%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP002-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n013.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 04:23:31 PM UTC 2026
% Result : Unsatisfiable 3.75s 3.13s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of clauses : 106 ( 70 unt; 0 nHn; 85 RR)
% Number of literals : 160 ( 26 equ; 56 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 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 : 130 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(x_cubed_is_identity_2,hypothesis,
( product(X2,X1,identity)
| ~ product(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(h_times_b_is_j,negated_conjecture,
product(h,b,j),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
product(d,inverse(b),h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
product(c,inverse(a),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
product(j,inverse(h),k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
~ product(k,inverse(b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(c_0_15,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_16,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_17,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_18,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_19,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_21,hypothesis,
( product(X2,X1,identity)
| ~ product(X1,X1,X2) ),
x_cubed_is_identity_2 ).
cnf(c_0_22,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_23,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_24,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( product(X1,identity,X2)
| ~ product(X1,inverse(X2),identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
product(multiply(X1,X1),X1,identity),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,identity,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_28,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
product(h,b,j),
h_times_b_is_j ).
cnf(c_0_30,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_31,hypothesis,
product(multiply(inverse(X1),inverse(X1)),identity,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
product(inverse(inverse(X1)),identity,X1),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_33,plain,
( product(X1,X2,X3)
| ~ product(X3,inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_28]) ).
cnf(c_0_34,negated_conjecture,
product(d,inverse(b),h),
d_times_inverse_b_is_h ).
cnf(c_0_35,negated_conjecture,
( X1 = j
| ~ product(h,b,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_36,hypothesis,
multiply(inverse(X1),inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]) ).
cnf(c_0_37,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_28]) ).
cnf(c_0_38,negated_conjecture,
product(h,b,d),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
multiply(h,b) = j,
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
cnf(c_0_40,hypothesis,
multiply(X1,X1) = inverse(X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
product(c,inverse(a),d),
c_times_inverse_a_is_d ).
cnf(c_0_42,negated_conjecture,
d = j,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_38]),c_0_39]) ).
cnf(c_0_43,hypothesis,
product(X1,X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
product(c,inverse(a),j),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_46,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
product(j,a,c),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( product(X1,c,b)
| ~ product(X1,a,identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( product(c,a,X1)
| ~ product(j,inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
( product(X1,inverse(X2),X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_51,negated_conjecture,
product(inverse(a),c,b),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_52,negated_conjecture,
product(c,a,multiply(j,inverse(a))),
inference(spm,[status(thm)],[c_0_49,c_0_22]) ).
cnf(c_0_53,hypothesis,
( product(multiply(X1,X2),X2,X3)
| ~ product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_22]) ).
cnf(c_0_54,negated_conjecture,
product(b,inverse(c),inverse(a)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( product(X1,inverse(b),X2)
| ~ product(X3,h,X2)
| ~ product(X3,d,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_56,negated_conjecture,
product(j,inverse(h),k),
j_times_inverse_h_is_k ).
cnf(c_0_57,negated_conjecture,
multiply(j,inverse(a)) = multiply(c,a),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
product(multiply(b,c),c,inverse(a)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( product(X1,inverse(b),X2)
| ~ product(X3,h,X2)
| ~ product(X3,j,X1) ),
inference(rw,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_60,negated_conjecture,
product(k,h,j),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
product(j,inverse(a),multiply(c,a)),
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_62,hypothesis,
( product(X1,X2,inverse(X3))
| ~ product(X4,X3,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_43]) ).
cnf(c_0_63,negated_conjecture,
product(inverse(a),inverse(c),multiply(b,c)),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( product(X1,inverse(b),j)
| ~ product(k,j,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,c,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_66,negated_conjecture,
product(multiply(c,a),a,j),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_61]),c_0_37]) ).
cnf(c_0_67,plain,
( X1 = X2
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_68,negated_conjecture,
( product(X1,j,a)
| ~ product(X1,c,inverse(a)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_44]),c_0_37]) ).
cnf(c_0_69,plain,
product(multiply(X1,inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_70,negated_conjecture,
multiply(inverse(a),inverse(c)) = multiply(b,c),
inference(spm,[status(thm)],[c_0_30,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
product(multiply(k,j),inverse(b),j),
inference(spm,[status(thm)],[c_0_64,c_0_22]) ).
