TSTP Solution File: GRP371-1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : GRP371-1 : TPTP v8.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 20:55:45 EDT 2024
% Result : Unsatisfiable 3.97s 0.96s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 25
% Syntax : Number of clauses : 142 ( 24 unt; 103 nHn; 121 RR)
% Number of literals : 355 ( 354 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 : 88 ( 3 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_18,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(X1,X2) != sk_c11
| inverse(X1) != X2
| multiply(X2,sk_c10) != sk_c11
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_44,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
cnf(c_0_25,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_30,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).
cnf(c_0_31,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_19 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c6 ),
prove_this_28 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c8 ),
prove_this_29 ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_8 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_38 ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c1),sk_c11) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c1) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_9 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_48 ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(X1,X2) != sk_c11
| inverse(X1) != X2
| multiply(X2,sk_c10) != sk_c11
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
inference(fof_simplification,[status(thm)],[prove_this_51]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_39 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_49 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(X1,X2) != sk_c11
| inverse(X1) != X2
| multiply(X2,sk_c10) != sk_c11
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
c_0_46 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_49]),c_0_26]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_31,c_0_50]) ).
cnf(c_0_57,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_53])])]) ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c2),sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c11,sk_c10) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c11,X1) = X1
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_49]),c_0_28]) ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c9),sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(spm,[status(thm)],[c_0_59,c_0_50]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c2) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c9) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(spm,[status(thm)],[c_0_65,c_0_58]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_31,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c10) = sk_c9
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_31,c_0_68]) ).
cnf(c_0_74,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_75,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X4) != sk_c11
| identity != sk_c9 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_31])]),c_0_26]) ).
cnf(c_0_76,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = sk_c2 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_74,c_0_30]) ).
cnf(c_0_79,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X4) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_78,c_0_55]) ).
cnf(c_0_81,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_31])]),c_0_26]),c_0_67]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c11) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_61]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c8
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_50,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_30 ).
cnf(c_0_85,negated_conjecture,
( sk_c7 = sk_c8
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| inverse(X2) != identity
| inverse(X2) != X2 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_30]),c_0_27]),c_0_30]),c_0_30])]),c_0_83]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( sk_c7 = sk_c8
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11 ),
inference(spm,[status(thm)],[c_0_85,c_0_78]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
prove_this_26 ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_25 ).
cnf(c_0_90,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
sk_c7 = sk_c8,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_82]),c_0_27]),c_0_30])]),c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_31,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_17 ).
cnf(c_0_95,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c8
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_26,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1)
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[c_0_86,c_0_91]) ).
cnf(c_0_99,negated_conjecture,
( multiply(inverse(sk_c1),sk_c11) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_15 ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c5,sk_c6) = multiply(sk_c11,sk_c8)
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c2) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_27 ).
cnf(c_0_105,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_26]) ).
cnf(c_0_108,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| inverse(sk_c2) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_106]),c_0_30]) ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_26]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c10,sk_c8) = identity
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_26]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c10) = sk_c8
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_116]),c_0_30]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c8,sk_c10) = identity
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_26,c_0_117]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_121,negated_conjecture,
identity = sk_c11,
inference(spm,[status(thm)],[c_0_107,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_31,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_43 ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_120]) ).
cnf(c_0_125,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c3 != sk_c10 ),
inference(ef,[status(thm)],[c_0_122]) ).
cnf(c_0_127,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_121]),c_0_121]) ).
cnf(c_0_128,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
prove_this_44 ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c3 = sk_c10 ),
inference(rw,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( sk_c10 = sk_c11
| sk_c3 != sk_c10 ),
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
sk_c10 = sk_c11,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_130]),c_0_127]),c_0_131]) ).
cnf(c_0_134,plain,
multiply(sk_c11,X1) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_121]) ).
cnf(c_0_135,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[c_0_26,c_0_121]) ).
cnf(c_0_136,negated_conjecture,
sk_c9 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133]),c_0_125]),c_0_133]),c_0_134]),c_0_133])]) ).
cnf(c_0_137,plain,
multiply(X1,inverse(X1)) = sk_c11,
inference(spm,[status(thm)],[c_0_135,c_0_31]) ).
cnf(c_0_138,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_59,c_0_127]),c_0_133]),c_0_125]),c_0_133]),c_0_125]),c_0_136]),c_0_133]),c_0_125]),c_0_137]),c_0_137]),c_0_133]),c_0_125]),c_0_136]),c_0_125]),c_0_133]),c_0_133]),c_0_133])])])]),c_0_127])]) ).
cnf(c_0_139,negated_conjecture,
( inverse(X1) != sk_c11
| inverse(X2) != sk_c11
| inverse(X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_125]),c_0_125]) ).
cnf(c_0_140,negated_conjecture,
inverse(X1) != sk_c11,
inference(spm,[status(thm)],[c_0_139,c_0_127]) ).
cnf(c_0_141,plain,
$false,
inference(sr,[status(thm)],[c_0_127,c_0_140]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP371-1 : TPTP v8.2.0. Released v2.5.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 06:00:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order model finding
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.97/0.96 # Version: 3.1.0
% 3.97/0.96 # Preprocessing class: FSMSSMSMSSSNFFN.
% 3.97/0.96 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.97/0.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.97/0.96 # Starting new_bool_3 with 300s (1) cores
% 3.97/0.96 # Starting new_bool_1 with 300s (1) cores
% 3.97/0.96 # Starting sh5l with 300s (1) cores
% 3.97/0.96 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 14897 completed with status 0
% 3.97/0.96 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 3.97/0.96 # Preprocessing class: FSMSSMSMSSSNFFN.
