%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP208-1 : 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 : n002.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 12:38:59 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.53s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 24
% Syntax : Number of clauses : 107 ( 25 unt; 70 nHn; 89 RR)
% Number of literals : 278 ( 277 equ; 108 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 : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 87 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_61,negated_conjecture,
( multiply(X10,sk_c12) != sk_c11
| inverse(X10) != sk_c11
| multiply(X9,sk_c12) != sk_c11
| inverse(X8) != X9
| multiply(X8,X9) != sk_c11
| multiply(X7,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != X3
| multiply(sk_c12,X3) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != X2
| multiply(X1,X2) != sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
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_c5,sk_c6) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c7) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c9,sk_c12) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c12
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c12,sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_47,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c10) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c7) = sk_c12
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_55,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(c_0_24,negated_conjecture,
( multiply(X10,sk_c12) != sk_c11
| inverse(X10) != sk_c11
| multiply(X9,sk_c12) != sk_c11
| inverse(X8) != X9
| multiply(X8,X9) != sk_c11
| multiply(X7,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != X3
| multiply(sk_c12,X3) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != X2
| multiply(X1,X2) != sk_c12 ),
inference(fof_simplification,[status(thm)],[prove_this_61]) ).
cnf(c_0_25,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_28,negated_conjecture,
( multiply(X10,sk_c12) != sk_c11
| inverse(X10) != sk_c11
| multiply(X9,sk_c12) != sk_c11
| inverse(X8) != X9
| multiply(X8,X9) != sk_c11
| multiply(X7,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != X3
| multiply(sk_c12,X3) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != X2
| multiply(X1,X2) != sk_c12 ),
c_0_24 ).
cnf(c_0_29,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_1 ).
cnf(c_0_31,negated_conjecture,
( inverse(X1) != sk_c12
| inverse(X6) != sk_c12
| inverse(X5) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| multiply(X5,sk_c12) != sk_c11
| multiply(X4,inverse(X4)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c11
| multiply(inverse(X4),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X2),sk_c12) != sk_c11
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_9 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_10 ).
cnf(c_0_34,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| multiply(inverse(sk_c5),sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_2 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_5 ).
cnf(c_0_38,negated_conjecture,
( inverse(X1) != sk_c12
| inverse(X5) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| multiply(X4,inverse(X4)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c11
| multiply(inverse(X4),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X2),sk_c12) != sk_c11
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c7) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_4 ).
cnf(c_0_40,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c6,sk_c12) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| multiply(inverse(sk_c7),sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(X1) != sk_c12
| multiply(X4,inverse(X4)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c11
| multiply(inverse(X4),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X2),sk_c12) != sk_c11
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_37]) ).
cnf(c_0_44,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( identity = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_26]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X1,inverse(X1)) != sk_c11
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_27]),c_0_45]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_7 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_6 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c9,sk_c12) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_8 ).
cnf(c_0_51,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c12
| multiply(X1,inverse(X1)) != sk_c12
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X1),sk_c11) != sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
prove_this_3 ).
cnf(c_0_53,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c12
| multiply(inverse(X1),sk_c11) != sk_c12
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_30]),c_0_52]) ).
cnf(c_0_54,negated_conjecture,
multiply(sk_c1,sk_c2) = sk_c12,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_36]),c_0_30]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
multiply(inverse(sk_c1),sk_c12) = sk_c2,
inference(spm,[status(thm)],[c_0_29,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c12
| inverse(sk_c1) = sk_c2 ),
prove_this_11 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c12 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c2
| multiply(inverse(sk_c5),sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_29,c_0_57]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
prove_this_12 ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c6,sk_c12) = sk_c6
| multiply(sk_c2,sk_c12) = sk_c2 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
prove_this_36 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c2
| multiply(sk_c6,sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_55,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(inverse(sk_c8),sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c12,sk_c4) = sk_c11 ),
prove_this_37 ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c4 ),
prove_this_46 ).
cnf(c_0_66,negated_conjecture,
( identity = sk_c12
| multiply(sk_c2,sk_c12) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_62]),c_0_26]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
prove_this_40 ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c9
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(inverse(sk_c8),sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c4 ),
prove_this_47 ).
cnf(c_0_72,negated_conjecture,
identity = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_66]),c_0_26])]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(inverse(sk_c10),sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_29,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c10) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
prove_this_39 ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c8,sk_c9) = multiply(sk_c11,sk_c11) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,plain,
multiply(inverse(X1),X1) = sk_c12,
inference(rw,[status(thm)],[c_0_26,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c7) = sk_c12
| inverse(sk_c3) = sk_c12 ),
prove_this_54 ).
