%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN581-1 : 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 05:39:37 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN581-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.11 % 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 12:38:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(p2_type, type, (
% 0.20/0.50 p2: ( $i * $i ) > $o)).
% 0.20/0.50 tff(c16_type, type, (
% 0.20/0.50 c16: $i)).
% 0.20/0.50 tff(f4_type, type, (
% 0.20/0.50 f4: $i > $i)).
% 0.20/0.50 tff(f6_type, type, (
% 0.20/0.50 f6: ( $i * $i ) > $i)).
% 0.20/0.50 tff(c18_type, type, (
% 0.20/0.50 c18: $i)).
% 0.20/0.50 tff(c15_type, type, (
% 0.20/0.50 c15: $i)).
% 0.20/0.50 tff(c14_type, type, (
% 0.20/0.50 c14: $i)).
% 0.20/0.50 tff(p5_type, type, (
% 0.20/0.50 p5: ( $i * $i ) > $o)).
% 0.20/0.50 tff(p11_type, type, (
% 0.20/0.50 p11: ( $i * $i ) > $o)).
% 0.20/0.50 tff(1,plain,
% 0.20/0.50 (^[X18: $i] : refl(p2(X18, X18) <=> p2(X18, X18))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(4,axiom,(![X18: $i] : p2(X18, X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_2')).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (![X18: $i] : p2(X18, X18)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.50 tff(6,plain,(
% 0.20/0.50 ![X18: $i] : p2(X18, X18)),
% 0.20/0.50 inference(skolemize,[status(sab)],[5])).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (![X18: $i] : p2(X18, X18)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 ((~![X18: $i] : p2(X18, X18)) | p2(c16, c16)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (p2(c16, c16)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.50 tff(10,assumption,(~p2(c18, c18)), introduced(assumption)).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 ((~![X18: $i] : p2(X18, X18)) | p2(c18, c18)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[11, 7, 10])).
% 0.20/0.50 tff(13,plain,(p2(c18, c18)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(14,assumption,(~p5(c15, c15)), introduced(assumption)).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (^[X31: $i] : refl(p5(X31, X31) <=> p5(X31, X31))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(18,axiom,(![X31: $i] : p5(X31, X31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_3')).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (![X31: $i] : p5(X31, X31)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.50 tff(20,plain,(
% 0.20/0.50 ![X31: $i] : p5(X31, X31)),
% 0.20/0.50 inference(skolemize,[status(sab)],[19])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (![X31: $i] : p5(X31, X31)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 ((~![X31: $i] : p5(X31, X31)) | p5(c15, c15)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.20/0.50 tff(24,plain,(p5(c15, c15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (^[X25: $i, X27: $i, X28: $i, X26: $i] : refl(((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 (^[X25: $i, X27: $i, X28: $i, X26: $i] : trans(monotonicity(rewrite((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) <=> ((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28)))), (((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> (((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28))) | (~p5(X25, X27))))), rewrite((((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28))) | (~p5(X25, X27))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))), (((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.50 tff(30,axiom,(![X25: $i, X27: $i, X28: $i, X26: $i] : ((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_23')).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.50 tff(33,plain,(
% 0.20/0.50 ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[32])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c18, c18)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c18)))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c18, c18)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c18)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c18, c18)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c18)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c18, c18)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c18))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 ((~p2(c18, c18)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c18))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (p2(f6(c15, c18), f6(c15, c18))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[38, 24, 13])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (p2(c18, c14) <=> p2(c18, c14)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(41,axiom,(p2(c18, c14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (p2(c18, c14)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14)))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 ((~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[45, 42, 34])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (p2(f6(c15, c18), f6(c15, c14))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[46, 24])).
% 0.20/0.50 tff(48,assumption,(~p2(f6(c15, c14), f6(c15, c18))), introduced(assumption)).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (^[X18: $i, X20: $i, X19: $i] : refl((p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(X19, X20) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))))), rewrite(((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.50 tff(54,axiom,(![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_18')).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.50 tff(57,plain,(
% 0.20/0.50 ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[56])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c14))) | (~p2(f6(c15, c18), f6(c15, c18))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c14))) | (~p2(f6(c15, c18), f6(c15, c18))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 ((p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14)))) <=> (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c14))) | (~p2(f6(c15, c18), f6(c15, c18))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c14))) | (~p2(f6(c15, c18), f6(c15, c18)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c14))) | (~p2(f6(c15, c18), f6(c15, c18))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c14))) | (~p2(f6(c15, c18), f6(c15, c18)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[64, 58, 48, 47, 39])).
% 0.20/0.50 tff(66,plain,(p2(f6(c15, c14), f6(c15, c18))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (^[X23: $i, X24: $i] : refl(((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (^[X23: $i, X24: $i] : rewrite((p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.51 tff(72,axiom,(![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_14')).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.51 tff(75,plain,(
% 0.20/0.51 ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[74])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18))))) <=> ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 ((~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (p2(f4(f6(c15, c14)), f4(f6(c15, c18)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[80, 66])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 (^[X9: $i, X10: $i, X7: $i, X8: $i] : refl(((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)) <=> ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 (^[X9: $i, X10: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p11(X7, X8) | (~p2(X9, X7))) <=> ((~p2(X9, X7)) | p11(X7, X8))), (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) <=> (((~p2(X9, X7)) | p11(X7, X8)) | (~p2(X10, X8))))), rewrite((((~p2(X9, X7)) | p11(X7, X8)) | (~p2(X10, X8))) <=> ((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8))), (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) <=> ((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8)))), ((((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10))) <=> (((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8)) | (~p11(X9, X10))))), rewrite((((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8)) | (~p11(X9, X10))) <=> ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))), ((((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10))) <=> ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (![X9: $i, X10: $i, X7: $i, X8: $i] : (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10))) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.51 tff(87,axiom,(![X9: $i, X10: $i, X7: $i, X8: $i] : (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_21')).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.51 tff(90,plain,(
% 0.20/0.51 ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(skolemize,[status(sab)],[89])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 ((~p11(f4(f6(c15, c18)), c16)) <=> (~p11(f4(f6(c15, c18)), c16))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(93,axiom,(~p11(f4(f6(c15, c18)), c16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p11_9')).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 (~p11(f4(f6(c15, c18)), c16)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 (p11(f4(f6(c15, c14)), c16) <=> p11(f4(f6(c15, c14)), c16)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(96,axiom,(p11(f4(f6(c15, c14)), c16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_8')).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 (p11(f4(f6(c15, c14)), c16)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))) <=> ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | (~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | (~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[100, 97, 94, 91, 81, 9])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------