TSTP Solution File: GRP113-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP113-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 00:16:06 EDT 2023
% Result : Unsatisfiable 3.64s 3.71s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 22
% Syntax : Number of formulae : 196 ( 43 unt; 6 typ; 0 def)
% Number of atoms : 510 ( 509 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 390 ( 70 ~; 320 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 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,
a: $i ).
tff(decl_26,type,
b: $i ).
tff(decl_27,type,
c: $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(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(all_of_group1,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| X1 = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(c_not_identity,hypothesis,
c != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_identity) ).
cnf(b_not_identity,hypothesis,
b != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_identity) ).
cnf(a_not_identity,hypothesis,
a != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_identity) ).
cnf(a_not_b,hypothesis,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_b) ).
cnf(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
cnf(b_not_c,hypothesis,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_c) ).
cnf(condition_b,negated_conjecture,
( multiply(b,b) != c
| multiply(b,multiply(b,b)) != a
| multiply(b,multiply(b,multiply(b,b))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_b) ).
cnf(square_identity,negated_conjecture,
( multiply(a,a) != identity
| multiply(b,b) != identity
| multiply(c,c) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_identity) ).
cnf(condition_a,negated_conjecture,
( multiply(a,a) != b
| multiply(a,multiply(a,a)) != c
| multiply(a,multiply(a,multiply(a,a))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_a) ).
cnf(condition_c,negated_conjecture,
( multiply(c,c) != a
| multiply(c,multiply(c,c)) != b
| multiply(c,multiply(c,multiply(c,c))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_c) ).
cnf(c_0_16,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_17,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_18,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_19,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_20,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| X1 = identity ),
all_of_group1 ).
cnf(c_0_22,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_23,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,hypothesis,
( multiply(X1,X2) = c
| multiply(X1,X2) = b
| multiply(X1,X2) = a
| inverse(X1) = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,hypothesis,
c != identity,
c_not_identity ).
cnf(c_0_26,hypothesis,
b != identity,
b_not_identity ).
cnf(c_0_27,hypothesis,
a != identity,
a_not_identity ).
cnf(c_0_28,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_29,hypothesis,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_23]),c_0_23]),c_0_25]),c_0_26]),c_0_27]) ).
cnf(c_0_30,hypothesis,
( inverse(X1) = X1
| X1 = c
| X1 = b
| X1 = a ),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_31,hypothesis,
multiply(X1,multiply(inverse(multiply(X2,X1)),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_32,hypothesis,
( multiply(X1,X1) = identity
| X1 = a
| X1 = b
| X1 = c ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_19]),c_0_18]) ).
cnf(c_0_34,hypothesis,
( multiply(inverse(X1),X2) = multiply(X1,X2)
| X1 = c
| X1 = b
| X1 = a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28]),c_0_18]) ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_22]) ).
cnf(c_0_36,hypothesis,
( X1 = c
| X1 = b
| X1 = a
| X2 = c
| X2 = b
| X2 = a
| X2 = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_37,hypothesis,
( multiply(X1,multiply(X1,X2)) = X2
| X1 = a
| X1 = b
| X1 = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_38,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = a
| inverse(X1) = b
| inverse(X1) = X2
| X2 = a
| X2 = b
| X2 = c ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_39,hypothesis,
( inverse(X1) = c
| inverse(X1) = b
| inverse(X1) = a
| inverse(X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_17]),c_0_22]) ).
cnf(c_0_40,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = b
| inverse(X1) = a
| inverse(X1) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_28]),c_0_28]),c_0_28]),c_0_27]),c_0_26]),c_0_25]) ).
cnf(c_0_41,hypothesis,
( inverse(b) = a
| inverse(b) = b
| inverse(b) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_39])]) ).
cnf(c_0_42,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_29]),c_0_35]) ).
cnf(c_0_43,hypothesis,
( multiply(inverse(X1),c) = identity
| X1 = a
| X1 = b
| identity = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_40]),c_0_35]),c_0_35]) ).
cnf(c_0_44,hypothesis,
( multiply(X1,inverse(multiply(X2,X1))) = c
| multiply(X1,inverse(multiply(X2,X1))) = b
| multiply(X1,inverse(multiply(X2,X1))) = a
| X2 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_22]) ).
