%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU157+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n006.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 05:10:50 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 130 ( 52 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 146 ( 60 ~; 66 |; 15 &)
% ( 4 <=>; 1 =>; 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 : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 127 ( 11 sgn 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t33_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_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(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(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(l55_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(c_0_5,plain,
! [X62,X63,X64,X65] :
( ( X62 = X64
| ordered_pair(X62,X63) != ordered_pair(X64,X65) )
& ( X63 = X65
| ordered_pair(X62,X63) != ordered_pair(X64,X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X52,X53] : ordered_pair(X52,X53) = unordered_pair(unordered_pair(X52,X53),singleton(X52)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,plain,
! [X35,X36,X37,X38,X41,X42,X43,X44,X45,X46,X48,X49] :
( ( in(esk1_4(X35,X36,X37,X38),X35)
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( in(esk2_4(X35,X36,X37,X38),X36)
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( X38 = ordered_pair(esk1_4(X35,X36,X37,X38),esk2_4(X35,X36,X37,X38))
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( ~ in(X42,X35)
| ~ in(X43,X36)
| X41 != ordered_pair(X42,X43)
| in(X41,X37)
| X37 != cartesian_product2(X35,X36) )
& ( ~ in(esk3_3(X44,X45,X46),X46)
| ~ in(X48,X44)
| ~ in(X49,X45)
| esk3_3(X44,X45,X46) != ordered_pair(X48,X49)
| X46 = cartesian_product2(X44,X45) )
& ( in(esk4_3(X44,X45,X46),X44)
| in(esk3_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) )
& ( in(esk5_3(X44,X45,X46),X45)
| in(esk3_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) )
& ( esk3_3(X44,X45,X46) = ordered_pair(esk4_3(X44,X45,X46),esk5_3(X44,X45,X46))
| in(esk3_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) ) ),
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])])])])])]) ).
cnf(c_0_8,plain,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X33,X34] : unordered_pair(X33,X34) = unordered_pair(X34,X33),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,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_7]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[l55_zfmisc_1]) ).
cnf(c_0_13,plain,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),singleton(X1)) != unordered_pair(unordered_pair(X2,X4),singleton(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,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_11,c_0_9]) ).
fof(c_0_16,negated_conjecture,
( ( ~ in(ordered_pair(esk6_0,esk7_0),cartesian_product2(esk8_0,esk9_0))
| ~ in(esk6_0,esk8_0)
| ~ in(esk7_0,esk9_0) )
& ( in(esk6_0,esk8_0)
| in(ordered_pair(esk6_0,esk7_0),cartesian_product2(esk8_0,esk9_0)) )
& ( in(esk7_0,esk9_0)
| in(ordered_pair(esk6_0,esk7_0),cartesian_product2(esk8_0,esk9_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_17,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_7]) ).
cnf(c_0_18,plain,
( in(esk1_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),singleton(X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,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_15,c_0_14])]) ).
cnf(c_0_21,plain,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(ordered_pair(esk6_0,esk7_0),cartesian_product2(esk8_0,esk9_0))
| ~ in(esk6_0,esk8_0)
| ~ in(esk7_0,esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17,c_0_9]) ).
cnf(c_0_24,plain,
( in(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( esk1_4(X1,X2,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X4),singleton(X3))) = X3
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
( in(esk6_0,esk8_0)
| in(ordered_pair(esk6_0,esk7_0),cartesian_product2(esk8_0,esk9_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),singleton(X3)) != unordered_pair(unordered_pair(X4,X2),singleton(X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_9]),c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(esk6_0,esk8_0)
| ~ in(esk7_0,esk9_0)
| ~ in(unordered_pair(unordered_pair(esk6_0,esk7_0),singleton(esk6_0)),cartesian_product2(esk8_0,esk9_0)) ),
inference(rw,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_29,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_23])]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( in(esk6_0,esk8_0)
| in(unordered_pair(unordered_pair(esk6_0,esk7_0),singleton(esk6_0)),cartesian_product2(esk8_0,esk9_0)) ),
inference(rw,[status(thm)],[c_0_26,c_0_9]) ).
cnf(c_0_32,plain,
( in(esk2_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,plain,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),singleton(X3)) != unordered_pair(singleton(X4),unordered_pair(X4,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( in(esk7_0,esk9_0)
| in(ordered_pair(esk6_0,esk7_0),cartesian_product2(esk8_0,esk9_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,negated_conjecture,
( ~ in(esk6_0,esk8_0)
| ~ in(esk7_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
in(esk6_0,esk8_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( esk2_4(X1,X2,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X4),singleton(X3))) = X4
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20])]) ).
cnf(c_0_39,negated_conjecture,
( in(esk7_0,esk9_0)
| in(unordered_pair(unordered_pair(esk6_0,esk7_0),singleton(esk6_0)),cartesian_product2(esk8_0,esk9_0)) ),
inference(rw,[status(thm)],[c_0_34,c_0_9]) ).
cnf(c_0_40,negated_conjecture,
~ in(esk7_0,esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_41,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
in(unordered_pair(unordered_pair(esk6_0,esk7_0),singleton(esk6_0)),cartesian_product2(esk8_0,esk9_0)),
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU157+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:45:31 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------