TSTP Solution File: GRP330-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP330-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 00:18:28 EDT 2023
% Result : Unsatisfiable 0.19s 0.75s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 33
% Syntax : Number of formulae : 111 ( 22 unt; 14 typ; 0 def)
% Number of atoms : 237 ( 236 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 224 ( 84 ~; 140 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 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 : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 67 ( 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_c10: $i ).
tff(decl_26,type,
sk_c11: $i ).
tff(decl_27,type,
sk_c9: $i ).
tff(decl_28,type,
sk_c3: $i ).
tff(decl_29,type,
sk_c4: $i ).
tff(decl_30,type,
sk_c5: $i ).
tff(decl_31,type,
sk_c8: $i ).
tff(decl_32,type,
sk_c7: $i ).
tff(decl_33,type,
sk_c6: $i ).
tff(decl_34,type,
sk_c1: $i ).
tff(decl_35,type,
sk_c2: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_41,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c10,sk_c11) != sk_c9
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c9
| 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/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_20,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_21,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_22,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_24,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_32 ).
cnf(c_0_29,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c2) = sk_c9 ),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c2,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_5 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_3 ).
cnf(c_0_37,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_41 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c11) = sk_c3
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_25]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_7 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_4 ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_6 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c4,multiply(sk_c10,X1)) = multiply(sk_c9,X1)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_47,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_25]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_31 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c3,sk_c11) = identity
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c8,multiply(sk_c10,X1)) = multiply(sk_c11,X1)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_19,c_0_42]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_24 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c9,inverse(sk_c10)) = sk_c4
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_29]),c_0_25]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c10) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_20]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c2,sk_c9) = identity
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c11,sk_c4) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_25]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c11,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_55]),c_0_22]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c4 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_25]) ).
cnf(c_0_65,negated_conjecture,
sk_c10 = identity,
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c4 = sk_c8 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c1 ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( sk_c4 = sk_c9
| sk_c9 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_21]) ).
cnf(c_0_69,negated_conjecture,
( sk_c4 = sk_c8
| sk_c9 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_65]),c_0_21]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c10,sk_c11) != sk_c9
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c9
| 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 ),
prove_this_51 ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c10) = sk_c1
| sk_c4 != sk_c1 ),
inference(ef,[status(thm)],[c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_23 ).
cnf(c_0_73,negated_conjecture,
( sk_c8 = sk_c11
| sk_c9 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_65]),c_0_21]),c_0_65]),c_0_25]) ).
cnf(c_0_74,negated_conjecture,
( sk_c9 = sk_c11
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_76,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c11) != sk_c9
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c9
| inverse(X6) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_70])]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| sk_c4 != sk_c1 ),
inference(spm,[status(thm)],[c_0_29,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
sk_c9 = sk_c11,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_15 ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c11) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c9
| inverse(X6) != sk_c10
| sk_c11 != identity ),
inference(rw,[status(thm)],[c_0_76,c_0_29]) ).
cnf(c_0_83,negated_conjecture,
( sk_c1 = identity
| sk_c4 != sk_c1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_65]),c_0_21]) ).
cnf(c_0_84,negated_conjecture,
( sk_c1 = identity
| sk_c4 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_65]),c_0_25]),c_0_65]),c_0_25]),c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_87,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X3,sk_c11) != identity
| multiply(X4,sk_c9) != identity
| inverse(sk_c9) != identity
| inverse(sk_c11) != identity
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c9
| sk_c9 != sk_c11
| sk_c11 != identity ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_82,c_0_65]),c_0_25]),c_0_65]),c_0_21]),c_0_65]),c_0_25]),c_0_65]),c_0_65]),c_0_65]),c_0_25]),c_0_65]),c_0_65])])]) ).
cnf(c_0_88,negated_conjecture,
( sk_c1 = identity
| sk_c1 != sk_c11 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
( sk_c11 = identity
| sk_c1 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_65]),c_0_25]) ).
cnf(c_0_90,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X3,sk_c11) != identity
| multiply(X4,sk_c11) != identity
| inverse(sk_c11) != identity
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11
| sk_c11 != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_79]),c_0_79]),c_0_79]),c_0_79])]) ).
cnf(c_0_92,negated_conjecture,
sk_c11 = identity,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_90]) ).
cnf(c_0_94,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)],[c_0_91,c_0_92]),c_0_25]),c_0_92]),c_0_25]),c_0_92]),c_0_93]),c_0_92]),c_0_92]),c_0_92]),c_0_92])])])]),c_0_93])]) ).
cnf(c_0_95,negated_conjecture,
inverse(X1) != identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_20]),c_0_93]),c_0_26])]) ).
cnf(c_0_96,plain,
$false,
inference(sr,[status(thm)],[c_0_93,c_0_95]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP330-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:42:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.74 % Version : CSE_E---1.5
% 0.19/0.75 % Problem : theBenchmark.p
% 0.19/0.75 % Proof found
% 0.19/0.75 % SZS status Theorem for theBenchmark.p
% 0.19/0.75 % SZS output start Proof
% See solution above
% 0.19/0.75 % Total time : 0.178000 s
% 0.19/0.75 % SZS output end Proof
% 0.19/0.76 % Total time : 0.181000 s
%------------------------------------------------------------------------------