cnf(c_0_45,hypothesis,
( multiply(c,b) = identity
| inverse(b) = b
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_46,hypothesis,
( multiply(c,X1) = identity
| multiply(c,X1) = b
| multiply(c,X1) = a
| inverse(X1) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,hypothesis,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_48,hypothesis,
( multiply(X1,inverse(multiply(X2,X1))) = c
| inverse(X2) = a
| inverse(X2) = b
| X2 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_29]),c_0_29]) ).
cnf(c_0_49,hypothesis,
( multiply(c,b) = a
| multiply(c,b) = b
| multiply(c,b) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_26]),c_0_27]) ).
cnf(c_0_50,hypothesis,
( inverse(X1) = b
| inverse(X1) = a
| inverse(c) = X1
| X1 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_16]),c_0_19]),c_0_22]) ).
cnf(c_0_51,hypothesis,
( inverse(c) = c
| inverse(c) = a
| inverse(c) = b ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_39])]) ).
cnf(c_0_52,hypothesis,
( multiply(c,b) = b
| multiply(c,b) = a
| inverse(c) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_49]),c_0_22]) ).
cnf(c_0_53,hypothesis,
( inverse(a) = a
| inverse(a) = b
| inverse(a) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_39])]) ).
cnf(c_0_54,hypothesis,
( inverse(c) = X1
| inverse(X1) = a
| inverse(b) = X1
| X1 = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_55,hypothesis,
( multiply(c,c) = identity
| inverse(c) = b
| inverse(c) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_51]) ).
cnf(c_0_56,hypothesis,
( multiply(b,c) = identity
| inverse(b) = b
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_57,hypothesis,
( multiply(c,b) = a
| multiply(c,b) = b
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
cnf(c_0_58,hypothesis,
( inverse(b) = b
| inverse(b) = a
| inverse(c) = b ),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_59,hypothesis,
( inverse(a) = b
| inverse(a) = a
| inverse(c) = a ),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
cnf(c_0_60,hypothesis,
a != b,
a_not_b ).
cnf(c_0_61,hypothesis,
( inverse(b) = X1
| inverse(c) = X1
| inverse(a) = X1
| X1 = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_54]) ).
cnf(c_0_62,hypothesis,
( multiply(c,c) = identity
| multiply(b,c) = identity
| inverse(c) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_55]) ).
cnf(c_0_63,hypothesis,
( multiply(b,c) = identity
| multiply(b,b) = identity
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_64,hypothesis,
( multiply(b,c) = identity
| multiply(c,b) = a
| inverse(c) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_57]),c_0_19]) ).
cnf(c_0_65,hypothesis,
( inverse(a) = a
| inverse(a) = b
| inverse(b) = a
| inverse(b) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_66,hypothesis,
( inverse(a) = X1
| inverse(b) = X1
| inverse(X1) = c
| X1 = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_61]) ).
cnf(c_0_67,hypothesis,
a != c,
a_not_c ).
cnf(c_0_68,hypothesis,
b != c,
b_not_c ).
cnf(c_0_69,hypothesis,
( multiply(b,c) = identity
| multiply(c,c) = identity
| inverse(a) = c ),
inference(spm,[status(thm)],[c_0_35,c_0_62]) ).
cnf(c_0_70,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = identity
| inverse(a) = b ),
inference(spm,[status(thm)],[c_0_35,c_0_63]) ).
cnf(c_0_71,hypothesis,
( multiply(c,b) = a
| multiply(b,c) = identity ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_64]),c_0_22]),c_0_25]) ).
cnf(c_0_72,hypothesis,
( multiply(c,a) = identity
| inverse(a) = b
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_53]) ).
cnf(c_0_73,hypothesis,
( inverse(b) = b
| inverse(a) = b
| inverse(a) = a ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]),c_0_26]) ).
cnf(c_0_74,hypothesis,
( inverse(X1) = c
| inverse(a) = X1
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_66]) ).
cnf(c_0_75,hypothesis,
( multiply(b,b) = identity
| multiply(c,c) = identity
| multiply(b,c) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_68]) ).
cnf(c_0_76,hypothesis,
( multiply(b,inverse(a)) = inverse(c)
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_71]) ).
