%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN613-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:41 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN613-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.14/0.33 % Computer : n012.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Jun 20 12:38:25 EDT 2025
% 0.14/0.33 % CPUTime :
% 0.21/0.58 % SZS status Unsatisfiable
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 tff(p11_type, type, (
% 0.21/0.58 p11: ( $i * $i ) > $o)).
% 0.21/0.58 tff(c23_type, type, (
% 0.21/0.58 c23: $i)).
% 0.21/0.58 tff(f12_type, type, (
% 0.21/0.58 f12: $i > $i)).
% 0.21/0.58 tff(f9_type, type, (
% 0.21/0.58 f9: $i > $i)).
% 0.21/0.58 tff(c21_type, type, (
% 0.21/0.58 c21: $i)).
% 0.21/0.58 tff(p17_type, type, (
% 0.21/0.58 p17: ( $i * $i * $i ) > $o)).
% 0.21/0.58 tff(f4_type, type, (
% 0.21/0.58 f4: $i > $i)).
% 0.21/0.58 tff(f7_type, type, (
% 0.21/0.58 f7: ( $i * $i ) > $i)).
% 0.21/0.58 tff(f8_type, type, (
% 0.21/0.58 f8: ( $i * $i ) > $i)).
% 0.21/0.58 tff(c22_type, type, (
% 0.21/0.58 c22: $i)).
% 0.21/0.58 tff(f10_type, type, (
% 0.21/0.58 f10: $i > $i)).
% 0.21/0.58 tff(c20_type, type, (
% 0.21/0.58 c20: $i)).
% 0.21/0.58 tff(c19_type, type, (
% 0.21/0.58 c19: $i)).
% 0.21/0.58 tff(p3_type, type, (
% 0.21/0.58 p3: ( $i * $i ) > $o)).
% 0.21/0.58 tff(p2_type, type, (
% 0.21/0.58 p2: ( $i * $i ) > $o)).
% 0.21/0.58 tff(p5_type, type, (
% 0.21/0.58 p5: ( $i * $i ) > $o)).
% 0.21/0.58 tff(p6_type, type, (
% 0.21/0.58 p6: ( $i * $i ) > $o)).
% 0.21/0.58 tff(p16_type, type, (
% 0.21/0.58 p16: ( $i * $i ) > $o)).
% 0.21/0.58 tff(c24_type, type, (
% 0.21/0.58 c24: $i)).
% 0.21/0.58 tff(1,assumption,(~p5(f10(c20), f10(c20))), introduced(assumption)).
% 0.21/0.58 tff(2,plain,
% 0.21/0.58 (^[X41: $i] : refl(p5(X41, X41) <=> p5(X41, X41))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(3,plain,
% 0.21/0.58 (![X41: $i] : p5(X41, X41) <=> ![X41: $i] : p5(X41, X41)),
% 0.21/0.58 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.58 tff(4,plain,
% 0.21/0.58 (![X41: $i] : p5(X41, X41) <=> ![X41: $i] : p5(X41, X41)),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(5,axiom,(![X41: $i] : p5(X41, X41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_3')).
% 0.21/0.58 tff(6,plain,
% 0.21/0.58 (![X41: $i] : p5(X41, X41)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.58 tff(7,plain,(
% 0.21/0.58 ![X41: $i] : p5(X41, X41)),
% 0.21/0.58 inference(skolemize,[status(sab)],[6])).
% 0.21/0.58 tff(8,plain,
% 0.21/0.58 (![X41: $i] : p5(X41, X41)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.58 tff(9,plain,
% 0.21/0.58 ((~![X41: $i] : p5(X41, X41)) | p5(f10(c20), f10(c20))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(10,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.58 tff(11,plain,(p5(f10(c20), f10(c20))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(12,assumption,(~p6(f8(f9(c21), c22), f8(f9(c21), c22))), introduced(assumption)).
% 0.21/0.58 tff(13,plain,
% 0.21/0.58 (^[X48: $i] : refl(p6(X48, X48) <=> p6(X48, X48))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(14,plain,
% 0.21/0.58 (![X48: $i] : p6(X48, X48) <=> ![X48: $i] : p6(X48, X48)),
% 0.21/0.58 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.58 tff(15,plain,
% 0.21/0.58 (![X48: $i] : p6(X48, X48) <=> ![X48: $i] : p6(X48, X48)),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(16,axiom,(![X48: $i] : p6(X48, X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p6_2')).
