%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP051-1 : 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 : 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 : Tue May 5 05:56:45 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 89 ( 89 unt; 0 nHn; 75 RR)
% Number of literals : 89 ( 88 equ; 5 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 : 13 ( 13 usr; 11 con; 0-10 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(involutory_quandle_01,axiom,
product(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
cnf(knot_07,axiom,
product(a6,a2) = a7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
cnf(knot,axiom,
product(a1,a6) = a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
cnf(knot_03,axiom,
product(a2,a7) = a3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
cnf(knot_08,axiom,
product(a7,a3) = a8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
cnf(knot_10,axiom,
product(a9,a4) = a10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
cnf(knot_05,axiom,
product(a4,a10) = a5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
cnf(knot_09,axiom,
product(a8,a6) = a9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
cnf(knot_04,axiom,
product(a3,a1) = a4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
cnf(knot_06,axiom,
product(a5,a9) = a6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
cnf(knot_11,axiom,
product(a10,a5) = a11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
cnf(goal,negated_conjecture,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_14,axiom,
product(product(X1,X2),X3) = product(product(X1,X3),product(X2,X3)),
involutory_quandle_02 ).
cnf(c_0_15,axiom,
product(X1,X1) = X1,
involutory_quandle ).
cnf(c_0_16,axiom,
product(product(X1,X2),X2) = X1,
involutory_quandle_01 ).
cnf(c_0_17,axiom,
product(a6,a2) = a7,
knot_07 ).
cnf(c_0_18,axiom,
product(a1,a6) = a2,
knot ).
cnf(c_0_19,axiom,
product(a2,a7) = a3,
knot_03 ).
cnf(c_0_20,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
product(a7,a2) = a6,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
product(a2,a6) = a1,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_23,plain,
product(a3,a7) = a2,
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_24,axiom,
product(a7,a3) = a8,
knot_08 ).
cnf(c_0_25,plain,
product(product(X1,a7),a3) = product(product(X1,a2),a7),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_26,plain,
product(a3,a2) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_21]),c_0_22]) ).
cnf(c_0_27,plain,
product(a3,a8) = product(a2,a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
product(product(X1,a2),a7) = product(product(X1,a6),a2),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_29,plain,
product(a1,a7) = product(a2,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_26]),c_0_24]),c_0_27]) ).
cnf(c_0_30,axiom,
product(a9,a4) = a10,
knot_10 ).
cnf(c_0_31,plain,
product(product(a3,a6),a2) = product(a2,a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).
cnf(c_0_32,plain,
product(a8,a3) = a7,
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_33,axiom,
product(a4,a10) = a5,
knot_05 ).
cnf(c_0_34,plain,
product(a10,a4) = a9,
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_35,axiom,
product(a8,a6) = a9,
knot_09 ).
cnf(c_0_36,plain,
product(product(X1,a1),a6) = product(product(X1,a6),a2),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_37,axiom,
product(a3,a1) = a4,
knot_04 ).
cnf(c_0_38,plain,
product(a3,a6) = product(a2,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_31]),c_0_20]),c_0_26]) ).
cnf(c_0_39,plain,
product(a1,a2) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_17]),c_0_19]) ).
cnf(c_0_40,plain,
product(product(X1,a3),a8) = product(product(X1,a7),a3),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_41,plain,
product(a8,a7) = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24]),c_0_23]),c_0_21]) ).
cnf(c_0_42,plain,
product(a8,product(a2,a3)) = product(a7,a8),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_32]),c_0_27]) ).
cnf(c_0_43,plain,
product(product(X1,a9),a4) = product(product(X1,a4),a10),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_44,axiom,
product(a5,a9) = a6,
knot_06 ).
cnf(c_0_45,plain,
product(a5,a4) = product(a4,a9),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_33]),c_0_34]) ).
cnf(c_0_46,plain,
product(a5,a10) = a4,
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_47,axiom,
product(a10,a5) = a11,
knot_11 ).
cnf(c_0_48,plain,
product(product(X1,a8),a6) = product(product(X1,a6),a9),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_49,plain,
product(a4,a6) = product(a2,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_20]),c_0_39]) ).
cnf(c_0_50,plain,
product(a7,a8) = product(a6,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_40]),c_0_41]),c_0_27]),c_0_42]) ).
cnf(c_0_51,plain,
product(a7,a6) = product(a6,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_22]) ).
cnf(c_0_52,plain,
product(product(X1,a10),a5) = product(product(X1,a4),a10),
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_53,plain,
product(product(a4,a9),a10) = product(a6,a4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_54,plain,
product(a5,a11) = product(a4,a5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_46]),c_0_47]) ).