cnf(c_0_77,hypothesis,
( multiply(c,a) = identity
| multiply(b,a) = identity
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_72]) ).
cnf(c_0_78,hypothesis,
( multiply(inverse(c),a) = b
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_71]) ).
cnf(c_0_79,hypothesis,
( multiply(b,b) = identity
| inverse(a) = a
| inverse(a) = b ),
inference(spm,[status(thm)],[c_0_19,c_0_73]) ).
cnf(c_0_80,hypothesis,
( multiply(a,X1) = identity
| inverse(X1) = b
| inverse(X1) = c
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_74]) ).
cnf(c_0_81,hypothesis,
( multiply(b,c) = identity
| multiply(b,b) = identity
| inverse(c) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_75]),c_0_22]) ).
cnf(c_0_82,hypothesis,
( inverse(c) = multiply(b,b)
| multiply(b,b) = identity
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_76,c_0_70]) ).
cnf(c_0_83,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = identity
| multiply(b,a) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_63]) ).
cnf(c_0_84,hypothesis,
( multiply(b,a) = identity
| multiply(c,a) = identity
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_77]) ).
cnf(c_0_85,hypothesis,
( multiply(X1,a) = identity
| inverse(X1) = b
| inverse(X1) = c
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_74]) ).
cnf(c_0_86,hypothesis,
( multiply(a,inverse(b)) = c
| multiply(b,c) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_78]),c_0_35]) ).
cnf(c_0_87,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = b
| inverse(a) = X1
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_74]) ).
cnf(c_0_88,hypothesis,
( multiply(a,c) = identity
| inverse(a) = b
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_89,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = identity
| inverse(a) = b ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_67]),c_0_68]),c_0_27]) ).
cnf(c_0_90,hypothesis,
( multiply(b,b) = c
| multiply(b,b) = identity
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,hypothesis,
( multiply(b,a) = identity
| multiply(b,b) = identity
| inverse(c) = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_83]),c_0_28]),c_0_18]) ).
cnf(c_0_92,hypothesis,
( multiply(a,a) = identity
| multiply(b,a) = identity
| inverse(c) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_84]),c_0_22]) ).
cnf(c_0_93,hypothesis,
( multiply(X1,a) = identity
| multiply(X1,c) = identity
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_85]) ).
cnf(c_0_94,hypothesis,
( multiply(b,c) = identity
| multiply(a,b) = c
| inverse(a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_26]) ).
cnf(c_0_95,hypothesis,
( multiply(a,c) = identity
| multiply(b,a) = identity
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_88]) ).
cnf(c_0_96,hypothesis,
( multiply(b,b) = identity
| multiply(a,a) = identity
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_35,c_0_89]) ).
cnf(c_0_97,hypothesis,
( multiply(b,b) = identity
| multiply(b,b) = c
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_90]),c_0_22]) ).
cnf(c_0_98,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = a
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_50]) ).
cnf(c_0_99,hypothesis,
( multiply(inverse(a),c) = inverse(b)
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_71]) ).
cnf(c_0_100,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = identity
| multiply(b,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_60]) ).
cnf(c_0_101,hypothesis,
( multiply(b,a) = identity
| multiply(b,c) = identity
| multiply(a,b) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_93]),c_0_26]) ).
cnf(c_0_102,hypothesis,
( multiply(a,b) = c
| multiply(c,c) = identity
| multiply(b,c) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_94]),c_0_68]) ).
cnf(c_0_103,hypothesis,
( multiply(b,a) = identity
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_95]) ).
cnf(c_0_104,hypothesis,
( multiply(b,b) = c
| multiply(a,a) = identity
| multiply(b,b) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_67]) ).
cnf(c_0_105,hypothesis,
( multiply(X1,c) = identity
| multiply(X1,b) = identity
| inverse(X1) = a
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_98]) ).
cnf(c_0_106,hypothesis,
( inverse(b) = multiply(b,c)
| multiply(b,b) = identity
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_99,c_0_70]) ).
cnf(c_0_107,hypothesis,
( multiply(b,a) = identity
| multiply(a,a) = identity
| inverse(b) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_100]),c_0_22]) ).
cnf(c_0_108,hypothesis,
( multiply(a,b) = c
| multiply(b,a) = identity
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_101]),c_0_22]) ).