% 0.21/0.58 tff(17,plain,
% 0.21/0.58 (![X48: $i] : p6(X48, X48)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.58 tff(18,plain,(
% 0.21/0.58 ![X48: $i] : p6(X48, X48)),
% 0.21/0.58 inference(skolemize,[status(sab)],[17])).
% 0.21/0.58 tff(19,plain,
% 0.21/0.58 (![X48: $i] : p6(X48, X48)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.58 tff(20,plain,
% 0.21/0.58 ((~![X48: $i] : p6(X48, X48)) | p6(f8(f9(c21), c22), f8(f9(c21), c22))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(21,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.21/0.58 tff(22,plain,(p6(f8(f9(c21), c22), f8(f9(c21), c22))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(23,plain,
% 0.21/0.58 (^[X32: $i, X35: $i, X34: $i, X33: $i] : refl(((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35))) <=> ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(24,plain,
% 0.21/0.58 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35))) <=> ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.58 tff(25,plain,
% 0.21/0.58 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35))) <=> ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(26,plain,
% 0.21/0.58 (^[X32: $i, X35: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p2(f7(X32, X33), f7(X34, X35)) | (~p5(X32, X34))) <=> ((~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))), (((p2(f7(X32, X33), f7(X34, X35)) | (~p5(X32, X34))) | (~p6(X33, X35))) <=> (((~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35))) | (~p6(X33, X35))))), rewrite((((~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35))) | (~p6(X33, X35))) <=> ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))), (((p2(f7(X32, X33), f7(X34, X35)) | (~p5(X32, X34))) | (~p6(X33, X35))) <=> ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(27,plain,
% 0.21/0.58 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((p2(f7(X32, X33), f7(X34, X35)) | (~p5(X32, X34))) | (~p6(X33, X35))) <=> ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.58 tff(28,axiom,(![X32: $i, X35: $i, X34: $i, X33: $i] : ((p2(f7(X32, X33), f7(X34, X35)) | (~p5(X32, X34))) | (~p6(X33, X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_26')).
% 0.21/0.58 tff(29,plain,
% 0.21/0.58 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.58 tff(30,plain,
% 0.21/0.58 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.58 tff(31,plain,(
% 0.21/0.58 ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(skolemize,[status(sab)],[30])).
% 0.21/0.58 tff(32,plain,
% 0.21/0.58 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.58 tff(33,plain,
% 0.21/0.58 (((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))) | ((~p6(f8(f9(c21), c22), f8(f9(c21), c22))) | (~p5(f10(c20), f10(c20))) | p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22))))) <=> ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))) | (~p6(f8(f9(c21), c22), f8(f9(c21), c22))) | (~p5(f10(c20), f10(c20))) | p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(34,plain,
% 0.21/0.58 ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))) | ((~p6(f8(f9(c21), c22), f8(f9(c21), c22))) | (~p5(f10(c20), f10(c20))) | p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(35,plain,
% 0.21/0.58 ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p6(X33, X35)) | (~p5(X32, X34)) | p2(f7(X32, X33), f7(X34, X35)))) | (~p6(f8(f9(c21), c22), f8(f9(c21), c22))) | (~p5(f10(c20), f10(c20))) | p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.58 tff(36,plain,
% 0.21/0.58 ((~p6(f8(f9(c21), c22), f8(f9(c21), c22))) | (~p5(f10(c20), f10(c20))) | p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.21/0.58 tff(37,plain,
% 0.21/0.58 (p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[36, 22, 11])).
% 0.21/0.58 tff(38,plain,
% 0.21/0.58 (^[X39: $i, X40: $i] : refl(((~p2(X39, X40)) | p3(f4(X39), f4(X40))) <=> ((~p2(X39, X40)) | p3(f4(X39), f4(X40))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(39,plain,
% 0.21/0.58 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.58 tff(40,plain,
% 0.21/0.58 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(41,plain,
% 0.21/0.58 (^[X39: $i, X40: $i] : rewrite((p3(f4(X39), f4(X40)) | (~p2(X39, X40))) <=> ((~p2(X39, X40)) | p3(f4(X39), f4(X40))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(42,plain,
% 0.21/0.58 (![X39: $i, X40: $i] : (p3(f4(X39), f4(X40)) | (~p2(X39, X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.58 tff(43,axiom,(![X39: $i, X40: $i] : (p3(f4(X39), f4(X40)) | (~p2(X39, X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_13')).
