%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET955+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 134 ( 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 predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 124 ( 4 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/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,
! [X36,X37,X38,X39,X42,X43,X44,X45,X46,X47,X49,X50] :
( ( in(esk1_4(X36,X37,X38,X39),X36)
| ~ in(X39,X38)
| X38 != cartesian_product2(X36,X37) )
& ( in(esk2_4(X36,X37,X38,X39),X37)
| ~ in(X39,X38)
| X38 != cartesian_product2(X36,X37) )
& ( X39 = ordered_pair(esk1_4(X36,X37,X38,X39),esk2_4(X36,X37,X38,X39))
| ~ in(X39,X38)
| X38 != cartesian_product2(X36,X37) )
& ( ~ in(X43,X36)
| ~ in(X44,X37)
| X42 != ordered_pair(X43,X44)
| in(X42,X38)
| X38 != cartesian_product2(X36,X37) )
& ( ~ in(esk3_3(X45,X46,X47),X47)
| ~ in(X49,X45)
| ~ in(X50,X46)
| esk3_3(X45,X46,X47) != ordered_pair(X49,X50)
| X47 = cartesian_product2(X45,X46) )
& ( in(esk4_3(X45,X46,X47),X45)
| in(esk3_3(X45,X46,X47),X47)
| X47 = cartesian_product2(X45,X46) )
& ( in(esk5_3(X45,X46,X47),X46)
| in(esk3_3(X45,X46,X47),X47)
| X47 = cartesian_product2(X45,X46) )
& ( esk3_3(X45,X46,X47) = ordered_pair(esk4_3(X45,X46,X47),esk5_3(X45,X46,X47))
| in(esk3_3(X45,X46,X47),X47)
| X47 = cartesian_product2(X45,X46) ) ),
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,
! [X53,X54] : ordered_pair(X53,X54) = unordered_pair(unordered_pair(X53,X54),singleton(X53)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
! [X63,X64] :
( ( ~ in(ordered_pair(X63,X64),cartesian_product2(esk8_0,esk9_0))
| in(ordered_pair(X63,X64),cartesian_product2(esk10_0,esk11_0)) )
& ( ~ in(ordered_pair(X63,X64),cartesian_product2(esk10_0,esk11_0))
| in(ordered_pair(X63,X64),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]) ).
fof(c_0_12,plain,
! [X34,X35] : unordered_pair(X34,X35) = unordered_pair(X35,X34),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,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_14,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_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,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_13])]) ).
cnf(c_0_17,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk8_0,esk9_0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk10_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,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_20,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_21,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_22,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,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_20,c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_4(X2,esk11_0,cartesian_product2(X2,esk11_0),X3))),cartesian_product2(esk8_0,esk9_0))
| ~ in(X3,cartesian_product2(X2,esk11_0))
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,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_23,c_0_15])]) ).
cnf(c_0_26,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_27,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_28,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_24,c_0_25]) ).
cnf(c_0_29,plain,
( in(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_26]) ).
fof(c_0_30,plain,
! [X65,X66] :
( ( ~ in(esk12_2(X65,X66),X65)
| ~ in(esk12_2(X65,X66),X66)
| X65 = X66 )
& ( in(esk12_2(X65,X66),X65)
| in(esk12_2(X65,X66),X66)
| X65 = X66 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_31,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_27,c_0_10]),c_0_10]) ).
cnf(c_0_32,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,esk9_0))
| ~ in(X1,cartesian_product2(esk10_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( in(esk12_2(X1,X2),X1)
| in(esk12_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,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_31,c_0_15]) ).
cnf(c_0_35,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_32,c_0_33]) ).
cnf(c_0_36,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_37,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_34,c_0_25]) ).
cnf(c_0_38,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_35]),c_0_36]) ).
cnf(c_0_39,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_37,c_0_38]) ).
cnf(c_0_40,plain,
( X1 = X2
| ~ in(esk12_2(X1,X2),X1)
| ~ in(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,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_39,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_38])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET955+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n023.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 02:40:39 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------