%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET885+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 : n028.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 05:08:54 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 74 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 86 ( 31 ~; 36 |; 11 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 2 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
inference(assume_negation,[status(cth)],[t26_zfmisc_1]) ).
fof(c_0_5,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])])])])])]) ).
fof(c_0_6,plain,
! [X46,X47,X48,X49,X50] :
( ( ~ subset(X46,X47)
| ~ in(X48,X46)
| in(X48,X47) )
& ( in(esk3_2(X49,X50),X49)
| subset(X49,X50) )
& ( ~ in(esk3_2(X49,X50),X50)
| subset(X49,X50) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_7,negated_conjecture,
( subset(unordered_pair(esk6_0,esk7_0),singleton(esk8_0))
& esk6_0 != esk8_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(unordered_pair(esk6_0,esk7_0),singleton(esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44] :
( ( ~ in(X40,X39)
| X40 = X37
| X40 = X38
| X39 != unordered_pair(X37,X38) )
& ( X41 != X37
| in(X41,X39)
| X39 != unordered_pair(X37,X38) )
& ( X41 != X38
| in(X41,X39)
| X39 != unordered_pair(X37,X38) )
& ( esk2_3(X42,X43,X44) != X42
| ~ in(esk2_3(X42,X43,X44),X44)
| X44 = unordered_pair(X42,X43) )
& ( esk2_3(X42,X43,X44) != X43
| ~ in(esk2_3(X42,X43,X44),X44)
| X44 = unordered_pair(X42,X43) )
& ( in(esk2_3(X42,X43,X44),X44)
| esk2_3(X42,X43,X44) = X42
| esk2_3(X42,X43,X44) = X43
| X44 = unordered_pair(X42,X43) ) ),
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_tarski])])])])])]) ).
cnf(c_0_12,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(X1,singleton(esk8_0))
| ~ in(X1,unordered_pair(esk6_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( X1 = esk8_0
| ~ in(X1,unordered_pair(esk6_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_17,negated_conjecture,
esk6_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET885+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.13/0.32 % Computer : n028.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 02:38:46 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------