%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:37:24 PM UTC 2026
% Result : Unsatisfiable 4.47s 1.12s
% Output : CNFRefutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 15
% Syntax : Number of clauses : 174 ( 117 unt; 0 nHn; 153 RR)
% Number of literals : 260 ( 45 equ; 89 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 186 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(h_times_b_is_j,negated_conjecture,
product(h,b,j),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_b_is_j) ).
cnf(x_cubed_is_identity_2,hypothesis,
( ~ product(X1,X1,X2)
| product(X2,X1,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
product(j,inverse(h),k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
product(d,inverse(b),h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
product(c,inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
~ product(k,inverse(b),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(c_0_15,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_16,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity2]) ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_15 ).
cnf(c_0_18,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_19,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_16 ).
cnf(c_0_20,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_21,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_23,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
product(h,b,j),
h_times_b_is_j ).
cnf(c_0_26,hypothesis,
( ~ product(X1,X1,X2)
| product(X2,X1,identity) ),
inference(fof_simplification,[status(thm)],[x_cubed_is_identity_2]) ).
cnf(c_0_27,negated_conjecture,
product(j,inverse(h),k),
j_times_inverse_h_is_k ).
cnf(c_0_28,plain,
( ~ product(X3,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
product(d,inverse(b),h),
d_times_inverse_b_is_h ).
cnf(c_0_30,negated_conjecture,
( ~ product(h,b,X1)
| X1 = j ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_31,hypothesis,
( ~ product(X1,X1,X2)
| product(X2,X1,identity) ),
c_0_26 ).
cnf(c_0_32,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_33,negated_conjecture,
( ~ product(X3,j,X1)
| ~ product(X3,k,X2)
| product(X1,inverse(h),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_34,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_35,negated_conjecture,
product(h,b,d),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
multiply(h,b) = j,
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_37,hypothesis,
product(multiply(X1,X1),X1,identity),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_38,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( ~ product(inverse(k),j,X1)
| product(X1,inverse(h),identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_40,negated_conjecture,
product(c,inverse(a),d),
c_times_inverse_a_is_d ).
cnf(c_0_41,negated_conjecture,
d = j,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_42,hypothesis,
product(identity,X1,multiply(inverse(X1),inverse(X1))),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_43,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_44,plain,
product(identity,X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_45,negated_conjecture,
product(multiply(inverse(k),j),inverse(h),identity),
inference(spm,[status(thm)],[c_0_39,c_0_22]) ).
cnf(c_0_46,negated_conjecture,
product(c,inverse(a),j),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,hypothesis,
multiply(inverse(X1),inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_43]) ).
cnf(c_0_48,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_44]),c_0_43]) ).
cnf(c_0_49,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_50,negated_conjecture,
product(identity,h,multiply(inverse(k),j)),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_51,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity1]) ).
cnf(c_0_52,negated_conjecture,
product(j,a,c),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_53,plain,
product(multiply(X1,inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_54,hypothesis,
multiply(X1,X1) = inverse(X1),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
( ~ product(X4,X2,X1)
| ~ product(X4,identity,X3)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
multiply(inverse(k),j) = h,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_50]),c_0_43]) ).
cnf(c_0_57,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_51 ).
cnf(c_0_58,negated_conjecture,
( ~ product(X3,j,X1)
| ~ product(X3,c,X2)
| product(X1,a,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_52]) ).
cnf(c_0_59,hypothesis,
product(X1,X1,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48]) ).
cnf(c_0_60,plain,
( ~ product(X3,X2,X1)
| product(X1,inverse(X2),X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_22]),c_0_24]) ).
cnf(c_0_61,negated_conjecture,
product(inverse(k),j,h),
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_63,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_32]) ).
cnf(c_0_64,negated_conjecture,
( ~ product(c,j,X1)
| product(X1,a,inverse(c)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( ~ product(X3,X4,X2)
| ~ product(X1,X3,inverse(X4))
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_66,negated_conjecture,
product(h,inverse(j),inverse(k)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( ~ product(X2,j,X1)
| product(X1,inverse(h),multiply(X2,k)) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_68,negated_conjecture,
( ~ product(X3,a,X1)
| ~ product(X3,c,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_62]) ).
