TSTP Solution File: GRP252-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP252-1 : 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 : n021.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 00:17:56 EDT 2023
% Result : Unsatisfiable 0.55s 0.71s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 34
% Syntax : Number of formulae : 130 ( 26 unt; 13 typ; 0 def)
% Number of atoms : 326 ( 325 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 355 ( 146 ~; 209 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 5 ( 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 96 ( 0 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_c1: $i ).
tff(decl_26,type,
sk_c10: $i ).
tff(decl_27,type,
sk_c9: $i ).
tff(decl_28,type,
sk_c4: $i ).
tff(decl_29,type,
sk_c5: $i ).
tff(decl_30,type,
sk_c8: $i ).
tff(decl_31,type,
sk_c7: $i ).
tff(decl_32,type,
sk_c6: $i ).
tff(decl_33,type,
sk_c2: $i ).
tff(decl_34,type,
sk_c3: $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_1,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_43,negated_conjecture,
( multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,sk_c8) != sk_c9
| inverse(X5) != sk_c8
| multiply(sk_c8,X6) != sk_c9
| multiply(X7,sk_c8) != X6
| inverse(X7) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_24,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_1 ).
cnf(c_0_26,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_2 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_8 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_9 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_34 ).
cnf(c_0_36,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
sk_c9 = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_36]),c_0_22]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c3 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_23]) ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| sk_c3 = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c8 ),
prove_this_35 ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
prove_this_33 ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(inverse(sk_c6)),sk_c8) = sk_c7
| sk_c3 = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c3) = identity
| inverse(sk_c6) = sk_c8 ),
inference(rw,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c9,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c3) = identity
| sk_c3 = identity
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_22]) ).
cnf(c_0_47,negated_conjecture,
( multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,sk_c8) != sk_c9
| inverse(X5) != sk_c8
| multiply(sk_c8,X6) != sk_c9
| multiply(X7,sk_c8) != X6
| inverse(X7) != sk_c8 ),
prove_this_43 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| inverse(sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c7) = identity
| sk_c3 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_38]),c_0_38]),c_0_23]) ).
cnf(c_0_50,negated_conjecture,
( sk_c7 = identity
| sk_c3 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_46]),c_0_23])]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| multiply(X6,sk_c10) != sk_c9
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c10
| inverse(X4) != sk_c9
| inverse(X5) != sk_c9
| inverse(X6) != sk_c10 ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_6 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
prove_this_7 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
prove_this_5 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| inverse(sk_c3) = identity ),
inference(rw,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c8,identity) = identity
| sk_c3 = identity ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X5,sk_c10) != sk_c9
| inverse(X1) != sk_c8
| inverse(X2) != sk_c10
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9
| inverse(X5) != sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
prove_this_3 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_4 ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_41 ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| sk_c3 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_55]),c_0_23]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c3 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_56]),c_0_23]),c_0_23]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
prove_this_19 ).
cnf(c_0_65,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c8 ),
prove_this_42 ).
cnf(c_0_67,negated_conjecture,
( sk_c3 = identity
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c10) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_25]),c_0_27]) ).
cnf(c_0_69,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
prove_this_26 ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( sk_c3 = identity
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_67]),c_0_23]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c10) != sk_c9
| inverse(sk_c5) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c10 ),
inference(spm,[status(thm)],[c_0_68,c_0_58]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = identity ),
inference(rw,[status(thm)],[c_0_71,c_0_38]) ).
cnf(c_0_76,negated_conjecture,
( sk_c3 = identity
| sk_c8 = identity ),
inference(spm,[status(thm)],[c_0_50,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c10
| sk_c8 != sk_c9 ),
inference(spm,[status(thm)],[c_0_73,c_0_59]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c7) = identity
| sk_c8 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_38]),c_0_38]),c_0_23]),c_0_38]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c8 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_23])]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| multiply(X1,identity) != sk_c8
| multiply(X2,sk_c10) != identity
| inverse(X1) != identity
| inverse(X2) != sk_c10
| sk_c8 != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_38]),c_0_38]),c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_81,negated_conjecture,
sk_c8 = identity,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_25 ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| multiply(X1,identity) != identity
| multiply(X2,sk_c10) != identity
| inverse(X1) != identity
| inverse(X2) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_81])]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c5,identity) = identity
| multiply(sk_c1,sk_c10) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_38]),c_0_38]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( inverse(sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_82,c_0_38]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| multiply(X1,sk_c10) != identity
| inverse(sk_c5) != identity
| inverse(X1) != sk_c10 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c5) = identity
| inverse(sk_c2) = identity ),
inference(rw,[status(thm)],[c_0_85,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c2) = identity
| multiply(X1,sk_c10) != identity
| inverse(X1) != sk_c10 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c4,sk_c10) = identity
| multiply(sk_c1,sk_c10) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_38]),c_0_38]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c4) = sk_c10 ),
inference(rw,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c2) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| multiply(sk_c2,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_91]),c_0_23]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c1,sk_c10) = identity
| multiply(X1,sk_c10) != identity
| inverse(X1) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_92]),c_0_91]) ).
