%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP389-1 : 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 : n014.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 12:43:31 PM UTC 2026
% Result : Unsatisfiable 5.05s 1.15s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 27
% Syntax : Number of clauses : 147 ( 25 unt; 110 nHn; 129 RR)
% Number of literals : 372 ( 371 equ; 116 neg)
% Maximal clause size : 15 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 84 ( 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_24,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_40,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_55,negated_conjecture,
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X2) != X3
| multiply(X2,X3) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_41,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_44,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_24 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(inverse(sk_c6),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_23 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
prove_this_34 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(inverse(sk_c1),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_15 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(inverse(sk_c7),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(inverse(inverse(sk_c7)),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c10 ),
prove_this_35 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(inverse(sk_c6),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_14 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_25 ).
cnf(c_0_45,negated_conjecture,
( identity = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_28]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c3 ),
prove_this_38 ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_40 ).
cnf(c_0_49,negated_conjecture,
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X2) != X3
| multiply(X2,X3) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(fof_simplification,[status(thm)],[prove_this_55]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(inverse(sk_c7),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c2),sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c11,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
multiply(sk_c11,sk_c11) = sk_c10,
inference(spm,[status(thm)],[c_0_36,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X2) != X3
| multiply(X2,X3) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| inverse(sk_c10) != sk_c9 ),
c_0_49 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(inverse(inverse(sk_c7)),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_26 ).
cnf(c_0_58,negated_conjecture,
( identity = sk_c10
| multiply(sk_c3,sk_c10) = sk_c3
| multiply(sk_c11,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_60,negated_conjecture,
multiply(inverse(sk_c11),sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c10
| multiply(sk_c3,sk_c10) = sk_c3
| multiply(sk_c10,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_51,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(X3) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(X6,sk_c10) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_55])]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c3 ),
prove_this_41 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c3 ),
prove_this_42 ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_28]) ).
cnf(c_0_66,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c4) = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_58]),c_0_28])]) ).
cnf(c_0_67,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_59]) ).
cnf(c_0_68,negated_conjecture,
multiply(inverse(sk_c11),multiply(sk_c10,X1)) = multiply(sk_c11,X1),
inference(spm,[status(thm)],[c_0_27,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c5) = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_61]),c_0_28])]) ).
cnf(c_0_70,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_39 ).
cnf(c_0_72,negated_conjecture,
( identity = sk_c10
| multiply(sk_c1,multiply(sk_c10,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c10
| inverse(sk_c11) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_66]),c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( identity = sk_c10
| inverse(sk_c11) = multiply(sk_c11,sk_c5) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(X3) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_48]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_37 ).
cnf(c_0_77,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_67]),c_0_67]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c10) = sk_c9 ),
prove_this_5 ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c10) = sk_c9 ),
prove_this_2 ).
cnf(c_0_80,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c5) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_69]),c_0_67]) ).
cnf(c_0_81,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( inverse(X3) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_46]),c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( inverse(sk_c11) = sk_c6
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c11) = sk_c4
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_77,c_0_79]) ).
cnf(c_0_85,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_67]) ).
cnf(c_0_86,negated_conjecture,
( sk_c4 = sk_c1
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c9 ),
prove_this_4 ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c10) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_63]),c_0_64]) ).
cnf(c_0_89,negated_conjecture,
( sk_c6 = sk_c4
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
prove_this_3 ).
cnf(c_0_91,negated_conjecture,
( sk_c4 = sk_c1
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c10) = sk_c5
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_77,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| sk_c6 = sk_c4
| inverse(sk_c2) = sk_c3 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
prove_this_44 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_43 ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_45 ).
cnf(c_0_97,negated_conjecture,
( sk_c9 = sk_c10
| sk_c4 = sk_c1
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( sk_c9 = sk_c10
| sk_c5 = sk_c10
| sk_c4 = sk_c1 ),
inference(spm,[status(thm)],[c_0_92,c_0_91]) ).
cnf(c_0_99,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| sk_c6 = sk_c4
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_11 ).
cnf(c_0_101,negated_conjecture,
( sk_c4 = sk_c1
| multiply(sk_c10,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_91]) ).
cnf(c_0_102,negated_conjecture,
( sk_c4 = sk_c1
| sk_c9 = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( sk_c6 = sk_c4
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_94]),c_0_95]),c_0_96]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
( identity = sk_c9
| sk_c4 = sk_c1
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( identity = sk_c10
| multiply(sk_c3,sk_c10) = sk_c3
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_51,c_0_76]) ).
cnf(c_0_107,negated_conjecture,
( identity = sk_c10
| multiply(sk_c4,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_73]) ).
