%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN583-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.45s 0.64s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN583-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:40:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.45/0.64 % SZS status Unsatisfiable
% 0.45/0.64 % SZS output start Proof
% 0.45/0.64 tff(p2_type, type, (
% 0.45/0.64 p2: ( $i * $i ) > $o)).
% 0.45/0.64 tff(c16_type, type, (
% 0.45/0.64 c16: $i)).
% 0.45/0.64 tff(f4_type, type, (
% 0.45/0.64 f4: $i > $i)).
% 0.45/0.64 tff(f6_type, type, (
% 0.45/0.64 f6: ( $i * $i ) > $i)).
% 0.45/0.64 tff(c18_type, type, (
% 0.45/0.64 c18: $i)).
% 0.45/0.64 tff(c15_type, type, (
% 0.45/0.64 c15: $i)).
% 0.45/0.64 tff(c13_type, type, (
% 0.45/0.64 c13: $i)).
% 0.45/0.64 tff(p5_type, type, (
% 0.45/0.64 p5: ( $i * $i ) > $o)).
% 0.45/0.64 tff(p12_type, type, (
% 0.45/0.64 p12: ( $i * $i ) > $o)).
% 0.45/0.64 tff(p11_type, type, (
% 0.45/0.64 p11: ( $i * $i ) > $o)).
% 0.45/0.64 tff(1,plain,
% 0.45/0.64 (^[X18: $i] : refl(p2(X18, X18) <=> p2(X18, X18))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(2,plain,
% 0.45/0.64 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.45/0.64 inference(quant_intro,[status(thm)],[1])).
% 0.45/0.64 tff(3,plain,
% 0.45/0.64 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(4,axiom,(![X18: $i] : p2(X18, X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_2')).
% 0.45/0.64 tff(5,plain,
% 0.45/0.64 (![X18: $i] : p2(X18, X18)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.45/0.64 tff(6,plain,(
% 0.45/0.64 ![X18: $i] : p2(X18, X18)),
% 0.45/0.64 inference(skolemize,[status(sab)],[5])).
% 0.45/0.64 tff(7,plain,
% 0.45/0.64 (![X18: $i] : p2(X18, X18)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.45/0.64 tff(8,plain,
% 0.45/0.64 ((~![X18: $i] : p2(X18, X18)) | p2(c16, c16)),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(9,plain,
% 0.45/0.64 (p2(c16, c16)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.45/0.64 tff(10,assumption,(~p5(c15, c15)), introduced(assumption)).
% 0.45/0.64 tff(11,plain,
% 0.45/0.64 (^[X31: $i] : refl(p5(X31, X31) <=> p5(X31, X31))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(12,plain,
% 0.45/0.64 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 0.45/0.64 inference(quant_intro,[status(thm)],[11])).
% 0.45/0.64 tff(13,plain,
% 0.45/0.64 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(14,axiom,(![X31: $i] : p5(X31, X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_3')).
% 0.45/0.64 tff(15,plain,
% 0.45/0.64 (![X31: $i] : p5(X31, X31)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.45/0.64 tff(16,plain,(
% 0.45/0.64 ![X31: $i] : p5(X31, X31)),
% 0.45/0.64 inference(skolemize,[status(sab)],[15])).
% 0.45/0.64 tff(17,plain,
% 0.45/0.64 (![X31: $i] : p5(X31, X31)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.45/0.64 tff(18,plain,
% 0.45/0.64 ((~![X31: $i] : p5(X31, X31)) | p5(c15, c15)),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(19,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.45/0.64 tff(20,plain,(p5(c15, c15)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(21,plain,
% 0.45/0.64 (^[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))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(22,plain,
% 0.45/0.64 (![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)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[21])).
% 0.45/0.64 tff(23,plain,
% 0.45/0.64 (![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)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(24,plain,
% 0.45/0.64 (^[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)))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(25,plain,
% 0.45/0.64 (![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)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[24])).
% 0.45/0.64 tff(26,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/sandbox2/benchmark/theBenchmark.p','p2_23')).
% 0.45/0.64 tff(27,plain,
% 0.45/0.64 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.45/0.64 tff(28,plain,
% 0.45/0.64 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.45/0.64 tff(29,plain,(
% 0.45/0.64 ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.45/0.64 inference(skolemize,[status(sab)],[28])).
