%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:05 PM UTC 2026
% Result : Unsatisfiable 0.59s 0.50s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 21
% Syntax : Number of clauses : 115 ( 35 unt; 65 nHn; 97 RR)
% Number of literals : 288 ( 287 equ; 113 neg)
% Maximal clause size : 13 ( 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 : 75 ( 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_1,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_43,negated_conjecture,
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_24,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
prove_this_1 ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
prove_this_2 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(inverse(sk_c1),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
prove_this_8 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_9 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
prove_this_41 ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ),
inference(fof_simplification,[status(thm)],[prove_this_43]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
prove_this_42 ).
cnf(c_0_39,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
prove_this_35 ).
cnf(c_0_41,negated_conjecture,
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ),
c_0_36 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
prove_this_19 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
identity = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_22]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( inverse(X6) != sk_c10
| inverse(X5) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c10
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c10 ),
prove_this_14 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(inverse(sk_c2),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
prove_this_26 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(inverse(sk_c3),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_51,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(rw,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( inverse(X5) != sk_c10
| inverse(X4) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c10
| inverse(X1) != sk_c8
| multiply(X5,sk_c10) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
prove_this_11 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
prove_this_10 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
prove_this_27 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( sk_c7 = sk_c9
| multiply(inverse(sk_c3),sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( sk_c6 = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( inverse(X4) != sk_c10
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c10) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
prove_this_20 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( sk_c7 = sk_c8
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_51]),c_0_51]) ).
cnf(c_0_64,negated_conjecture,
( sk_c8 = sk_c9
| sk_c7 = sk_c9
| sk_c6 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_51]) ).
cnf(c_0_65,negated_conjecture,
( inverse(X3) != sk_c10
| inverse(X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_33]),c_0_30]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
prove_this_21 ).
cnf(c_0_68,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_44]),c_0_51]) ).
cnf(c_0_69,negated_conjecture,
( sk_c8 = sk_c9
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( inverse(X2) != sk_c10
| inverse(X1) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(spm,[status(thm)],[c_0_65,c_0_47]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( sk_c7 = sk_c9
| sk_c2 = sk_c9
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_51]) ).
cnf(c_0_73,negated_conjecture,
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(sk_c6,sk_c9) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(spm,[status(thm)],[c_0_70,c_0_47]) ).
cnf(c_0_74,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[c_0_71,c_0_51]) ).
cnf(c_0_75,negated_conjecture,
( sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_63,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c6,sk_c9) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_33]),c_0_30]) ).
cnf(c_0_77,negated_conjecture,
( sk_c8 = sk_c9
| sk_c7 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_51])]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c10 ),
prove_this_13 ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c10 ),
prove_this_12 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c6,sk_c8) != sk_c9
| multiply(sk_c6,sk_c9) != sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_51])]) ).
cnf(c_0_81,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_63,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_22,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(rw,[status(thm)],[c_0_79,c_0_51]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c6,sk_c9) != sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_81])]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c10,sk_c1) = sk_c9 ),
inference(rw,[status(thm)],[c_0_82,c_0_44]) ).
cnf(c_0_86,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(rw,[status(thm)],[c_0_83,c_0_81]) ).
cnf(c_0_87,plain,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c1) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_89,negated_conjecture,
multiply(sk_c10,sk_c1) = sk_c9,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_90,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c1,
inference(spm,[status(thm)],[c_0_24,c_0_89]) ).
cnf(c_0_91,negated_conjecture,
multiply(inverse(inverse(sk_c10)),sk_c1) = sk_c9,
inference(spm,[status(thm)],[c_0_24,c_0_90]) ).
cnf(c_0_92,negated_conjecture,
multiply(inverse(sk_c10),X1) = multiply(sk_c1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_90]),c_0_51]) ).
cnf(c_0_93,negated_conjecture,
multiply(inverse(inverse(sk_c10)),multiply(sk_c1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_91]),c_0_51]) ).
