TSTP Solution File: GRP304-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP304-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 00:18:18 EDT 2023
% Result : Unsatisfiable 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 33
% Syntax : Number of formulae : 146 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 323 ( 322 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 287 ( 100 ~; 187 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 59 ( 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_c7: $i ).
tff(decl_26,type,
sk_c6: $i ).
tff(decl_27,type,
sk_c5: $i ).
tff(decl_28,type,
sk_c2: $i ).
tff(decl_29,type,
sk_c4: $i ).
tff(decl_30,type,
sk_c3: $i ).
tff(decl_31,type,
sk_c1: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_1,negated_conjecture,
multiply(sk_c7,sk_c6) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(sk_c7,X3) != sk_c6
| multiply(X4,sk_c7) != X3
| inverse(X4) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_24,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_25,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_12 ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
prove_this_13 ).
cnf(c_0_30,negated_conjecture,
multiply(sk_c7,sk_c6) = sk_c5,
prove_this_1 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_17 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
multiply(inverse(sk_c7),sk_c5) = sk_c6,
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_7 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_2 ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c7 ),
prove_this_18 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
prove_this_3 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6
| sk_c5 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_30])]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(sk_c7,X3) != sk_c6
| multiply(X4,sk_c7) != X3
| inverse(X4) != sk_c7 ),
prove_this_22 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_14 ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
prove_this_8 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_30]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| inverse(X1) != sk_c7
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6 ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_30])])]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_9 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_4 ).
cnf(c_0_53,negated_conjecture,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_19 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c5,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30]) ).
cnf(c_0_56,negated_conjecture,
( sk_c5 = sk_c7
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_58,negated_conjecture,
multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c5,X1),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c5,sk_c5) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( sk_c5 = sk_c7
| sk_c6 != sk_c7 ),
inference(ef,[status(thm)],[c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c7,multiply(X1,multiply(X2,sk_c7))) != sk_c6
| inverse(multiply(X1,X2)) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_30]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c6
| sk_c5 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_56]),c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c7,multiply(X1,sk_c5)) != sk_c6
| inverse(multiply(X1,sk_c5)) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_67,negated_conjecture,
( sk_c5 = sk_c7
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_64]),c_0_24]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(multiply(sk_c6,sk_c5)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_58]),c_0_66]) ).
cnf(c_0_69,negated_conjecture,
sk_c6 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_67]),c_0_24])]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| multiply(X1,sk_c7) != identity
| multiply(X2,identity) != sk_c7
| inverse(sk_c5) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != 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_68,c_0_69]),c_0_69]),c_0_25]),c_0_69]),c_0_69]),c_0_69]) ).
cnf(c_0_71,negated_conjecture,
sk_c5 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_69]),c_0_25])]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| multiply(X1,sk_c7) != identity
| multiply(X2,identity) != sk_c7
| inverse(sk_c7) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != identity ),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c7) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_69]),c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| multiply(X1,sk_c7) != identity
| multiply(X2,identity) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != identity ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| inverse(inverse(sk_c7)) != sk_c7
| multiply(X1,identity) != sk_c7
| inverse(X1) != identity ),
inference(spm,[status(thm)],[c_0_74,c_0_24]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c5,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_51]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| multiply(X1,identity) != sk_c7
| inverse(X1) != identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_73]),c_0_73]) ).
cnf(c_0_78,negated_conjecture,
multiply(sk_c7,identity) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_69]),c_0_71]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| sk_c5 = identity ),
inference(spm,[status(thm)],[c_0_76,c_0_63]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c7,sk_c4) = identity
| sk_c7 != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_73]),c_0_78])]) ).
cnf(c_0_81,negated_conjecture,
multiply(sk_c7,sk_c4) = identity,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_69]),c_0_71]),c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
prove_this_10 ).
cnf(c_0_83,negated_conjecture,
multiply(inverse(sk_c7),identity) = sk_c4,
inference(spm,[status(thm)],[c_0_26,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c7 ),
inference(rw,[status(thm)],[c_0_82,c_0_71]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| sk_c4 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_78]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c7) = sk_c7 ),
inference(rw,[status(thm)],[c_0_85,c_0_71]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c7
| sk_c4 = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
prove_this_11 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c7,sk_c2) = identity
| sk_c4 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_87]),c_0_78]) ).
cnf(c_0_91,negated_conjecture,
( multiply(inverse(inverse(sk_c3)),sk_c7) = sk_c4
| sk_c4 = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference(rw,[status(thm)],[c_0_89,c_0_71]) ).
cnf(c_0_93,negated_conjecture,
( sk_c4 = sk_c7
| sk_c4 = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_90]),c_0_83]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c4 = sk_c7
| sk_c4 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_24]) ).
