%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP282-1 : 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 : 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 12:39:10 PM UTC 2026
% Result : Unsatisfiable 2.24s 0.77s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 41
% Syntax : Number of clauses : 242 ( 25 unt; 208 nHn; 217 RR)
% Number of literals : 560 ( 559 equ; 98 neg)
% Maximal clause size : 14 ( 2 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 : 74 ( 1 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_47,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_43,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_44,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_49,negated_conjecture,
( multiply(X6,sk_c9) != sk_c7
| inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| multiply(X4,sk_c7) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(c_0_41,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_42,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_43,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_44,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_45,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_46,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_44]) ).
cnf(c_0_47,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c9 ),
prove_this_47 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
prove_this_23 ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
prove_this_43 ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
prove_this_19 ).
cnf(c_0_52,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_20 ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_44 ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(inverse(sk_c9),identity) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(inverse(sk_c9),identity) = sk_c1 ),
inference(spm,[status(thm)],[c_0_45,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c9) = sk_c4
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
prove_this_46 ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
prove_this_22 ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c6,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_52,c_0_54]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c6,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c9) = sk_c4
| inverse(sk_c2) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c6,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_6 ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_45 ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_21 ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c9) = sk_c2
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( sk_c4 = sk_c7
| sk_c2 = sk_c1
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c6) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_69]),c_0_47]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_7 ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c4,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( sk_c4 = sk_c1
| sk_c2 = sk_c1
| sk_c4 = sk_c7 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( sk_c1 = sk_c7
| sk_c2 = sk_c1
| sk_c4 = sk_c7 ),
inference(spm,[status(thm)],[c_0_65,c_0_74]) ).
cnf(c_0_83,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_84,negated_conjecture,
( sk_c2 = sk_c1
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_75]) ).
cnf(c_0_85,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_52,c_0_76]) ).
cnf(c_0_86,negated_conjecture,
( multiply(X6,sk_c9) != sk_c7
| inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| multiply(X4,sk_c7) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_49]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_42 ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_18 ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
prove_this_41 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
prove_this_17 ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_3 ).
cnf(c_0_93,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c4,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_94,negated_conjecture,
( sk_c4 = sk_c7
| sk_c2 = sk_c1 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_81]),c_0_82]) ).
cnf(c_0_95,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_83]) ).
cnf(c_0_96,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_97,negated_conjecture,
( multiply(X6,sk_c9) != sk_c7
| inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| multiply(X4,sk_c7) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
c_0_86 ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_87]) ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_88]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_89]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_90]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c6,multiply(sk_c7,X1)) = multiply(sk_c6,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_91]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c7,sk_c9) = identity
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_92]) ).
cnf(c_0_104,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c7,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_105,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_42,c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( identity = sk_c7
| sk_c2 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_96]),c_0_42]) ).
cnf(c_0_107,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c7) != sk_c9
| multiply(X2,inverse(X2)) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(inverse(X2),sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_97])]) ).
cnf(c_0_108,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_109,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_8 ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_47]) ).
cnf(c_0_112,negated_conjecture,
( sk_c2 = sk_c1
| multiply(inverse(sk_c7),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_104]) ).
cnf(c_0_113,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c7) != sk_c9
| multiply(X2,inverse(X2)) != sk_c7
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(inverse(X2),sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| sk_c2 = sk_c1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_65]),c_0_108]),c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_65]) ).
cnf(c_0_118,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c7) != sk_c9
| multiply(X2,inverse(X2)) != sk_c7
| multiply(inverse(X2),sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| sk_c2 = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( identity = sk_c9
| sk_c2 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_116]),c_0_42]) ).
cnf(c_0_120,negated_conjecture,
( sk_c7 = sk_c9
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_117,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X2,inverse(X2)) != sk_c7
| multiply(inverse(X2),sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| sk_c6 = sk_c7
| sk_c2 = sk_c1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_105]),c_0_43]),c_0_119]),c_0_120]) ).
cnf(c_0_122,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_105,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( sk_c6 = sk_c7
| multiply(inverse(sk_c9),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_115]) ).
cnf(c_0_124,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(inverse(X1),sk_c9) != sk_c7
| sk_c2 = sk_c1
| sk_c6 = sk_c7 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_105]),c_0_43]),c_0_119]) ).
cnf(c_0_125,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c9,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c7,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_113]) ).
cnf(c_0_127,negated_conjecture,
( sk_c6 = sk_c7
| sk_c2 = sk_c1
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_123,c_0_65]) ).
cnf(c_0_128,negated_conjecture,
( identity != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c9) != sk_c7
| sk_c6 = sk_c7
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( identity = sk_c8
| sk_c2 = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_30 ).
