%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET872+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 : n026.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 05:08:52 PM UTC 2026
% Result : Theorem 1.23s 1.72s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 71 ( 33 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 81 ( 29 ~; 36 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 52 ( 2 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t12_zfmisc_1,conjecture,
! [X1,X2] : subset(singleton(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_4,plain,
! [X29,X30,X31,X32,X33,X34] :
( ( ~ in(X31,X30)
| X31 = X29
| X30 != singleton(X29) )
& ( X32 != X29
| in(X32,X30)
| X30 != singleton(X29) )
& ( ~ in(esk1_2(X33,X34),X34)
| esk1_2(X33,X34) != X33
| X34 = singleton(X33) )
& ( in(esk1_2(X33,X34),X34)
| esk1_2(X33,X34) = X33
| X34 = singleton(X33) ) ),
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_5,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X45,X46,X47,X48,X49] :
( ( ~ subset(X45,X46)
| ~ in(X47,X45)
| in(X47,X46) )
& ( in(esk3_2(X48,X49),X48)
| subset(X48,X49) )
& ( ~ in(esk3_2(X48,X49),X49)
| subset(X48,X49) ) ),
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,
~ ! [X1,X2] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[t12_zfmisc_1]) ).
cnf(c_0_8,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X36,X37,X38,X39,X40,X41,X42,X43] :
( ( ~ in(X39,X38)
| X39 = X36
| X39 = X37
| X38 != unordered_pair(X36,X37) )
& ( X40 != X36
| in(X40,X38)
| X38 != unordered_pair(X36,X37) )
& ( X40 != X37
| in(X40,X38)
| X38 != unordered_pair(X36,X37) )
& ( esk2_3(X41,X42,X43) != X41
| ~ in(esk2_3(X41,X42,X43),X43)
| X43 = unordered_pair(X41,X42) )
& ( esk2_3(X41,X42,X43) != X42
| ~ in(esk2_3(X41,X42,X43),X43)
| X43 = unordered_pair(X41,X42) )
& ( in(esk2_3(X41,X42,X43),X43)
| esk2_3(X41,X42,X43) = X41
| esk2_3(X41,X42,X43) = X42
| X43 = unordered_pair(X41,X42) ) ),
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])])])])])]) ).
fof(c_0_11,negated_conjecture,
~ subset(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( esk3_2(singleton(X1),X2) = X1
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ subset(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET872+1 : TPTP v9.2.1. Released v3.2.0.
% 0.11/0.13 % 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
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 5 02:38:23 EDT 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 1.23/1.72 % Version : CSE_E---1.7
% 1.23/1.72 % Problem : theBenchmark.p
% 1.23/1.72 % SZS status Theorem for theBenchmark.p
% 1.23/1.72 % SZS output start CNFRefutation
% See solution above
% 1.23/1.72 % Total time : 1.367s
%------------------------------------------------------------------------------