cnf(c_0_72,negated_conjecture,
( product(X1,b,multiply(X2,c))
| ~ product(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_22]) ).
cnf(c_0_73,negated_conjecture,
( product(X1,j,inverse(a))
| ~ product(X1,c,identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_44]) ).
cnf(c_0_74,negated_conjecture,
( product(X1,j,a)
| ~ product(X1,multiply(c,a),identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_66]) ).
cnf(c_0_75,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_22]) ).
cnf(c_0_76,negated_conjecture,
product(multiply(b,c),j,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_77,negated_conjecture,
product(j,b,multiply(k,j)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_71]),c_0_37]) ).
cnf(c_0_78,negated_conjecture,
product(j,b,multiply(multiply(c,a),c)),
inference(spm,[status(thm)],[c_0_72,c_0_66]) ).
cnf(c_0_79,hypothesis,
( product(X1,multiply(X2,X3),inverse(X3))
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_62,c_0_22]) ).
cnf(c_0_80,negated_conjecture,
product(inverse(c),j,inverse(a)),
inference(spm,[status(thm)],[c_0_73,c_0_20]) ).
cnf(c_0_81,negated_conjecture,
product(inverse(multiply(c,a)),j,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_69]),c_0_75]) ).
cnf(c_0_82,negated_conjecture,
product(a,inverse(j),multiply(b,c)),
inference(spm,[status(thm)],[c_0_50,c_0_76]) ).
cnf(c_0_83,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_84,negated_conjecture,
multiply(k,j) = multiply(j,b),
inference(spm,[status(thm)],[c_0_30,c_0_77]) ).
cnf(c_0_85,plain,
product(multiply(X1,X2),inverse(X2),X1),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_86,negated_conjecture,
multiply(multiply(c,a),c) = multiply(j,b),
inference(spm,[status(thm)],[c_0_30,c_0_78]) ).
cnf(c_0_87,negated_conjecture,
product(inverse(c),multiply(c,a),a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_57]),c_0_37]) ).
cnf(c_0_88,negated_conjecture,
product(a,inverse(j),inverse(multiply(c,a))),
inference(spm,[status(thm)],[c_0_50,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
multiply(a,inverse(j)) = multiply(b,c),
inference(spm,[status(thm)],[c_0_30,c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( product(X1,c,multiply(X2,a))
| ~ product(X1,j,X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_47]) ).
cnf(c_0_91,negated_conjecture,
product(k,j,multiply(j,b)),
inference(spm,[status(thm)],[c_0_22,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
product(multiply(j,b),inverse(c),multiply(c,a)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
multiply(inverse(c),multiply(c,a)) = a,
inference(spm,[status(thm)],[c_0_30,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
inverse(multiply(c,a)) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_88]),c_0_89]) ).
cnf(c_0_95,negated_conjecture,
product(k,c,multiply(multiply(j,b),a)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
( X1 = X2
| ~ product(multiply(X2,inverse(X3)),X3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_69]) ).
cnf(c_0_97,hypothesis,
product(multiply(j,b),a,multiply(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_98,negated_conjecture,
multiply(multiply(j,b),a) = multiply(k,c),
inference(spm,[status(thm)],[c_0_30,c_0_95]) ).
cnf(c_0_99,plain,
( X1 = X2
| ~ product(multiply(X2,X3),inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_37]) ).
cnf(c_0_100,hypothesis,
multiply(k,c) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_97]),c_0_98]) ).
cnf(c_0_101,hypothesis,
( X1 = k
| ~ product(multiply(b,c),inverse(c),X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_102,negated_conjecture,
~ product(k,inverse(b),identity),
prove_k_times_inverse_b_is_e ).
cnf(c_0_103,hypothesis,
k = b,
inference(spm,[status(thm)],[c_0_101,c_0_85]) ).
cnf(c_0_104,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_105,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103]),c_0_104])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP002-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n013.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:16:26 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 3.75/3.13 % Version : CSE_E---1.7
% 3.75/3.13 % Problem : theBenchmark.p
% 3.75/3.13 % SZS status Unsatisfiable for theBenchmark.p
% 3.75/3.13 % SZS output start CNFRefutation
% See solution above
% 3.75/3.14 % Total time : 2.371s
%------------------------------------------------------------------------------