%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET961+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 : 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 05:09:03 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 93 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 94 ( 39 ~; 40 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 13 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l55_zfmisc_1,axiom,
! [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(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(t114_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
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,plain,
! [X38,X39,X40,X41] :
( ( in(X38,X40)
| ~ in(ordered_pair(X38,X39),cartesian_product2(X40,X41)) )
& ( in(X39,X41)
| ~ in(ordered_pair(X38,X39),cartesian_product2(X40,X41)) )
& ( ~ in(X38,X40)
| ~ in(X39,X41)
| in(ordered_pair(X38,X39),cartesian_product2(X40,X41)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X34,X35] : ordered_pair(X34,X35) = unordered_pair(unordered_pair(X34,X35),singleton(X34)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
inference(assume_negation,[status(cth)],[t114_zfmisc_1]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
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,negated_conjecture,
( cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk5_0,esk4_0)
& esk4_0 != empty_set
& esk5_0 != empty_set
& esk4_0 != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_15,plain,
! [X30,X31,X32] :
( ( X30 != empty_set
| ~ in(X31,X30) )
& ( in(esk1_1(X32),X32)
| X32 = 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_11])])])])]) ).
cnf(c_0_16,negated_conjecture,
( in(X1,esk5_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_14,c_0_9]) ).
fof(c_0_18,plain,
! [X46,X47] :
( ( ~ in(esk6_2(X46,X47),X46)
| ~ in(esk6_2(X46,X47),X47)
| X46 = X47 )
& ( in(esk6_2(X46,X47),X46)
| in(esk6_2(X46,X47),X47)
| X46 = X47 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_19,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk4_0)
| ~ in(X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( in(esk6_2(X1,X2),X1)
| in(esk6_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( esk4_0 = X1
| in(esk6_2(esk4_0,X1),esk5_0)
| in(esk6_2(esk4_0,X1),X1)
| ~ in(X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( empty_set = X1
| in(esk6_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( esk4_0 = X1
| in(esk6_2(esk4_0,X1),esk5_0)
| in(esk6_2(esk4_0,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk4_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_13]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ in(esk6_2(X1,X2),X1)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,negated_conjecture,
in(esk6_2(esk4_0,esk5_0),esk5_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_28]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X2,esk4_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_34,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
~ in(esk6_2(esk4_0,esk5_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk5_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET961+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
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:40:16 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------