%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP246-1 : 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 12:39:04 PM UTC 2026
% Result : Unsatisfiable 0.98s 0.58s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 24
% Syntax : Number of clauses : 134 ( 30 unt; 82 nHn; 109 RR)
% Number of literals : 408 ( 407 equ; 200 neg)
% Maximal clause size : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 135 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
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_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
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_29,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
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_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_13,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_41,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_50,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_25,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_26,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_21 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(inverse(sk_c5),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_22 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(inverse(sk_c4),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_2 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,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_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_55]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(inverse(sk_c2),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_30 ).
cnf(c_0_39,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_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
c_0_35 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_10 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( inverse(X7) != sk_c11
| inverse(X6) != sk_c10
| inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| multiply(X7,sk_c11) != sk_c10
| multiply(X6,sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10 ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c10 ),
prove_this_32 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
prove_this_33 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(inverse(sk_c5),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_31 ).
cnf(c_0_49,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X6,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X4,sk_c9) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(inverse(sk_c4),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_11 ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(X3) != sk_c11
| inverse(X2) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_38]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
prove_this_29 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_28 ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
multiply(sk_c11,sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_40,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
identity = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_57]),c_0_25]) ).
cnf(c_0_61,negated_conjecture,
( inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(sk_c6,sk_c9) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_58,c_0_44]) ).
cnf(c_0_62,negated_conjecture,
sk_c9 = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_59]),c_0_25]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_62]),c_0_62]),c_0_45]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_65,negated_conjecture,
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(sk_c5,sk_c10) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_63,c_0_48]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_60]),c_0_62]),c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_68,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_54]),c_0_55]) ).
cnf(c_0_69,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c10,
inference(rw,[status(thm)],[c_0_57,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_48]),c_0_69])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c10
| multiply(sk_c10,multiply(sk_c2,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_70]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c10
| multiply(inverse(sk_c10),X1) = multiply(sk_c2,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c10
| multiply(sk_c2,multiply(sk_c10,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_72]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c10
| multiply(inverse(sk_c2),X1) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_73]) ).
cnf(c_0_75,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_60]),c_0_62]) ).
cnf(c_0_76,negated_conjecture,
( sk_c2 = sk_c10
| multiply(inverse(sk_c2),X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_75]) ).
cnf(c_0_77,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_60]),c_0_62]) ).
cnf(c_0_78,negated_conjecture,
sk_c2 = sk_c10,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[c_0_48,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_14 ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_15 ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c5,X1) = X1
| inverse(sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_79]),c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X6,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X4,sk_c9) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_80]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_13 ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
prove_this_12 ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c10) = sk_c10
| multiply(inverse(sk_c5),X1) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(X3) != sk_c11
| inverse(X2) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c10) = sk_c10
| multiply(inverse(inverse(sk_c5)),X1) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_51]),c_0_41]) ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c10) = sk_c10
| multiply(inverse(sk_c10),X1) = X1 ),
inference(spm,[status(thm)],[c_0_88,c_0_79]) ).
cnf(c_0_91,negated_conjecture,
( inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(sk_c6,sk_c9) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_89,c_0_80]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c10) = sk_c10
| multiply(inverse(inverse(sk_c10)),X1) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_90]) ).
cnf(c_0_93,negated_conjecture,
( inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_62]),c_0_62]),c_0_62]),c_0_81]) ).
cnf(c_0_94,negated_conjecture,
inverse(sk_c10) = sk_c10,
inference(spm,[status(thm)],[c_0_77,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_41 ).
cnf(c_0_96,negated_conjecture,
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_75])]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
prove_this_51 ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_51]),c_0_41]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c11
| multiply(inverse(sk_c6),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
prove_this_50 ).
cnf(c_0_102,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c6) = sk_c9 ),
inference(rw,[status(thm)],[c_0_98,c_0_60]) ).
cnf(c_0_103,negated_conjecture,
inverse(sk_c1) = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_94]),c_0_75])]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c6) = sk_c10 ),
inference(rw,[status(thm)],[c_0_102,c_0_62]) ).