% 0.21/0.58 tff(44,plain,
% 0.21/0.58 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.58 tff(45,plain,
% 0.21/0.58 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.21/0.58 tff(46,plain,(
% 0.21/0.58 ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(skolemize,[status(sab)],[45])).
% 0.21/0.58 tff(47,plain,
% 0.21/0.58 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.21/0.58 tff(48,plain,
% 0.21/0.58 (((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | ((~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))))) <=> ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | (~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(49,plain,
% 0.21/0.58 ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | ((~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(50,plain,
% 0.21/0.58 ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | (~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.58 tff(51,plain,
% 0.21/0.58 (p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 0.21/0.58 tff(52,assumption,(~p16(c19, c19)), introduced(assumption)).
% 0.21/0.58 tff(53,plain,
% 0.21/0.58 (^[X14: $i] : refl(p16(X14, X14) <=> p16(X14, X14))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(54,plain,
% 0.21/0.58 (![X14: $i] : p16(X14, X14) <=> ![X14: $i] : p16(X14, X14)),
% 0.21/0.58 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.58 tff(55,plain,
% 0.21/0.58 (![X14: $i] : p16(X14, X14) <=> ![X14: $i] : p16(X14, X14)),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(56,axiom,(![X14: $i] : p16(X14, X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p16_6')).
% 0.21/0.58 tff(57,plain,
% 0.21/0.58 (![X14: $i] : p16(X14, X14)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.58 tff(58,plain,(
% 0.21/0.58 ![X14: $i] : p16(X14, X14)),
% 0.21/0.58 inference(skolemize,[status(sab)],[57])).
% 0.21/0.58 tff(59,plain,
% 0.21/0.58 (![X14: $i] : p16(X14, X14)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.21/0.58 tff(60,plain,
% 0.21/0.58 ((~![X14: $i] : p16(X14, X14)) | p16(c19, c19)),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(61,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.21/0.58 tff(62,plain,(p16(c19, c19)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(63,plain,
% 0.21/0.58 (^[X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : refl(((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) <=> ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(64,plain,
% 0.21/0.58 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) <=> ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.58 tff(65,plain,
% 0.21/0.58 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) <=> ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(66,plain,
% 0.21/0.58 (^[X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p17(X17, X18, X19) | (~p3(X22, X18))) <=> ((~p3(X22, X18)) | p17(X17, X18, X19))), (((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) <=> (((~p3(X22, X18)) | p17(X17, X18, X19)) | (~p16(X21, X17))))), rewrite((((~p3(X22, X18)) | p17(X17, X18, X19)) | (~p16(X21, X17))) <=> ((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))), (((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) <=> ((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)))), ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) <=> (((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p11(X20, X19))))), rewrite((((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p11(X20, X19))) <=> ((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))), ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) <=> ((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)))), (((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20))) <=> (((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p17(X21, X22, X20))))), rewrite((((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p17(X21, X22, X20))) <=> ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))), (((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20))) <=> ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(67,plain,
% 0.21/0.58 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20))) <=> ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.58 tff(68,axiom,(![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_29')).
% 0.21/0.58 tff(69,plain,
% 0.21/0.58 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.58 tff(70,plain,
% 0.21/0.58 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.58 tff(71,plain,(
% 0.21/0.58 ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(skolemize,[status(sab)],[70])).
% 0.21/0.58 tff(72,plain,
% 0.21/0.58 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.58 tff(73,plain,
% 0.21/0.58 (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24) <=> p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(74,axiom,(p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_21')).
% 0.21/0.58 tff(75,plain,
% 0.21/0.58 (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.58 tff(76,plain,
% 0.21/0.58 (p11(c24, f12(f9(c21))) <=> p11(c24, f12(f9(c21)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(77,axiom,(p11(c24, f12(f9(c21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_8')).
% 0.21/0.59 tff(78,plain,
% 0.21/0.59 (p11(c24, f12(f9(c21)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.59 tff(79,plain,
% 0.21/0.59 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(80,plain,
% 0.21/0.59 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(81,plain,
% 0.21/0.59 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.59 tff(82,plain,
% 0.21/0.59 (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[81, 78, 75, 72, 62, 51])).
% 0.21/0.59 tff(83,plain,
% 0.21/0.59 ((~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)) <=> (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(84,axiom,(~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p17_22')).