cnf(c_0_94,negated_conjecture,
multiply(sk_c1,multiply(sk_c10,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
multiply(inverse(inverse(sk_c10)),X1) = multiply(sk_c10,X1),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_96,negated_conjecture,
multiply(sk_c10,inverse(sk_c10)) = sk_c9,
inference(spm,[status(thm)],[c_0_87,c_0_95]) ).
cnf(c_0_97,negated_conjecture,
multiply(sk_c1,sk_c9) = sk_c1,
inference(rw,[status(thm)],[c_0_90,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
multiply(inverse(inverse(inverse(sk_c10))),sk_c9) = sk_c1,
inference(spm,[status(thm)],[c_0_24,c_0_91]) ).
cnf(c_0_99,negated_conjecture,
inverse(sk_c10) = sk_c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_96]),c_0_92]),c_0_97]) ).
cnf(c_0_100,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_101,negated_conjecture,
multiply(inverse(inverse(sk_c1)),sk_c9) = sk_c1,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_102,negated_conjecture,
multiply(sk_c1,sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_87,c_0_92]) ).
cnf(c_0_103,plain,
multiply(inverse(sk_c9),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_51]) ).
cnf(c_0_104,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_87]),c_0_100]) ).
cnf(c_0_105,negated_conjecture,
multiply(inverse(inverse(sk_c1)),X1) = multiply(sk_c1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_101]),c_0_51]) ).
cnf(c_0_106,negated_conjecture,
multiply(inverse(sk_c1),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_24,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( inverse(X6) != sk_c10
| inverse(X5) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c10
| inverse(X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c9
| multiply(X4,sk_c9) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c9
| multiply(X1,sk_c9) != sk_c9 ),
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_46,c_0_51]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]) ).
cnf(c_0_108,plain,
inverse(sk_c9) = sk_c9,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
multiply(sk_c1,inverse(sk_c1)) = sk_c9,
inference(spm,[status(thm)],[c_0_87,c_0_105]) ).
cnf(c_0_110,negated_conjecture,
multiply(inverse(sk_c1),X1) = multiply(sk_c10,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_106]),c_0_51]) ).
cnf(c_0_111,negated_conjecture,
( inverse(X2) != sk_c10
| inverse(X1) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,sk_c10) != sk_c9 ),
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)],[c_0_107,c_0_104]),c_0_104]),c_0_104]),c_0_104])])])])]),c_0_108])]) ).
cnf(c_0_112,negated_conjecture,
inverse(sk_c1) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_109]),c_0_110]),c_0_39]) ).
cnf(c_0_113,negated_conjecture,
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_102])]) ).
cnf(c_0_114,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_112]),c_0_102])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n010.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 20 20:07:54 UTC 2026
% 0.05/0.38 % CPUTime :
% 0.05/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.42 Running first-order theorem proving
% 0.05/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.50 % Version: 3.5.1
% 0.59/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.59/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.59/0.50 % Starting sh5l with 300s (1) cores
% 0.59/0.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3402841 completed with status 0
% 0.59/0.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.59/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.59/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.50 % No SInE strategy applied
% 0.59/0.50 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.59/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.59/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.59/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.59/0.50 % new_bool_1 with pid 3402852 completed with status 0
% 0.59/0.50 % Result found by new_bool_1
% 0.59/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.59/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.50 % No SInE strategy applied
% 0.59/0.50 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.59/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.59/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.59/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.59/0.50 % Preprocessing time : 0.002 s
% 0.59/0.50 % Presaturation interreduction done
% 0.59/0.50
% 0.59/0.50 % Proof found!