cnf(c_0_109,hypothesis,
( multiply(b,c) = identity
| multiply(a,b) = c
| inverse(c) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_102]),c_0_22]) ).
cnf(c_0_110,hypothesis,
( inverse(c) = multiply(b,b)
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_76,c_0_94]) ).
cnf(c_0_111,hypothesis,
( multiply(b,c) = identity
| multiply(a,b) = c
| inverse(b) = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_98]),c_0_26]) ).
cnf(c_0_112,hypothesis,
( inverse(b) = multiply(b,c)
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_99,c_0_94]) ).
cnf(c_0_113,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = identity
| inverse(b) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_103]),c_0_22]) ).
cnf(c_0_114,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = c
| inverse(b) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_104]),c_0_22]) ).
cnf(c_0_115,hypothesis,
( multiply(b,c) = a
| multiply(b,b) = identity
| multiply(b,c) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_26]) ).
cnf(c_0_116,hypothesis,
( multiply(a,b) = c
| multiply(a,a) = identity
| multiply(b,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_68]) ).
cnf(c_0_117,hypothesis,
( multiply(b,b) = c
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,hypothesis,
( multiply(b,c) = a
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( multiply(b,b) != c
| multiply(b,multiply(b,b)) != a
| multiply(b,multiply(b,multiply(b,b))) != identity ),
condition_b ).
cnf(c_0_120,hypothesis,
( multiply(b,b) = c
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_60]) ).
cnf(c_0_121,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = a
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_115]),c_0_22]) ).
cnf(c_0_122,hypothesis,
( multiply(a,a) = identity
| multiply(a,b) = c
| inverse(b) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_116]),c_0_22]) ).
cnf(c_0_123,hypothesis,
( multiply(a,b) = c
| multiply(b,b) = c
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_117]),c_0_22]) ).
cnf(c_0_124,hypothesis,
( multiply(a,b) = c
| multiply(b,c) = a
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_118]),c_0_22]) ).
cnf(c_0_125,negated_conjecture,
( multiply(a,a) = identity
| multiply(a,c) = identity
| multiply(b,multiply(b,c)) != identity
| multiply(b,c) != a ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,hypothesis,
( multiply(b,c) = a
| multiply(a,a) = identity
| multiply(b,b) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_121]),c_0_67]) ).
cnf(c_0_127,hypothesis,
( multiply(b,b) = c
| multiply(a,b) = c
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_67]) ).
cnf(c_0_128,hypothesis,
( multiply(b,c) = a
| multiply(a,b) = c
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_124]),c_0_67]) ).
cnf(c_0_129,hypothesis,
( multiply(b,b) = identity
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_100]) ).
cnf(c_0_130,negated_conjecture,
( multiply(a,a) = identity
| multiply(a,b) = c
| multiply(b,multiply(b,c)) != identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_127]),c_0_128]) ).
cnf(c_0_131,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_129]),c_0_25]) ).
cnf(c_0_132,negated_conjecture,
( multiply(a,a) != identity
| multiply(b,b) != identity
| multiply(c,c) != identity ),
square_identity ).
cnf(c_0_133,hypothesis,
( multiply(X1,b) = identity
| multiply(X1,c) = identity
| multiply(X1,a) = identity
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_105]) ).
cnf(c_0_134,hypothesis,
( multiply(a,b) = c
| multiply(a,a) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_128]),c_0_116]) ).
cnf(c_0_135,hypothesis,
( multiply(a,a) = identity
| inverse(a) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_131]),c_0_22]) ).
cnf(c_0_136,negated_conjecture,
( multiply(c,a) = identity
| multiply(c,b) = identity
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_25]) ).
cnf(c_0_137,hypothesis,
( multiply(inverse(a),c) = b
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_134]) ).
cnf(c_0_138,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_135]),c_0_67]),c_0_68]) ).
cnf(c_0_139,negated_conjecture,
( multiply(c,a) = identity
| inverse(c) = b
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_136]),c_0_22]) ).
cnf(c_0_140,hypothesis,
( multiply(c,inverse(b)) = a
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_137]),c_0_35]) ).
cnf(c_0_141,hypothesis,
( multiply(a,a) = identity
| inverse(b) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_138]),c_0_22]) ).
