TSTP Solution File: SET955+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET955+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 14:36:25 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 60 ( 10 unt; 18 typ; 0 def)
% Number of atoms : 133 ( 41 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 153 ( 62 ~; 71 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 12 >; 17 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 120 ( 4 sgn; 43 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_25,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton: $i > $i ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_29,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_30,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk6_0: $i ).
tff(decl_34,type,
esk7_0: $i ).
tff(decl_35,type,
esk8_0: $i ).
tff(decl_36,type,
esk9_0: $i ).
tff(decl_37,type,
esk10_0: $i ).
tff(decl_38,type,
esk11_0: $i ).
tff(decl_39,type,
esk12_2: ( $i * $i ) > $i ).
fof(t108_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
<=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
=> cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
<=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
=> cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
inference(assume_negation,[status(cth)],[t108_zfmisc_1]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X17,X18,X19,X20,X21,X22,X24,X25] :
( ( in(esk1_4(X11,X12,X13,X14),X11)
| ~ in(X14,X13)
| X13 != cartesian_product2(X11,X12) )
& ( in(esk2_4(X11,X12,X13,X14),X12)
| ~ in(X14,X13)
| X13 != cartesian_product2(X11,X12) )
& ( X14 = ordered_pair(esk1_4(X11,X12,X13,X14),esk2_4(X11,X12,X13,X14))
| ~ in(X14,X13)
| X13 != cartesian_product2(X11,X12) )
& ( ~ in(X18,X11)
| ~ in(X19,X12)
| X17 != ordered_pair(X18,X19)
| in(X17,X13)
| X13 != cartesian_product2(X11,X12) )
& ( ~ in(esk3_3(X20,X21,X22),X22)
| ~ in(X24,X20)
| ~ in(X25,X21)
| esk3_3(X20,X21,X22) != ordered_pair(X24,X25)
| X22 = cartesian_product2(X20,X21) )
& ( in(esk4_3(X20,X21,X22),X20)
| in(esk3_3(X20,X21,X22),X22)
| X22 = cartesian_product2(X20,X21) )
& ( in(esk5_3(X20,X21,X22),X21)
| in(esk3_3(X20,X21,X22),X22)
| X22 = cartesian_product2(X20,X21) )
& ( esk3_3(X20,X21,X22) = ordered_pair(esk4_3(X20,X21,X22),esk5_3(X20,X21,X22))
| in(esk3_3(X20,X21,X22),X22)
| X22 = cartesian_product2(X20,X21) ) ),
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_7,plain,
! [X28,X29] : ordered_pair(X28,X29) = unordered_pair(unordered_pair(X28,X29),singleton(X28)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
! [X38,X39] :
( ( ~ in(ordered_pair(X38,X39),cartesian_product2(esk8_0,esk9_0))
| in(ordered_pair(X38,X39),cartesian_product2(esk10_0,esk11_0)) )
& ( ~ in(ordered_pair(X38,X39),cartesian_product2(esk10_0,esk11_0))
| in(ordered_pair(X38,X39),cartesian_product2(esk8_0,esk9_0)) )
& cartesian_product2(esk8_0,esk9_0) != cartesian_product2(esk10_0,esk11_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,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_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( in(ordered_pair(X1,X2),cartesian_product2(esk8_0,esk9_0))
| ~ in(ordered_pair(X1,X2),cartesian_product2(esk10_0,esk11_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,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_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk8_0,esk9_0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk10_0,esk11_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
cnf(c_0_14,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_12])]) ).
fof(c_0_15,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( X1 = ordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk8_0,esk9_0))
| ~ in(X2,esk11_0)
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( X1 = unordered_pair(unordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1)),singleton(esk1_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk8_0,esk9_0))
| ~ in(X2,esk11_0)
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( unordered_pair(singleton(esk1_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),esk2_4(X1,X2,cartesian_product2(X1,X2),X3))) = X3
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_18])]) ).
cnf(c_0_22,plain,
( in(esk2_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,esk9_0))
| ~ in(esk2_4(X2,X3,cartesian_product2(X2,X3),X1),esk11_0)
| ~ in(esk1_4(X2,X3,cartesian_product2(X2,X3),X1),esk10_0)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
( in(esk1_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( in(ordered_pair(X1,X2),cartesian_product2(esk10_0,esk11_0))
| ~ in(ordered_pair(X1,X2),cartesian_product2(esk8_0,esk9_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,esk9_0))
| ~ in(esk1_4(X2,esk11_0,cartesian_product2(X2,esk11_0),X1),esk10_0)
| ~ in(X1,cartesian_product2(X2,esk11_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( in(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X40,X41] :
( ( ~ in(esk12_2(X40,X41),X40)
| ~ in(esk12_2(X40,X41),X41)
| X40 = X41 )
& ( in(esk12_2(X40,X41),X40)
| in(esk12_2(X40,X41),X41)
| X40 = X41 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_30,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk10_0,esk11_0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk8_0,esk9_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_10]),c_0_10]) ).
cnf(c_0_31,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,esk9_0))
| ~ in(X1,cartesian_product2(esk10_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( in(esk12_2(X1,X2),X1)
| in(esk12_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk10_0,esk11_0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk8_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( X1 = cartesian_product2(esk10_0,esk11_0)
| in(esk12_2(X1,cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0))
| in(esk12_2(X1,cartesian_product2(esk10_0,esk11_0)),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
cartesian_product2(esk8_0,esk9_0) != cartesian_product2(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,esk11_0))
| ~ in(X1,cartesian_product2(esk8_0,esk9_0))
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
in(esk12_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0)),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_34]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( in(esk12_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk10_0,esk11_0))
| ~ in(esk12_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
( X1 = X2
| ~ in(esk12_2(X1,X2),X1)
| ~ in(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,negated_conjecture,
in(esk12_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk10_0,esk11_0)),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_37])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET955+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 14:36:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.028000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.031000 s
%------------------------------------------------------------------------------