TSTP Solution File: GRP219-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP219-1 : 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 : n023.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 00:17:47 EDT 2023
% Result : Unsatisfiable 0.56s 0.66s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 32
% Syntax : Number of formulae : 112 ( 20 unt; 12 typ; 0 def)
% Number of atoms : 260 ( 259 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 252 ( 92 ~; 160 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 70 ( 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_c1: $i ).
tff(decl_26,type,
sk_c9: $i ).
tff(decl_27,type,
sk_c6: $i ).
tff(decl_28,type,
sk_c8: $i ).
tff(decl_29,type,
sk_c7: $i ).
tff(decl_30,type,
sk_c2: $i ).
tff(decl_31,type,
sk_c3: $i ).
tff(decl_32,type,
sk_c5: $i ).
tff(decl_33,type,
sk_c4: $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_6,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_33,negated_conjecture,
( inverse(X1) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,X3) != sk_c8
| inverse(X2) != X3
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c9,X4) != sk_c8
| multiply(X5,sk_c9) != X4
| inverse(X5) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c8) != sk_c9
| multiply(X7,sk_c8) != sk_c9
| inverse(X7) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(c_0_20,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_21,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_22,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_23,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_6 ).
cnf(c_0_25,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_2 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(sk_c6),sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_5 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
prove_this_23 ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_1 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_22 ).
cnf(c_0_35,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| inverse(sk_c7) = sk_c8 ),
prove_this_24 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c9,X1)
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c8,
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c9 ),
prove_this_27 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
multiply(inverse(sk_c9),sk_c8) = sk_c9,
inference(spm,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( sk_c8 = sk_c9
| sk_c5 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
prove_this_31 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40])]) ).
cnf(c_0_50,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| inverse(sk_c7) = sk_c8 ),
prove_this_28 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
( inverse(X1) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,X3) != sk_c8
| inverse(X2) != X3
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c9,X4) != sk_c8
| multiply(X5,sk_c9) != X4
| inverse(X5) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c8) != sk_c9
| multiply(X7,sk_c8) != sk_c9
| inverse(X7) != sk_c8 ),
prove_this_33 ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(inverse(X2),sk_c9) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,sk_c8) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c9
| inverse(X1) != sk_c9
| inverse(X5) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_53])]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_26 ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_30 ).
cnf(c_0_58,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c7) = sk_c8 ),
prove_this_32 ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(inverse(X1),sk_c9) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_34]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_14 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_10 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_18 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| inverse(sk_c7) = sk_c8
| sk_c8 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_40])]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_50,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(sk_c1) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9 ),
inference(spm,[status(thm)],[c_0_65,c_0_24]) ).
cnf(c_0_68,negated_conjecture,
( sk_c8 = sk_c9
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_66]),c_0_21]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| sk_c8 != sk_c9 ),
inference(spm,[status(thm)],[c_0_67,c_0_26]) ).
cnf(c_0_70,negated_conjecture,
sk_c9 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_68]),c_0_21])]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| multiply(X1,sk_c8) != identity
| multiply(X2,sk_c8) != identity
| inverse(X1) != identity
| inverse(X2) != identity
| sk_c8 != identity ),
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_69,c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_72,negated_conjecture,
sk_c8 = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_70]),c_0_70]),c_0_22]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c6,identity) = identity
| multiply(X1,identity) != identity
| multiply(X2,identity) != identity
| inverse(X1) != identity
| inverse(X2) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_72]),c_0_72]),c_0_72])]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c1,identity) = identity
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_70]),c_0_70]),c_0_22]),c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c6,identity) = identity
| sk_c6 = identity
| multiply(X1,identity) != identity
| inverse(sk_c1) != identity
| inverse(X1) != identity ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c6,identity) = identity
| inverse(sk_c1) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_70]),c_0_70]),c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c6,identity) = identity
| sk_c6 = identity
| multiply(X1,identity) != identity
| inverse(X1) != identity ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c6,identity) = identity
| sk_c6 = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_75]),c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c6,X1) = X1
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_79]),c_0_22]),c_0_22]) ).
cnf(c_0_81,negated_conjecture,
( multiply(inverse(sk_c6),X1) = X1
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c6) = identity
| inverse(sk_c1) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_70]),c_0_70]) ).
cnf(c_0_83,negated_conjecture,
sk_c6 = identity,
inference(spm,[status(thm)],[c_0_21,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c1) = identity
| inverse(identity) = identity ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_85,negated_conjecture,
( inverse(identity) = identity
| multiply(sk_c1,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_84]),c_0_22]) ).
cnf(c_0_86,negated_conjecture,
( multiply(inverse(sk_c1),X1) = X1
| inverse(identity) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_85]) ).
cnf(c_0_87,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),X1) = X1
| inverse(identity) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_86]) ).
cnf(c_0_89,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_87]) ).
cnf(c_0_90,negated_conjecture,
( multiply(inverse(identity),X1) = X1
| inverse(identity) = identity ),
inference(spm,[status(thm)],[c_0_88,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( multiply(inverse(X1),sk_c9) != sk_c8
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(identity) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
inference(spm,[status(thm)],[c_0_55,c_0_22]) ).
cnf(c_0_92,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_89]),c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(inverse(identity)),X1) = X1
| inverse(identity) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( multiply(inverse(X1),sk_c9) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(identity) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_40])]) ).
cnf(c_0_95,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_87,c_0_92]) ).
cnf(c_0_96,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_21,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_21,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
inverse(X1) != identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_95]),c_0_72]),c_0_96]),c_0_72]),c_0_72]),c_0_95]),c_0_72]),c_0_95]),c_0_72]),c_0_95]),c_0_97]),c_0_72])])])])]),c_0_97])]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_97,c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP219-1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 02:12:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.56/0.66 % Version : CSE_E---1.5
% 0.56/0.66 % Problem : theBenchmark.p
% 0.56/0.66 % Proof found
% 0.56/0.66 % SZS status Theorem for theBenchmark.p
% 0.56/0.66 % SZS output start Proof
% See solution above
% 0.56/0.67 % Total time : 0.079000 s
% 0.56/0.67 % SZS output end Proof
% 0.56/0.67 % Total time : 0.083000 s
%------------------------------------------------------------------------------