TSTP Solution File: GRP243-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP243-1 : 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 : n002.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 00:17:54 EDT 2023
% Result : Unsatisfiable 0.73s 0.85s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 42
% Syntax : Number of formulae : 152 ( 21 unt; 15 typ; 0 def)
% Number of atoms : 373 ( 372 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 365 ( 129 ~; 236 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 85 ( 2 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_c12: $i ).
tff(decl_27,type,
sk_c11: $i ).
tff(decl_28,type,
sk_c6: $i ).
tff(decl_29,type,
sk_c7: $i ).
tff(decl_30,type,
sk_c10: $i ).
tff(decl_31,type,
sk_c8: $i ).
tff(decl_32,type,
sk_c9: $i ).
tff(decl_33,type,
sk_c2: $i ).
tff(decl_34,type,
sk_c3: $i ).
tff(decl_35,type,
sk_c4: $i ).
tff(decl_36,type,
sk_c5: $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_37,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_64,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != sk_c11
| multiply(X7,sk_c10) != sk_c11
| multiply(X8,X9) != sk_c11
| inverse(X8) != X9
| multiply(X9,sk_c10) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_64) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_55,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_62,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_62) ).
cnf(prove_this_47,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_53,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_61,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_37 ).
cnf(c_0_32,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( multiply(inverse(sk_c3),sk_c12) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_30 ).
cnf(c_0_35,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != sk_c11
| multiply(X7,sk_c10) != sk_c11
| multiply(X8,X9) != sk_c11
| inverse(X8) != X9
| multiply(X9,sk_c10) != sk_c11 ),
prove_this_64 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_46 ).
cnf(c_0_39,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c7) = sk_c11 ),
prove_this_31 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c7) = sk_c11 ),
prove_this_10 ).
cnf(c_0_42,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_36 ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| multiply(X6,sk_c11) != sk_c10
| multiply(X7,sk_c12) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12
| inverse(X5) != sk_c12
| inverse(X6) != sk_c11
| inverse(X7) != sk_c12 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_37])]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c8) = sk_c9 ),
prove_this_55 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_48 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_62 ).
cnf(c_0_48,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c12) = sk_c1 ),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_47 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| multiply(X6,sk_c12) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_53 ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c12) = sk_c3
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c12) = sk_c1
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(inverse(sk_c3),sk_c12) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_29 ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(X1,sk_c10) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c12) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_28]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c11) = sk_c7
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c12 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c5) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_54 ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c11 = identity
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| inverse(sk_c7) != sk_c11
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c7) = sk_c11
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_39,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
multiply(sk_c12,sk_c12) = sk_c11,
inference(spm,[status(thm)],[c_0_42,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_28]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c3 = sk_c1
| sk_c11 = identity
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
multiply(inverse(sk_c12),sk_c11) = sk_c12,
inference(spm,[status(thm)],[c_0_30,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c9
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c11 = identity
| sk_c3 = sk_c1
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_39])]) ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(inverse(sk_c8)),sk_c9) = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c9 ),
prove_this_20 ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c3 = sk_c1
| sk_c11 = identity
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c12) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_72]),c_0_39])]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_28])]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_27 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_6 ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c11 = identity
| sk_c3 = sk_c1
| multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_80]),c_0_28])]) ).
cnf(c_0_83,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c9 ),
prove_this_13 ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c3 = sk_c1
| sk_c11 = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c8) = sk_c9 ),
prove_this_41 ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c9
| sk_c3 = sk_c1
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_73,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_85]),c_0_28])]) ).
cnf(c_0_88,negated_conjecture,
( sk_c3 = sk_c1
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_86]),c_0_28])]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c11,sk_c2) = identity
| inverse(sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c1,multiply(sk_c11,X1)) = multiply(sk_c12,X1)
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c11,sk_c2) = identity
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_90]),c_0_28])]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c12,sk_c2) = sk_c1
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_35]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_61 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c12,multiply(sk_c2,X1)) = multiply(sk_c1,X1)
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c9
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_94]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c1,sk_c11) = multiply(sk_c12,sk_c10)
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_95,c_0_78]) ).
