%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET957+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : Tue May 5 05:09:02 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 94 ( 21 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 38 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 84 ( 4 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t110_zfmisc_1,conjecture,
! [X1,X2,X3,X4,X5,X6] :
( ( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( in(ordered_pair(X7,X8),X1)
<=> in(ordered_pair(X7,X8),X4) ) )
=> X1 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_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(t103_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
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] :
( ( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( in(ordered_pair(X7,X8),X1)
<=> in(ordered_pair(X7,X8),X4) ) )
=> X1 = X4 ),
inference(assume_negation,[status(cth)],[t110_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
! [X61,X62] :
( subset(esk5_0,cartesian_product2(esk6_0,esk7_0))
& subset(esk8_0,cartesian_product2(esk9_0,esk10_0))
& ( ~ in(ordered_pair(X61,X62),esk5_0)
| in(ordered_pair(X61,X62),esk8_0) )
& ( ~ in(ordered_pair(X61,X62),esk8_0)
| in(ordered_pair(X61,X62),esk5_0) )
& esk5_0 != esk8_0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X42,X43] : ordered_pair(X42,X43) = unordered_pair(unordered_pair(X42,X43),singleton(X42)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X49,X50,X51,X52] :
( ( in(esk3_4(X49,X50,X51,X52),X50)
| ~ subset(X49,cartesian_product2(X50,X51))
| ~ in(X52,X49) )
& ( in(esk4_4(X49,X50,X51,X52),X51)
| ~ subset(X49,cartesian_product2(X50,X51))
| ~ in(X52,X49) )
& ( X52 = ordered_pair(esk3_4(X49,X50,X51,X52),esk4_4(X49,X50,X51,X52))
| ~ subset(X49,cartesian_product2(X50,X51))
| ~ in(X52,X49) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t103_zfmisc_1])])])]) ).
cnf(c_0_9,negated_conjecture,
( in(ordered_pair(X1,X2),esk5_0)
| ~ in(ordered_pair(X1,X2),esk8_0) ),
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]) ).
fof(c_0_11,plain,
! [X40,X41] : unordered_pair(X40,X41) = unordered_pair(X41,X40),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( X1 = ordered_pair(esk3_4(X2,X3,X4,X1),esk4_4(X2,X3,X4,X1))
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk5_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk8_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = unordered_pair(unordered_pair(esk3_4(X2,X3,X4,X1),esk4_4(X2,X3,X4,X1)),singleton(esk3_4(X2,X3,X4,X1)))
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk5_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk8_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( unordered_pair(singleton(esk3_4(X1,X2,X3,X4)),unordered_pair(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4))) = X4
| ~ subset(X1,cartesian_product2(X2,X3))
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( in(X1,esk5_0)
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,esk8_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
subset(esk8_0,cartesian_product2(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_20,plain,
! [X63,X64] :
( ( ~ in(esk11_2(X63,X64),X63)
| ~ in(esk11_2(X63,X64),X64)
| X63 = X64 )
& ( in(esk11_2(X63,X64),X63)
| in(esk11_2(X63,X64),X64)
| X63 = X64 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_21,negated_conjecture,
( in(ordered_pair(X1,X2),esk8_0)
| ~ in(ordered_pair(X1,X2),esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( in(esk11_2(X1,X2),X1)
| in(esk11_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk8_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_10]),c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( esk8_0 = X1
| in(esk11_2(esk8_0,X1),esk5_0)
| in(esk11_2(esk8_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
esk5_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk8_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ in(esk11_2(X1,X2),X1)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
in(esk11_2(esk8_0,esk5_0),esk5_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk8_0)
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,esk5_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
subset(esk5_0,cartesian_product2(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk11_2(esk8_0,esk5_0),esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,esk8_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET957+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:43:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.367s
%------------------------------------------------------------------------------