% 0.45/0.64 tff(30,plain,
% 0.45/0.64 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.45/0.64 tff(31,plain,
% 0.45/0.64 (p2(c13, c18) <=> p2(c13, c18)),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(32,axiom,(p2(c13, c18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.45/0.64 tff(33,plain,
% 0.45/0.64 (p2(c13, c18)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.45/0.64 tff(34,plain,
% 0.45/0.64 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), 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(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(35,plain,
% 0.45/0.64 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(36,plain,
% 0.45/0.64 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.45/0.64 tff(37,plain,
% 0.45/0.64 ((~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[36, 33, 30])).
% 0.45/0.64 tff(38,plain,
% 0.45/0.64 (p2(f6(c15, c13), f6(c15, c18))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[37, 20])).
% 0.45/0.64 tff(39,plain,
% 0.45/0.64 (^[X23: $i, X24: $i] : refl(((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(40,plain,
% 0.45/0.64 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[39])).
% 0.45/0.64 tff(41,plain,
% 0.45/0.64 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(42,plain,
% 0.45/0.64 (^[X23: $i, X24: $i] : rewrite((p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(43,plain,
% 0.45/0.64 (![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[42])).
% 0.45/0.64 tff(44,axiom,(![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 0.45/0.64 tff(45,plain,
% 0.45/0.64 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.45/0.64 tff(46,plain,
% 0.45/0.64 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.45/0.64 tff(47,plain,(
% 0.45/0.64 ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(skolemize,[status(sab)],[46])).
% 0.45/0.64 tff(48,plain,
% 0.45/0.64 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.45/0.64 tff(49,plain,
% 0.45/0.64 (((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18))))) <=> ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18))))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(50,plain,
% 0.45/0.64 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18))))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(51,plain,
% 0.45/0.64 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.45/0.64 tff(52,plain,
% 0.45/0.64 ((~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18)))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.45/0.64 tff(53,plain,
% 0.45/0.64 (p2(f4(f6(c15, c13)), f4(f6(c15, c18)))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[52, 38])).
% 0.45/0.64 tff(54,plain,
% 0.45/0.64 (^[X12: $i, X11: $i] : refl(((~p12(X11, X12)) | p11(X11, X12)) <=> ((~p12(X11, X12)) | p11(X11, X12)))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(55,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12)) <=> ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[54])).
% 0.45/0.64 tff(56,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12)) <=> ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(57,plain,
% 0.45/0.64 (^[X12: $i, X11: $i] : rewrite((p11(X11, X12) | (~p12(X11, X12))) <=> ((~p12(X11, X12)) | p11(X11, X12)))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(58,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p12(X11, X12))) <=> ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[57])).
% 0.45/0.64 tff(59,axiom,(![X12: $i, X11: $i] : (p11(X11, X12) | (~p12(X11, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_10')).
% 0.45/0.64 tff(60,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.45/0.64 tff(61,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.45/0.64 tff(62,plain,(
% 0.45/0.64 ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(skolemize,[status(sab)],[61])).
% 0.45/0.64 tff(63,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.45/0.64 tff(64,plain,
% 0.45/0.64 ((~p11(f4(f6(c15, c18)), c16)) <=> (~p11(f4(f6(c15, c18)), c16))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(65,axiom,(~p11(f4(f6(c15, c18)), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_9')).
% 0.45/0.64 tff(66,plain,
% 0.45/0.64 (~p11(f4(f6(c15, c18)), c16)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.45/0.64 tff(67,plain,
% 0.45/0.64 (((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | ((~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16))) <=> ((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | (~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(68,plain,
% 0.45/0.64 ((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | ((~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(69,plain,
% 0.45/0.64 ((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | (~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.45/0.64 tff(70,plain,
% 0.45/0.64 (~p12(f4(f6(c15, c18)), c16)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[69, 66, 63])).
% 0.45/0.64 tff(71,assumption,(~p2(f6(c15, c13), f6(c15, c13))), introduced(assumption)).
% 0.45/0.64 tff(72,plain,
% 0.45/0.64 ((~![X18: $i] : p2(X18, X18)) | p2(f6(c15, c13), f6(c15, c13))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(73,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[72, 7, 71])).
% 0.45/0.64 tff(74,plain,(p2(f6(c15, c13), f6(c15, c13))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(75,plain,
% 0.45/0.64 (((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c13), f6(c15, c13))) | p2(f4(f6(c15, c13)), f4(f6(c15, c13))))) <=> ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c13), f6(c15, c13))) | p2(f4(f6(c15, c13)), f4(f6(c15, c13))))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(76,plain,
% 0.45/0.64 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c13), f6(c15, c13))) | p2(f4(f6(c15, c13)), f4(f6(c15, c13))))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(77,plain,
% 0.45/0.64 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c13), f6(c15, c13))) | p2(f4(f6(c15, c13)), f4(f6(c15, c13)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.45/0.64 tff(78,plain,
% 0.45/0.64 ((~p2(f6(c15, c13), f6(c15, c13))) | p2(f4(f6(c15, c13)), f4(f6(c15, c13)))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[77, 48])).