cnf(c_0_108,negated_conjecture,
( sk_c6 = sk_c4
| inverse(sk_c3) = sk_c2 ),
inference(spm,[status(thm)],[c_0_77,c_0_103]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c11,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( sk_c9 = sk_c10
| sk_c4 = sk_c1 ),
inference(spm,[status(thm)],[c_0_86,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( identity = sk_c10
| multiply(sk_c3,sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( sk_c6 = sk_c4
| multiply(sk_c2,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
identity = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_111]),c_0_28])]) ).
cnf(c_0_115,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c11,sk_c1) = sk_c10 ),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c10) = sk_c9 ),
prove_this_6 ).
cnf(c_0_118,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_114]),c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( sk_c6 = sk_c4
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_85,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_100,c_0_110]) ).
cnf(c_0_121,negated_conjecture,
( sk_c1 = sk_c11
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_116]),c_0_60]) ).
cnf(c_0_122,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( sk_c9 = sk_c10
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_89,c_0_119]) ).
cnf(c_0_124,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c11) = sk_c4 ),
inference(rw,[status(thm)],[c_0_84,c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
multiply(sk_c11,multiply(sk_c11,X1)) = multiply(sk_c10,X1),
inference(spm,[status(thm)],[c_0_27,c_0_53]) ).
cnf(c_0_127,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c4,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( sk_c4 = sk_c11
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
multiply(sk_c11,sk_c10) = multiply(sk_c10,sk_c11),
inference(spm,[status(thm)],[c_0_126,c_0_53]) ).
cnf(c_0_130,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c10) = sk_c5 ),
inference(rw,[status(thm)],[c_0_92,c_0_118]) ).
cnf(c_0_131,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_132,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c11) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_90,c_0_118]) ).
cnf(c_0_134,negated_conjecture,
( sk_c5 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_118,c_0_130]) ).
cnf(c_0_135,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_68]),c_0_126]) ).
cnf(c_0_136,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_137,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_67,c_0_114]) ).
cnf(c_0_138,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[c_0_28,c_0_114]) ).
cnf(c_0_139,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_77])]),c_0_60])]) ).
cnf(c_0_140,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_141,negated_conjecture,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[c_0_60,c_0_137]) ).
cnf(c_0_142,plain,
multiply(X1,inverse(X1)) = sk_c10,
inference(spm,[status(thm)],[c_0_138,c_0_77]) ).
cnf(c_0_143,negated_conjecture,
( inverse(X1) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,sk_c11) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[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(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_139,c_0_118]),c_0_140]),c_0_137]),c_0_140]),c_0_137]),c_0_137]),c_0_140]),c_0_137]),c_0_140])])])]),c_0_118]),c_0_141])]),c_0_142]),c_0_142])]) ).
cnf(c_0_144,negated_conjecture,
( inverse(X1) != sk_c11
| inverse(X2) != sk_c10
| multiply(X1,sk_c11) != sk_c10 ),
inference(spm,[status(thm)],[c_0_143,c_0_118]) ).
cnf(c_0_145,negated_conjecture,
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
inference(spm,[status(thm)],[c_0_144,c_0_118]) ).
cnf(c_0_146,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_141]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP389-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:10:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 5.05/1.15 % Version: 3.5.1
% 5.05/1.15 % Preprocessing class: FSMSSMSMSSSNFFN.
% 5.05/1.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.05/1.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 5.05/1.15 % Starting new_bool_3 with 300s (1) cores
% 5.05/1.15 % Starting new_bool_1 with 300s (1) cores
% 5.05/1.15 % Starting sh5l with 300s (1) cores
% 5.05/1.15 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2250133 completed with status 0
% 5.05/1.15 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 5.05/1.15 % Preprocessing class: FSMSSMSMSSSNFFN.
% 5.05/1.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.05/1.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 5.05/1.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.05/1.15 % No SInE strategy applied
% 5.05/1.15 % Search class: FGHPS-FFMM21-SFFFFFNN
% 5.05/1.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.05/1.15 % Starting SubtermCWHack with 136s (1) cores
% 5.05/1.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 5.05/1.15 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.05/1.15 % Starting new_bool_3 with 136s (1) cores
% 5.05/1.15 % Starting new_bool_1 with 136s (1) cores
% 5.05/1.15 % new_bool_3 with pid 2250141 completed with status 0
% 5.05/1.15 % Result found by new_bool_3
% 5.05/1.15 % Preprocessing class: FSMSSMSMSSSNFFN.