cnf(c_0_94,negated_conjecture,
multiply(sk_c1,sk_c10) = identity,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_90]),c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c8,multiply(X1,multiply(X2,sk_c8))) != sk_c9
| inverse(multiply(X1,X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c8) != sk_c9
| multiply(X6,sk_c9) != sk_c8
| multiply(X7,sk_c10) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c10
| inverse(X5) != sk_c9
| inverse(X6) != sk_c9
| inverse(X7) != sk_c10 ),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_96,negated_conjecture,
multiply(inverse(sk_c1),identity) = sk_c10,
inference(spm,[status(thm)],[c_0_24,c_0_94]) ).
cnf(c_0_97,negated_conjecture,
( inverse(multiply(inverse(multiply(X1,sk_c8)),X1)) != sk_c8
| multiply(sk_c8,identity) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| multiply(X6,sk_c10) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c10
| inverse(X4) != sk_c9
| inverse(X5) != sk_c9
| inverse(X6) != sk_c10 ),
inference(spm,[status(thm)],[c_0_95,c_0_22]) ).
cnf(c_0_98,negated_conjecture,
multiply(inverse(inverse(sk_c1)),sk_c10) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
multiply(inverse(sk_c1),X1) = multiply(sk_c10,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_96]),c_0_23]) ).
cnf(c_0_100,negated_conjecture,
( inverse(multiply(inverse(multiply(X1,sk_c8)),X1)) != sk_c8
| multiply(sk_c8,identity) != identity
| multiply(X2,sk_c8) != identity
| multiply(X3,sk_c10) != identity
| multiply(X4,sk_c8) != identity
| multiply(X5,identity) != sk_c8
| multiply(X6,sk_c10) != identity
| inverse(X2) != sk_c8
| inverse(X3) != sk_c10
| inverse(X4) != identity
| inverse(X5) != identity
| inverse(X6) != sk_c10 ),
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_97,c_0_38]),c_0_38]),c_0_38]),c_0_38]),c_0_38]),c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_101,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_102,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_103,negated_conjecture,
multiply(inverse(inverse(sk_c1)),multiply(sk_c10,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_98]),c_0_23]) ).
cnf(c_0_104,negated_conjecture,
multiply(sk_c10,multiply(sk_c1,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( inverse(multiply(inverse(multiply(X1,identity)),X1)) != identity
| multiply(X2,identity) != identity
| multiply(X3,sk_c10) != identity
| multiply(X4,identity) != identity
| multiply(X5,identity) != identity
| multiply(X6,sk_c10) != identity
| inverse(X2) != identity
| inverse(X3) != sk_c10
| inverse(X4) != identity
| inverse(X5) != identity
| inverse(X6) != sk_c10 ),
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)],[c_0_100,c_0_81]),c_0_81]),c_0_81]),c_0_23]),c_0_81]),c_0_81]),c_0_81]),c_0_81])]) ).
cnf(c_0_106,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_108,negated_conjecture,
multiply(inverse(inverse(sk_c1)),X1) = multiply(sk_c1,X1),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( multiply(X1,sk_c10) != identity
| multiply(X2,sk_c10) != identity
| inverse(identity) != identity
| inverse(X1) != sk_c10
| inverse(X2) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106]),c_0_22]),c_0_106]),c_0_106]),c_0_106])])])]) ).
cnf(c_0_110,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_107,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
multiply(sk_c1,inverse(sk_c1)) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_108]) ).
cnf(c_0_112,negated_conjecture,
multiply(sk_c10,identity) = sk_c10,
inference(rw,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_113,negated_conjecture,
( multiply(X1,sk_c10) != identity
| multiply(X2,sk_c10) != identity
| inverse(X1) != sk_c10
| inverse(X2) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_114,negated_conjecture,
inverse(sk_c1) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_111]),c_0_99]),c_0_112]) ).
cnf(c_0_115,negated_conjecture,
( multiply(X1,sk_c10) != identity
| inverse(X1) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_94]),c_0_114])]) ).
cnf(c_0_116,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_114]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP252-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n021.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 : Mon Aug 28 23:10:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.55/0.71 % Version : CSE_E---1.5
% 0.55/0.71 % Problem : theBenchmark.p
% 0.55/0.71 % Proof found
% 0.55/0.71 % SZS status Theorem for theBenchmark.p
% 0.55/0.71 % SZS output start Proof
% See solution above
% 0.55/0.72 % Total time : 0.136000 s
% 0.55/0.72 % SZS output end Proof
% 0.55/0.72 % Total time : 0.139000 s
%------------------------------------------------------------------------------