%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET975+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n019.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 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 101 ( 33 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 104 ( 43 ~; 46 |; 10 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 4 con; 0-2 aty)
% Number of variables : 82 ( 10 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t128_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
<=> ( X1 = X3
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
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/sandbox/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/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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
<=> ( X1 = X3
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[t128_zfmisc_1]) ).
fof(c_0_6,plain,
! [X41,X42,X43,X44] :
( ( in(X41,X43)
| ~ in(ordered_pair(X41,X42),cartesian_product2(X43,X44)) )
& ( in(X42,X44)
| ~ in(ordered_pair(X41,X42),cartesian_product2(X43,X44)) )
& ( ~ in(X41,X43)
| ~ in(X42,X44)
| in(ordered_pair(X41,X42),cartesian_product2(X43,X44)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_7,plain,
! [X37,X38] : ordered_pair(X37,X38) = unordered_pair(unordered_pair(X37,X38),singleton(X37)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
( ( ~ in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0))
| esk4_0 != esk6_0
| ~ in(esk5_0,esk7_0) )
& ( esk4_0 = esk6_0
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) )
& ( in(esk5_0,esk7_0)
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) ) ),
inference(distribute,[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(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
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,
! [X28,X29] : unordered_pair(X28,X29) = unordered_pair(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,negated_conjecture,
( in(esk5_0,esk7_0)
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0))
| esk4_0 != esk6_0
| ~ in(esk5_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( in(esk5_0,esk7_0)
| in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( esk4_0 = esk6_0
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_19,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ in(X32,X31)
| X32 = X30
| X31 != singleton(X30) )
& ( X33 != X30
| in(X33,X31)
| X31 != singleton(X30) )
& ( ~ in(esk1_2(X34,X35),X35)
| esk1_2(X34,X35) != X34
| X35 = singleton(X34) )
& ( in(esk1_2(X34,X35),X35)
| esk1_2(X34,X35) = X34
| X35 = singleton(X34) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_20,negated_conjecture,
( esk6_0 != esk4_0
| ~ in(esk5_0,esk7_0)
| ~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( in(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),cartesian_product2(singleton(esk6_0),esk7_0))
| in(esk5_0,esk7_0) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( esk6_0 = esk4_0
| in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(rw,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_25,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( esk4_0 != esk6_0
| ~ in(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),cartesian_product2(singleton(esk6_0),esk7_0))
| ~ in(esk5_0,esk7_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_27,negated_conjecture,
in(esk5_0,esk7_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,negated_conjecture,
( esk4_0 = esk6_0
| in(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(rw,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
( esk4_0 != esk6_0
| ~ in(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
esk4_0 = esk6_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,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_31,c_0_10]) ).
cnf(c_0_35,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_36,negated_conjecture,
~ in(unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk5_0)),cartesian_product2(singleton(esk6_0),esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]),c_0_33])]) ).
cnf(c_0_37,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_38,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_35])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET975+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:41:29 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.27/1.71 % Version : CSE_E---1.7
% 1.27/1.71 % Problem : theBenchmark.p
% 1.27/1.71 % SZS status Theorem for theBenchmark.p
% 1.27/1.71 % SZS output start CNFRefutation
% See solution above
% 1.27/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------