TSTP Solution File: NUN062+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUN062+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 : n019.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 12:45:48 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 30
% Syntax : Number of formulae : 51 ( 7 unt; 26 typ; 0 def)
% Number of atoms : 73 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 88 ( 40 ~; 28 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 24 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 5 sgn; 26 !; 12 ?; 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 ).
tff(decl_46,type,
esk21_0: $i ).
tff(decl_47,type,
esk22_2: ( $i * $i ) > $i ).
fof(infiniteNumbers,conjecture,
! [X14] :
? [X22,X39] :
( ! [X16] :
( ~ r1(X16)
| X39 != X16 )
& ? [X23] :
( r3(X14,X39,X23)
& X23 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbers) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
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_4,negated_conjecture,
~ ! [X14] :
? [X22,X39] :
( ! [X16] :
( ~ r1(X16)
| X39 != X16 )
& ? [X23] :
( r3(X14,X39,X23)
& X23 = X22 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[infiniteNumbers])]) ).
fof(c_0_5,plain,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_6,negated_conjecture,
! [X88,X89,X91] :
( ( r1(esk22_2(X88,X89))
| ~ r3(esk21_0,X89,X91)
| X91 != X88 )
& ( X89 = esk22_2(X88,X89)
| ~ r3(esk21_0,X89,X91)
| X91 != X88 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
fof(c_0_7,plain,
! [X84,X85,X86] :
( ~ r1(X86)
| X86 != X85
| ~ r2(X84,X85) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
cnf(c_0_8,negated_conjecture,
( r1(esk22_2(X1,X2))
| ~ r3(esk21_0,X2,X3)
| X3 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X57,X58] :
( r2(X58,esk7_2(X57,X58))
& r3(X57,esk7_2(X57,X58),esk6_2(X57,X58))
& esk6_2(X57,X58) = esk5_2(X57,X58)
& r2(esk8_2(X57,X58),esk5_2(X57,X58))
& r3(X57,X58,esk8_2(X57,X58)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_10,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_11,plain,
( ~ r1(X1)
| X1 != X2
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( r1(esk22_2(X1,X2))
| ~ r3(esk21_0,X2,X1) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( X1 = esk22_2(X2,X1)
| ~ r3(esk21_0,X1,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_15,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_10])])]) ).
cnf(c_0_16,plain,
( ~ r2(X1,X2)
| ~ r1(X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
r1(esk22_2(esk8_2(esk21_0,X1),X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( esk22_2(X1,X2) = X2
| ~ r3(esk21_0,X2,X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
~ r2(X1,esk22_2(esk8_2(esk21_0,X2),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
esk22_2(esk8_2(esk21_0,X1),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_22,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
~ r2(X1,X2),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
$false,
inference(sr,[status(thm)],[c_0_22,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.36 % Computer : n019.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Aug 27 09:03:43 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.60 start to proof: theBenchmark
% 0.21/0.62 % Version : CSE_E---1.5
% 0.21/0.62 % Problem : theBenchmark.p
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark.p
% 0.21/0.62 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.007000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.010000 s
%------------------------------------------------------------------------------