% 0.45/0.64 tff(79,plain,
% 0.45/0.64 (p2(f4(f6(c15, c13)), f4(f6(c15, c13)))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[78, 74])).
% 0.45/0.64 tff(80,plain,
% 0.45/0.64 (^[X12: $i, X11: $i] : refl((p11(X11, X12) | (~p2(X11, X12))) <=> (p11(X11, X12) | (~p2(X11, X12))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(81,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12))) <=> ![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[80])).
% 0.45/0.64 tff(82,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12))) <=> ![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(83,axiom,(![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_11')).
% 0.45/0.64 tff(84,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.45/0.64 tff(85,plain,(
% 0.45/0.64 ![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 0.45/0.64 inference(skolemize,[status(sab)],[84])).
% 0.45/0.64 tff(86,plain,
% 0.45/0.64 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.45/0.64 tff(87,plain,
% 0.45/0.64 (((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | ((~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))) | p11(f4(f6(c15, c13)), f4(f6(c15, c13))))) <=> ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))) | p11(f4(f6(c15, c13)), f4(f6(c15, c13))))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(88,plain,
% 0.45/0.64 ((p11(f4(f6(c15, c13)), f4(f6(c15, c13))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13))))) <=> ((~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))) | p11(f4(f6(c15, c13)), f4(f6(c15, c13))))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(89,plain,
% 0.45/0.64 (((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (p11(f4(f6(c15, c13)), f4(f6(c15, c13))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))))) <=> ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | ((~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))) | p11(f4(f6(c15, c13)), f4(f6(c15, c13)))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[88])).
% 0.45/0.64 tff(90,plain,
% 0.45/0.64 (((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (p11(f4(f6(c15, c13)), f4(f6(c15, c13))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))))) <=> ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))) | p11(f4(f6(c15, c13)), f4(f6(c15, c13))))),
% 0.45/0.64 inference(transitivity,[status(thm)],[89, 87])).
% 0.45/0.64 tff(91,plain,
% 0.45/0.64 ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (p11(f4(f6(c15, c13)), f4(f6(c15, c13))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(92,plain,
% 0.45/0.64 ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c13)))) | p11(f4(f6(c15, c13)), f4(f6(c15, c13)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.45/0.64 tff(93,plain,
% 0.45/0.64 (p11(f4(f6(c15, c13)), f4(f6(c15, c13)))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[92, 86, 79])).
% 0.45/0.64 tff(94,assumption,(p2(f4(f6(c15, c13)), c16)), introduced(assumption)).
% 0.45/0.64 tff(95,plain,
% 0.45/0.64 (^[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)))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(96,plain,
% 0.45/0.64 (![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))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[95])).
% 0.45/0.64 tff(97,plain,
% 0.45/0.64 (![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))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(98,plain,
% 0.45/0.64 (^[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))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(99,plain,
% 0.45/0.64 (![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))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[98])).
% 0.45/0.64 tff(100,axiom,(![X9: $i, X10: $i, X7: $i, X8: $i] : (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_21')).
% 0.45/0.64 tff(101,plain,
% 0.45/0.64 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.45/0.64 tff(102,plain,
% 0.45/0.64 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.45/0.64 tff(103,plain,(
% 0.45/0.64 ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.45/0.64 inference(skolemize,[status(sab)],[102])).
% 0.45/0.64 tff(104,plain,
% 0.45/0.64 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.45/0.64 tff(105,plain,
% 0.45/0.64 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | (p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), c16)))) <=> ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), c16)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(106,plain,
% 0.45/0.64 (((~p2(f4(f6(c15, c13)), c16)) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16)) <=> (p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), c16)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(107,plain,
% 0.45/0.64 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(f4(f6(c15, c13)), c16)) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), 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))) | (p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), c16))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[106])).
% 0.45/0.65 tff(108,plain,
% 0.45/0.65 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(f4(f6(c15, c13)), c16)) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), 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))) | p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), c16)))),
% 0.45/0.65 inference(transitivity,[status(thm)],[107, 105])).
% 0.45/0.65 tff(109,plain,
% 0.45/0.65 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(f4(f6(c15, c13)), c16)) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
% 0.45/0.65 tff(110,plain,
% 0.45/0.65 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | (~p11(f4(f6(c15, c13)), f4(f6(c15, c13)))) | (~p2(f4(f6(c15, c13)), c16))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.45/0.65 tff(111,plain,
% 0.45/0.65 ($false),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[110, 66, 104, 94, 53, 93])).