cnf(c_0_69,plain,
( ~ product(X1,X3,X2)
| product(inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_20]) ).
cnf(c_0_70,negated_conjecture,
product(multiply(c,j),a,inverse(c)),
inference(spm,[status(thm)],[c_0_64,c_0_22]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(inverse(j),k,X1)
| product(h,X1,identity) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
product(multiply(inverse(j),inverse(j)),inverse(h),k),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_42]),c_0_43]) ).
cnf(c_0_73,negated_conjecture,
product(k,h,j),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(X2,a,X1)
| product(X1,b,multiply(X2,c)) ),
inference(spm,[status(thm)],[c_0_68,c_0_22]) ).
cnf(c_0_75,negated_conjecture,
product(inverse(multiply(c,j)),inverse(c),a),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(X1,X3,j)
| ~ product(X3,inverse(h),X2)
| product(X1,X2,k) ),
inference(spm,[status(thm)],[c_0_57,c_0_27]) ).
cnf(c_0_77,negated_conjecture,
product(h,multiply(inverse(j),k),identity),
inference(spm,[status(thm)],[c_0_71,c_0_22]) ).
cnf(c_0_78,negated_conjecture,
product(k,h,multiply(inverse(j),inverse(j))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_72]),c_0_48]) ).
cnf(c_0_79,negated_conjecture,
multiply(k,h) = j,
inference(spm,[status(thm)],[c_0_34,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
product(inverse(a),b,multiply(a,c)),
inference(spm,[status(thm)],[c_0_74,c_0_59]) ).
cnf(c_0_81,negated_conjecture,
product(a,c,inverse(multiply(c,j))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_75]),c_0_48]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(identity,inverse(h),X1)
| product(j,X1,k) ),
inference(spm,[status(thm)],[c_0_76,c_0_18]) ).
cnf(c_0_83,negated_conjecture,
product(identity,inverse(multiply(inverse(j),k)),h),
inference(spm,[status(thm)],[c_0_60,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
multiply(inverse(j),inverse(j)) = j,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_78]),c_0_79]) ).
cnf(c_0_85,negated_conjecture,
product(a,multiply(a,c),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_80]),c_0_48]) ).
cnf(c_0_86,negated_conjecture,
inverse(multiply(c,j)) = multiply(a,c),
inference(spm,[status(thm)],[c_0_34,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
product(j,multiply(h,h),k),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_42]),c_0_48]),c_0_48]) ).
cnf(c_0_88,negated_conjecture,
inverse(multiply(inverse(j),k)) = h,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_83]),c_0_43]) ).
cnf(c_0_89,negated_conjecture,
product(j,j,inverse(j)),
inference(spm,[status(thm)],[c_0_53,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
product(b,inverse(multiply(a,c)),a),
inference(spm,[status(thm)],[c_0_60,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
inverse(multiply(a,c)) = multiply(c,j),
inference(spm,[status(thm)],[c_0_48,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
product(inverse(j),k,multiply(h,h)),
inference(spm,[status(thm)],[c_0_69,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
multiply(inverse(j),k) = inverse(h),
inference(spm,[status(thm)],[c_0_48,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
product(inverse(j),inverse(h),multiply(j,k)),
inference(spm,[status(thm)],[c_0_67,c_0_89]) ).
cnf(c_0_95,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_96,negated_conjecture,
product(b,multiply(c,j),a),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(X3,h,X1)
| ~ product(X3,j,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_98,negated_conjecture,
multiply(h,h) = inverse(h),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_92]),c_0_93]) ).
cnf(c_0_99,negated_conjecture,
product(multiply(j,k),h,inverse(j)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_94]),c_0_48]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(b,c,X1)
| product(X1,j,a) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( ~ product(X2,h,X1)
| product(X1,b,multiply(X2,j)) ),
inference(spm,[status(thm)],[c_0_97,c_0_22]) ).
