%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET977+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 : n015.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 05:09:04 PM UTC 2026
% Result : Theorem 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 72 ( 36 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 36 ~; 25 |; 10 &)
% ( 4 <=>; 2 =>; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t128_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
<=> ( X1 = X3
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_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(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(t130_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(singleton(X2),X1) != empty_set
& cartesian_product2(X1,singleton(X2)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(t129_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(c_0_6,plain,
! [X41,X42,X43,X44] :
( ( X41 = X43
| ~ in(ordered_pair(X41,X42),cartesian_product2(singleton(X43),X44)) )
& ( in(X42,X44)
| ~ in(ordered_pair(X41,X42),cartesian_product2(singleton(X43),X44)) )
& ( X41 != X43
| ~ in(X42,X44)
| in(ordered_pair(X41,X42),cartesian_product2(singleton(X43),X44)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t128_zfmisc_1])])]) ).
fof(c_0_7,plain,
! [X35,X36] : ordered_pair(X35,X36) = unordered_pair(unordered_pair(X35,X36),singleton(X35)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),X4))
| X1 != X2
| ~ in(X3,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]) ).
fof(c_0_11,plain,
! [X29,X30] : unordered_pair(X29,X30) = unordered_pair(X30,X29),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(singleton(X2),X1) != empty_set
& cartesian_product2(X1,singleton(X2)) != empty_set ) ),
inference(assume_negation,[status(cth)],[t130_zfmisc_1]) ).
fof(c_0_13,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_8])])])])]) ).
fof(c_0_14,plain,
! [X45,X46,X47,X48] :
( ( in(X45,X47)
| ~ in(ordered_pair(X45,X46),cartesian_product2(X47,singleton(X48))) )
& ( X46 = X48
| ~ in(ordered_pair(X45,X46),cartesian_product2(X47,singleton(X48))) )
& ( ~ in(X45,X47)
| X46 != X48
| in(ordered_pair(X45,X46),cartesian_product2(X47,singleton(X48))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t129_zfmisc_1])])]) ).
cnf(c_0_15,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(singleton(X2),X4))
| X1 != X2
| ~ in(X3,X4) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
( esk4_0 != empty_set
& ( cartesian_product2(singleton(esk5_0),esk4_0) = empty_set
| cartesian_product2(esk4_0,singleton(esk5_0)) = empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_18,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,singleton(X4)))
| ~ in(X1,X2)
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(singleton(X1),X3))
| ~ in(X2,X3) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_21,negated_conjecture,
( cartesian_product2(singleton(esk5_0),esk4_0) = empty_set
| cartesian_product2(esk4_0,singleton(esk5_0)) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,singleton(X4)))
| X3 != X4
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( cartesian_product2(esk4_0,singleton(esk5_0)) = empty_set
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,singleton(X2)))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16])]) ).
cnf(c_0_28,negated_conjecture,
cartesian_product2(esk4_0,singleton(esk5_0)) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
~ in(X1,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET977+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.13/0.32 % Computer : n015.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:41:32 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Theorem for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------