%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP354-1 : 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 : n001.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 04:25:41 PM UTC 2026
% Result : Unsatisfiable 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of clauses : 59 ( 24 unt; 26 nHn; 43 RR)
% Number of literals : 161 ( 160 equ; 85 neg)
% Maximal clause size : 14 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 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_9,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,X6) != sk_c8
| inverse(X5) != X6
| multiply(X6,sk_c7) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(c_0_11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_12,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_13,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_14,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
prove_this_9 ).
cnf(c_0_16,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c9 ),
prove_this_10 ).
cnf(c_0_18,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
prove_this_17 ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
prove_this_18 ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
multiply(sk_c9,sk_c8) = sk_c9,
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
identity = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_25]),c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
prove_this_5 ).
cnf(c_0_28,plain,
multiply(inverse(X1),X1) = sk_c8,
inference(rw,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
prove_this_4 ).
cnf(c_0_31,plain,
multiply(inverse(inverse(X1)),sk_c8) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_32,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_35,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( multiply(inverse(sk_c8),sk_c9) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_37,plain,
multiply(inverse(sk_c8),X1) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_38,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_27 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,X6) != sk_c8
| inverse(X5) != X6
| multiply(X6,sk_c7) != sk_c8 ),
prove_this_49 ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
multiply(sk_c9,sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(X5,sk_c9) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c7
| inverse(X5) != sk_c9 ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_48,negated_conjecture,
inverse(sk_c9) = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_44]),c_0_35]) ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(X5,sk_c9) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c7
| inverse(X5) != sk_c9
| sk_c7 != sk_c9 ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
sk_c7 = sk_c9,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(sk_c9) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c7
| inverse(X4) != sk_c9
| sk_c7 != sk_c9 ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_35])]) ).
cnf(c_0_52,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c8,
inference(rw,[status(thm)],[c_0_44,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( multiply(inverse(X1),sk_c9) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_40])]),c_0_50]),c_0_50]),c_0_52]),c_0_50]),c_0_48]),c_0_50]),c_0_50]),c_0_48]),c_0_50]),c_0_50]),c_0_50])]) ).
cnf(c_0_54,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_52])]) ).
cnf(c_0_56,negated_conjecture,
( multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_52]),c_0_48]),c_0_50])]) ).
cnf(c_0_57,negated_conjecture,
( multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_52]),c_0_48]),c_0_50])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_54]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP354-1 : 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
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:38:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------