% 0.21/0.59 tff(85,plain,
% 0.21/0.59 (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.59 tff(86,plain,
% 0.21/0.59 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(87,plain,
% 0.21/0.59 (((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)) <=> (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(88,plain,
% 0.21/0.59 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))))),
% 0.21/0.59 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.59 tff(89,plain,
% 0.21/0.59 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))),
% 0.21/0.59 inference(transitivity,[status(thm)],[88, 86])).
% 0.21/0.59 tff(90,plain,
% 0.21/0.59 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(91,plain,
% 0.21/0.59 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.59 tff(92,plain,
% 0.21/0.59 (~p11(f12(f9(c21)), c23)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[91, 85, 72, 62, 51, 82])).
% 0.21/0.59 tff(93,plain,
% 0.21/0.59 (^[X0: $i] : refl(p11(X0, X0) <=> p11(X0, X0))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(94,plain,
% 0.21/0.59 (![X0: $i] : p11(X0, X0) <=> ![X0: $i] : p11(X0, X0)),
% 0.21/0.59 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.59 tff(95,plain,
% 0.21/0.59 (![X0: $i] : p11(X0, X0) <=> ![X0: $i] : p11(X0, X0)),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(96,axiom,(![X0: $i] : p11(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_1')).
% 0.21/0.59 tff(97,plain,
% 0.21/0.59 (![X0: $i] : p11(X0, X0)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.59 tff(98,plain,(
% 0.21/0.59 ![X0: $i] : p11(X0, X0)),
% 0.21/0.59 inference(skolemize,[status(sab)],[97])).
% 0.21/0.59 tff(99,plain,
% 0.21/0.59 (![X0: $i] : p11(X0, X0)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.59 tff(100,plain,
% 0.21/0.59 ((~![X0: $i] : p11(X0, X0)) | p11(c23, c23)),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(101,plain,
% 0.21/0.59 (p11(c23, c23)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.59 tff(102,plain,
% 0.21/0.59 (^[X0: $i, X2: $i, X1: $i] : refl((p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))) <=> (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(103,plain,
% 0.21/0.59 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.59 tff(104,plain,
% 0.21/0.59 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(105,plain,
% 0.21/0.59 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p11(X1, X2) | (~p11(X0, X1))) <=> (p11(X1, X2) | (~p11(X0, X1)))), (((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))))), rewrite(((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))), (((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(106,plain,
% 0.21/0.59 (![X0: $i, X2: $i, X1: $i] : ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.59 tff(107,axiom,(![X0: $i, X2: $i, X1: $i] : ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_15')).
% 0.21/0.59 tff(108,plain,
% 0.21/0.59 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.59 tff(109,plain,
% 0.21/0.59 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.21/0.59 tff(110,plain,(
% 0.21/0.59 ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(skolemize,[status(sab)],[109])).
% 0.21/0.59 tff(111,plain,
% 0.21/0.59 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.21/0.59 tff(112,plain,
% 0.21/0.59 (p11(c23, f12(f9(c21))) <=> p11(c23, f12(f9(c21)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(113,axiom,(p11(c23, f12(f9(c21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_7')).
% 0.21/0.59 tff(114,plain,
% 0.21/0.59 (p11(c23, f12(f9(c21)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.59 tff(115,plain,
% 0.21/0.59 (((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | ((~p11(c23, f12(f9(c21)))) | (~p11(c23, c23)) | p11(f12(f9(c21)), c23))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (~p11(c23, f12(f9(c21)))) | (~p11(c23, c23)) | p11(f12(f9(c21)), c23))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(116,plain,
% 0.21/0.59 ((p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21))))) <=> ((~p11(c23, f12(f9(c21)))) | (~p11(c23, c23)) | p11(f12(f9(c21)), c23))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(117,plain,
% 0.21/0.59 (((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | ((~p11(c23, f12(f9(c21)))) | (~p11(c23, c23)) | p11(f12(f9(c21)), c23)))),
% 0.21/0.59 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.59 tff(118,plain,
% 0.21/0.59 (((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (~p11(c23, f12(f9(c21)))) | (~p11(c23, c23)) | p11(f12(f9(c21)), c23))),
% 0.21/0.59 inference(transitivity,[status(thm)],[117, 115])).
% 0.21/0.59 tff(119,plain,
% 0.21/0.59 ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21)))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(120,plain,
% 0.21/0.59 ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (~p11(c23, f12(f9(c21)))) | (~p11(c23, c23)) | p11(f12(f9(c21)), c23)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.59 tff(121,plain,
% 0.21/0.59 ($false),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[120, 114, 111, 101, 92])).
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % E exiting
%------------------------------------------------------------------------------