cnf(c_0_142,negated_conjecture,
( multiply(c,a) = identity
| multiply(b,c) = identity
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(spm,[status(thm)],[c_0_17,c_0_139]) ).
cnf(c_0_143,hypothesis,
( multiply(a,a) = identity
| multiply(c,b) = a ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_144,negated_conjecture,
( multiply(b,c) = identity
| inverse(c) = a
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_142]),c_0_22]) ).
cnf(c_0_145,hypothesis,
( multiply(inverse(c),a) = b
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_143]) ).
cnf(c_0_146,hypothesis,
( multiply(inverse(c),a) = inverse(b)
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_134]) ).
cnf(c_0_147,hypothesis,
( multiply(a,a) = identity
| inverse(c) = a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_131]),c_0_28]),c_0_18]) ).
cnf(c_0_148,hypothesis,
( multiply(b,c) = identity
| inverse(a) = c
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_142]),c_0_28]),c_0_18]) ).
cnf(c_0_149,negated_conjecture,
( multiply(b,c) = identity
| multiply(a,a) = b
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(spm,[status(thm)],[c_0_78,c_0_144]) ).
cnf(c_0_150,hypothesis,
( multiply(a,inverse(b)) = c
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_145]),c_0_35]) ).
cnf(c_0_151,hypothesis,
( inverse(b) = multiply(a,a)
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,hypothesis,
( inverse(c) = multiply(b,c)
| multiply(b,c) = identity
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(spm,[status(thm)],[c_0_76,c_0_148]) ).
cnf(c_0_153,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = identity
| multiply(a,a) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_105]),c_0_26]) ).
cnf(c_0_154,negated_conjecture,
( multiply(a,a) = b
| inverse(b) = c
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_149]),c_0_22]) ).
cnf(c_0_155,negated_conjecture,
( multiply(a,a) != b
| multiply(a,multiply(a,a)) != c
| multiply(a,multiply(a,multiply(a,a))) != identity ),
condition_a ).
cnf(c_0_156,hypothesis,
( multiply(a,multiply(a,a)) = c
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_157,hypothesis,
( multiply(a,a) = identity
| multiply(a,a) = b ),
inference(spm,[status(thm)],[c_0_145,c_0_147]) ).
cnf(c_0_158,negated_conjecture,
( multiply(b,c) = a
| multiply(b,c) = identity
| multiply(a,a) != identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_152]),c_0_115]) ).
cnf(c_0_159,hypothesis,
( multiply(a,a) = c
| multiply(b,b) = identity
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_153]),c_0_22]) ).
cnf(c_0_160,negated_conjecture,
( multiply(a,a) = b
| multiply(c,b) = identity
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(spm,[status(thm)],[c_0_17,c_0_154]) ).
cnf(c_0_161,negated_conjecture,
multiply(a,a) = identity,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_131]) ).
cnf(c_0_162,negated_conjecture,
( multiply(b,c) = a
| inverse(b) = c
| multiply(a,a) != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_158]),c_0_22]) ).
cnf(c_0_163,hypothesis,
( multiply(inverse(b),X1) = multiply(c,X1)
| multiply(b,c) = a
| multiply(a,a) != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_158]),c_0_28]),c_0_18]) ).
cnf(c_0_164,hypothesis,
( multiply(b,b) = identity
| multiply(a,a) = c
| multiply(c,b) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_159]) ).
cnf(c_0_165,negated_conjecture,
( multiply(c,b) = identity
| multiply(b,b) != identity ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_161]),c_0_161])]),c_0_26]) ).
cnf(c_0_166,negated_conjecture,
( multiply(c,multiply(b,X1)) = X1
| multiply(b,c) = a
| multiply(a,a) != identity ),
inference(spm,[status(thm)],[c_0_20,c_0_162]) ).
cnf(c_0_167,hypothesis,
( multiply(X1,inverse(c)) = multiply(X1,b)
| multiply(b,c) = a
| multiply(a,a) != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_163]),c_0_47]),c_0_35]) ).
cnf(c_0_168,hypothesis,
multiply(c,b) = identity,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_161]),c_0_25]),c_0_165]) ).
cnf(c_0_169,hypothesis,
( multiply(c,a) = a
| multiply(c,a) = b
| multiply(c,a) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_46]),c_0_26]),c_0_27]) ).
