%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU158+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n005.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 05:10:50 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 71 ( 19 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 70 ( 27 ~; 29 |; 7 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_zfmisc_1,conjecture,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
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(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
inference(assume_negation,[status(cth)],[t37_zfmisc_1]) ).
fof(c_0_6,lemma,
! [X307,X308] :
( ( ~ subset(singleton(X307),X308)
| in(X307,X308) )
& ( ~ in(X307,X308)
| subset(singleton(X307),X308) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(c_0_7,lemma,
! [X393] : unordered_pair(X393,X393) = singleton(X393),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_8,negated_conjecture,
( ( ~ subset(singleton(esk20_0),esk21_0)
| ~ in(esk20_0,esk21_0) )
& ( subset(singleton(esk20_0),esk21_0)
| in(esk20_0,esk21_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( subset(singleton(esk20_0),esk21_0)
| in(esk20_0,esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X197,X198,X199,X200,X201,X202] :
( ( ~ in(X199,X198)
| X199 = X197
| X198 != singleton(X197) )
& ( X200 != X197
| in(X200,X198)
| X198 != singleton(X197) )
& ( ~ in(esk1_2(X201,X202),X202)
| esk1_2(X201,X202) != X201
| X202 = singleton(X201) )
& ( in(esk1_2(X201,X202),X202)
| esk1_2(X201,X202) = X201
| X202 = singleton(X201) ) ),
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_13,negated_conjecture,
( ~ subset(singleton(esk20_0),esk21_0)
| ~ in(esk20_0,esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( in(esk20_0,esk21_0)
| subset(unordered_pair(esk20_0,esk20_0),esk21_0) ),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(esk20_0,esk21_0)
| ~ subset(unordered_pair(esk20_0,esk20_0),esk21_0) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
in(esk20_0,esk21_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X250,X251,X252,X253,X254] :
( ( ~ subset(X250,X251)
| ~ in(X252,X250)
| in(X252,X251) )
& ( in(esk11_2(X253,X254),X253)
| subset(X253,X254) )
& ( ~ in(esk11_2(X253,X254),X254)
| subset(X253,X254) ) ),
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])])])])])]) ).
cnf(c_0_20,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_21,negated_conjecture,
~ subset(unordered_pair(esk20_0,esk20_0),esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_22,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
in(esk11_2(unordered_pair(esk20_0,esk20_0),esk21_0),unordered_pair(esk20_0,esk20_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
esk11_2(unordered_pair(esk20_0,esk20_0),esk21_0) = esk20_0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU158+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.16/0.32 % Computer : n005.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:46:15 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------