%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP053-1 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 05:56:55 PM UTC 2026
% Result : Unsatisfiable 1.35s 1.76s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 75 RR)
% Number of literals : 87 ( 86 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-14 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(involutory_quandle_02,axiom,
product(product(X1,X2),X3) = product(product(X1,X3),product(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
cnf(involutory_quandle,axiom,
product(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
cnf(involutory_quandle_01,axiom,
product(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
cnf(knot_04,axiom,
product(a5,a6) = a7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
cnf(knot,axiom,
product(a1,a2) = a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
cnf(knot_06,axiom,
product(a8,a2) = a9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
cnf(knot_05,axiom,
product(a7,a3) = a8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
cnf(knot_09,axiom,
product(a12,a3) = a13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
cnf(knot_12,axiom,
product(a2,a12) = a14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_12) ).
cnf(knot_15,axiom,
product(a4,a7) = a11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_15) ).
cnf(knot_03,axiom,
product(a3,a4) = a5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
cnf(knot_11,axiom,
product(a6,a7) = a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
cnf(knot_07,axiom,
product(a9,a1) = a10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
cnf(knot_10,axiom,
product(a13,a8) = a6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
cnf(knot_13,axiom,
product(a14,a3) = a15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_13) ).
cnf(knot_14,axiom,
product(a15,a8) = a4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_14) ).
cnf(knot_08,axiom,
product(a10,a11) = a12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
cnf(goal,negated_conjecture,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c_0_18,axiom,
product(product(X1,X2),X3) = product(product(X1,X3),product(X2,X3)),
involutory_quandle_02 ).
cnf(c_0_19,axiom,
product(X1,X1) = X1,
involutory_quandle ).
cnf(c_0_20,axiom,
product(product(X1,X2),X2) = X1,
involutory_quandle_01 ).
cnf(c_0_21,axiom,
product(a5,a6) = a7,
knot_04 ).
cnf(c_0_22,axiom,
product(a1,a2) = a3,
knot ).
cnf(c_0_23,axiom,
product(a8,a2) = a9,
knot_06 ).
cnf(c_0_24,axiom,
product(a7,a3) = a8,
knot_05 ).
cnf(c_0_25,axiom,
product(a12,a3) = a13,
knot_09 ).
cnf(c_0_26,axiom,
product(a2,a12) = a14,
knot_12 ).
cnf(c_0_27,axiom,
product(a4,a7) = a11,
knot_15 ).
cnf(c_0_28,axiom,
product(a3,a4) = a5,
knot_03 ).
cnf(c_0_29,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,plain,
product(a7,a6) = a5,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,axiom,
product(a6,a7) = a2,
knot_11 ).
cnf(c_0_32,plain,
product(product(X1,a1),a2) = product(product(X1,a2),a3),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_33,axiom,
product(a9,a1) = a10,
knot_07 ).
cnf(c_0_34,plain,
product(a9,a2) = a8,
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_35,plain,
product(a8,a3) = a7,
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_36,axiom,
product(a13,a8) = a6,
knot_10 ).
cnf(c_0_37,plain,
product(product(X1,a12),a3) = product(product(X1,a3),a13),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_38,plain,
product(a14,a12) = a2,
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_39,axiom,
product(a14,a3) = a15,
knot_13 ).
cnf(c_0_40,plain,
product(product(X1,a4),a7) = product(product(X1,a7),a11),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_41,plain,
product(a5,a4) = a3,
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_42,plain,
product(a5,a7) = product(a7,a2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_43,plain,
product(a10,a2) = a7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_44,plain,
product(product(X1,a13),a8) = product(product(X1,a8),a6),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_45,plain,
product(a15,a13) = product(a2,a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_46,axiom,
product(a15,a8) = a4,
knot_14 ).
cnf(c_0_47,plain,
product(product(a7,a2),a11) = product(a3,a7),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,plain,
product(a7,a2) = a10,
inference(spm,[status(thm)],[c_0_20,c_0_43]) ).
cnf(c_0_49,axiom,
product(a10,a11) = a12,
knot_08 ).
cnf(c_0_50,plain,
product(product(X1,a7),a3) = product(product(X1,a3),a8),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_51,plain,
product(a2,a7) = a6,
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_52,plain,
product(product(a2,a3),a8) = product(a4,a6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_53,plain,
product(a3,a7) = a12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_54,plain,
product(a6,a3) = product(a4,a6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_55,plain,
product(a12,a7) = a3,
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_56,plain,
product(product(a4,a6),a3) = a6,
inference(spm,[status(thm)],[c_0_20,c_0_54]) ).
