TSTP Solution File: SET960+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET960+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n017.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 14:36:27 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 53 ( 12 unt; 17 typ; 0 def)
% Number of atoms : 111 ( 62 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 127 ( 52 ~; 57 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 12 >; 16 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 80 ( 13 sgn; 31 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_26,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
singleton: $i > $i ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
esk1_1: $i > $i ).
tff(decl_30,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_31,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk7_0: $i ).
tff(decl_36,type,
esk8_0: $i ).
tff(decl_37,type,
esk9_0: $i ).
tff(decl_38,type,
esk10_0: $i ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t113_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(c_0_4,plain,
! [X15,X16,X17,X18,X21,X22,X23,X24,X25,X26,X28,X29] :
( ( in(esk2_4(X15,X16,X17,X18),X15)
| ~ in(X18,X17)
| X17 != cartesian_product2(X15,X16) )
& ( in(esk3_4(X15,X16,X17,X18),X16)
| ~ in(X18,X17)
| X17 != cartesian_product2(X15,X16) )
& ( X18 = ordered_pair(esk2_4(X15,X16,X17,X18),esk3_4(X15,X16,X17,X18))
| ~ in(X18,X17)
| X17 != cartesian_product2(X15,X16) )
& ( ~ in(X22,X15)
| ~ in(X23,X16)
| X21 != ordered_pair(X22,X23)
| in(X21,X17)
| X17 != cartesian_product2(X15,X16) )
& ( ~ in(esk4_3(X24,X25,X26),X26)
| ~ in(X28,X24)
| ~ in(X29,X25)
| esk4_3(X24,X25,X26) != ordered_pair(X28,X29)
| X26 = cartesian_product2(X24,X25) )
& ( in(esk5_3(X24,X25,X26),X24)
| in(esk4_3(X24,X25,X26),X26)
| X26 = cartesian_product2(X24,X25) )
& ( in(esk6_3(X24,X25,X26),X25)
| in(esk4_3(X24,X25,X26),X26)
| X26 = cartesian_product2(X24,X25) )
& ( esk4_3(X24,X25,X26) = ordered_pair(esk5_3(X24,X25,X26),esk6_3(X24,X25,X26))
| in(esk4_3(X24,X25,X26),X26)
| X26 = cartesian_product2(X24,X25) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])]) ).
fof(c_0_5,plain,
! [X32,X33] : ordered_pair(X32,X33) = unordered_pair(unordered_pair(X32,X33),singleton(X32)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_6,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_7,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[t113_zfmisc_1]) ).
fof(c_0_10,plain,
! [X11,X12,X13] :
( ( X11 != empty_set
| ~ in(X12,X11) )
& ( in(esk1_1(X13),X13)
| X13 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_11,plain,
( in(X5,X6)
| X6 != cartesian_product2(X2,X4)
| X5 != unordered_pair(unordered_pair(X1,X3),singleton(X1))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_12,negated_conjecture,
( ( esk9_0 != empty_set
| cartesian_product2(esk9_0,esk10_0) != empty_set )
& ( esk10_0 != empty_set
| cartesian_product2(esk9_0,esk10_0) != empty_set )
& ( cartesian_product2(esk9_0,esk10_0) = empty_set
| esk9_0 = empty_set
| esk10_0 = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_13,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(esk3_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).
cnf(c_0_16,negated_conjecture,
( cartesian_product2(esk9_0,esk10_0) = empty_set
| esk9_0 = empty_set
| esk10_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(esk3_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( empty_set = esk10_0
| empty_set = esk9_0
| ~ in(X1,esk10_0)
| ~ in(X2,esk9_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
~ in(X1,cartesian_product2(X2,empty_set)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( empty_set = esk9_0
| empty_set = esk10_0
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( in(esk2_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_24,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( empty_set = esk10_0
| empty_set = esk9_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_26,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( esk10_0 != empty_set
| cartesian_product2(esk9_0,esk10_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,negated_conjecture,
( cartesian_product2(X1,esk10_0) = esk10_0
| empty_set = esk9_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( esk9_0 != empty_set
| cartesian_product2(esk9_0,esk10_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,negated_conjecture,
empty_set = esk9_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]) ).
cnf(c_0_32,plain,
cartesian_product2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_33,negated_conjecture,
cartesian_product2(esk9_0,esk10_0) != esk9_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31])]) ).
cnf(c_0_34,plain,
cartesian_product2(esk9_0,X1) = esk9_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET960+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.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 : Sat Aug 26 10:43:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 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
% 0.19/0.60 % Total time : 0.009000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.012000 s
%------------------------------------------------------------------------------