%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP049-1 : 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 : n011.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 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 64 RR)
% Number of literals : 75 ( 74 equ; 6 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 : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 18 ( 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_11,axiom,
a9 = product(a4,a8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
cnf(knot_08,axiom,
a8 = product(a7,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
cnf(knot_09,axiom,
a10 = product(a8,a9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
cnf(knot_10,axiom,
a4 = product(a10,a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
cnf(knot_05,axiom,
a5 = product(a2,a10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
cnf(knot_04,axiom,
a2 = product(a3,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
cnf(knot_03,axiom,
a3 = product(a1,a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
cnf(knot_06,axiom,
a6 = product(a5,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
cnf(knot_07,axiom,
a7 = product(a6,a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
cnf(knot,axiom,
a1 = product(a9,a7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
cnf(goal,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
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,
a9 = product(a4,a8),
knot_11 ).
cnf(c_0_18,axiom,
a8 = product(a7,a4),
knot_08 ).
cnf(c_0_19,axiom,
a10 = product(a8,a9),
knot_09 ).
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(a9,a8) = a4,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
product(a8,a4) = a7,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_23,axiom,
a4 = product(a10,a3),
knot_10 ).
cnf(c_0_24,plain,
product(product(X1,a8),a9) = product(product(X1,a9),a10),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_25,plain,
product(a10,a8) = a7,
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_26,plain,
product(a10,a9) = a8,
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_27,axiom,
a5 = product(a2,a10),
knot_05 ).
cnf(c_0_28,axiom,
a2 = product(a3,a4),
knot_04 ).
cnf(c_0_29,plain,
product(a4,a3) = a10,
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_30,plain,
product(a9,a10) = product(a4,a9),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_15]) ).
cnf(c_0_31,plain,
product(a8,a10) = product(a7,a9),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
product(product(X1,a10),a3) = product(product(X1,a3),a4),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_33,plain,
product(a5,a10) = a2,
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_34,plain,
product(a2,a3) = product(a3,a10),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_28]),c_0_29]) ).
cnf(c_0_35,axiom,
a3 = product(a1,a2),
knot_03 ).
cnf(c_0_36,plain,
product(product(X1,a9),a10) = product(product(X1,a4),a8),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_24]) ).
cnf(c_0_37,plain,
product(a10,a4) = product(a4,a2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_28]) ).
cnf(c_0_38,plain,
product(a10,product(a4,a9)) = product(a7,a9),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_30]),c_0_31]) ).
cnf(c_0_39,plain,
product(product(a5,a3),a4) = product(a3,a10),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,plain,
product(product(X1,a3),a4) = product(product(X1,a4),a2),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_41,axiom,
a6 = product(a5,a4),
knot_06 ).
cnf(c_0_42,plain,
product(a3,a2) = a1,
inference(spm,[status(thm)],[c_0_16,c_0_35]) ).
cnf(c_0_43,plain,
product(product(a4,a2),a8) = product(a7,a9),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_37]),c_0_30]),c_0_38]) ).
cnf(c_0_44,plain,
product(product(a7,a9),a8) = product(a8,a7),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_25]) ).
cnf(c_0_45,plain,
product(a6,a2) = product(a3,a10),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_46,plain,
product(product(a3,a10),a2) = product(a2,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_42]) ).
cnf(c_0_47,plain,
product(a8,a7) = product(a4,a2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
product(a2,a1) = a6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_45]),c_0_46]) ).
cnf(c_0_49,axiom,
a7 = product(a6,a1),
knot_07 ).
cnf(c_0_50,plain,
product(product(a4,a2),a7) = a8,
inference(spm,[status(thm)],[c_0_16,c_0_47]) ).
cnf(c_0_51,plain,
a2 = a7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_48]),c_0_49]) ).
cnf(c_0_52,axiom,
a1 = product(a9,a7),
knot ).
cnf(c_0_53,plain,
product(a2,a4) = a3,
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_54,plain,
a8 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_16]) ).
cnf(c_0_55,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
goal ).
cnf(c_0_56,plain,
product(a1,a7) = a9,
inference(spm,[status(thm)],[c_0_16,c_0_52]) ).
cnf(c_0_57,plain,
a3 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_51]),c_0_18]),c_0_54]) ).
cnf(c_0_58,plain,
product(a7,a8) = a10,
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_59,plain,
product(product(a3,a10),a4) = product(a5,a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_34]) ).
cnf(c_0_60,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a7,a3,a4,a5) != tuple(a7,a10,a9,a7,a8,a3,a4,a5,a6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_51]),c_0_51]) ).
cnf(c_0_61,plain,
a9 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_51]),c_0_56]),c_0_57]) ).
cnf(c_0_62,plain,
a7 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_54]),c_0_15]) ).
cnf(c_0_63,plain,
a10 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_54]),c_0_18]),c_0_54]) ).
cnf(c_0_64,plain,
product(a5,a3) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_59]),c_0_53]),c_0_42]) ).
cnf(c_0_65,plain,
product(a7,product(a4,a7)) = product(a8,a7),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_66,negated_conjecture,
tuple(a1,a4,a4,a6,a4,a4,a4,a4,a5) != tuple(a4,a4,a4,a4,a4,a4,a4,a5,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_60,c_0_54]),c_0_54]),c_0_61]),c_0_62]),c_0_62]),c_0_57]),c_0_62]),c_0_63]),c_0_61]),c_0_62]),c_0_57]) ).
cnf(c_0_67,plain,
a6 = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_57]),c_0_41]) ).
cnf(c_0_68,plain,
product(a2,product(a4,a2)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_53]),c_0_42]) ).
cnf(c_0_69,plain,
product(a7,product(a4,a7)) = product(a4,a2),
inference(rw,[status(thm)],[c_0_65,c_0_47]) ).
cnf(c_0_70,negated_conjecture,
tuple(a1,a4,a4,a1,a4,a4,a4,a4,a5) != tuple(a4,a4,a4,a4,a4,a4,a4,a5,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_67]) ).
cnf(c_0_71,plain,
a1 = a4,
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_51]),c_0_51]),c_0_69]),c_0_51]),c_0_62]),c_0_15]) ).
cnf(c_0_72,negated_conjecture,
tuple(a4,a4,a4,a4,a4,a4,a4,a5,a4) != tuple(a4,a4,a4,a4,a4,a4,a4,a4,a5),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_71]),c_0_71]) ).
cnf(c_0_73,plain,
a5 = a4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_51]),c_0_62]),c_0_63]),c_0_15]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : TOP049-1 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n011.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:06:47 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------