%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP336-1 : 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 : n020.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 12:43:15 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.48s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of clauses : 95 ( 23 unt; 63 nHn; 79 RR)
% Number of literals : 240 ( 239 equ; 89 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 : 66 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_49,negated_conjecture,
( multiply(X7,sk_c8) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
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_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(c_0_22,negated_conjecture,
( multiply(X7,sk_c8) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(fof_simplification,[status(thm)],[prove_this_49]) ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_24,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_25,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_26,negated_conjecture,
( multiply(X7,sk_c8) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
c_0_22 ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_21 ).
cnf(c_0_29,negated_conjecture,
( inverse(X5) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_36 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_37 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_35 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_6 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(inverse(sk_c5),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_20 ).
cnf(c_0_36,negated_conjecture,
( inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_34 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_33 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(inverse(sk_c6),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_7 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_13 ).
cnf(c_0_46,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_31]) ).
cnf(c_0_47,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_24]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| identity = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
prove_this_39 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_38 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_40 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c5),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_12 ).
cnf(c_0_55,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9
| identity = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c10,sk_c10) != sk_c9
| identity = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_38]) ).
cnf(c_0_58,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_44,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_60,negated_conjecture,
( identity = sk_c9
| multiply(sk_c3,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_30 ).
cnf(c_0_62,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c3),identity) = sk_c2 ),
inference(spm,[status(thm)],[c_0_27,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(inverse(sk_c6),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_31 ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c3),X1) = multiply(sk_c2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_62]),c_0_25]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_27 ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c9
| multiply(sk_c2,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(inverse(sk_c2),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c9
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_69,c_0_32]) ).
cnf(c_0_72,negated_conjecture,
identity = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_70]),c_0_24])]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_71]),c_0_24]) ).
cnf(c_0_74,plain,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_24,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_27,c_0_58]) ).
cnf(c_0_77,plain,
multiply(inverse(inverse(X1)),sk_c9) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_74]) ).
cnf(c_0_78,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( sk_c8 = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_77]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_3 ).
cnf(c_0_82,negated_conjecture,
( sk_c8 = sk_c10
| multiply(sk_c9,X1) = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_79]) ).
cnf(c_0_83,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_77,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
multiply(inverse(inverse(sk_c10)),sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_27,c_0_76]) ).
cnf(c_0_85,negated_conjecture,
( sk_c8 = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_83]),c_0_83]) ).
cnf(c_0_87,negated_conjecture,
multiply(inverse(inverse(inverse(sk_c10))),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_27,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
sk_c8 = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_85]),c_0_76])]) ).
cnf(c_0_89,plain,
multiply(X1,inverse(X1)) = sk_c9,
inference(spm,[status(thm)],[c_0_74,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[c_0_87,c_0_77]) ).
cnf(c_0_91,negated_conjecture,
( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9 ),
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(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_29,c_0_88]),c_0_88]),c_0_88]),c_0_58])]),c_0_78]),c_0_89]),c_0_89]),c_0_83]),c_0_83])])])]),c_0_90])]) ).
cnf(c_0_92,negated_conjecture,
( multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_90]),c_0_58])]) ).
cnf(c_0_93,negated_conjecture,
multiply(inverse(X1),sk_c10) != sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_90]),c_0_58])]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_90]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP336-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:10:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.48 % Version: 3.5.1
% 0.11/0.48 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.11/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.11/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.48 % Starting sh5l with 300s (1) cores
% 0.11/0.48 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1118591 completed with status 0
% 0.11/0.48 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.11/0.48 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.11/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.11/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.48 % No SInE strategy applied
% 0.11/0.48 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.11/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.11/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.48 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.48 % new_bool_1 with pid 1118602 completed with status 0
% 0.11/0.48 % Result found by new_bool_1
% 0.11/0.48 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.11/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.11/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.48 % No SInE strategy applied
% 0.11/0.48 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.11/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.11/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.48 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.48 % Preprocessing time : 0.002 s
% 0.11/0.48 % Presaturation interreduction done
% 0.11/0.48
% 0.11/0.48 % Proof found!
