%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP258-1 : TPTP v9.2.1. Released v2.5.0.
% 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 : n008.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 04:24:57 PM UTC 2026
% Result : Unsatisfiable 1.81s 1.89s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of clauses : 73 ( 29 unt; 38 nHn; 53 RR)
% Number of literals : 185 ( 184 equ; 81 neg)
% Maximal clause size : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_71,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(sk_c10,sk_c12) != sk_c11
| multiply(X3,sk_c10) != sk_c12
| inverse(X3) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| inverse(X4) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| inverse(X5) != sk_c11
| multiply(X6,X7) != sk_c12
| inverse(X6) != X7
| multiply(X7,sk_c11) != sk_c12
| inverse(X8) != X9
| inverse(X9) != X7
| multiply(X8,X7) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_71) ).
cnf(c_0_14,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_15,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_16,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_17,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
prove_this_23 ).
cnf(c_0_19,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
prove_this_1 ).
cnf(c_0_20,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
prove_this_33 ).
cnf(c_0_21,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c11 ),
prove_this_24 ).
cnf(c_0_23,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
prove_this_11 ).
cnf(c_0_24,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
prove_this_2 ).
cnf(c_0_26,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c5) = sk_c11 ),
prove_this_34 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c11,multiply(sk_c2,X1)) = X1
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c4) = sk_c12 ),
prove_this_12 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c12,multiply(sk_c1,X1)) = X1
| multiply(sk_c4,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c12,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c11,multiply(sk_c5,X1)) = X1
| inverse(sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
prove_this_45 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c12,multiply(sk_c4,X1)) = X1
| inverse(sk_c1) = sk_c12 ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c12,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c9
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c9 ),
prove_this_46 ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c1),sk_c11) = sk_c12
| multiply(sk_c12,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c12,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
multiply(sk_c11,sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_45,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c9,sk_c12) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
multiply(sk_c12,sk_c11) = sk_c12,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
identity = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_43]),c_0_15]) ).
cnf(c_0_49,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_50,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_46]),c_0_15]) ).
cnf(c_0_52,negated_conjecture,
sk_c10 = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_47]),c_0_15]),c_0_48]) ).
cnf(c_0_53,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(sk_c10,sk_c12) != sk_c11
| multiply(X3,sk_c10) != sk_c12
| inverse(X3) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| inverse(X4) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| inverse(X5) != sk_c11
| multiply(X6,X7) != sk_c12
| inverse(X6) != X7
| multiply(X7,sk_c11) != sk_c12
| inverse(X8) != X9
| inverse(X9) != X7
| multiply(X8,X7) != X9 ),
prove_this_71 ).
cnf(c_0_55,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_50]),c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c11
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_48]),c_0_52]),c_0_52]) ).
cnf(c_0_57,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c12) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c10) != sk_c12
| multiply(X6,sk_c11) != sk_c10
| multiply(X7,sk_c12) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11
| inverse(X7) != sk_c12 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_54])]) ).
cnf(c_0_59,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
multiply(sk_c11,sk_c11) = sk_c11,
inference(rw,[status(thm)],[c_0_43,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
sk_c11 = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_56]),c_0_15]),c_0_48]),c_0_52])]) ).
cnf(c_0_62,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_48]),c_0_48]) ).
cnf(c_0_63,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c12) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c10) != sk_c12
| multiply(X6,sk_c11) != sk_c10
| multiply(X7,sk_c12) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11
| inverse(X7) != sk_c12
| identity != sk_c12 ),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
multiply(sk_c12,sk_c12) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_61]),c_0_61]) ).
cnf(c_0_65,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_52]),c_0_52]) ).
cnf(c_0_66,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c12) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X3,sk_c12) != sk_c12
| multiply(X4,sk_c12) != sk_c12
| multiply(X5,sk_c12) != sk_c12
| multiply(X6,sk_c12) != sk_c12
| multiply(X7,sk_c12) != sk_c12
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c12
| inverse(X6) != sk_c12
| inverse(X7) != sk_c12 ),
inference(cn,[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)],[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_63,c_0_48]),c_0_61]),c_0_52]),c_0_61]),c_0_64]),c_0_61]),c_0_61]),c_0_52]),c_0_61]),c_0_61]),c_0_52]),c_0_61]),c_0_61]),c_0_52]),c_0_61]),c_0_61]),c_0_61]),c_0_52]),c_0_61]),c_0_61]),c_0_52]),c_0_61])]) ).
cnf(c_0_67,plain,
multiply(X1,sk_c12) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_48]),c_0_52]),c_0_61]) ).
cnf(c_0_68,plain,
inverse(sk_c12) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_61]),c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[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_66,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67])])])])])]),c_0_68])]) ).
cnf(c_0_70,plain,
multiply(X1,inverse(X1)) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_48]),c_0_52]),c_0_61]) ).
cnf(c_0_71,negated_conjecture,
inverse(X1) != sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_68])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_29,c_0_71]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP258-1 : TPTP v9.2.1. Released v2.5.0.
% 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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:29:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.81/1.89 % Version : CSE_E---1.7
% 1.81/1.89 % Problem : theBenchmark.p
% 1.81/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 1.81/1.89 % SZS output start CNFRefutation
% See solution above
% 1.91/1.90 % Total time : 1.369s
%------------------------------------------------------------------------------