%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP373-1 : 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 : 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 04:25:58 PM UTC 2026
% Result : Unsatisfiable 1.90s 1.91s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of clauses : 73 ( 19 unt; 48 nHn; 60 RR)
% Number of literals : 181 ( 180 equ; 65 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 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_11,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_61,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(c_0_15,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_16,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_17,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_18,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_19,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_20,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_22,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_21 ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_33 ).
cnf(c_0_27,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_22 ).
cnf(c_0_29,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_34 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_4 ).
cnf(c_0_34,negated_conjecture,
multiply(sk_c11,sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_16]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c10,sk_c4) = identity
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
identity = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_34]),c_0_16]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_23 ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c9
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_16,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c9
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c4 = sk_c10 ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c11,sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( sk_c4 = sk_c10
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_41])]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_35 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c11,sk_c1) = sk_c10
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41])]) ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_36 ).
cnf(c_0_51,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c1
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_18,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_3 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c9 = sk_c10
| sk_c1 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_41]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_53]),c_0_16]) ).
cnf(c_0_56,negated_conjecture,
( sk_c9 = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_43,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( sk_c1 = sk_c10
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_41])]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| sk_c10 = sk_c11 ),
inference(rw,[status(thm)],[c_0_55,c_0_37]) ).
cnf(c_0_59,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
sk_c10 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_34])]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
prove_this_61 ).
cnf(c_0_62,plain,
multiply(sk_c11,X1) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_63,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_37]),c_0_60]) ).
cnf(c_0_64,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_65,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c9
| inverse(X6) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_61])]) ).
cnf(c_0_66,plain,
multiply(inverse(sk_c11),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_62]) ).
cnf(c_0_67,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_63]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c11) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| multiply(X4,sk_c11) != sk_c11
| multiply(X5,sk_c11) != sk_c11
| multiply(X6,sk_c11) != sk_c11
| inverse(sk_c11) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11
| inverse(X5) != sk_c11
| inverse(X6) != sk_c11 ),
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)],[c_0_65,c_0_59]),c_0_34]),c_0_59]),c_0_59]),c_0_59]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60])]) ).
cnf(c_0_69,plain,
inverse(sk_c11) = sk_c11,
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| inverse(X2) != sk_c11 ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67])])])])]),c_0_69])]) ).
cnf(c_0_71,negated_conjecture,
( inverse(X1) != sk_c11
| inverse(X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_69]),c_0_67]),c_0_67]),c_0_62])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_71,c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP373-1 : 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 : n013.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 18:33:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.90/1.91 % Version : CSE_E---1.7
% 1.90/1.91 % Problem : theBenchmark.p
% 1.90/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.90/1.91 % SZS output start CNFRefutation
% See solution above
% 1.90/1.91 % Total time : 1.371s
%------------------------------------------------------------------------------