% 0.11/0.48 % SZS status Unsatisfiable
% 0.11/0.48 % SZS output start CNFRefutation
% See solution above
% 0.11/0.48 % Parsed axioms : 52
% 0.11/0.48 % Removed by relevancy pruning/SinE : 0
% 0.11/0.48 % Initial clauses : 52
% 0.11/0.48 % Removed in clause preprocessing : 0
% 0.11/0.48 % Initial clauses in saturation : 52
% 0.11/0.48 % Processed clauses : 516
% 0.11/0.48 % ...of these trivial : 16
% 0.11/0.48 % ...subsumed : 141
% 0.11/0.48 % ...remaining for further processing : 359
% 0.11/0.48 % Other redundant clauses eliminated : 5
% 0.11/0.48 % Clauses deleted for lack of memory : 0
% 0.11/0.48 % Backward-subsumed : 43
% 0.11/0.48 % Backward-rewritten : 177
% 0.11/0.48 % Generated clauses : 1862
% 0.11/0.48 % ...of the previous two non-redundant : 1738
% 0.11/0.48 % ...aggressively subsumed : 0
% 0.11/0.48 % Contextual simplify-reflections : 18
% 0.11/0.48 % Paramodulations : 1857
% 0.11/0.48 % Factorizations : 0
% 0.11/0.48 % NegExts : 0
% 0.11/0.48 % Equation resolutions : 5
% 0.11/0.48 % Disequality decompositions : 0
% 0.11/0.48 % Total rewrite steps : 709
% 0.11/0.48 % ...of those cached : 641
% 0.11/0.48 % Propositional unsat checks : 0
% 0.11/0.48 % Propositional check models : 0
% 0.11/0.48 % Propositional check unsatisfiable : 0
% 0.11/0.48 % Propositional clauses : 0
% 0.11/0.48 % Propositional clauses after purity: 0
% 0.11/0.48 % Propositional unsat core size : 0
% 0.11/0.48 % Propositional preprocessing time : 0.000
% 0.11/0.48 % Propositional encoding time : 0.000
% 0.11/0.48 % Propositional solver time : 0.000
% 0.11/0.48 % Success case prop preproc time : 0.000
% 0.11/0.48 % Success case prop encoding time : 0.000
% 0.11/0.48 % Success case prop solver time : 0.000
% 0.11/0.48 % Current number of processed clauses : 83
% 0.11/0.48 % Positive orientable unit clauses : 15
% 0.11/0.48 % Positive unorientable unit clauses: 0
% 0.11/0.48 % Negative unit clauses : 1
% 0.11/0.48 % Non-unit-clauses : 67
% 0.11/0.48 % Current number of unprocessed clauses: 1059
% 0.11/0.48 % ...number of literals in the above : 3612
% 0.11/0.48 % Current number of archived formulas : 0
% 0.11/0.48 % Current number of archived clauses : 274
% 0.11/0.48 % Clause-clause subsumption calls (NU) : 2929
% 0.11/0.48 % Rec. Clause-clause subsumption calls : 2279
% 0.11/0.48 % Non-unit clause-clause subsumptions : 192
% 0.11/0.48 % Unit Clause-clause subsumption calls : 340
% 0.11/0.48 % Rewrite failures with RHS unbound : 0
% 0.11/0.48 % BW rewrite match attempts : 38
% 0.11/0.48 % BW rewrite match successes : 25
% 0.11/0.48 % Condensation attempts : 0
% 0.11/0.48 % Condensation successes : 0
% 0.11/0.48 % Termbank termtop insertions : 27385
% 0.11/0.48 % Search garbage collected termcells : 39
% 0.11/0.48
% 0.11/0.48 % -------------------------------------------------
% 0.11/0.48 % User time : 0.037 s
% 0.11/0.48 % System time : 0.006 s
% 0.11/0.48 % Total time : 0.043 s
% 0.11/0.48 % Maximum resident set size: 3656 pages
% 0.11/0.48
% 0.11/0.48 % -------------------------------------------------
% 0.11/0.48 % User time : 0.179 s
% 0.11/0.48 % System time : 0.025 s
% 0.11/0.48 % Total time : 0.204 s
% 0.11/0.48 % Maximum resident set size: 4608 pages
% 0.11/0.48 % E exiting
%------------------------------------------------------------------------------