((~![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))) | p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14))))) | (~p2(f6(c9, f4(c12)), f6(c9, f4(c12)))) | (~p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14)))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(132,plain,
% 0.40/0.57 ((~![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))) | (p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14))))) | (~p2(f6(c9, f4(c12)), f6(c9, f4(c12)))) | (~p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14)))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(133,plain,
% 0.40/0.57 ((~![X22: $i, X21: $i, X20: $i, X23: $i] : (p8(X20, X21) | (~p2(X22, X20)) | (~p8(X22, X23)) | (~p2(X23, X21)))) | p8(f6(c9, f4(c12)), f6(c9, f4(f4(f5(c12, c14))))) | (~p2(f6(c9, f4(c12)), f6(c9, f4(c12)))) | (~p8(f6(c9, f4(c12)), f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))))) | (~p2(f6(c9, f5(f4(f5(c12, c14)), f3(f7(c10)))), f6(c9, f4(f4(f5(c12, c14))))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.40/0.57 tff(134,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[133, 130, 127, 117, 103, 33])).
% 0.40/0.57 % SZS output end Proof
% 0.40/0.57 % E exiting
%------------------------------------------------------------------------------