cnf(c_0_57,plain,
a6 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_55]),c_0_19]),c_0_25]),c_0_36]) ).
cnf(c_0_58,negated_conjecture,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
goal ).
cnf(c_0_59,plain,
product(a4,a8) = a15,
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
cnf(c_0_60,plain,
a4 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_20]),c_0_57]) ).
cnf(c_0_61,plain,
a5 = a8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_57]),c_0_24]) ).
cnf(c_0_62,negated_conjecture,
tuple(a1,a2,a3,a4,a5,a3,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a3,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_57]),c_0_57]) ).
cnf(c_0_63,plain,
a12 = a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_57]),c_0_53]) ).
cnf(c_0_64,plain,
product(a4,product(a8,a4)) = product(a15,a4),
inference(spm,[status(thm)],[c_0_29,c_0_59]) ).
cnf(c_0_65,plain,
product(a15,a3) = a14,
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
cnf(c_0_66,plain,
product(product(a5,a3),a8) = product(product(a7,a2),a3),
inference(spm,[status(thm)],[c_0_50,c_0_42]) ).
cnf(c_0_67,plain,
a8 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_60]),c_0_19]),c_0_61]) ).
cnf(c_0_68,negated_conjecture,
tuple(a1,a2,a3,a3,a5,a3,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a3,a5,a3,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_60]),c_0_60]) ).
cnf(c_0_69,plain,
a11 = a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_60]),c_0_53]),c_0_63]) ).
cnf(c_0_70,plain,
a14 = a2,
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_64,c_0_60]),c_0_60]),c_0_35]),c_0_53]),c_0_60]),c_0_65]),c_0_63]) ).
cnf(c_0_71,plain,
product(a10,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_66,c_0_48]),c_0_61]),c_0_67]),c_0_19]),c_0_67]),c_0_19]) ).
cnf(c_0_72,negated_conjecture,
tuple(a1,a2,a3,a3,a3,a3,a7,a3,a9,a10,a2,a2,a13,a2) != tuple(a2,a3,a3,a3,a3,a7,a3,a9,a10,a2,a2,a13,a2,a15),
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_68,c_0_61]),c_0_61]),c_0_67]),c_0_67]),c_0_69]),c_0_63]),c_0_70]),c_0_67]),c_0_67]),c_0_69]),c_0_63]),c_0_70]) ).
cnf(c_0_73,plain,
a7 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_67]),c_0_19]) ).
cnf(c_0_74,plain,
product(a3,a2) = a1,
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_75,plain,
a10 = a3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_71]),c_0_19]) ).
cnf(c_0_76,negated_conjecture,
tuple(a1,a2,a3,a3,a3,a3,a3,a3,a9,a10,a2,a2,a13,a2) != tuple(a2,a3,a3,a3,a3,a3,a3,a9,a10,a2,a2,a13,a2,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_73]) ).
cnf(c_0_77,plain,
a9 = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_67]),c_0_74]) ).
cnf(c_0_78,plain,
a1 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_73]),c_0_74]),c_0_75]) ).
cnf(c_0_79,plain,
product(a2,a3) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_57]),c_0_73]) ).
cnf(c_0_80,plain,
product(a6,a8) = a13,
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_81,negated_conjecture,
tuple(a2,a3,a3,a3,a3,a3,a3,a3,a3,a2,a2,a13,a2,a15) != tuple(a3,a2,a3,a3,a3,a3,a3,a3,a3,a3,a2,a2,a13,a2),
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_76,c_0_77]),c_0_77]),c_0_78]),c_0_78]),c_0_75]),c_0_78]),c_0_75]) ).
cnf(c_0_82,plain,
a2 = a3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_79]),c_0_19]) ).
cnf(c_0_83,plain,
a13 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_57]),c_0_67]),c_0_19]) ).
cnf(c_0_84,negated_conjecture,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a15) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_83]),c_0_83]) ).
cnf(c_0_85,plain,
a15 = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_67]),c_0_19]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : TOP053-1 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 10:07:06 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.35/1.76 % Version : CSE_E---1.7
% 1.35/1.76 % Problem : theBenchmark.p
% 1.35/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.35/1.76 % SZS output start CNFRefutation
% See solution above
% 1.35/1.76 % Total time : 1.374s
%------------------------------------------------------------------------------