% 0.45/0.65 tff(112,plain,(~p2(f4(f6(c15, c13)), c16)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.65 tff(113,plain,
% 0.45/0.65 (^[X12: $i, X11: $i] : refl((p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))) <=> (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(114,plain,
% 0.45/0.65 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))) <=> ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[113])).
% 0.45/0.65 tff(115,plain,
% 0.45/0.65 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))) <=> ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(116,plain,
% 0.45/0.65 (^[X12: $i, X11: $i] : rewrite(((p12(X11, X12) | p2(X11, X12)) | (~p11(X11, X12))) <=> (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(117,plain,
% 0.45/0.65 (![X12: $i, X11: $i] : ((p12(X11, X12) | p2(X11, X12)) | (~p11(X11, X12))) <=> ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[116])).
% 0.45/0.65 tff(118,axiom,(![X12: $i, X11: $i] : ((p12(X11, X12) | p2(X11, X12)) | (~p11(X11, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_16')).
% 0.45/0.65 tff(119,plain,
% 0.45/0.65 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.45/0.65 tff(120,plain,
% 0.45/0.65 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.45/0.65 tff(121,plain,(
% 0.45/0.65 ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(skolemize,[status(sab)],[120])).
% 0.45/0.65 tff(122,plain,
% 0.45/0.65 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.45/0.65 tff(123,plain,
% 0.45/0.65 (p11(f4(f6(c15, c13)), c16) <=> p11(f4(f6(c15, c13)), c16)),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(124,axiom,(p11(f4(f6(c15, c13)), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_7')).
% 0.45/0.65 tff(125,plain,
% 0.45/0.65 (p11(f4(f6(c15, c13)), c16)),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.45/0.65 tff(126,plain,
% 0.45/0.65 (((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | (p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16)))) <=> ((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(127,plain,
% 0.45/0.65 ((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | (p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16)))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
% 0.45/0.65 tff(128,plain,
% 0.45/0.65 ((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.45/0.65 tff(129,plain,
% 0.45/0.65 (p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16)),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[128, 125, 122])).
% 0.45/0.65 tff(130,plain,
% 0.45/0.65 (p12(f4(f6(c15, c13)), c16)),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[129, 112])).
% 0.45/0.65 tff(131,plain,
% 0.45/0.65 (^[X14: $i, X17: $i, X16: $i, X15: $i] : refl(((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)) <=> ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(132,plain,
% 0.45/0.65 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[131])).
% 0.45/0.65 tff(133,plain,
% 0.45/0.65 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(134,plain,
% 0.45/0.65 (^[X14: $i, X17: $i, X16: $i, X15: $i] : trans(monotonicity(trans(monotonicity(rewrite((p12(X14, X15) | (~p2(X16, X14))) <=> ((~p2(X16, X14)) | p12(X14, X15))), (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) <=> (((~p2(X16, X14)) | p12(X14, X15)) | (~p2(X17, X15))))), rewrite((((~p2(X16, X14)) | p12(X14, X15)) | (~p2(X17, X15))) <=> ((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15))), (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) <=> ((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15)))), ((((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17))) <=> (((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15)) | (~p12(X16, X17))))), rewrite((((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15)) | (~p12(X16, X17))) <=> ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))), ((((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17))) <=> ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(135,plain,
% 0.45/0.65 (![X14: $i, X17: $i, X16: $i, X15: $i] : (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[134])).
% 0.45/0.65 tff(136,axiom,(![X14: $i, X17: $i, X16: $i, X15: $i] : (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_22')).
% 0.45/0.65 tff(137,plain,
% 0.45/0.65 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.45/0.65 tff(138,plain,
% 0.45/0.65 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.45/0.65 tff(139,plain,(
% 0.45/0.65 ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(skolemize,[status(sab)],[138])).
% 0.45/0.65 tff(140,plain,
% 0.45/0.65 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.45/0.65 tff(141,plain,
% 0.45/0.65 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | ((~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | (~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(142,plain,
% 0.45/0.65 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | ((~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
% 0.45/0.65 tff(143,plain,
% 0.45/0.65 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | (~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16)),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.45/0.65 tff(144,plain,
% 0.45/0.65 ($false),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[143, 140, 130, 70, 53, 9])).
% 0.45/0.65 % SZS output end Proof
% 0.45/0.65 % E exiting
%------------------------------------------------------------------------------