% 0.59/0.50 % SZS status Unsatisfiable
% 0.59/0.50 % SZS output start CNFRefutation
% See solution above
% 0.59/0.51 % Parsed axioms : 46
% 0.59/0.51 % Removed by relevancy pruning/SinE : 0
% 0.59/0.51 % Initial clauses : 46
% 0.59/0.51 % Removed in clause preprocessing : 0
% 0.59/0.51 % Initial clauses in saturation : 46
% 0.59/0.51 % Processed clauses : 789
% 0.59/0.51 % ...of these trivial : 43
% 0.59/0.51 % ...subsumed : 293
% 0.59/0.51 % ...remaining for further processing : 453
% 0.59/0.51 % Other redundant clauses eliminated : 5
% 0.59/0.51 % Clauses deleted for lack of memory : 0
% 0.59/0.51 % Backward-subsumed : 87
% 0.59/0.51 % Backward-rewritten : 263
% 0.59/0.51 % Generated clauses : 2615
% 0.59/0.51 % ...of the previous two non-redundant : 2169
% 0.59/0.51 % ...aggressively subsumed : 0
% 0.59/0.51 % Contextual simplify-reflections : 12
% 0.59/0.51 % Paramodulations : 2610
% 0.59/0.51 % Factorizations : 0
% 0.59/0.51 % NegExts : 0
% 0.59/0.51 % Equation resolutions : 5
% 0.59/0.51 % Disequality decompositions : 0
% 0.59/0.51 % Total rewrite steps : 1664
% 0.59/0.51 % ...of those cached : 1533
% 0.59/0.51 % Propositional unsat checks : 0
% 0.59/0.51 % Propositional check models : 0
% 0.59/0.51 % Propositional check unsatisfiable : 0
% 0.59/0.51 % Propositional clauses : 0
% 0.59/0.51 % Propositional clauses after purity: 0
% 0.59/0.51 % Propositional unsat core size : 0
% 0.59/0.51 % Propositional preprocessing time : 0.000
% 0.59/0.51 % Propositional encoding time : 0.000
% 0.59/0.51 % Propositional solver time : 0.000
% 0.59/0.51 % Success case prop preproc time : 0.000
% 0.59/0.51 % Success case prop encoding time : 0.000
% 0.59/0.51 % Success case prop solver time : 0.000
% 0.59/0.51 % Current number of processed clauses : 56
% 0.59/0.51 % Positive orientable unit clauses : 17
% 0.59/0.51 % Positive unorientable unit clauses: 0
% 0.59/0.51 % Negative unit clauses : 0
% 0.59/0.51 % Non-unit-clauses : 39
% 0.59/0.51 % Current number of unprocessed clauses: 491
% 0.59/0.51 % ...number of literals in the above : 2256
% 0.59/0.51 % Current number of archived formulas : 0
% 0.59/0.51 % Current number of archived clauses : 396
% 0.59/0.51 % Clause-clause subsumption calls (NU) : 5332
% 0.59/0.51 % Rec. Clause-clause subsumption calls : 3669
% 0.59/0.51 % Non-unit clause-clause subsumptions : 338
% 0.59/0.51 % Unit Clause-clause subsumption calls : 446
% 0.59/0.51 % Rewrite failures with RHS unbound : 0
% 0.59/0.51 % BW rewrite match attempts : 90
% 0.59/0.51 % BW rewrite match successes : 58
% 0.59/0.51 % Condensation attempts : 0
% 0.59/0.51 % Condensation successes : 0
% 0.59/0.51 % Termbank termtop insertions : 36765
% 0.59/0.51 % Search garbage collected termcells : 38
% 0.59/0.51
% 0.59/0.51 % -------------------------------------------------
% 0.59/0.51 % User time : 0.058 s
% 0.59/0.51 % System time : 0.003 s
% 0.59/0.51 % Total time : 0.061 s
% 0.59/0.51 % Maximum resident set size: 3656 pages
% 0.59/0.51
% 0.59/0.51 % -------------------------------------------------
% 0.59/0.51 % User time : 0.288 s
% 0.59/0.51 % System time : 0.020 s
% 0.59/0.51 % Total time : 0.308 s
% 0.59/0.51 % Maximum resident set size: 4864 pages
% 0.59/0.51 % E exiting
%------------------------------------------------------------------------------