cnf(c_0_98,negated_conjecture,
( multiply(inverse(inverse(sk_c8)),sk_c9) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c12,sk_c10) = sk_c12
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_89,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| inverse(sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_47]),c_0_28]) ).
cnf(c_0_102,negated_conjecture,
( sk_c11 = identity
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_99]),c_0_28]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_100]),c_0_28])]) ).
cnf(c_0_104,negated_conjecture,
( sk_c11 = identity
| sk_c5 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_35]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_18 ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c11,sk_c4) = identity
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_108,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c11 ),
prove_this_24 ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_46]),c_0_28])]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c11) = sk_c4
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_106]),c_0_35]) ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_25 ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c11) = sk_c2 ),
inference(spm,[status(thm)],[c_0_39,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_109,c_0_104]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c4,sk_c11) = identity
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_110]) ).
cnf(c_0_116,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c11 ),
prove_this_17 ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_28]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c11) = sk_c2
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
sk_c11 = identity,
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_121,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_116,c_0_35]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_117]) ).
cnf(c_0_123,negated_conjecture,
( multiply(inverse(sk_c7),sk_c11) = sk_c10
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
( sk_c7 = identity
| sk_c2 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_120]),c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( sk_c7 = identity
| sk_c2 = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_120]),c_0_35]),c_0_120]),c_0_121]) ).
cnf(c_0_126,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| multiply(X6,sk_c12) != sk_c11
| inverse(identity) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12
| sk_c10 != sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_116]),c_0_29]) ).
cnf(c_0_127,negated_conjecture,
( inverse(sk_c7) = sk_c10
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_120]),c_0_35]) ).
cnf(c_0_128,negated_conjecture,
( sk_c10 = identity
| sk_c7 = identity ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| multiply(X6,sk_c12) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12
| sk_c11 != identity
| sk_c10 != sk_c11 ),
inference(rw,[status(thm)],[c_0_126,c_0_121]) ).
cnf(c_0_130,negated_conjecture,
sk_c10 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_121])]) ).
cnf(c_0_131,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
cnf(c_0_132,negated_conjecture,
inverse(sk_c12) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_120]),c_0_35]) ).
cnf(c_0_133,negated_conjecture,
( multiply(X1,sk_c12) != identity
| inverse(X2) != identity
| inverse(X1) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[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(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)],[c_0_129,c_0_120]),c_0_120]),c_0_120]),c_0_120]),c_0_35]),c_0_120]),c_0_35]),c_0_120]),c_0_35]),c_0_120]),c_0_120]),c_0_120]),c_0_120]),c_0_120])])])])]),c_0_130]),c_0_35]),c_0_131]),c_0_130]),c_0_35]),c_0_132]),c_0_130]),c_0_121]),c_0_130])])]),c_0_121])]) ).
cnf(c_0_134,negated_conjecture,
multiply(sk_c12,sk_c12) = identity,
inference(rw,[status(thm)],[c_0_69,c_0_120]) ).
cnf(c_0_135,negated_conjecture,
inverse(X1) != identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_132])]) ).
cnf(c_0_136,plain,
$false,
inference(sr,[status(thm)],[c_0_121,c_0_135]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP243-1 : TPTP v8.1.2. Released v2.5.0.
% 0.09/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.30 % Computer : n002.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Aug 28 23:32:04 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.52 start to proof: theBenchmark
% 0.73/0.85 % Version : CSE_E---1.5
% 0.73/0.85 % Problem : theBenchmark.p
% 0.73/0.85 % Proof found
% 0.73/0.85 % SZS status Theorem for theBenchmark.p
% 0.73/0.85 % SZS output start Proof
% See solution above
% 0.73/0.86 % Total time : 0.321000 s
% 0.73/0.86 % SZS output end Proof
% 0.73/0.86 % Total time : 0.324000 s
%------------------------------------------------------------------------------