%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP050-1 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 : Tue May 5 05:56:45 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.69s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 35
% Syntax : Number of clauses : 178 ( 178 unt; 0 nHn; 156 RR)
% Number of literals : 178 ( 177 equ; 19 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 32 con; 0-31 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(involutory_quandle_01,axiom,
product(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
cnf(knot_24,axiom,
product(a24,a3) = a25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_24) ).
cnf(involutory_quandle_02,axiom,
product(product(X1,X2),X3) = product(product(X1,X3),product(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).
cnf(involutory_quandle,axiom,
product(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).
cnf(knot_30,axiom,
product(a30,a23) = a31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_30) ).
cnf(knot_22,axiom,
product(a22,a31) = a23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_22) ).
cnf(knot_32,axiom,
product(a32,a21) = a1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_32) ).
cnf(knot_03,axiom,
product(a2,a25) = a3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
cnf(knot,axiom,
product(a1,a31) = a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
cnf(knot_26,axiom,
product(a26,a1) = a27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_26) ).
cnf(knot_23,axiom,
product(a23,a21) = a24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_23) ).
cnf(knot_25,axiom,
product(a25,a23) = a26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_25) ).
cnf(knot_29,axiom,
product(a29,a1) = a30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_29) ).
cnf(knot_31,axiom,
product(a31,a3) = a32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_31) ).
cnf(knot_28,axiom,
product(a28,a3) = a29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_28) ).
cnf(knot_27,axiom,
product(a27,a21) = a28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_27) ).
cnf(knot_21,axiom,
product(a21,a25) = a22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_21) ).
cnf(goal,negated_conjecture,
tuple(a1,a30,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27) != tuple(a2,a31,a32,a3,a25,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(knot_20,axiom,
product(a20,a29) = a21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_20) ).
cnf(knot_19,axiom,
product(a19,a11) = a20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_19) ).
cnf(knot_04,axiom,
product(a3,a29) = a4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
cnf(knot_07,axiom,
product(a7,a19) = a8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
cnf(knot_05,axiom,
product(a4,a11) = a5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
cnf(knot_08,axiom,
product(a8,a5) = a9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
cnf(knot_18,axiom,
product(a18,a15) = a19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_18) ).
cnf(knot_15,axiom,
product(a15,a5) = a16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).
cnf(knot_06,axiom,
product(a5,a15) = a6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
cnf(knot_11,axiom,
product(a11,a5) = a12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
cnf(knot_14,axiom,
product(a14,a17) = a15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).
cnf(knot_16,axiom,
product(a16,a19) = a17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).
cnf(knot_12,axiom,
product(a12,a19) = a13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).
cnf(knot_10,axiom,
product(a10,a7) = a11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
cnf(knot_13,axiom,
product(a13,a7) = a14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).
cnf(knot_17,axiom,
product(a17,a9) = a18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_17) ).
cnf(knot_09,axiom,
product(a9,a17) = a10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
cnf(c_0_35,axiom,
product(product(X1,X2),X2) = X1,
involutory_quandle_01 ).
cnf(c_0_36,axiom,
product(a24,a3) = a25,
knot_24 ).
cnf(c_0_37,axiom,
product(product(X1,X2),X3) = product(product(X1,X3),product(X2,X3)),
involutory_quandle_02 ).
cnf(c_0_38,axiom,
product(X1,X1) = X1,
involutory_quandle ).
cnf(c_0_39,axiom,
product(a30,a23) = a31,
knot_30 ).
cnf(c_0_40,axiom,
product(a22,a31) = a23,
knot_22 ).
cnf(c_0_41,axiom,
product(a32,a21) = a1,
knot_32 ).
cnf(c_0_42,axiom,
product(a2,a25) = a3,
knot_03 ).
cnf(c_0_43,plain,
product(a25,a3) = a24,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,axiom,
product(a1,a31) = a2,
knot ).