cnf(c_0_106,negated_conjecture,
multiply(sk_c11,sk_c1) = sk_c10,
inference(spm,[status(thm)],[c_0_77,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(inverse(sk_c3),sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c11,sk_c6) = sk_c10 ),
inference(spm,[status(thm)],[c_0_77,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
multiply(inverse(sk_c11),sk_c10) = sk_c1,
inference(spm,[status(thm)],[c_0_27,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(inverse(sk_c3),sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[c_0_107,c_0_62]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_112,negated_conjecture,
( sk_c6 = sk_c1
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_108]),c_0_109]) ).
cnf(c_0_113,negated_conjecture,
multiply(inverse(sk_c11),X1) = multiply(sk_c1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_109]),c_0_75]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( sk_c3 = sk_c1
| sk_c6 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_112]),c_0_109]) ).
cnf(c_0_116,negated_conjecture,
multiply(sk_c1,sk_c10) = sk_c1,
inference(rw,[status(thm)],[c_0_109,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( sk_c1 = sk_c11
| sk_c3 = sk_c1
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_118,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_119,negated_conjecture,
( sk_c1 = sk_c11
| sk_c3 = sk_c1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_117]),c_0_113]),c_0_116])]) ).
cnf(c_0_120,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_121,plain,
multiply(X1,inverse(X1)) = sk_c10,
inference(spm,[status(thm)],[c_0_77,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( sk_c1 = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_119]),c_0_103])]) ).
cnf(c_0_123,negated_conjecture,
( inverse(X7) != sk_c11
| inverse(X6) != sk_c10
| inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| multiply(X7,sk_c11) != sk_c10
| multiply(X6,sk_c10) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_62]),c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_124,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_94]),c_0_75]) ).
cnf(c_0_125,negated_conjecture,
sk_c1 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_122]),c_0_113]),c_0_116])]) ).
cnf(c_0_126,negated_conjecture,
( inverse(X7) != sk_c11
| inverse(X6) != sk_c10
| inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| multiply(X7,sk_c11) != sk_c10
| multiply(X6,sk_c10) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| multiply(inverse(X1),sk_c10) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_121])]) ).
cnf(c_0_127,plain,
multiply(X1,sk_c10) = X1,
inference(spm,[status(thm)],[c_0_124,c_0_77]) ).
cnf(c_0_128,negated_conjecture,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[c_0_103,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( inverse(X2) != sk_c11
| inverse(X1) != sk_c11
| inverse(X3) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c11) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[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)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127])])])])]),c_0_128]),c_0_94])]) ).
cnf(c_0_130,negated_conjecture,
( inverse(X2) != sk_c11
| inverse(X1) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c11) != sk_c10 ),
inference(spm,[status(thm)],[c_0_129,c_0_94]) ).
cnf(c_0_131,negated_conjecture,
multiply(sk_c11,sk_c11) = sk_c10,
inference(rw,[status(thm)],[c_0_106,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_128]),c_0_131])]) ).
cnf(c_0_133,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_128]),c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP246-1 : 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 20:08:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 0.98/0.58 % Version: 3.5.1
% 0.98/0.58 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.98/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.98/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.98/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.98/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.98/0.58 % Starting sh5l with 300s (1) cores
% 0.98/0.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1112022 completed with status 0
% 0.98/0.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.98/0.58 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.98/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.98/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.98/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.98/0.58 % No SInE strategy applied
% 0.98/0.58 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.98/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.98/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.98/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.98/0.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.98/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.98/0.58 % Starting new_bool_1 with 136s (1) cores
% 0.98/0.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1112030 completed with status 0
% 0.98/0.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.98/0.58 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.98/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.98/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.98/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.98/0.58 % No SInE strategy applied
% 0.98/0.58 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.98/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.98/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.98/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.98/0.58 % Preprocessing time : 0.003 s
% 0.98/0.58 % Presaturation interreduction done
% 0.98/0.58
% 0.98/0.58 % Proof found!