cnf(c_0_131,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c9) != sk_c7
| sk_c2 = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_31 ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_35 ).
cnf(c_0_135,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c9) != sk_c7
| sk_c6 = sk_c7
| sk_c2 = sk_c1 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_52])]),c_0_42]),c_0_129]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_27 ).
cnf(c_0_138,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_11 ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c7,sk_c9) = identity
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_42,c_0_134]) ).
cnf(c_0_140,negated_conjecture,
( sk_c2 = sk_c1
| sk_c6 = sk_c7 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_105]),c_0_43]),c_0_43]),c_0_106]),c_0_120]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_38 ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c6,multiply(sk_c7,X1)) = multiply(sk_c6,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_136]) ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c7,sk_c9) = identity
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c7,sk_c9) = identity
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c1,sk_c9) = sk_c3
| multiply(sk_c7,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_14 ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_141]) ).
cnf(c_0_148,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_39 ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_32 ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_47]) ).
cnf(c_0_151,negated_conjecture,
( sk_c3 = sk_c8
| sk_c6 = sk_c7
| multiply(sk_c7,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_146]) ).
cnf(c_0_153,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_15 ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_155,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_156,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c8
| inverse(sk_c7) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_151]),c_0_47]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c1,sk_c9) = sk_c3
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_154,c_0_140]) ).
cnf(c_0_159,negated_conjecture,
( sk_c6 = sk_c7
| multiply(inverse(sk_c9),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_44,c_0_155]) ).
cnf(c_0_160,negated_conjecture,
( sk_c3 = sk_c8
| sk_c6 = sk_c7
| inverse(sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_156]) ).
cnf(c_0_161,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_162,negated_conjecture,
( sk_c3 = sk_c8
| sk_c6 = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_16 ).
cnf(c_0_164,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c8
| multiply(sk_c7,sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_165,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c8
| multiply(sk_c7,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_44]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_40 ).
cnf(c_0_167,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_163]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
prove_this_24 ).
cnf(c_0_169,negated_conjecture,
( sk_c3 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,multiply(sk_c6,X1)) = multiply(sk_c7,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_130]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_149]) ).
cnf(c_0_172,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_133]) ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(inverse(sk_c2),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_166]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
prove_this_48 ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_176,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c9,sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_155,c_0_169]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c7) = multiply(sk_c7,sk_c9) ),
inference(spm,[status(thm)],[c_0_170,c_0_149]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_175]) ).
cnf(c_0_181,negated_conjecture,
( sk_c8 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_115,c_0_176]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_179]) ).
cnf(c_0_184,negated_conjecture,
( identity = sk_c9
| sk_c8 = sk_c7
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_42]) ).
cnf(c_0_185,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_143,c_0_182]) ).
cnf(c_0_186,negated_conjecture,
( identity = sk_c9
| sk_c8 = sk_c7
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_181]),c_0_42]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_2 ).
cnf(c_0_188,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c7
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_184]),c_0_42]) ).
cnf(c_0_189,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c9
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_5 ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_9 ).
cnf(c_0_192,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c8,multiply(sk_c7,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_187]) ).
cnf(c_0_193,negated_conjecture,
( identity = sk_c9
| sk_c8 = sk_c7 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_188]),c_0_189]) ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(inverse(sk_c4),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_190]) ).
cnf(c_0_195,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_4 ).
cnf(c_0_196,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_191]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_103]),c_0_47]) ).
cnf(c_0_198,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c9,X1) = X1 ),
inference(spm,[status(thm)],[c_0_43,c_0_193]) ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_200,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c5,multiply(sk_c6,X1)) = multiply(sk_c7,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_70]) ).
cnf(c_0_201,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_110]) ).
cnf(c_0_202,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_78]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_196,c_0_90]) ).
cnf(c_0_204,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_205,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c9,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_199,c_0_198]) ).
cnf(c_0_206,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c5,sk_c7) = multiply(sk_c7,sk_c9) ),
inference(spm,[status(thm)],[c_0_200,c_0_110]) ).
cnf(c_0_207,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(inverse(sk_c8),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_203]) ).
cnf(c_0_209,negated_conjecture,
sk_c8 = sk_c7,
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_211,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_208,c_0_209]),c_0_42]),c_0_209]) ).
cnf(c_0_212,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_12 ).
cnf(c_0_213,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_103,c_0_210]) ).
cnf(c_0_214,negated_conjecture,
( identity = sk_c7
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_211]),c_0_42]) ).