cnf(c_0_45,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
product(a31,a23) = a30,
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_47,plain,
product(a23,a31) = a22,
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_48,plain,
product(a1,a21) = a32,
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_49,axiom,
product(a26,a1) = a27,
knot_26 ).
cnf(c_0_50,axiom,
product(a23,a21) = a24,
knot_23 ).
cnf(c_0_51,axiom,
product(a25,a23) = a26,
knot_25 ).
cnf(c_0_52,plain,
product(product(X1,a2),a25) = product(product(X1,a25),a3),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_53,plain,
product(product(X1,a25),a3) = product(product(X1,a3),a24),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_54,plain,
product(product(X1,a1),a31) = product(product(X1,a31),a2),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_55,axiom,
product(a29,a1) = a30,
knot_29 ).
cnf(c_0_56,plain,
product(a30,a31) = product(a31,a22),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_57,axiom,
product(a31,a3) = a32,
knot_31 ).
cnf(c_0_58,axiom,
product(a28,a3) = a29,
knot_28 ).
cnf(c_0_59,plain,
product(product(X1,a1),a21) = product(product(X1,a21),a32),
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
cnf(c_0_60,plain,
product(a27,a1) = a26,
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_61,axiom,
product(a27,a21) = a28,
knot_27 ).
cnf(c_0_62,plain,
product(product(X1,a23),a21) = product(product(X1,a21),a24),
inference(spm,[status(thm)],[c_0_37,c_0_50]) ).
cnf(c_0_63,plain,
product(a26,a23) = a25,
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_64,plain,
product(product(X1,a2),a25) = product(product(X1,a3),a24),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,plain,
product(product(a29,a31),a2) = product(a31,a22),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_66,plain,
product(product(X1,a31),a3) = product(product(X1,a3),a32),
inference(spm,[status(thm)],[c_0_37,c_0_57]) ).
cnf(c_0_67,plain,
product(a29,a3) = a28,
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_68,plain,
product(a28,a32) = product(a26,a21),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_69,plain,
product(product(a26,a21),a24) = product(a25,a21),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
product(product(a31,a22),a25) = product(a25,a21),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_69]) ).
cnf(c_0_71,axiom,
product(a21,a25) = a22,
knot_21 ).
cnf(c_0_72,plain,
product(a25,a22) = product(a31,a22),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_70]),c_0_45]),c_0_71]) ).
cnf(c_0_73,plain,
a25 = a31,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_72]),c_0_35]) ).
cnf(c_0_74,plain,
product(a22,a25) = a21,
inference(spm,[status(thm)],[c_0_35,c_0_71]) ).
cnf(c_0_75,plain,
product(a2,a31) = a1,
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_76,negated_conjecture,
tuple(a1,a30,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27) != tuple(a2,a31,a32,a3,a25,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28),
goal ).
cnf(c_0_77,axiom,
product(a20,a29) = a21,
knot_20 ).
cnf(c_0_78,plain,
a32 = a24,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_73]),c_0_57]) ).
cnf(c_0_79,plain,
product(a24,a21) = a23,
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_80,plain,
a23 = a21,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_73]),c_0_40]) ).
cnf(c_0_81,plain,
a1 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_73]),c_0_75]) ).
cnf(c_0_82,negated_conjecture,
tuple(a2,a31,a32,a3,a31,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28) != tuple(a1,a30,a31,a2,a24,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_73]),c_0_73]) ).
cnf(c_0_83,axiom,
product(a19,a11) = a20,
knot_19 ).
cnf(c_0_84,plain,
product(a21,a29) = a20,
inference(spm,[status(thm)],[c_0_35,c_0_77]) ).
cnf(c_0_85,plain,
a21 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_78]),c_0_79]),c_0_80]),c_0_81]) ).
cnf(c_0_86,axiom,
product(a3,a29) = a4,
knot_04 ).