cnf(c_0_55,plain,
product(product(a2,a1),a9) = product(product(a2,a3),a6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_27]),c_0_38]) ).
cnf(c_0_56,plain,
product(product(a2,a3),a6) = a4,
inference(spm,[status(thm)],[c_0_16,c_0_49]) ).
cnf(c_0_57,plain,
product(a6,a7) = a8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]),c_0_24]) ).
cnf(c_0_58,plain,
product(product(a8,a2),a7) = product(a6,a3),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_59,plain,
product(product(a6,a3),a7) = product(a6,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_50]),c_0_41]),c_0_51]) ).
cnf(c_0_60,plain,
product(a4,a5) = product(a6,a4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_52]),c_0_45]),c_0_53]),c_0_47]),c_0_54]) ).
cnf(c_0_61,plain,
product(product(a2,a1),a9) = a4,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
product(a1,product(a2,a1)) = a4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_39]),c_0_37]) ).
cnf(c_0_63,plain,
product(a6,product(a6,a1)) = a9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_57]),c_0_35]),c_0_51]) ).
cnf(c_0_64,plain,
product(a8,a2) = product(a6,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_58]),c_0_59]) ).
cnf(c_0_65,plain,
product(a4,product(a4,a9)) = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_60]),c_0_16]),c_0_45]) ).
cnf(c_0_66,plain,
product(a4,a9) = product(a2,a1),
inference(spm,[status(thm)],[c_0_16,c_0_61]) ).
cnf(c_0_67,plain,
product(a4,product(a2,a1)) = a1,
inference(spm,[status(thm)],[c_0_16,c_0_62]) ).
cnf(c_0_68,plain,
product(a9,product(a6,a1)) = a6,
inference(spm,[status(thm)],[c_0_16,c_0_63]) ).
cnf(c_0_69,plain,
product(a6,a9) = a5,
inference(spm,[status(thm)],[c_0_16,c_0_44]) ).
cnf(c_0_70,plain,
product(product(a6,a1),a2) = a8,
inference(spm,[status(thm)],[c_0_16,c_0_64]) ).
cnf(c_0_71,plain,
a1 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_72,plain,
product(a9,product(product(a6,a1),a9)) = a5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_68]),c_0_69]) ).
cnf(c_0_73,plain,
product(a9,a6) = a8,
inference(spm,[status(thm)],[c_0_16,c_0_35]) ).
cnf(c_0_74,plain,
a8 = a7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_15]),c_0_17]) ).
cnf(c_0_75,plain,
product(a5,product(product(a6,a1),a9)) = a9,
inference(spm,[status(thm)],[c_0_16,c_0_72]) ).
cnf(c_0_76,plain,
a5 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_71]),c_0_22]),c_0_71]),c_0_69]) ).
cnf(c_0_77,negated_conjecture,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
goal ).
cnf(c_0_78,plain,
a7 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_71]),c_0_15]),c_0_73]),c_0_74]) ).
cnf(c_0_79,plain,
a9 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_71]),c_0_15]),c_0_69]),c_0_15]),c_0_76]) ).
cnf(c_0_80,negated_conjecture,
tuple(a2,a6,a6,a3,a6,a4,a4,a10,a11,a4) != tuple(a6,a6,a4,a2,a6,a3,a4,a4,a10,a6),
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_77,c_0_71]),c_0_78]),c_0_74]),c_0_78]),c_0_76]),c_0_79]),c_0_76]),c_0_78]),c_0_79]),c_0_74]),c_0_78]) ).
cnf(c_0_81,plain,
a4 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_71]),c_0_71]),c_0_22]),c_0_71]),c_0_15]) ).
cnf(c_0_82,negated_conjecture,
tuple(a2,a6,a6,a3,a6,a6,a6,a10,a11,a6) != tuple(a6,a6,a6,a2,a6,a3,a6,a6,a10,a6),
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_80,c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]) ).
cnf(c_0_83,plain,
a3 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_71]),c_0_17]),c_0_78]) ).
cnf(c_0_84,plain,
a2 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_71]),c_0_15]) ).
cnf(c_0_85,plain,
a11 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_76]),c_0_34]),c_0_79]),c_0_81]) ).
cnf(c_0_86,negated_conjecture,
tuple(a6,a6,a6,a6,a6,a6,a6,a10,a6,a6) != tuple(a6,a6,a6,a6,a6,a6,a6,a6,a10,a6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_83]),c_0_84]),c_0_85]),c_0_84]) ).
cnf(c_0_87,plain,
a10 = a6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_79]),c_0_15]),c_0_81]) ).
cnf(c_0_88,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP051-1 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n002.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 10:07:16 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.370s
%------------------------------------------------------------------------------