cnf(c_0_102,negated_conjecture,
product(h,h,inverse(h)),
inference(spm,[status(thm)],[c_0_22,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
product(inverse(multiply(j,k)),inverse(j),h),
inference(spm,[status(thm)],[c_0_69,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
product(multiply(b,c),j,a),
inference(spm,[status(thm)],[c_0_100,c_0_22]) ).
cnf(c_0_105,negated_conjecture,
product(inverse(h),b,multiply(h,j)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_106,negated_conjecture,
product(h,j,inverse(multiply(j,k))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_103]),c_0_48]) ).
cnf(c_0_107,negated_conjecture,
product(a,inverse(j),multiply(b,c)),
inference(spm,[status(thm)],[c_0_60,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( ~ product(j,h,X1)
| product(X1,b,inverse(j)) ),
inference(spm,[status(thm)],[c_0_97,c_0_59]) ).
cnf(c_0_109,negated_conjecture,
product(h,multiply(h,j),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_105]),c_0_48]) ).
cnf(c_0_110,negated_conjecture,
inverse(multiply(j,k)) = multiply(h,j),
inference(spm,[status(thm)],[c_0_34,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
product(inverse(a),multiply(b,c),inverse(j)),
inference(spm,[status(thm)],[c_0_69,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
product(multiply(j,h),b,inverse(j)),
inference(spm,[status(thm)],[c_0_108,c_0_22]) ).
cnf(c_0_113,negated_conjecture,
product(b,inverse(multiply(h,j)),h),
inference(spm,[status(thm)],[c_0_60,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
inverse(multiply(h,j)) = multiply(j,k),
inference(spm,[status(thm)],[c_0_48,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( ~ product(j,h,X1)
| product(X1,h,k) ),
inference(spm,[status(thm)],[c_0_95,c_0_87]) ).
cnf(c_0_116,plain,
( ~ product(X1,X5,X3)
| ~ product(X5,X4,X2)
| product(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_117,negated_conjecture,
product(c,inverse(b),a),
inference(spm,[status(thm)],[c_0_60,c_0_62]) ).
cnf(c_0_118,negated_conjecture,
( ~ product(inverse(a),b,X1)
| product(X1,c,inverse(j)) ),
inference(spm,[status(thm)],[c_0_95,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
multiply(inverse(a),b) = multiply(a,c),
inference(spm,[status(thm)],[c_0_34,c_0_80]) ).
cnf(c_0_120,negated_conjecture,
product(inverse(j),inverse(b),multiply(j,h)),
inference(spm,[status(thm)],[c_0_60,c_0_112]) ).
cnf(c_0_121,negated_conjecture,
product(b,multiply(j,k),h),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
product(multiply(j,h),h,k),
inference(spm,[status(thm)],[c_0_115,c_0_22]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(X1,c,X2)
| product(X1,a,multiply(X2,inverse(b))) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
product(multiply(a,c),c,inverse(j)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_22]),c_0_119]) ).
cnf(c_0_125,negated_conjecture,
multiply(inverse(j),inverse(b)) = multiply(j,h),
inference(spm,[status(thm)],[c_0_34,c_0_120]) ).
cnf(c_0_126,negated_conjecture,
( ~ product(b,j,X1)
| product(X1,k,h) ),
inference(spm,[status(thm)],[c_0_95,c_0_121]) ).
cnf(c_0_127,negated_conjecture,
product(inverse(multiply(j,h)),k,h),
inference(spm,[status(thm)],[c_0_69,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( ~ product(X3,d,X1)
| ~ product(X3,h,X2)
| product(X1,inverse(b),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_129,negated_conjecture,
product(multiply(a,c),a,multiply(j,h)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_130,negated_conjecture,
product(multiply(b,j),k,h),
inference(spm,[status(thm)],[c_0_126,c_0_22]) ).