cnf(c_0_87,negated_conjecture,
tuple(a2,a31,a32,a3,a31,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a21,a24,a27,a28) != tuple(a1,a30,a31,a2,a24,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a21,a26,a27),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_80]),c_0_80]) ).
cnf(c_0_88,plain,
a24 = a21,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_80]),c_0_38]) ).
cnf(c_0_89,plain,
a30 = a26,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_73]),c_0_46]) ).
cnf(c_0_90,plain,
product(a30,a1) = a29,
inference(spm,[status(thm)],[c_0_35,c_0_55]) ).
cnf(c_0_91,axiom,
product(a7,a19) = a8,
knot_07 ).
cnf(c_0_92,plain,
product(a20,a11) = a19,
inference(spm,[status(thm)],[c_0_35,c_0_83]) ).
cnf(c_0_93,plain,
a20 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_94,axiom,
product(a4,a11) = a5,
knot_05 ).
cnf(c_0_95,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a26,a4,a29,a26,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a3,a22,a3,a3,a27,a28) != tuple(a3,a26,a31,a2,a3,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a3,a22,a3,a26,a27),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_78]),c_0_88]),c_0_85]),c_0_89]),c_0_85]),c_0_85]),c_0_88]),c_0_85]),c_0_81]),c_0_89]),c_0_88]),c_0_85]),c_0_85]),c_0_85]) ).
cnf(c_0_96,plain,
a27 = a29,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_89]),c_0_49]) ).
cnf(c_0_97,plain,
product(a8,a19) = a7,
inference(spm,[status(thm)],[c_0_35,c_0_91]) ).
cnf(c_0_98,plain,
a19 = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_99,axiom,
product(a8,a5) = a9,
knot_08 ).
cnf(c_0_100,axiom,
product(a18,a15) = a19,
knot_18 ).
cnf(c_0_101,axiom,
product(a15,a5) = a16,
knot_15 ).
cnf(c_0_102,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a26,a4,a29,a26,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a3,a22,a3,a3,a29,a28) != tuple(a3,a26,a31,a2,a3,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a3,a22,a3,a26,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96]),c_0_96]) ).
cnf(c_0_103,plain,
a9 = a7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_104,plain,
product(a19,a15) = a18,
inference(spm,[status(thm)],[c_0_35,c_0_100]) ).
cnf(c_0_105,axiom,
product(a5,a15) = a6,
knot_06 ).
cnf(c_0_106,axiom,
product(a11,a5) = a12,
knot_11 ).
cnf(c_0_107,axiom,
product(a14,a17) = a15,
knot_14 ).
cnf(c_0_108,axiom,
product(a16,a19) = a17,
knot_16 ).
cnf(c_0_109,plain,
product(a16,a5) = a15,
inference(spm,[status(thm)],[c_0_35,c_0_101]) ).
cnf(c_0_110,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a26,a4,a29,a26,a5,a11,a12,a6,a15,a16,a7,a8,a5,a4,a7,a10,a17,a18,a13,a14,a3,a22,a3,a3,a29,a28) != tuple(a3,a26,a31,a2,a3,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a5,a8,a7,a16,a17,a12,a13,a4,a3,a22,a3,a26,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_93]),c_0_93]),c_0_98]),c_0_103]),c_0_98]),c_0_103]) ).
cnf(c_0_111,plain,
a6 = a18,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_98]),c_0_105]) ).
cnf(c_0_112,axiom,
product(a12,a19) = a13,
knot_12 ).
cnf(c_0_113,plain,
product(a12,a5) = a11,
inference(spm,[status(thm)],[c_0_35,c_0_106]) ).
cnf(c_0_114,axiom,
product(a10,a7) = a11,
knot_10 ).
cnf(c_0_115,plain,
product(a15,a17) = a14,
inference(spm,[status(thm)],[c_0_35,c_0_107]) ).
cnf(c_0_116,plain,
a17 = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_98]),c_0_109]) ).
