TSTP Solution File: GRP318-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP318-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 : Thu Aug 31 00:18:23 EDT 2023
% Result : Unsatisfiable 39.00s 39.14s
% Output : CNFRefutation 39.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 39
% Syntax : Number of formulae : 179 ( 20 unt; 15 typ; 0 def)
% Number of atoms : 361 ( 360 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 263 ( 66 ~; 197 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 65 ( 1 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
sk_c11: $i ).
tff(decl_26,type,
sk_c12: $i ).
tff(decl_27,type,
sk_c10: $i ).
tff(decl_28,type,
sk_c4: $i ).
tff(decl_29,type,
sk_c5: $i ).
tff(decl_30,type,
sk_c6: $i ).
tff(decl_31,type,
sk_c9: $i ).
tff(decl_32,type,
sk_c8: $i ).
tff(decl_33,type,
sk_c7: $i ).
tff(decl_34,type,
sk_c1: $i ).
tff(decl_35,type,
sk_c3: $i ).
tff(decl_36,type,
sk_c2: $i ).
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_40,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_61,negated_conjecture,
( multiply(sk_c11,sk_c12) != sk_c10
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c11
| multiply(sk_c12,X2) != sk_c11
| multiply(X3,sk_c12) != X2
| inverse(X3) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| inverse(X4) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| inverse(X5) != sk_c11
| multiply(X6,X7) != sk_c12
| inverse(X6) != X7
| multiply(X7,sk_c11) != sk_c12
| inverse(X8) != X9
| inverse(X9) != X7
| multiply(X8,X7) != X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
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_c12,sk_c3) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_40 ).
cnf(c_0_29,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c8) = sk_c7 ),
prove_this_38 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c12 ),
prove_this_37 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_34,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( multiply(inverse(sk_c9),sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c12 ),
prove_this_32 ).
cnf(c_0_37,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c9 ),
prove_this_39 ).
cnf(c_0_39,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c9),multiply(sk_c12,X1)) = multiply(sk_c11,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c12,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
prove_this_31 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
prove_this_35 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_39]),c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c9) = multiply(sk_c11,sk_c4)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c4,multiply(sk_c12,X1)) = multiply(sk_c11,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c6,multiply(sk_c9,X1)) = multiply(sk_c12,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_50,negated_conjecture,
( multiply(inverse(sk_c9),sk_c7) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( inverse(multiply(sk_c11,sk_c4)) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c11,sk_c4) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_39]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c9 ),
prove_this_36 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c12,sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_39]) ).
cnf(c_0_55,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c7,X1)) = multiply(sk_c9,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_57,negated_conjecture,
( multiply(inverse(sk_c9),multiply(sk_c7,X1)) = multiply(sk_c9,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c9,multiply(sk_c9,X1)) = multiply(sk_c7,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( multiply(inverse(sk_c12),sk_c6) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_36]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c9,sk_c8)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_39]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c9) = multiply(sk_c9,sk_c8)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_56]),c_0_39]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c6) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_39]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c4,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( inverse(multiply(sk_c9,sk_c8)) = sk_c8
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c7,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c12) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_53]) ).
cnf(c_0_73,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c6
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(sk_c7),multiply(sk_c9,X1)) = multiply(sk_c7,X1)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_76,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c6
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c12)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c7) = multiply(sk_c7,sk_c6)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_60]),c_0_39]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = X1
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( inverse(multiply(sk_c7,sk_c6)) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c6,sk_c9) = sk_c12 ),
prove_this_15 ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c9 ),
prove_this_26 ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c9,multiply(sk_c7,X1)) = X1
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_74,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_27,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c12,sk_c6) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_60]),c_0_39]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c6) = sk_c12 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( multiply(inverse(inverse(sk_c6)),sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_27,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c9 ),
prove_this_16 ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c9) = sk_c6
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_45,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_69,c_0_94]) ).
cnf(c_0_101,negated_conjecture,
( multiply(inverse(sk_c12),sk_c6) = sk_c6
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c12) = sk_c7 ),
inference(spm,[status(thm)],[c_0_84,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c4) = sk_c12 ),
prove_this_52 ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
prove_this_25 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| sk_c12 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_25]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c6,sk_c9) = identity
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_25,c_0_99]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c8,sk_c12) = multiply(sk_c7,sk_c11)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_71,c_0_31]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c8,sk_c12) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_100]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c6) = sk_c6 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c11,multiply(sk_c1,X1)) = X1
| multiply(sk_c6,sk_c9) = sk_c12 ),
inference(spm,[status(thm)],[c_0_27,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( multiply(inverse(sk_c1),sk_c12) = sk_c11
| sk_c12 = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c6,sk_c9) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c4) = sk_c12 ),
prove_this_42 ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_84,c_0_109]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
prove_this_3 ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c12) = sk_c4
| inverse(sk_c12) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_110]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c11
| sk_c12 = identity ),
inference(spm,[status(thm)],[c_0_111,c_0_105]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c6,sk_c9) = identity
| multiply(sk_c11,sk_c12) = sk_c11
| sk_c12 = identity ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_114]) ).