cnf(c_0_131,negated_conjecture,
product(h,inverse(k),inverse(multiply(j,h))),
inference(spm,[status(thm)],[c_0_60,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( ~ product(X3,j,X1)
| ~ product(X3,h,X2)
| product(X1,inverse(b),X2) ),
inference(rw,[status(thm)],[c_0_128,c_0_41]) ).
cnf(c_0_133,plain,
( ~ product(inverse(X1),X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_49]) ).
cnf(c_0_134,plain,
( ~ product(multiply(X2,inverse(X3)),X3,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_53]) ).
cnf(c_0_135,negated_conjecture,
product(multiply(c,j),multiply(j,h),a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_129]),c_0_91]) ).
cnf(c_0_136,negated_conjecture,
product(h,inverse(k),multiply(b,j)),
inference(spm,[status(thm)],[c_0_60,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
multiply(h,inverse(k)) = inverse(multiply(j,h)),
inference(spm,[status(thm)],[c_0_34,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
product(inverse(b),a,inverse(multiply(a,c))),
inference(spm,[status(thm)],[c_0_69,c_0_90]) ).
cnf(c_0_139,negated_conjecture,
( ~ product(k,j,X1)
| product(X1,inverse(b),j) ),
inference(spm,[status(thm)],[c_0_132,c_0_73]) ).
cnf(c_0_140,plain,
product(X1,multiply(inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_133,c_0_22]) ).
cnf(c_0_141,plain,
( ~ product(multiply(X2,X3),inverse(X3),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_134,c_0_48]) ).
cnf(c_0_142,negated_conjecture,
multiply(multiply(c,j),multiply(j,h)) = a,
inference(spm,[status(thm)],[c_0_34,c_0_135]) ).
cnf(c_0_143,negated_conjecture,
inverse(multiply(j,h)) = multiply(b,j),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_136]),c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( ~ product(X1,X3,j)
| ~ product(X3,a,X2)
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_57,c_0_52]) ).
cnf(c_0_145,negated_conjecture,
product(inverse(b),a,multiply(c,j)),
inference(rw,[status(thm)],[c_0_138,c_0_91]) ).
cnf(c_0_146,negated_conjecture,
product(multiply(k,j),inverse(b),j),
inference(spm,[status(thm)],[c_0_139,c_0_22]) ).
cnf(c_0_147,plain,
( ~ product(X3,multiply(inverse(X3),X2),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_140]) ).
cnf(c_0_148,negated_conjecture,
( ~ product(a,multiply(b,j),X1)
| X1 = multiply(c,j) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]) ).
cnf(c_0_149,negated_conjecture,
( ~ product(X1,inverse(b),j)
| product(X1,multiply(c,j),c) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
product(j,b,multiply(k,j)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_146]),c_0_48]) ).
cnf(c_0_151,plain,
( ~ product(inverse(X3),multiply(X3,X2),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_147,c_0_48]) ).
cnf(c_0_152,negated_conjecture,
multiply(a,multiply(b,j)) = multiply(c,j),
inference(spm,[status(thm)],[c_0_148,c_0_22]) ).
cnf(c_0_153,negated_conjecture,
product(multiply(j,b),multiply(c,j),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_53]),c_0_48]) ).
cnf(c_0_154,negated_conjecture,
multiply(k,j) = multiply(j,b),
inference(spm,[status(thm)],[c_0_34,c_0_150]) ).
cnf(c_0_155,negated_conjecture,
product(inverse(c),inverse(a),multiply(c,j)),
inference(spm,[status(thm)],[c_0_60,c_0_70]) ).
cnf(c_0_156,negated_conjecture,
( ~ product(inverse(a),multiply(c,j),X1)
| X1 = multiply(b,j) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_157,negated_conjecture,
multiply(multiply(j,b),multiply(c,j)) = c,
inference(spm,[status(thm)],[c_0_34,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
product(k,j,multiply(j,b)),
inference(spm,[status(thm)],[c_0_22,c_0_154]) ).
cnf(c_0_159,hypothesis,
( ~ product(X1,X2,X3)
| product(X1,inverse(X2),multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_116,c_0_59]) ).