cnf(c_0_79,plain,
multiply(sk_c12,X1) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c12
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_61,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( identity = sk_c11
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_76]),c_0_26]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c12 ),
prove_this_55 ).
cnf(c_0_84,negated_conjecture,
( sk_c7 = sk_c12
| inverse(sk_c3) = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_85,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_86,negated_conjecture,
( sk_c11 = sk_c12
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c3),sk_c4) = sk_c12 ),
inference(spm,[status(thm)],[c_0_29,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( sk_c3 = sk_c12
| multiply(sk_c7,sk_c11) = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_83]),c_0_79]) ).
cnf(c_0_89,negated_conjecture,
( sk_c3 = sk_c12
| sk_c7 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_84]),c_0_79]) ).
cnf(c_0_90,plain,
multiply(inverse(inverse(X1)),sk_c12) = X1,
inference(rw,[status(thm)],[c_0_85,c_0_72]) ).
cnf(c_0_91,negated_conjecture,
( sk_c11 = sk_c12
| multiply(inverse(sk_c12),sk_c11) = sk_c4 ),
inference(spm,[status(thm)],[c_0_29,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( sk_c11 = sk_c12
| multiply(inverse(sk_c3),sk_c4) = sk_c12 ),
inference(rw,[status(thm)],[c_0_87,c_0_72]) ).
cnf(c_0_93,negated_conjecture,
( sk_c11 = sk_c12
| sk_c3 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_79]) ).
cnf(c_0_94,plain,
inverse(sk_c12) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_72]),c_0_72]) ).
cnf(c_0_95,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_90]),c_0_79]) ).
cnf(c_0_96,negated_conjecture,
( sk_c11 = sk_c12
| multiply(inverse(inverse(sk_c12)),sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_29,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( sk_c4 = sk_c12
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_79]) ).
cnf(c_0_98,plain,
multiply(X1,sk_c12) = X1,
inference(rw,[status(thm)],[c_0_90,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
sk_c11 = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_90])]) ).
cnf(c_0_100,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_98]),c_0_98]) ).
cnf(c_0_101,negated_conjecture,
( inverse(X4) != sk_c12
| inverse(X6) != sk_c12
| inverse(X5) != sk_c12
| multiply(X6,sk_c12) != sk_c12
| multiply(X5,sk_c12) != sk_c12
| multiply(X4,sk_c12) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X1,inverse(X1)) != sk_c12
| multiply(inverse(X3),sk_c12) != sk_c12
| multiply(inverse(X2),sk_c12) != sk_c12
| multiply(inverse(X1),sk_c12) != sk_c12 ),
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_31,c_0_79]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]) ).
cnf(c_0_102,plain,
multiply(X1,inverse(X1)) = sk_c12,
inference(spm,[status(thm)],[c_0_77,c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( inverse(X3) != sk_c12
| inverse(X2) != sk_c12
| inverse(X1) != sk_c12 ),
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(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)],[inference(rw,[status(thm)],[c_0_101,c_0_98]),c_0_98]),c_0_98]),c_0_98]),c_0_98]),c_0_98])])])]),c_0_94])]),c_0_102]),c_0_102]),c_0_102])]) ).
cnf(c_0_104,negated_conjecture,
( inverse(X2) != sk_c12
| inverse(X1) != sk_c12 ),
inference(spm,[status(thm)],[c_0_103,c_0_94]) ).
cnf(c_0_105,negated_conjecture,
inverse(X1) != sk_c12,
inference(spm,[status(thm)],[c_0_104,c_0_94]) ).
cnf(c_0_106,plain,
$false,
inference(sr,[status(thm)],[c_0_94,c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP208-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.37 % Computer : n002.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Sun Sep 20 20:08:52 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.53 % Version: 3.5.1
% 0.16/5.53 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.16/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.16/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.53 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.53 % Starting sh5l with 300s (1) cores
% 0.16/5.53 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1593864 completed with status 0
% 0.16/5.53 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.16/5.53 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.16/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.16/5.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.53 % No SInE strategy applied
% 0.16/5.53 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.16/5.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.53 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.16/5.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/5.53 % Starting new_bool_3 with 136s (1) cores
% 0.16/5.53 % Starting new_bool_1 with 136s (1) cores
% 0.16/5.53 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1593869 completed with status 0
% 0.16/5.53 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.16/5.53 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.16/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.16/5.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.53 % No SInE strategy applied
% 0.16/5.53 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.16/5.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.53 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.16/5.53 % Preprocessing time : 0.001 s
% 0.16/5.53 % Presaturation interreduction done
% 0.16/5.53
% 0.16/5.53 % Proof found!
