%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP224-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:39:01 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.57s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 24
% Syntax : Number of clauses : 111 ( 23 unt; 74 nHn; 96 RR)
% Number of literals : 296 ( 295 equ; 117 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 : 87 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_51,negated_conjecture,
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X8,sk_c11) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != X2
| multiply(sk_c11,X2) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_49,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_44,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_47,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
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_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_15 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(inverse(sk_c6),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_14 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(inverse(sk_c1),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_5 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c6,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_c11,sk_c3) = sk_c10 ),
prove_this_26 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
prove_this_31 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(inverse(sk_c6),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_4 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(inverse(sk_c7),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c11,sk_c3) = sk_c10 ),
prove_this_27 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
prove_this_21 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(inverse(sk_c4),sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
prove_this_32 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(inverse(sk_c4),sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
prove_this_22 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c4,multiply(sk_c5,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
multiply(sk_c11,sk_c11) = sk_c10,
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_45]),c_0_25]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c11),sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
multiply(inverse(sk_c11),sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_52]),c_0_25]) ).
cnf(c_0_57,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( sk_c3 = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( sk_c3 = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_56]),c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X8,sk_c11) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != X2
| multiply(sk_c11,X2) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11 ),
inference(fof_simplification,[status(thm)],[prove_this_51]) ).
cnf(c_0_61,negated_conjecture,
( sk_c10 = sk_c11
| multiply(inverse(sk_c2),sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( sk_c10 = sk_c11
| sk_c3 = sk_c11 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X8,sk_c11) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != X2
| multiply(sk_c11,X2) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11 ),
c_0_60 ).
cnf(c_0_64,negated_conjecture,
( sk_c10 = sk_c11
| multiply(inverse(sk_c2),sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
prove_this_41 ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c11 ),
prove_this_46 ).
cnf(c_0_67,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X1) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c10
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_63])])]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c2) = sk_c11 ),
prove_this_49 ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
prove_this_50 ).
cnf(c_0_70,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_50])]) ).
cnf(c_0_71,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_66]),c_0_50])]) ).
cnf(c_0_72,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X1) != sk_c11
| inverse(X4) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c10
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c11 ),
prove_this_44 ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
prove_this_45 ).
cnf(c_0_75,negated_conjecture,
( sk_c10 = sk_c11
| multiply(inverse(sk_c4),sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c11 ),
prove_this_42 ).
cnf(c_0_77,negated_conjecture,
( sk_c10 = sk_c11
| multiply(inverse(sk_c7),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c11 ),
prove_this_47 ).
cnf(c_0_79,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(X1) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c10
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( sk_c10 = sk_c11
| inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( sk_c10 = sk_c11
| inverse(sk_c2) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( inverse(X3) != sk_c11
| multiply(X3,sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X1),sk_c11) != sk_c10
| multiply(sk_c11,multiply(sk_c6,sk_c11)) != sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_79,c_0_73]) ).
cnf(c_0_83,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c5,sk_c11) = sk_c5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_80]),c_0_50])]) ).
cnf(c_0_84,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c8,sk_c10) = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_81]),c_0_50])]) ).
cnf(c_0_85,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X1),sk_c11) != sk_c10
| multiply(sk_c11,multiply(sk_c6,sk_c11)) != sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_73]),c_0_74]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
prove_this_48 ).
cnf(c_0_87,negated_conjecture,
( identity = sk_c11
| sk_c10 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_83]),c_0_25]) ).
cnf(c_0_88,negated_conjecture,
( identity = sk_c10
| sk_c10 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_84]),c_0_25]) ).
cnf(c_0_89,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c11
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(sk_c11,multiply(sk_c6,sk_c11)) != sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_78]),c_0_66]),c_0_86]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
prove_this_43 ).
cnf(c_0_91,negated_conjecture,
sk_c10 = sk_c11,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c11,multiply(sk_c6,sk_c11)) != sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_76]),c_0_65]),c_0_90]) ).
cnf(c_0_93,negated_conjecture,
identity = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_91]),c_0_25]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c11,multiply(sk_c6,sk_c11)) != sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(rw,[status(thm)],[c_0_92,c_0_91]) ).
cnf(c_0_95,plain,
multiply(sk_c11,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c11 ),
inference(rw,[status(thm)],[c_0_74,c_0_91]) ).
cnf(c_0_97,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[c_0_25,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
inverse(sk_c2) = sk_c11,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_99,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_100,negated_conjecture,
sk_c2 = sk_c11,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_95]) ).
cnf(c_0_101,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_102,plain,
multiply(X1,inverse(X1)) = sk_c11,
inference(spm,[status(thm)],[c_0_97,c_0_99]) ).
cnf(c_0_103,negated_conjecture,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[c_0_98,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X3) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| multiply(X6,sk_c11) != sk_c11
| multiply(X5,sk_c11) != sk_c11
| multiply(X4,sk_c11) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c11
| multiply(inverse(X1),sk_c11) != sk_c11 ),
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_67,c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_95]) ).
cnf(c_0_105,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X3) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| multiply(X6,sk_c11) != sk_c11
| multiply(X5,sk_c11) != sk_c11
| multiply(X4,sk_c11) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c11
| multiply(inverse(X1),sk_c11) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_102]),c_0_102])]) ).
cnf(c_0_107,plain,
multiply(X1,sk_c11) = X1,
inference(spm,[status(thm)],[c_0_105,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( inverse(X2) != sk_c11
| inverse(X1) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107]),c_0_107]),c_0_107]),c_0_107]),c_0_107]),c_0_107])])])])]),c_0_103])]) ).