cnf(c_0_160,negated_conjecture,
product(c,multiply(c,j),inverse(a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_155]),c_0_48]) ).
cnf(c_0_161,negated_conjecture,
multiply(inverse(a),multiply(c,j)) = multiply(b,j),
inference(spm,[status(thm)],[c_0_156,c_0_22]) ).
cnf(c_0_162,negated_conjecture,
( ~ product(c,multiply(a,c),X1)
| X1 = multiply(j,b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_157]),c_0_86]) ).
cnf(c_0_163,negated_conjecture,
product(multiply(j,b),inverse(j),k),
inference(spm,[status(thm)],[c_0_60,c_0_158]) ).
cnf(c_0_164,negated_conjecture,
product(c,multiply(a,c),multiply(b,j)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_86]),c_0_161]) ).
cnf(c_0_165,negated_conjecture,
multiply(c,multiply(a,c)) = multiply(j,b),
inference(spm,[status(thm)],[c_0_162,c_0_22]) ).
cnf(c_0_166,negated_conjecture,
product(multiply(b,j),inverse(j),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_112]),c_0_143]) ).
cnf(c_0_167,negated_conjecture,
~ product(k,inverse(b),identity),
inference(fof_simplification,[status(thm)],[prove_k_times_inverse_b_is_e]) ).
cnf(c_0_168,negated_conjecture,
multiply(multiply(j,b),inverse(j)) = k,
inference(spm,[status(thm)],[c_0_34,c_0_163]) ).
cnf(c_0_169,negated_conjecture,
multiply(j,b) = multiply(b,j),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_164]),c_0_165]) ).
cnf(c_0_170,negated_conjecture,
multiply(multiply(b,j),inverse(j)) = b,
inference(spm,[status(thm)],[c_0_34,c_0_166]) ).
cnf(c_0_171,negated_conjecture,
~ product(k,inverse(b),identity),
c_0_167 ).
cnf(c_0_172,negated_conjecture,
k = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_169]),c_0_170]) ).
cnf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 19:53:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.47/1.12 % Version: 3.5.1
% 4.47/1.12 % Preprocessing class: FSMSSMSMSSSNFFN.
% 4.47/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.47/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 4.47/1.12 % Starting new_bool_3 with 300s (1) cores
% 4.47/1.12 % Starting new_bool_1 with 300s (1) cores
% 4.47/1.12 % Starting sh5l with 300s (1) cores
% 4.47/1.12 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3470676 completed with status 0
% 4.47/1.12 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 4.47/1.12 % Preprocessing class: FSMSSMSMSSSNFFN.
% 4.47/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.47/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 4.47/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.47/1.12 % No SInE strategy applied
% 4.47/1.12 % Search class: FHUSM-FFSS21-SFFFFFNN
% 4.47/1.12 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.47/1.12 % Starting SubtermCWHack with 136s (1) cores
% 4.47/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 4.47/1.12 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 4.47/1.12 % Starting new_bool_3 with 136s (1) cores
% 4.47/1.12 % Starting new_bool_1 with 136s (1) cores
% 4.47/1.12 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3470682 completed with status 0
% 4.47/1.12 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 4.47/1.12 % Preprocessing class: FSMSSMSMSSSNFFN.
% 4.47/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.47/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 4.47/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.47/1.12 % No SInE strategy applied
% 4.47/1.12 % Search class: FHUSM-FFSS21-SFFFFFNN
% 4.47/1.12 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.47/1.12 % Starting SubtermCWHack with 136s (1) cores
% 4.47/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 4.47/1.12 % Preprocessing time : 0.001 s
% 4.47/1.12 % Presaturation interreduction done
% 4.47/1.12
% 4.47/1.12 % Proof found!