cnf(c_0_117,plain,
product(product(a2,X1),a25) = product(a3,product(X1,a25)),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_118,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a26,a4,a29,a26,a5,a11,a12,a18,a15,a16,a7,a8,a5,a4,a7,a10,a17,a18,a13,a14,a3,a22,a3,a3,a29,a28) != tuple(a3,a26,a31,a2,a3,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a18,a7,a18,a5,a8,a7,a16,a17,a12,a13,a4,a3,a22,a3,a26,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111]),c_0_111]) ).
cnf(c_0_119,axiom,
product(a13,a7) = a14,
knot_13 ).
cnf(c_0_120,plain,
a13 = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_98]),c_0_113]) ).
cnf(c_0_121,plain,
product(a11,a7) = a10,
inference(spm,[status(thm)],[c_0_35,c_0_114]) ).
cnf(c_0_122,plain,
a14 = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116]),c_0_38]) ).
cnf(c_0_123,plain,
product(product(a22,X1),a31) = product(a23,product(X1,a31)),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_124,plain,
product(a3,product(a31,a25)) = product(a1,a25),
inference(spm,[status(thm)],[c_0_117,c_0_75]) ).
cnf(c_0_125,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a26,a4,a29,a26,a5,a11,a12,a18,a15,a16,a7,a8,a5,a4,a7,a10,a15,a18,a13,a14,a3,a22,a3,a3,a29,a28) != tuple(a3,a26,a31,a2,a3,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a18,a7,a18,a5,a8,a7,a16,a15,a12,a13,a4,a3,a22,a3,a26,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_116]),c_0_116]) ).
cnf(c_0_126,plain,
a26 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_73]),c_0_45]),c_0_40]),c_0_46]),c_0_73]),c_0_85]),c_0_57]),c_0_78]),c_0_88]),c_0_85]),c_0_89]) ).
cnf(c_0_127,plain,
a10 = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_122]) ).
cnf(c_0_128,plain,
product(a23,product(a25,a31)) = product(a21,a31),
inference(spm,[status(thm)],[c_0_123,c_0_74]) ).
cnf(c_0_129,plain,
product(a3,a31) = a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_73]),c_0_38]),c_0_73]),c_0_44]) ).
cnf(c_0_130,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a3,a4,a29,a3,a5,a11,a12,a18,a15,a16,a7,a8,a5,a4,a7,a15,a15,a18,a11,a15,a3,a22,a3,a3,a29,a28) != tuple(a3,a3,a31,a2,a3,a31,a3,a28,a29,a4,a15,a11,a5,a15,a15,a18,a7,a18,a5,a8,a7,a16,a15,a12,a11,a4,a3,a22,a3,a3,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_120]),c_0_120]),c_0_126]),c_0_126]),c_0_127]),c_0_122]),c_0_126]),c_0_127]),c_0_122]),c_0_126]) ).
cnf(c_0_131,plain,
a22 = a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_73]),c_0_38]),c_0_47]),c_0_85]),c_0_129]) ).
cnf(c_0_132,plain,
a31 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_73]),c_0_126]),c_0_80]),c_0_85]),c_0_38]) ).
cnf(c_0_133,plain,
product(product(a26,a21),a32) = a28,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_49]),c_0_61]) ).
cnf(c_0_134,plain,
product(product(X1,a15),a5) = product(product(X1,a5),a16),
inference(spm,[status(thm)],[c_0_37,c_0_101]) ).
cnf(c_0_135,negated_conjecture,
tuple(a2,a31,a3,a3,a31,a3,a4,a29,a3,a5,a11,a12,a18,a15,a16,a7,a8,a5,a4,a7,a15,a15,a18,a11,a15,a3,a2,a3,a3,a29,a28) != tuple(a3,a3,a31,a2,a3,a31,a3,a28,a29,a4,a15,a11,a5,a15,a15,a18,a7,a18,a5,a8,a7,a16,a15,a12,a11,a4,a3,a2,a3,a3,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131]),c_0_131]) ).
