TSTP Solution File: NUN076+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUN076+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 12:45:54 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 63 ( 18 unt; 24 typ; 0 def)
% Number of atoms : 112 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 49 ~; 37 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 23 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 89 ( 15 sgn; 21 !; 25 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
r1: $i > $o ).
tff(decl_23,type,
r2: ( $i * $i ) > $o ).
tff(decl_24,type,
r3: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
r4: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
esk1_0: $i ).
tff(decl_27,type,
esk2_1: $i > $i ).
tff(decl_28,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk13_1: $i > $i ).
tff(decl_39,type,
esk14_1: $i > $i ).
tff(decl_40,type,
esk15_1: $i > $i ).
tff(decl_41,type,
esk16_1: $i > $i ).
tff(decl_42,type,
esk17_1: $i > $i ).
tff(decl_43,type,
esk18_1: $i > $i ).
tff(decl_44,type,
esk19_1: $i > $i ).
tff(decl_45,type,
esk20_1: $i > $i ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_5a,axiom,
! [X33] :
? [X34] :
( ? [X35] :
( r1(X35)
& r4(X33,X35,X34) )
& ? [X36] :
( r1(X36)
& X34 = X36 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(thereexistsanevennumber,conjecture,
? [X39,X22,X23] :
( ? [X16] :
( X16 = X39
& ? [X25] :
( r4(X25,X22,X16)
& ? [X19] :
( r2(X19,X25)
& ? [X34] :
( r1(X34)
& r2(X34,X19) ) ) ) )
& ? [X17] :
( r3(X22,X23,X17)
& X17 = X39 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thereexistsanevennumber) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(c_0_5,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_6,plain,
! [X76] :
( r1(esk16_1(X76))
& r4(X76,esk16_1(X76),esk15_1(X76))
& r1(esk17_1(X76))
& esk15_1(X76) = esk17_1(X76) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_7,negated_conjecture,
~ ? [X39,X22,X23] :
( ? [X16] :
( X16 = X39
& ? [X25] :
( r4(X25,X22,X16)
& ? [X19] :
( r2(X19,X25)
& ? [X34] :
( r1(X34)
& r2(X34,X19) ) ) ) )
& ? [X17] :
( r3(X22,X23,X17)
& X17 = X39 ) ),
inference(assume_negation,[status(cth)],[thereexistsanevennumber]) ).
fof(c_0_8,plain,
! [X45] :
( ( r1(X45)
| ~ r1(X45) )
& ( X45 = esk1_0
| ~ r1(X45) )
& ( r1(X45)
| X45 != esk1_0 )
& ( X45 = esk1_0
| X45 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
! [X87,X88,X89,X90,X91,X92,X93,X94] :
( X90 != X87
| ~ r4(X91,X88,X90)
| ~ r2(X92,X91)
| ~ r1(X93)
| ~ r2(X93,X92)
| ~ r3(X88,X89,X94)
| X94 != X87 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_15,plain,
! [X73] :
( r1(esk14_1(X73))
& r3(X73,esk14_1(X73),esk13_1(X73))
& esk13_1(X73) = X73 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_16,negated_conjecture,
( X1 != X2
| ~ r4(X3,X4,X1)
| ~ r2(X5,X3)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r3(X4,X7,X8)
| X8 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_20,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( ~ r4(X1,X2,X3)
| ~ r3(X2,X4,X3)
| ~ r2(X5,X6)
| ~ r2(X6,X1)
| ~ r1(X5) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_24,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
fof(c_0_27,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_28,negated_conjecture,
( ~ r3(esk1_0,X1,esk1_0)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_31,plain,
! [X46,X48] :
( ( r2(X46,X48)
| ~ r2(X46,X48) )
& ( X48 = esk2_1(X46)
| ~ r2(X46,X48) )
& ( r2(X46,X48)
| X48 != esk2_1(X46) )
& ( X48 = esk2_1(X46)
| X48 != esk2_1(X46) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_27])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( ~ r2(esk1_0,X1)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
~ r2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_37,c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN076+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 10:12:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.008000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.011000 s
%------------------------------------------------------------------------------