cnf(c_0_215,negated_conjecture,
( inverse(sk_c9) = sk_c4
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_212]) ).
cnf(c_0_216,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[c_0_58,c_0_47]) ).
cnf(c_0_217,negated_conjecture,
( sk_c4 != sk_c1
| inverse(sk_c9) = sk_c1 ),
inference(ef,[status(thm)],[c_0_66]) ).
cnf(c_0_218,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c7) = sk_c7 ),
inference(rw,[status(thm)],[c_0_213,c_0_209]) ).
cnf(c_0_219,negated_conjecture,
( sk_c7 != sk_c9
| identity = sk_c9 ),
inference(ef,[status(thm)],[c_0_214]) ).
cnf(c_0_220,negated_conjecture,
( sk_c4 = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_138,c_0_215]) ).
cnf(c_0_221,negated_conjecture,
( sk_c4 = sk_c7
| inverse(sk_c9) = sk_c1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_66]),c_0_217]) ).
cnf(c_0_222,negated_conjecture,
identity = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_211]),c_0_219]) ).
cnf(c_0_223,negated_conjecture,
( inverse(sk_c9) = sk_c4
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_195]) ).
cnf(c_0_224,negated_conjecture,
( sk_c4 = sk_c7
| multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_220]) ).
cnf(c_0_225,negated_conjecture,
( sk_c4 = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_221]) ).
cnf(c_0_226,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[c_0_212,c_0_209]) ).
cnf(c_0_227,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_222]) ).
cnf(c_0_228,negated_conjecture,
( sk_c4 = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_92,c_0_223]) ).
cnf(c_0_229,negated_conjecture,
( sk_c4 = sk_c7
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_230,negated_conjecture,
( sk_c1 = sk_c7
| inverse(sk_c4) = sk_c9 ),
inference(rw,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_231,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_222]),c_0_222]) ).
cnf(c_0_232,negated_conjecture,
( sk_c1 != sk_c7
| inverse(sk_c9) = sk_c7 ),
inference(ef,[status(thm)],[c_0_216]) ).
cnf(c_0_233,negated_conjecture,
( sk_c7 = sk_c9
| sk_c4 = sk_c7 ),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
cnf(c_0_234,negated_conjecture,
( sk_c4 = sk_c9
| sk_c1 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_230]),c_0_231]) ).
cnf(c_0_235,negated_conjecture,
( sk_c1 != sk_c7
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[c_0_232,c_0_231]) ).
cnf(c_0_236,plain,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_42,c_0_222]) ).
cnf(c_0_237,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_43,c_0_222]) ).
cnf(c_0_238,negated_conjecture,
sk_c7 = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_235]) ).
cnf(c_0_239,plain,
multiply(X1,inverse(X1)) = sk_c9,
inference(spm,[status(thm)],[c_0_236,c_0_52]) ).
cnf(c_0_240,negated_conjecture,
inverse(X1) != sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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)],[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_107,c_0_209]),c_0_209]),c_0_209]),c_0_209]),c_0_209]),c_0_227]),c_0_237]),c_0_238]),c_0_227]),c_0_238]),c_0_237]),c_0_238]),c_0_238]),c_0_227]),c_0_238]),c_0_238]),c_0_238]),c_0_238]),c_0_227]),c_0_239]),c_0_238]),c_0_238]),c_0_227]),c_0_227]),c_0_238]),c_0_231]),c_0_238])])])])]),c_0_231])]) ).
cnf(c_0_241,plain,
$false,
inference(sr,[status(thm)],[c_0_231,c_0_240]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP282-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:09:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 2.24/0.77 % Version: 3.5.1
% 2.24/0.77 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.24/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.24/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.24/0.77 % Starting new_bool_3 with 300s (1) cores
% 2.24/0.77 % Starting new_bool_1 with 300s (1) cores
% 2.24/0.77 % Starting sh5l with 300s (1) cores
% 2.24/0.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1116146 completed with status 0
% 2.24/0.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.24/0.77 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.24/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.24/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.24/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.24/0.77 % No SInE strategy applied
% 2.24/0.77 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.24/0.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.24/0.77 % Starting SubtermCWHack with 136s (1) cores
% 2.24/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.24/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.24/0.77 % Starting new_bool_3 with 136s (1) cores
% 2.24/0.77 % Starting new_bool_1 with 136s (1) cores
% 2.24/0.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1116152 completed with status 0
% 2.24/0.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.24/0.77 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.24/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.24/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.24/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.24/0.77 % No SInE strategy applied
% 2.24/0.77 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.24/0.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.24/0.77 % Starting SubtermCWHack with 136s (1) cores
% 2.24/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.24/0.77 % Preprocessing time : 0.002 s
% 2.24/0.77 % Presaturation interreduction done
% 2.24/0.77
% 2.24/0.77 % Proof found!