% 0.16/5.53 % SZS status Unsatisfiable
% 0.16/5.53 % SZS output start CNFRefutation
% See solution above
% 0.16/5.53 % Parsed axioms : 64
% 0.16/5.53 % Removed by relevancy pruning/SinE : 0
% 0.16/5.53 % Initial clauses : 64
% 0.16/5.53 % Removed in clause preprocessing : 0
% 0.16/5.53 % Initial clauses in saturation : 64
% 0.16/5.53 % Processed clauses : 2433
% 0.16/5.53 % ...of these trivial : 110
% 0.16/5.53 % ...subsumed : 1440
% 0.16/5.53 % ...remaining for further processing : 883
% 0.16/5.53 % Other redundant clauses eliminated : 62
% 0.16/5.53 % Clauses deleted for lack of memory : 0
% 0.16/5.53 % Backward-subsumed : 133
% 0.16/5.53 % Backward-rewritten : 667
% 0.16/5.53 % Generated clauses : 6441
% 0.16/5.53 % ...of the previous two non-redundant : 6041
% 0.16/5.53 % ...aggressively subsumed : 0
% 0.16/5.53 % Contextual simplify-reflections : 43
% 0.16/5.53 % Paramodulations : 6382
% 0.16/5.53 % Factorizations : 0
% 0.16/5.53 % NegExts : 0
% 0.16/5.53 % Equation resolutions : 62
% 0.16/5.53 % Disequality decompositions : 0
% 0.16/5.53 % Total rewrite steps : 4290
% 0.16/5.53 % ...of those cached : 4148
% 0.16/5.53 % Propositional unsat checks : 0
% 0.16/5.53 % Propositional check models : 0
% 0.16/5.53 % Propositional check unsatisfiable : 0
% 0.16/5.53 % Propositional clauses : 0
% 0.16/5.53 % Propositional clauses after purity: 0
% 0.16/5.53 % Propositional unsat core size : 0
% 0.16/5.53 % Propositional preprocessing time : 0.000
% 0.16/5.53 % Propositional encoding time : 0.000
% 0.16/5.53 % Propositional solver time : 0.000
% 0.16/5.53 % Success case prop preproc time : 0.000
% 0.16/5.53 % Success case prop encoding time : 0.000
% 0.16/5.53 % Success case prop solver time : 0.000
% 0.16/5.53 % Current number of processed clauses : 16
% 0.16/5.53 % Positive orientable unit clauses : 15
% 0.16/5.53 % Positive unorientable unit clauses: 0
% 0.16/5.53 % Negative unit clauses : 1
% 0.16/5.53 % Non-unit-clauses : 0
% 0.16/5.53 % Current number of unprocessed clauses: 1256
% 0.16/5.53 % ...number of literals in the above : 7712
% 0.16/5.53 % Current number of archived formulas : 0
% 0.16/5.53 % Current number of archived clauses : 865
% 0.16/5.53 % Clause-clause subsumption calls (NU) : 24114
% 0.16/5.53 % Rec. Clause-clause subsumption calls : 11288
% 0.16/5.53 % Non-unit clause-clause subsumptions : 1571
% 0.16/5.53 % Unit Clause-clause subsumption calls : 1112
% 0.16/5.53 % Rewrite failures with RHS unbound : 0
% 0.16/5.53 % BW rewrite match attempts : 107
% 0.16/5.53 % BW rewrite match successes : 60
% 0.16/5.53 % Condensation attempts : 0
% 0.16/5.53 % Condensation successes : 0
% 0.16/5.53 % Termbank termtop insertions : 94679
% 0.16/5.53 % Search garbage collected termcells : 47
% 0.16/5.53
% 0.16/5.53 % -------------------------------------------------
% 0.16/5.53 % User time : 0.091 s
% 0.16/5.53 % System time : 0.003 s
% 0.16/5.53 % Total time : 0.094 s
% 0.16/5.53 % Maximum resident set size: 3664 pages
% 0.16/5.53
% 0.16/5.53 % -------------------------------------------------
% 0.16/5.53 % User time : 0.443 s
% 0.16/5.53 % System time : 0.028 s
% 0.16/5.53 % Total time : 0.471 s
% 0.16/5.53 % Maximum resident set size: 4608 pages
% 0.16/5.53 % E exiting
%------------------------------------------------------------------------------