% 5.05/1.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.05/1.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 5.05/1.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.05/1.15 % No SInE strategy applied
% 5.05/1.15 % Search class: FGHPS-FFMM21-SFFFFFNN
% 5.05/1.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.05/1.15 % Starting SubtermCWHack with 136s (1) cores
% 5.05/1.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 5.05/1.15 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.05/1.15 % Starting new_bool_3 with 136s (1) cores
% 5.05/1.15 % Preprocessing time : 0.002 s
% 5.05/1.15 % Presaturation interreduction done
% 5.05/1.15
% 5.05/1.15 % Proof found!
% 5.05/1.15 % SZS status Unsatisfiable
% 5.05/1.15 % SZS output start CNFRefutation
% See solution above
% 5.05/1.15 % Parsed axioms : 58
% 5.05/1.15 % Removed by relevancy pruning/SinE : 0
% 5.05/1.15 % Initial clauses : 58
% 5.05/1.15 % Removed in clause preprocessing : 0
% 5.05/1.15 % Initial clauses in saturation : 58
% 5.05/1.15 % Processed clauses : 10209
% 5.05/1.15 % ...of these trivial : 283
% 5.05/1.15 % ...subsumed : 8180
% 5.05/1.15 % ...remaining for further processing : 1746
% 5.05/1.15 % Other redundant clauses eliminated : 48
% 5.05/1.15 % Clauses deleted for lack of memory : 0
% 5.05/1.15 % Backward-subsumed : 136
% 5.05/1.15 % Backward-rewritten : 1471
% 5.05/1.15 % Generated clauses : 42100
% 5.05/1.15 % ...of the previous two non-redundant : 40889
% 5.05/1.15 % ...aggressively subsumed : 0
% 5.05/1.15 % Contextual simplify-reflections : 58
% 5.05/1.15 % Paramodulations : 42052
% 5.05/1.15 % Factorizations : 6
% 5.05/1.15 % NegExts : 0
% 5.05/1.15 % Equation resolutions : 48
% 5.05/1.15 % Disequality decompositions : 0
% 5.05/1.15 % Total rewrite steps : 12455
% 5.05/1.15 % ...of those cached : 11897
% 5.05/1.15 % Propositional unsat checks : 0
% 5.05/1.15 % Propositional check models : 0
% 5.05/1.15 % Propositional check unsatisfiable : 0
% 5.05/1.15 % Propositional clauses : 0
% 5.05/1.15 % Propositional clauses after purity: 0
% 5.05/1.15 % Propositional unsat core size : 0
% 5.05/1.15 % Propositional preprocessing time : 0.000
% 5.05/1.15 % Propositional encoding time : 0.000
% 5.05/1.15 % Propositional solver time : 0.000
% 5.05/1.15 % Success case prop preproc time : 0.000
% 5.05/1.15 % Success case prop encoding time : 0.000
% 5.05/1.15 % Success case prop solver time : 0.000
% 5.05/1.15 % Current number of processed clauses : 62
% 5.05/1.15 % Positive orientable unit clauses : 16
% 5.05/1.15 % Positive unorientable unit clauses: 0
% 5.05/1.15 % Negative unit clauses : 0
% 5.05/1.15 % Non-unit-clauses : 46
% 5.05/1.15 % Current number of unprocessed clauses: 26142
% 5.05/1.15 % ...number of literals in the above : 103695
% 5.05/1.15 % Current number of archived formulas : 0
% 5.05/1.15 % Current number of archived clauses : 1665
% 5.05/1.15 % Clause-clause subsumption calls (NU) : 142578
% 5.05/1.15 % Rec. Clause-clause subsumption calls : 101927
% 5.05/1.15 % Non-unit clause-clause subsumptions : 8359
% 5.05/1.15 % Unit Clause-clause subsumption calls : 1581
% 5.05/1.15 % Rewrite failures with RHS unbound : 0
% 5.05/1.15 % BW rewrite match attempts : 100
% 5.05/1.15 % BW rewrite match successes : 75
% 5.05/1.15 % Condensation attempts : 0
% 5.05/1.15 % Condensation successes : 0
% 5.05/1.15 % Termbank termtop insertions : 508506
% 5.05/1.15 % Search garbage collected termcells : 43
% 5.05/1.15
% 5.05/1.15 % -------------------------------------------------
% 5.05/1.15 % User time : 0.667 s
% 5.05/1.15 % System time : 0.026 s
% 5.05/1.15 % Total time : 0.694 s
% 5.05/1.15 % Maximum resident set size: 3660 pages
% 5.05/1.15
% 5.05/1.15 % -------------------------------------------------
% 5.05/1.15 % User time : 3.263 s
% 5.05/1.15 % System time : 0.163 s
% 5.05/1.15 % Total time : 3.426 s
% 5.05/1.15 % Maximum resident set size: 4608 pages
% 5.05/1.15 % E exiting
%------------------------------------------------------------------------------