%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU154+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n001.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 05:10:49 PM UTC 2026
% Result : Theorem 1.16s 1.86s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 62 ( 19 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 69 ( 30 ~; 19 |; 16 &)
% ( 2 <=>; 2 =>; 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 : 41 ( 0 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l28_zfmisc_1,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l28_zfmisc_1])]) ).
fof(c_0_5,plain,
! [X169,X170,X171,X172,X173,X174] :
( ( ~ in(X171,X170)
| X171 = X169
| X170 != singleton(X169) )
& ( X172 != X169
| in(X172,X170)
| X170 != singleton(X169) )
& ( ~ in(esk1_2(X173,X174),X174)
| esk1_2(X173,X174) != X173
| X174 = singleton(X173) )
& ( in(esk1_2(X173,X174),X174)
| esk1_2(X173,X174) = X173
| X174 = singleton(X173) ) ),
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,lemma,
! [X321] : unordered_pair(X321,X321) = singleton(X321),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
( ~ in(esk9_0,esk10_0)
& ~ disjoint(singleton(esk9_0),esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
cnf(c_0_9,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
~ disjoint(singleton(esk9_0),esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,lemma,
! [X296,X297,X299,X300,X301] :
( ( in(esk14_2(X296,X297),X296)
| disjoint(X296,X297) )
& ( in(esk14_2(X296,X297),X297)
| disjoint(X296,X297) )
& ( ~ in(X301,X299)
| ~ in(X301,X300)
| ~ disjoint(X299,X300) ) ),
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)],[c_0_8])])])])])]) ).
cnf(c_0_13,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ disjoint(unordered_pair(esk9_0,esk9_0),esk10_0),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,lemma,
( in(esk14_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,lemma,
( in(esk14_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
in(esk14_2(unordered_pair(esk9_0,esk9_0),esk10_0),unordered_pair(esk9_0,esk9_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
in(esk14_2(unordered_pair(esk9_0,esk9_0),esk10_0),esk10_0),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
esk14_2(unordered_pair(esk9_0,esk9_0),esk10_0) = esk9_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : SEU154+2 : TPTP v9.2.1. Released v3.3.0.
% 0.02/0.21 % 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
% 0.12/0.45 % Computer : n001.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8042.1875MB
% 0.12/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Tue May 5 02:46:03 EDT 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.46 % start to proof: theBenchmark
% 1.16/1.86 % Version : CSE_E---1.7
% 1.16/1.86 % Problem : theBenchmark.p
% 1.16/1.86 % SZS status Theorem for theBenchmark.p
% 1.16/1.86 % SZS output start CNFRefutation
% See solution above
% 1.16/1.86 % Total time : 1.390s
%------------------------------------------------------------------------------