% 3.97/0.96 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.97/0.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.97/0.96 # No SInE strategy applied
% 3.97/0.96 # Search class: FGHPS-FFMM21-SFFFFFNN
% 3.97/0.96 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.97/0.96 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 3.97/0.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 3.97/0.96 # Starting new_bool_3 with 136s (1) cores
% 3.97/0.96 # Starting new_bool_1 with 136s (1) cores
% 3.97/0.96 # Starting sh5l with 136s (1) cores
% 3.97/0.96 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 14902 completed with status 0
% 3.97/0.96 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 3.97/0.96 # Preprocessing class: FSMSSMSMSSSNFFN.
% 3.97/0.96 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.97/0.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.97/0.96 # No SInE strategy applied
% 3.97/0.96 # Search class: FGHPS-FFMM21-SFFFFFNN
% 3.97/0.96 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.97/0.96 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 3.97/0.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 3.97/0.96 # Preprocessing time : 0.002 s
% 3.97/0.96 # Presaturation interreduction done
% 3.97/0.96
% 3.97/0.96 # Proof found!
% 3.97/0.96 # SZS status Unsatisfiable
% 3.97/0.96 # SZS output start CNFRefutation
% See solution above
% 3.97/0.96 # Parsed axioms : 54
% 3.97/0.96 # Removed by relevancy pruning/SinE : 0
% 3.97/0.96 # Initial clauses : 54
% 3.97/0.96 # Removed in clause preprocessing : 0
% 3.97/0.96 # Initial clauses in saturation : 54
% 3.97/0.96 # Processed clauses : 6863
% 3.97/0.96 # ...of these trivial : 231
% 3.97/0.96 # ...subsumed : 5098
% 3.97/0.96 # ...remaining for further processing : 1534
% 3.97/0.96 # Other redundant clauses eliminated : 149
% 3.97/0.96 # Clauses deleted for lack of memory : 0
% 3.97/0.96 # Backward-subsumed : 101
% 3.97/0.96 # Backward-rewritten : 1006
% 3.97/0.96 # Generated clauses : 28831
% 3.97/0.96 # ...of the previous two non-redundant : 28897
% 3.97/0.96 # ...aggressively subsumed : 0
% 3.97/0.96 # Contextual simplify-reflections : 26
% 3.97/0.96 # Paramodulations : 28660
% 3.97/0.96 # Factorizations : 3
% 3.97/0.96 # NegExts : 0
% 3.97/0.96 # Equation resolutions : 149
% 3.97/0.96 # Disequality decompositions : 0
% 3.97/0.96 # Total rewrite steps : 8880
% 3.97/0.96 # ...of those cached : 8567
% 3.97/0.96 # Propositional unsat checks : 0
% 3.97/0.96 # Propositional check models : 0
% 3.97/0.96 # Propositional check unsatisfiable : 0
% 3.97/0.96 # Propositional clauses : 0
% 3.97/0.96 # Propositional clauses after purity: 0
% 3.97/0.96 # Propositional unsat core size : 0
% 3.97/0.96 # Propositional preprocessing time : 0.000
% 3.97/0.96 # Propositional encoding time : 0.000
% 3.97/0.96 # Propositional solver time : 0.000
% 3.97/0.96 # Success case prop preproc time : 0.000
% 3.97/0.96 # Success case prop encoding time : 0.000
% 3.97/0.96 # Success case prop solver time : 0.000
% 3.97/0.96 # Current number of processed clauses : 280
% 3.97/0.96 # Positive orientable unit clauses : 12
% 3.97/0.96 # Positive unorientable unit clauses: 0
% 3.97/0.96 # Negative unit clauses : 1
% 3.97/0.96 # Non-unit-clauses : 267
% 3.97/0.96 # Current number of unprocessed clauses: 21264
% 3.97/0.96 # ...number of literals in the above : 124585
% 3.97/0.96 # Current number of archived formulas : 0
% 3.97/0.96 # Current number of archived clauses : 1196
% 3.97/0.96 # Clause-clause subsumption calls (NU) : 131153
% 3.97/0.96 # Rec. Clause-clause subsumption calls : 62230
% 3.97/0.96 # Non-unit clause-clause subsumptions : 5206
% 3.97/0.96 # Unit Clause-clause subsumption calls : 1701
% 3.97/0.96 # Rewrite failures with RHS unbound : 0
% 3.97/0.96 # BW rewrite match attempts : 64
% 3.97/0.96 # BW rewrite match successes : 55
% 3.97/0.96 # Condensation attempts : 0
% 3.97/0.96 # Condensation successes : 0
% 3.97/0.96 # Termbank termtop insertions : 518441
% 3.97/0.96 # Search garbage collected termcells : 42
% 3.97/0.96
% 3.97/0.96 # -------------------------------------------------
% 3.97/0.96 # User time : 0.445 s
% 3.97/0.96 # System time : 0.013 s
% 3.97/0.96 # Total time : 0.458 s
% 3.97/0.96 # Maximum resident set size: 1652 pages
% 3.97/0.96
% 3.97/0.96 # -------------------------------------------------
% 3.97/0.96 # User time : 2.325 s
% 3.97/0.96 # System time : 0.040 s
% 3.97/0.96 # Total time : 2.365 s
% 3.97/0.96 # Maximum resident set size: 1760 pages
% 3.97/0.96 % E---3.1 exiting
%------------------------------------------------------------------------------