cnf(c_0_109,negated_conjecture,
inverse(X1) != sk_c11,
inference(spm,[status(thm)],[c_0_108,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_103,c_0_109]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP224-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.38 % Computer : n008.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sun Sep 20 20:07:44 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/5.57 % Version: 3.5.1
% 0.16/5.57 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.16/5.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.16/5.57 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.57 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.57 % Starting sh5l with 300s (1) cores
% 0.16/5.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3494470 completed with status 0
% 0.16/5.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.16/5.57 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.16/5.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.16/5.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.57 % No SInE strategy applied
% 0.16/5.57 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.16/5.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.57 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.16/5.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/5.57 % Starting new_bool_3 with 136s (1) cores
% 0.16/5.57 % Starting new_bool_1 with 136s (1) cores
% 0.16/5.57 % new_bool_3 with pid 3494478 completed with status 0
% 0.16/5.57 % Result found by new_bool_3
% 0.16/5.57 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.16/5.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.16/5.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.57 % No SInE strategy applied
% 0.16/5.57 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.16/5.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.57 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.16/5.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/5.57 % Starting new_bool_3 with 136s (1) cores
% 0.16/5.57 % Preprocessing time : 0.002 s
% 0.16/5.57 % Presaturation interreduction done
% 0.16/5.57
% 0.16/5.57 % Proof found!
% 0.16/5.57 % SZS status Unsatisfiable
% 0.16/5.57 % SZS output start CNFRefutation
% See solution above
% 0.16/5.57 % Parsed axioms : 54
% 0.16/5.57 % Removed by relevancy pruning/SinE : 0
% 0.16/5.57 % Initial clauses : 54
% 0.16/5.57 % Removed in clause preprocessing : 0
% 0.16/5.57 % Initial clauses in saturation : 54
% 0.16/5.57 % Processed clauses : 1967
% 0.16/5.57 % ...of these trivial : 72
% 0.16/5.57 % ...subsumed : 1263
% 0.16/5.57 % ...remaining for further processing : 632
% 0.16/5.57 % Other redundant clauses eliminated : 22
% 0.16/5.57 % Clauses deleted for lack of memory : 0
% 0.16/5.57 % Backward-subsumed : 82
% 0.16/5.57 % Backward-rewritten : 389
% 0.16/5.57 % Generated clauses : 5119
% 0.16/5.57 % ...of the previous two non-redundant : 4897
% 0.16/5.57 % ...aggressively subsumed : 0
% 0.16/5.57 % Contextual simplify-reflections : 37
% 0.16/5.57 % Paramodulations : 5086
% 0.16/5.57 % Factorizations : 0
% 0.16/5.57 % NegExts : 0
% 0.16/5.57 % Equation resolutions : 22
% 0.16/5.57 % Disequality decompositions : 0
% 0.16/5.57 % Total rewrite steps : 2520
% 0.16/5.57 % ...of those cached : 2301
% 0.16/5.57 % Propositional unsat checks : 0
% 0.16/5.57 % Propositional check models : 0
% 0.16/5.57 % Propositional check unsatisfiable : 0
% 0.16/5.57 % Propositional clauses : 0
% 0.16/5.57 % Propositional clauses after purity: 0
% 0.16/5.57 % Propositional unsat core size : 0
% 0.16/5.57 % Propositional preprocessing time : 0.000
% 0.16/5.57 % Propositional encoding time : 0.000
% 0.16/5.57 % Propositional solver time : 0.000
% 0.16/5.57 % Success case prop preproc time : 0.000
% 0.16/5.57 % Success case prop encoding time : 0.000
% 0.16/5.57 % Success case prop solver time : 0.000
% 0.16/5.57 % Current number of processed clauses : 93
% 0.16/5.57 % Positive orientable unit clauses : 13
% 0.16/5.57 % Positive unorientable unit clauses: 0
% 0.16/5.57 % Negative unit clauses : 1
% 0.16/5.57 % Non-unit-clauses : 79
% 0.16/5.57 % Current number of unprocessed clauses: 1006
% 0.16/5.57 % ...number of literals in the above : 4546
% 0.16/5.57 % Current number of archived formulas : 0
% 0.16/5.57 % Current number of archived clauses : 538
% 0.16/5.57 % Clause-clause subsumption calls (NU) : 20571
% 0.16/5.57 % Rec. Clause-clause subsumption calls : 17728
% 0.16/5.57 % Non-unit clause-clause subsumptions : 1360
% 0.16/5.57 % Unit Clause-clause subsumption calls : 387
% 0.16/5.57 % Rewrite failures with RHS unbound : 0
% 0.16/5.57 % BW rewrite match attempts : 98
% 0.16/5.57 % BW rewrite match successes : 51
% 0.16/5.57 % Condensation attempts : 0
% 0.16/5.57 % Condensation successes : 0
% 0.16/5.57 % Termbank termtop insertions : 78624
% 0.16/5.57 % Search garbage collected termcells : 44
% 0.16/5.57
% 0.16/5.57 % -------------------------------------------------
% 0.16/5.57 % User time : 0.114 s
% 0.16/5.57 % System time : 0.005 s
% 0.16/5.57 % Total time : 0.120 s
% 0.16/5.57 % Maximum resident set size: 3608 pages
% 0.16/5.57
% 0.16/5.57 % -------------------------------------------------
% 0.16/5.57 % User time : 0.564 s
% 0.16/5.57 % System time : 0.034 s
% 0.16/5.57 % Total time : 0.598 s
% 0.16/5.57 % Maximum resident set size: 4608 pages
% 0.16/5.57 % E exiting
%------------------------------------------------------------------------------