cnf(c_0_136,plain,
a2 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_132]),c_0_38]) ).
cnf(c_0_137,plain,
a28 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_78]),c_0_69]),c_0_73]),c_0_132]),c_0_85]),c_0_38]) ).
cnf(c_0_138,plain,
product(product(X1,a7),a19) = product(product(X1,a19),a8),
inference(spm,[status(thm)],[c_0_37,c_0_91]) ).
cnf(c_0_139,plain,
product(product(X1,a16),a19) = product(product(X1,a19),a17),
inference(spm,[status(thm)],[c_0_37,c_0_108]) ).
cnf(c_0_140,plain,
product(product(a18,a5),a16) = product(a19,a5),
inference(spm,[status(thm)],[c_0_134,c_0_100]) ).
cnf(c_0_141,axiom,
product(a17,a9) = a18,
knot_17 ).
cnf(c_0_142,axiom,
product(a9,a17) = a10,
knot_09 ).
cnf(c_0_143,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a4,a29,a3,a5,a11,a12,a18,a15,a16,a7,a8,a5,a4,a7,a15,a15,a18,a11,a15,a3,a3,a3,a3,a29,a28) != tuple(a3,a3,a3,a3,a3,a3,a3,a28,a29,a4,a15,a11,a5,a15,a15,a18,a7,a18,a5,a8,a7,a16,a15,a12,a11,a4,a3,a3,a3,a3,a29),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_132]),c_0_132]),c_0_132]),c_0_132]),c_0_136]),c_0_136]),c_0_136]),c_0_136]) ).
cnf(c_0_144,plain,
a29 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_137]),c_0_38]) ).
cnf(c_0_145,plain,
product(product(X1,a8),a5) = product(product(X1,a5),a9),
inference(spm,[status(thm)],[c_0_37,c_0_99]) ).
cnf(c_0_146,plain,
product(product(a10,a19),a8) = product(a11,a19),
inference(spm,[status(thm)],[c_0_138,c_0_114]) ).
cnf(c_0_147,plain,
product(product(product(a18,a5),a19),a17) = product(a19,product(a5,a19)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_45]) ).
cnf(c_0_148,plain,
product(a18,a17) = product(a17,a10),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_141]),c_0_142]) ).
cnf(c_0_149,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a4,a3,a3,a5,a11,a12,a18,a15,a16,a7,a8,a5,a4,a7,a15,a15,a18,a11,a15,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a4,a15,a11,a5,a15,a15,a18,a7,a18,a5,a8,a7,a16,a15,a12,a11,a4,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_137]),c_0_137]),c_0_144]),c_0_144]),c_0_144]),c_0_144]) ).
cnf(c_0_150,plain,
a4 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_144]),c_0_38]) ).
cnf(c_0_151,plain,
product(product(product(a10,a19),a5),a9) = product(product(a11,a19),a5),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,plain,
product(product(a11,X1),a5) = product(a12,product(X1,a5)),
inference(spm,[status(thm)],[c_0_37,c_0_106]) ).
cnf(c_0_153,plain,
a15 = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_98]),c_0_35]),c_0_148]),c_0_98]),c_0_98]),c_0_38]),c_0_38]),c_0_116]),c_0_127]),c_0_38]) ).
cnf(c_0_154,plain,
product(product(a8,X1),a5) = product(a9,product(X1,a5)),
inference(spm,[status(thm)],[c_0_37,c_0_99]) ).
cnf(c_0_155,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a12,a18,a15,a16,a7,a8,a5,a3,a7,a15,a15,a18,a11,a15,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a15,a11,a5,a15,a15,a18,a7,a18,a5,a8,a7,a16,a15,a12,a11,a3,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150]),c_0_150]),c_0_150]),c_0_150]) ).
cnf(c_0_156,plain,
product(product(product(a10,a19),a5),a9) = product(a12,product(a19,a5)),
inference(rw,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_157,plain,
product(a10,a9) = product(a9,a18),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_142]),c_0_141]) ).
