%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP214-1 : 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 : n005.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 04:24:50 PM UTC 2026
% Result : Unsatisfiable 1.42s 1.74s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of clauses : 70 ( 24 unt; 32 nHn; 58 RR)
% Number of literals : 162 ( 161 equ; 67 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 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 ( 16 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_3,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_13,negated_conjecture,
( multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X4
| inverse(X3) != sk_c7
| multiply(X5,X4) != sk_c6
| inverse(X5) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
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_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_3 ).
cnf(c_0_16,negated_conjecture,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c5 ),
prove_this_4 ).
cnf(c_0_18,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_7 ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X4
| inverse(X3) != sk_c7
| multiply(X5,X4) != sk_c6
| inverse(X5) != X4 ),
prove_this_13 ).
cnf(c_0_23,negated_conjecture,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
prove_this_8 ).
cnf(c_0_25,negated_conjecture,
( multiply(X1,multiply(X2,sk_c7)) != sk_c6
| inverse(X1) != multiply(X2,sk_c7)
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,X4) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7 ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c5 ),
prove_this_1 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
prove_this_2 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(X1,sk_c5) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c7,X3) != sk_c6
| inverse(X1) != sk_c5
| inverse(X2) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_6 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_15]),c_0_17]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c7 ),
inference(spm,[status(thm)],[c_0_12,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(X1,multiply(X2,sk_c7)) != sk_c6
| inverse(multiply(X1,X2)) != sk_c7
| multiply(sk_c7,X3) != sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_11]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_12,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
identity = sk_c6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_34]),c_0_12])]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(multiply(X1,identity)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_13]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c7,sk_c1) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(multiply(X1,sk_c6)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6 ),
inference(rw,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c3
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(spm,[status(thm)],[c_0_14,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c7,sk_c1) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c7,X1) != sk_c6 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_12]),c_0_37])]),c_0_27]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(spm,[status(thm)],[c_0_14,c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(spm,[status(thm)],[c_0_14,c_0_44]) ).
cnf(c_0_46,plain,
multiply(inverse(X1),X1) = sk_c6,
inference(rw,[status(thm)],[c_0_12,c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(inverse(inverse(sk_c1))),sk_c6) = sk_c7
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(spm,[status(thm)],[c_0_14,c_0_45]) ).
cnf(c_0_48,plain,
multiply(inverse(inverse(X1)),sk_c6) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c7,sk_c1) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,negated_conjecture,
multiply(sk_c7,sk_c1) = sk_c6,
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_51,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_52,negated_conjecture,
multiply(inverse(sk_c7),sk_c6) = sk_c1,
inference(spm,[status(thm)],[c_0_14,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( inverse(identity) != multiply(X1,sk_c7)
| multiply(X1,sk_c7) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c7,X3) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_54,plain,
multiply(inverse(sk_c6),X1) = X1,
inference(rw,[status(thm)],[c_0_51,c_0_37]) ).
cnf(c_0_55,negated_conjecture,
multiply(inverse(inverse(sk_c7)),sk_c1) = sk_c6,
inference(spm,[status(thm)],[c_0_14,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| inverse(identity) != identity
| inverse(X1) != sk_c7
| identity != sk_c6 ),
inference(spm,[status(thm)],[c_0_53,c_0_12]) ).
cnf(c_0_57,plain,
multiply(inverse(inverse(sk_c6)),X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
inverse(sk_c7) = sk_c1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_55]),c_0_48]) ).
cnf(c_0_59,negated_conjecture,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(X1) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_37]),c_0_37]),c_0_37])]) ).
cnf(c_0_60,plain,
inverse(sk_c6) = sk_c6,
inference(spm,[status(thm)],[c_0_46,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
multiply(inverse(sk_c1),sk_c6) = sk_c7,
inference(spm,[status(thm)],[c_0_48,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_63,negated_conjecture,
multiply(inverse(inverse(sk_c1)),sk_c7) = sk_c6,
inference(spm,[status(thm)],[c_0_14,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| inverse(sk_c1) != sk_c7
| inverse(X1) != sk_c7 ),
inference(rw,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
inverse(sk_c1) = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_63]),c_0_48]) ).
cnf(c_0_66,negated_conjecture,
( multiply(X1,sk_c7) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_67,negated_conjecture,
multiply(sk_c1,sk_c7) = sk_c6,
inference(spm,[status(thm)],[c_0_46,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
multiply(sk_c7,X1) != sk_c6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_65])]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_50,c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP214-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.10 % 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
% 0.12/0.30 % Computer : n005.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Mon May 4 18:28:45 EDT 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.31 % start to proof: theBenchmark
% 1.42/1.74 % Version : CSE_E---1.7
% 1.42/1.74 % Problem : theBenchmark.p
% 1.42/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.74 % SZS output start CNFRefutation
% See solution above
% 1.42/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------