cnf(c_0_123,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_115]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_116]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c12 ),
prove_this_7 ).
cnf(c_0_126,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_117]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c5) = sk_c11 ),
prove_this_4 ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c12) = sk_c2
| sk_c4 != sk_c2 ),
inference(ef,[status(thm)],[c_0_118]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c11
| sk_c12 = identity ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
prove_this_51 ).
cnf(c_0_131,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_121]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c4,sk_c12) = sk_c11 ),
prove_this_41 ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c4,sk_c12) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_122]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c6,sk_c9) = multiply(sk_c12,sk_c12)
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_48,c_0_72]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c9,multiply(sk_c11,X1)) = multiply(sk_c12,X1)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_24,c_0_125]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c2,sk_c12) = identity
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_25,c_0_128]) ).
cnf(c_0_139,negated_conjecture,
sk_c12 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_129]),c_0_25])]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c12) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_130]) ).
cnf(c_0_141,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_131]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c9,sk_c11) = multiply(sk_c12,sk_c10)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_145,negated_conjecture,
( sk_c2 = identity
| sk_c4 != sk_c2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_139]),c_0_39]) ).
cnf(c_0_146,negated_conjecture,
( sk_c2 = identity
| sk_c4 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_139]),c_0_39]),c_0_139]),c_0_141]) ).
cnf(c_0_147,negated_conjecture,
( sk_c11 = identity
| sk_c3 = sk_c2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_139]),c_0_39]) ).
cnf(c_0_148,negated_conjecture,
( sk_c11 = identity
| sk_c3 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_139]),c_0_26]),c_0_139]),c_0_139]),c_0_39]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c11,sk_c12) != sk_c10
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c11
| multiply(sk_c12,X2) != sk_c11
| multiply(X3,sk_c12) != X2
| inverse(X3) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| inverse(X4) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| inverse(X5) != sk_c11
| multiply(X6,X7) != sk_c12
| inverse(X6) != X7
| multiply(X7,sk_c11) != sk_c12
| inverse(X8) != X9
| inverse(X9) != X7
| multiply(X8,X7) != X9 ),
prove_this_61 ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c12,sk_c10) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_125,c_0_144]) ).
cnf(c_0_151,negated_conjecture,
( sk_c2 = identity
| sk_c2 != sk_c11 ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,negated_conjecture,
( sk_c2 = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(sk_c11,sk_c12) != sk_c10
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c12) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12
| inverse(X1) != sk_c12
| inverse(X6) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_149])])]) ).
cnf(c_0_154,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_155,negated_conjecture,
( sk_c10 = sk_c11
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_139]),c_0_26]),c_0_139]),c_0_139]),c_0_39]) ).
cnf(c_0_156,negated_conjecture,
sk_c11 = identity,
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(sk_c11,sk_c12) != sk_c10
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c12) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12
| inverse(X1) != sk_c12
| inverse(X6) != sk_c11
| sk_c12 != identity ),
inference(rw,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_158,negated_conjecture,
sk_c10 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156])]) ).
cnf(c_0_159,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c5) = sk_c11 ),
prove_this_54 ).
cnf(c_0_160,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != identity ),
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(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)],[c_0_157,c_0_139]),c_0_139]),c_0_39]),c_0_26]),c_0_139]),c_0_139]),c_0_39]),c_0_139]),c_0_39]),c_0_139]),c_0_139]),c_0_139]),c_0_139])])])]),c_0_156]),c_0_39]),c_0_158]),c_0_156]),c_0_156]),c_0_39]),c_0_158]),c_0_156]),c_0_39]),c_0_156]),c_0_156]),c_0_141]),c_0_156])])])]),c_0_141])]) ).
cnf(c_0_161,negated_conjecture,
( inverse(sk_c2) = identity
| inverse(sk_c5) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_139]),c_0_156]) ).
cnf(c_0_162,negated_conjecture,
inverse(X1) != identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_25]),c_0_141]),c_0_45])]) ).
cnf(c_0_163,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_161,c_0_162]),c_0_162]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP318-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 21:10:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.63 start to proof: theBenchmark
% 39.00/39.14 % Version : CSE_E---1.5
% 39.00/39.14 % Problem : theBenchmark.p
% 39.00/39.14 % Proof found
% 39.00/39.14 % SZS status Theorem for theBenchmark.p
% 39.00/39.14 % SZS output start Proof
% See solution above
% 39.06/39.16 % Total time : 38.403000 s
% 39.06/39.16 % SZS output end Proof
% 39.06/39.16 % Total time : 38.407000 s
%------------------------------------------------------------------------------