cnf(c_0_170,hypothesis,
( multiply(a,a) = b
| inverse(a) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_157]),c_0_22]) ).
cnf(c_0_171,negated_conjecture,
( inverse(c) = multiply(c,multiply(b,b))
| multiply(b,c) = a
| multiply(a,a) != identity ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_172,hypothesis,
multiply(b,c) = identity,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_168]),c_0_27]) ).
cnf(c_0_173,hypothesis,
( multiply(c,a) = b
| multiply(c,a) = a
| inverse(a) = c ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_169]),c_0_28]),c_0_18]) ).
cnf(c_0_174,hypothesis,
inverse(a) = a,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_161]),c_0_26]) ).
cnf(c_0_175,negated_conjecture,
inverse(c) = multiply(c,multiply(b,b)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_161])]),c_0_172]),c_0_27]) ).
cnf(c_0_176,hypothesis,
( multiply(c,a) = a
| multiply(c,a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_67]) ).
cnf(c_0_177,hypothesis,
multiply(c,multiply(b,b)) = b,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_168]),c_0_168]),c_0_26]),c_0_27]),c_0_175]) ).
cnf(c_0_178,negated_conjecture,
( multiply(c,c) != a
| multiply(c,multiply(c,c)) != b
| multiply(c,multiply(c,multiply(c,c))) != identity ),
condition_c ).
cnf(c_0_179,hypothesis,
( multiply(c,a) = a
| multiply(b,b) = a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_176]),c_0_175]),c_0_177]) ).
cnf(c_0_180,hypothesis,
( multiply(c,multiply(c,multiply(c,c))) = c
| multiply(c,multiply(c,multiply(c,c))) = b
| multiply(c,multiply(c,multiply(c,c))) = a
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
inference(spm,[status(thm)],[c_0_178,c_0_21]) ).
cnf(c_0_181,hypothesis,
multiply(b,b) = a,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_179]),c_0_19]),c_0_175]),c_0_177]),c_0_26]) ).
cnf(c_0_182,hypothesis,
( multiply(c,b) = b
| multiply(c,b) = a
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_49]),c_0_28]),c_0_18]) ).
cnf(c_0_183,plain,
multiply(X1,multiply(X2,multiply(X3,inverse(multiply(X1,multiply(X2,X3)))))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_23]),c_0_16]) ).
cnf(c_0_184,hypothesis,
( multiply(c,multiply(c,multiply(c,c))) = a
| multiply(c,multiply(c,multiply(c,c))) = b
| multiply(c,multiply(c,c)) = identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_180]),c_0_16]),c_0_16]),c_0_19]),c_0_22]) ).
cnf(c_0_185,hypothesis,
multiply(c,a) = b,
inference(rw,[status(thm)],[c_0_177,c_0_181]) ).
cnf(c_0_186,hypothesis,
inverse(b) = c,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_168]),c_0_168]),c_0_26]),c_0_27]) ).
cnf(c_0_187,hypothesis,
( multiply(c,multiply(c,multiply(c,multiply(c,inverse(b))))) = identity
| multiply(c,multiply(c,multiply(c,c))) = a
| multiply(c,multiply(c,c)) = identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_16]) ).
cnf(c_0_188,hypothesis,
multiply(c,c) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_185]),c_0_186]),c_0_174]) ).
cnf(c_0_189,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[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_187,c_0_186]),c_0_188]),c_0_185]),c_0_168]),c_0_22]),c_0_188]),c_0_185]),c_0_168]),c_0_188]),c_0_185]),c_0_188]),c_0_185]),c_0_188])]),c_0_25]),c_0_27]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP113-1 : TPTP v8.1.2. Released v1.1.0.
% 0.03/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 19:51:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 3.64/3.71 % Version : CSE_E---1.5
% 3.64/3.71 % Problem : theBenchmark.p
% 3.64/3.71 % Proof found
% 3.64/3.71 % SZS status Theorem for theBenchmark.p
% 3.64/3.71 % SZS output start Proof
% See solution above
% 3.64/3.72 % Total time : 3.126000 s
% 3.64/3.72 % SZS output end Proof
% 3.64/3.72 % Total time : 3.130000 s
%------------------------------------------------------------------------------