% 2.24/0.77 % SZS status Unsatisfiable
% 2.24/0.77 % SZS output start CNFRefutation
% See solution above
% 2.24/0.77 % Parsed axioms : 52
% 2.24/0.77 % Removed by relevancy pruning/SinE : 0
% 2.24/0.77 % Initial clauses : 52
% 2.24/0.77 % Removed in clause preprocessing : 0
% 2.24/0.77 % Initial clauses in saturation : 52
% 2.24/0.77 % Processed clauses : 4221
% 2.24/0.77 % ...of these trivial : 325
% 2.24/0.77 % ...subsumed : 2810
% 2.24/0.77 % ...remaining for further processing : 1086
% 2.24/0.77 % Other redundant clauses eliminated : 35
% 2.24/0.77 % Clauses deleted for lack of memory : 0
% 2.24/0.77 % Backward-subsumed : 177
% 2.24/0.77 % Backward-rewritten : 824
% 2.24/0.77 % Generated clauses : 18810
% 2.24/0.77 % ...of the previous two non-redundant : 18828
% 2.24/0.77 % ...aggressively subsumed : 0
% 2.24/0.77 % Contextual simplify-reflections : 43
% 2.24/0.77 % Paramodulations : 18772
% 2.24/0.77 % Factorizations : 10
% 2.24/0.77 % NegExts : 0
% 2.24/0.77 % Equation resolutions : 35
% 2.24/0.77 % Disequality decompositions : 0
% 2.24/0.77 % Total rewrite steps : 6456
% 2.24/0.77 % ...of those cached : 6168
% 2.24/0.77 % Propositional unsat checks : 0
% 2.24/0.77 % Propositional check models : 0
% 2.24/0.77 % Propositional check unsatisfiable : 0
% 2.24/0.77 % Propositional clauses : 0
% 2.24/0.77 % Propositional clauses after purity: 0
% 2.24/0.77 % Propositional unsat core size : 0
% 2.24/0.77 % Propositional preprocessing time : 0.000
% 2.24/0.77 % Propositional encoding time : 0.000
% 2.24/0.77 % Propositional solver time : 0.000
% 2.24/0.77 % Success case prop preproc time : 0.000
% 2.24/0.77 % Success case prop encoding time : 0.000
% 2.24/0.77 % Success case prop solver time : 0.000
% 2.24/0.77 % Current number of processed clauses : 23
% 2.24/0.77 % Positive orientable unit clauses : 21
% 2.24/0.77 % Positive unorientable unit clauses: 0
% 2.24/0.77 % Negative unit clauses : 1
% 2.24/0.77 % Non-unit-clauses : 1
% 2.24/0.77 % Current number of unprocessed clauses: 4781
% 2.24/0.77 % ...number of literals in the above : 26108
% 2.24/0.77 % Current number of archived formulas : 0
% 2.24/0.77 % Current number of archived clauses : 1057
% 2.24/0.77 % Clause-clause subsumption calls (NU) : 48454
% 2.24/0.77 % Rec. Clause-clause subsumption calls : 15227
% 2.24/0.77 % Non-unit clause-clause subsumptions : 3018
% 2.24/0.77 % Unit Clause-clause subsumption calls : 585
% 2.24/0.77 % Rewrite failures with RHS unbound : 0
% 2.24/0.77 % BW rewrite match attempts : 35
% 2.24/0.77 % BW rewrite match successes : 31
% 2.24/0.77 % Condensation attempts : 0
% 2.24/0.77 % Condensation successes : 0
% 2.24/0.77 % Termbank termtop insertions : 228114
% 2.24/0.77 % Search garbage collected termcells : 37
% 2.24/0.77
% 2.24/0.77 % -------------------------------------------------
% 2.24/0.77 % User time : 0.314 s
% 2.24/0.77 % System time : 0.017 s
% 2.24/0.77 % Total time : 0.331 s
% 2.24/0.77 % Maximum resident set size: 3656 pages
% 2.24/0.77
% 2.24/0.77 % -------------------------------------------------
% 2.24/0.77 % User time : 1.487 s
% 2.24/0.77 % System time : 0.092 s
% 2.24/0.77 % Total time : 1.579 s
% 2.24/0.77 % Maximum resident set size: 4608 pages
% 2.24/0.77 % E exiting
%------------------------------------------------------------------------------