%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP336-1 : 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 04:25:36 PM UTC 2026
% Result : Unsatisfiable 1.42s 1.79s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 20
% Syntax : Number of clauses : 97 ( 23 unt; 67 nHn; 78 RR)
% Number of literals : 249 ( 248 equ; 86 neg)
% Maximal clause size : 14 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 68 ( 3 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_21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c9,sk_c10) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,X3) != sk_c9
| inverse(X2) != X3
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X5) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,X7) != sk_c9
| inverse(X6) != X7
| multiply(X7,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(c_0_20,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_21,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_22,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_23,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
prove_this_21 ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
prove_this_6 ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
prove_this_27 ).
cnf(c_0_27,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c10 ),
prove_this_20 ).
cnf(c_0_29,negated_conjecture,
( multiply(inverse(sk_c6),sk_c9) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| inverse(sk_c6) = sk_c7 ),
prove_this_7 ).
cnf(c_0_31,negated_conjecture,
( multiply(inverse(sk_c2),sk_c9) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
prove_this_35 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c9,sk_c10) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,X3) != sk_c9
| inverse(X2) != X3
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X5) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,X7) != sk_c9
| inverse(X6) != X7
| multiply(X7,sk_c8) != sk_c9 ),
prove_this_49 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
prove_this_13 ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(X1),sk_c8) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_35]),c_0_21]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_36]),c_0_21]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( identity = sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c7 ),
prove_this_15 ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c9 ),
prove_this_14 ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c9 ),
prove_this_16 ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c10 ),
prove_this_12 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c1) = sk_c10
| identity = sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_10 ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_9 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c1) = sk_c10
| identity = sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c10
| inverse(X3) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c1) = sk_c10
| identity = sk_c9
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c10
| inverse(X3) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10
| identity = sk_c9
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_24]),c_0_28]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_17 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_18 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10
| identity = sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c8
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_61,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_23,c_0_54]) ).
cnf(c_0_62,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_24]),c_0_28]) ).
cnf(c_0_64,negated_conjecture,
( identity = sk_c9
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( multiply(inverse(sk_c10),identity) = sk_c1
| multiply(sk_c1,sk_c9) = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c10,sk_c8) = sk_c9 ),
prove_this_3 ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c9,X1) = X1
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_22,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( multiply(inverse(sk_c10),X1) = multiply(sk_c1,X1)
| multiply(sk_c1,sk_c9) = sk_c10
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_65]),c_0_22]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_61,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
sk_c8 = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_69]),c_0_61])]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c1,multiply(sk_c9,X1)) = multiply(sk_c10,X1)
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_20,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c10
| identity = sk_c9 ),
inference(rw,[status(thm)],[c_0_40,c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_54]) ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_74]) ).
cnf(c_0_76,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c10) = sk_c9
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_75]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c4) = identity
| inverse(sk_c1) = sk_c10 ),
inference(spm,[status(thm)],[c_0_21,c_0_50]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c10,sk_c4) = identity
| identity = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_21])]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c10,multiply(sk_c4,X1)) = X1
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_78]),c_0_22]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_51]),c_0_21])]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
identity = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_81]),c_0_21])]) ).
cnf(c_0_83,plain,
multiply(inverse(inverse(X1)),sk_c9) = X1,
inference(rw,[status(thm)],[c_0_62,c_0_82]) ).
cnf(c_0_84,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_82]) ).
cnf(c_0_85,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_83]),c_0_84]) ).
cnf(c_0_86,negated_conjecture,
multiply(inverse(inverse(sk_c10)),sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_23,c_0_61]) ).
cnf(c_0_87,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_83,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
multiply(inverse(inverse(inverse(sk_c10))),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_23,c_0_86]) ).
cnf(c_0_89,plain,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_21,c_0_82]) ).
cnf(c_0_90,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_87]),c_0_87]) ).
cnf(c_0_91,negated_conjecture,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[c_0_88,c_0_83]) ).
cnf(c_0_92,plain,
multiply(X1,inverse(X1)) = sk_c9,
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_71]),c_0_71]),c_0_71]),c_0_54])]),c_0_84]),c_0_87]),c_0_87])])])]),c_0_91])]),c_0_92]),c_0_92])]) ).
cnf(c_0_94,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X2) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_91]),c_0_54])]) ).
cnf(c_0_95,negated_conjecture,
( multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_91]),c_0_54])]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_91]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP336-1 : 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
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 18:32:11 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.42/1.79 % Version : CSE_E---1.7
% 1.42/1.79 % Problem : theBenchmark.p
% 1.42/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.79 % SZS output start CNFRefutation
% See solution above
% 1.42/1.79 % Total time : 1.374s
%------------------------------------------------------------------------------