% 0.98/0.58 % SZS status Unsatisfiable
% 0.98/0.58 % SZS output start CNFRefutation
% See solution above
% 0.98/0.58 % Parsed axioms : 58
% 0.98/0.58 % Removed by relevancy pruning/SinE : 0
% 0.98/0.58 % Initial clauses : 58
% 0.98/0.58 % Removed in clause preprocessing : 0
% 0.98/0.58 % Initial clauses in saturation : 58
% 0.98/0.58 % Processed clauses : 988
% 0.98/0.58 % ...of these trivial : 40
% 0.98/0.58 % ...subsumed : 406
% 0.98/0.58 % ...remaining for further processing : 542
% 0.98/0.58 % Other redundant clauses eliminated : 7
% 0.98/0.58 % Clauses deleted for lack of memory : 0
% 0.98/0.58 % Backward-subsumed : 61
% 0.98/0.58 % Backward-rewritten : 310
% 0.98/0.58 % Generated clauses : 3715
% 0.98/0.58 % ...of the previous two non-redundant : 2957
% 0.98/0.58 % ...aggressively subsumed : 0
% 0.98/0.58 % Contextual simplify-reflections : 11
% 0.98/0.58 % Paramodulations : 3707
% 0.98/0.58 % Factorizations : 1
% 0.98/0.58 % NegExts : 0
% 0.98/0.58 % Equation resolutions : 7
% 0.98/0.58 % Disequality decompositions : 0
% 0.98/0.58 % Total rewrite steps : 2446
% 0.98/0.58 % ...of those cached : 2312
% 0.98/0.58 % Propositional unsat checks : 0
% 0.98/0.58 % Propositional check models : 0
% 0.98/0.58 % Propositional check unsatisfiable : 0
% 0.98/0.58 % Propositional clauses : 0
% 0.98/0.58 % Propositional clauses after purity: 0
% 0.98/0.58 % Propositional unsat core size : 0
% 0.98/0.58 % Propositional preprocessing time : 0.000
% 0.98/0.58 % Propositional encoding time : 0.000
% 0.98/0.58 % Propositional solver time : 0.000
% 0.98/0.58 % Success case prop preproc time : 0.000
% 0.98/0.58 % Success case prop encoding time : 0.000
% 0.98/0.58 % Success case prop solver time : 0.000
% 0.98/0.58 % Current number of processed clauses : 112
% 0.98/0.58 % Positive orientable unit clauses : 18
% 0.98/0.58 % Positive unorientable unit clauses: 0
% 0.98/0.58 % Negative unit clauses : 0
% 0.98/0.58 % Non-unit-clauses : 94
% 0.98/0.58 % Current number of unprocessed clauses: 962
% 0.98/0.58 % ...number of literals in the above : 3490
% 0.98/0.58 % Current number of archived formulas : 0
% 0.98/0.58 % Current number of archived clauses : 429
% 0.98/0.58 % Clause-clause subsumption calls (NU) : 6103
% 0.98/0.58 % Rec. Clause-clause subsumption calls : 5065
% 0.98/0.58 % Non-unit clause-clause subsumptions : 447
% 0.98/0.58 % Unit Clause-clause subsumption calls : 482
% 0.98/0.58 % Rewrite failures with RHS unbound : 0
% 0.98/0.58 % BW rewrite match attempts : 54
% 0.98/0.58 % BW rewrite match successes : 38
% 0.98/0.58 % Condensation attempts : 0
% 0.98/0.58 % Condensation successes : 0
% 0.98/0.58 % Termbank termtop insertions : 49963
% 0.98/0.58 % Search garbage collected termcells : 44
% 0.98/0.58
% 0.98/0.58 % -------------------------------------------------
% 0.98/0.58 % User time : 0.127 s
% 0.98/0.58 % System time : 0.007 s
% 0.98/0.58 % Total time : 0.134 s
% 0.98/0.58 % Maximum resident set size: 3608 pages
% 0.98/0.58
% 0.98/0.58 % -------------------------------------------------
% 0.98/0.58 % User time : 0.587 s
% 0.98/0.58 % System time : 0.036 s
% 0.98/0.58 % Total time : 0.623 s
% 0.98/0.58 % Maximum resident set size: 4608 pages
% 0.98/0.58 % E exiting
%------------------------------------------------------------------------------