%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET960+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : 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 : Tue May 5 05:09:03 PM UTC 2026
% Result : Theorem 1.25s 1.73s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 107 ( 58 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 125 ( 51 ~; 56 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 78 ( 11 sgn 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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,
! [X35,X36,X37,X38,X41,X42,X43,X44,X45,X46,X48,X49] :
( ( in(esk2_4(X35,X36,X37,X38),X35)
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( in(esk3_4(X35,X36,X37,X38),X36)
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( X38 = ordered_pair(esk2_4(X35,X36,X37,X38),esk3_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(esk4_3(X44,X45,X46),X46)
| ~ in(X48,X44)
| ~ in(X49,X45)
| esk4_3(X44,X45,X46) != ordered_pair(X48,X49)
| X46 = cartesian_product2(X44,X45) )
& ( in(esk5_3(X44,X45,X46),X44)
| in(esk4_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) )
& ( in(esk6_3(X44,X45,X46),X45)
| in(esk4_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) )
& ( esk4_3(X44,X45,X46) = ordered_pair(esk5_3(X44,X45,X46),esk6_3(X44,X45,X46))
| in(esk4_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])])])])])]) ).
fof(c_0_5,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_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,
! [X31,X32,X33] :
( ( X31 != empty_set
| ~ in(X32,X31) )
& ( in(esk1_1(X33),X33)
| X33 = 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(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_15,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_16,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,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_18,negated_conjecture,
( esk10_0 = empty_set
| esk9_0 = empty_set
| ~ in(X1,esk10_0)
| ~ in(X2,esk9_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( in(esk3_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,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_22,negated_conjecture,
( esk9_0 = empty_set
| esk10_0 = empty_set
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
~ in(X1,cartesian_product2(X2,empty_set)),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_24,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_25,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_26,negated_conjecture,
( esk10_0 = empty_set
| esk9_0 = empty_set ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_27,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_28,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_29,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_30,negated_conjecture,
esk9_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
cartesian_product2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET960+1 : TPTP v9.2.1. Released v3.2.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:41:18 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.19/0.35 % start to proof: theBenchmark
% 1.25/1.73 % Version : CSE_E---1.7
% 1.25/1.73 % Problem : theBenchmark.p
% 1.25/1.73 % SZS status Theorem for theBenchmark.p
% 1.25/1.73 % SZS output start CNFRefutation
% See solution above
% 1.25/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------