cnf(c_0_158,plain,
product(a18,a5) = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_98]),c_0_153]) ).
cnf(c_0_159,plain,
product(a9,product(a19,a5)) = product(a7,a5),
inference(spm,[status(thm)],[c_0_154,c_0_97]) ).
cnf(c_0_160,plain,
product(a9,a5) = a8,
inference(spm,[status(thm)],[c_0_35,c_0_99]) ).
cnf(c_0_161,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a12,a18,a5,a16,a7,a8,a5,a3,a7,a5,a5,a18,a11,a5,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a5,a5,a5,a18,a7,a18,a5,a8,a7,a16,a5,a12,a11,a3,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_153]),c_0_153]),c_0_153]),c_0_153]),c_0_153]),c_0_153]),c_0_153]),c_0_153]) ).
cnf(c_0_162,plain,
a16 = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_153]),c_0_38]) ).
cnf(c_0_163,plain,
product(a7,a18) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_98]),c_0_35]),c_0_157]),c_0_98]),c_0_38]),c_0_113]),c_0_103]) ).
cnf(c_0_164,plain,
a18 = a5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_158]),c_0_38]) ).
cnf(c_0_165,plain,
product(a7,a5) = a8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_98]),c_0_38]),c_0_160]) ).
cnf(c_0_166,plain,
product(a10,a17) = a9,
inference(spm,[status(thm)],[c_0_35,c_0_142]) ).
cnf(c_0_167,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a12,a18,a5,a5,a7,a8,a5,a3,a7,a5,a5,a18,a11,a5,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a5,a5,a5,a18,a7,a18,a5,a8,a7,a5,a5,a12,a11,a3,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_162]),c_0_162]) ).
cnf(c_0_168,plain,
a8 = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164]),c_0_165]) ).
cnf(c_0_169,plain,
a7 = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_103]),c_0_127]),c_0_153]),c_0_116]),c_0_153]),c_0_38]) ).
cnf(c_0_170,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a12,a5,a5,a5,a7,a8,a5,a3,a7,a5,a5,a5,a11,a5,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a5,a5,a5,a5,a7,a5,a5,a8,a7,a5,a5,a12,a11,a3,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_164]),c_0_164]),c_0_164]),c_0_164]) ).
cnf(c_0_171,plain,
a12 = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_103]),c_0_168]),c_0_106]),c_0_169]) ).
cnf(c_0_172,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a12,a5,a5,a5,a5,a11,a5,a3,a5,a5,a5,a5,a11,a5,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a11,a5,a5,a5,a5,a5,a5,a5,a11,a5,a5,a5,a12,a11,a3,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_168]),c_0_168]),c_0_169]),c_0_169]),c_0_169]),c_0_169]) ).
cnf(c_0_173,plain,
a11 = a5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_171]),c_0_38]) ).
cnf(c_0_174,plain,
product(a5,a11) = a4,
inference(spm,[status(thm)],[c_0_35,c_0_94]) ).
cnf(c_0_175,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a5,a5,a5,a5,a5,a5,a5,a5,a3,a5,a5,a5,a5,a5,a5,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a5,a5,a5,a5,a5,a5,a5,a5,a5,a5,a5,a5,a5,a5,a5,a3,a3,a3,a3,a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_171]),c_0_171]),c_0_173]),c_0_173]),c_0_173]),c_0_173]),c_0_173]),c_0_173]) ).
cnf(c_0_176,plain,
a5 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_150]),c_0_173]),c_0_38]) ).
cnf(c_0_177,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176]),c_0_176])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : TOP050-1 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 05:06:56 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.30/1.69 % Version : CSE_E---1.7
% 1.30/1.69 % Problem : theBenchmark.p
% 1.30/1.69 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.69 % SZS output start CNFRefutation
% See solution above
% 1.30/1.69 % Total time : 1.363s
%------------------------------------------------------------------------------