cnf(c_0_95,negated_conjecture,
( sk_c4 = sk_c7
| sk_c2 != sk_c7 ),
inference(ef,[status(thm)],[c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c4 ),
prove_this_20 ).
cnf(c_0_97,negated_conjecture,
( sk_c4 = identity
| sk_c4 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_94]),c_0_78])]) ).
cnf(c_0_98,negated_conjecture,
( multiply(inverse(sk_c3),sk_c2) = sk_c7
| sk_c4 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_93]),c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c6,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c7,multiply(sk_c4,X1)) = X1
| sk_c7 != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_80]),c_0_25]) ).
cnf(c_0_101,negated_conjecture,
( sk_c4 = identity
| sk_c7 != identity ),
inference(ef,[status(thm)],[c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c7
| inverse(sk_c7) = sk_c7
| sk_c4 = sk_c7 ),
inference(spm,[status(thm)],[c_0_98,c_0_92]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c4 = sk_c7
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_92]),c_0_81]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
prove_this_15 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| sk_c1 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_69]),c_0_25]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c7 != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_25]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c7
| sk_c4 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_102]),c_0_78])]) ).
cnf(c_0_108,negated_conjecture,
( sk_c7 = identity
| sk_c4 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_103]),c_0_78])]) ).
cnf(c_0_109,negated_conjecture,
( multiply(inverse(sk_c7),identity) = sk_c4
| sk_c7 != identity ),
inference(spm,[status(thm)],[c_0_26,c_0_80]) ).
cnf(c_0_110,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c7
| sk_c1 = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
sk_c4 = sk_c7,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_95]) ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
prove_this_21 ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c7),X1) = multiply(sk_c4,X1)
| sk_c7 != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_109]),c_0_25]) ).
cnf(c_0_115,negated_conjecture,
( multiply(inverse(inverse(sk_c3)),sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_110]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_16 ).
cnf(c_0_117,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c7
| sk_c1 = identity ),
inference(rw,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c1) = identity
| inverse(sk_c3) = sk_c7 ),
inference(rw,[status(thm)],[c_0_113,c_0_69]) ).
cnf(c_0_119,negated_conjecture,
multiply(sk_c7,sk_c7) = identity,
inference(rw,[status(thm)],[c_0_81,c_0_112]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c4,sk_c7) = identity
| sk_c7 != identity ),
inference(spm,[status(thm)],[c_0_24,c_0_114]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| sk_c4 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_24]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c1) = identity
| sk_c1 = identity
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( multiply(inverse(sk_c4),identity) = sk_c7
| sk_c7 != identity ),
inference(spm,[status(thm)],[c_0_26,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c1,identity) = sk_c7
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_69]),c_0_112]) ).
cnf(c_0_125,negated_conjecture,
( sk_c7 = identity
| sk_c1 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_122]),c_0_25])]) ).
cnf(c_0_126,negated_conjecture,
( multiply(inverse(sk_c4),X1) = multiply(sk_c7,X1)
| sk_c7 != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_123]),c_0_25]) ).
cnf(c_0_127,negated_conjecture,
sk_c7 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_25])]) ).
cnf(c_0_128,negated_conjecture,
multiply(inverse(identity),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_112]),c_0_127]),c_0_127]),c_0_25]),c_0_127])]) ).
cnf(c_0_129,negated_conjecture,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_128]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c7,multiply(X1,sk_c7)) != identity
| multiply(X2,sk_c7) != identity
| multiply(X3,identity) != sk_c7
| inverse(sk_c7) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != sk_c7
| inverse(X3) != identity ),
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_50,c_0_69]),c_0_69]),c_0_25]),c_0_69]),c_0_69]),c_0_69]),c_0_71]),c_0_71])]) ).
cnf(c_0_131,negated_conjecture,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( multiply(X1,identity) != identity
| multiply(X2,identity) != identity
| multiply(X3,identity) != identity
| inverse(X1) != identity
| inverse(X2) != identity
| inverse(X3) != identity ),
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_130,c_0_127]),c_0_127]),c_0_25]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_131])]) ).
cnf(c_0_133,negated_conjecture,
( 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(spm,[status(thm)],[c_0_132,c_0_129]),c_0_131]),c_0_131]),c_0_131])]) ).
cnf(c_0_134,negated_conjecture,
( multiply(X1,identity) != identity
| inverse(X1) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_129]),c_0_131]),c_0_131]),c_0_131])]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_131]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP304-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n010.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 21:24:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.64 % Version : CSE_E---1.5
% 0.19/0.64 % Problem : theBenchmark.p
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark.p
% 0.19/0.64 % SZS output start Proof
% See solution above
% 0.19/0.64 % Total time : 0.062000 s
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time : 0.066000 s
%------------------------------------------------------------------------------