% 4.47/1.12 % SZS status Unsatisfiable
% 4.47/1.12 % SZS output start CNFRefutation
% See solution above
% 4.47/1.12 % Parsed axioms : 16
% 4.47/1.12 % Removed by relevancy pruning/SinE : 0
% 4.47/1.12 % Initial clauses : 16
% 4.47/1.12 % Removed in clause preprocessing : 0
% 4.47/1.12 % Initial clauses in saturation : 16
% 4.47/1.12 % Processed clauses : 5360
% 4.47/1.12 % ...of these trivial : 472
% 4.47/1.12 % ...subsumed : 2093
% 4.47/1.12 % ...remaining for further processing : 2795
% 4.47/1.12 % Other redundant clauses eliminated : 0
% 4.47/1.12 % Clauses deleted for lack of memory : 0
% 4.47/1.12 % Backward-subsumed : 100
% 4.47/1.12 % Backward-rewritten : 817
% 4.47/1.12 % Generated clauses : 22609
% 4.47/1.12 % ...of the previous two non-redundant : 16822
% 4.47/1.12 % ...aggressively subsumed : 0
% 4.47/1.12 % Contextual simplify-reflections : 0
% 4.47/1.12 % Paramodulations : 22609
% 4.47/1.12 % Factorizations : 0
% 4.47/1.12 % NegExts : 0
% 4.47/1.12 % Equation resolutions : 0
% 4.47/1.12 % Disequality decompositions : 0
% 4.47/1.12 % Total rewrite steps : 15187
% 4.47/1.12 % ...of those cached : 14047
% 4.47/1.12 % Propositional unsat checks : 0
% 4.47/1.12 % Propositional check models : 0
% 4.47/1.12 % Propositional check unsatisfiable : 0
% 4.47/1.12 % Propositional clauses : 0
% 4.47/1.12 % Propositional clauses after purity: 0
% 4.47/1.12 % Propositional unsat core size : 0
% 4.47/1.12 % Propositional preprocessing time : 0.000
% 4.47/1.12 % Propositional encoding time : 0.000
% 4.47/1.12 % Propositional solver time : 0.000
% 4.47/1.12 % Success case prop preproc time : 0.000
% 4.47/1.12 % Success case prop encoding time : 0.000
% 4.47/1.12 % Success case prop solver time : 0.000
% 4.47/1.12 % Current number of processed clauses : 1862
% 4.47/1.12 % Positive orientable unit clauses : 476
% 4.47/1.12 % Positive unorientable unit clauses: 0
% 4.47/1.12 % Negative unit clauses : 0
% 4.47/1.12 % Non-unit-clauses : 1386
% 4.47/1.12 % Current number of unprocessed clauses: 9952
% 4.47/1.12 % ...number of literals in the above : 17683
% 4.47/1.12 % Current number of archived formulas : 0
% 4.47/1.12 % Current number of archived clauses : 933
% 4.47/1.12 % Clause-clause subsumption calls (NU) : 301098
% 4.47/1.12 % Rec. Clause-clause subsumption calls : 269961
% 4.47/1.12 % Non-unit clause-clause subsumptions : 2193
% 4.47/1.12 % Unit Clause-clause subsumption calls : 167
% 4.47/1.12 % Rewrite failures with RHS unbound : 0
% 4.47/1.12 % BW rewrite match attempts : 1271
% 4.47/1.12 % BW rewrite match successes : 125
% 4.47/1.12 % Condensation attempts : 0
% 4.47/1.12 % Condensation successes : 0
% 4.47/1.12 % Termbank termtop insertions : 310127
% 4.47/1.12 % Search garbage collected termcells : 22
% 4.47/1.12
% 4.47/1.12 % -------------------------------------------------
% 4.47/1.12 % User time : 0.637 s
% 4.47/1.12 % System time : 0.022 s
% 4.47/1.12 % Total time : 0.660 s
% 4.47/1.12 % Maximum resident set size: 3612 pages
% 4.47/1.12
% 4.47/1.12 % -------------------------------------------------
% 4.47/1.12 % User time : 2.956 s
% 4.47/1.12 % System time : 0.119 s
% 4.47/1.12 % Total time : 3.075 s
% 4.47/1.12 % Maximum resident set size: 4864 pages
% 4.47/1.12 % E exiting
%------------------------------------------------------------------------------