%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET921+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 : n013.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 05:08:58 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 97 ( 34 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 115 ( 45 ~; 48 |; 14 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 5 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t64_zfmisc_1,conjecture,
! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( in(X1,X2)
& X1 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_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(c_0_3,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_4,plain,
! [X28,X29,X30,X31,X32,X33,X34,X35] :
( ( in(X31,X28)
| ~ in(X31,X30)
| X30 != set_difference(X28,X29) )
& ( ~ in(X31,X29)
| ~ in(X31,X30)
| X30 != set_difference(X28,X29) )
& ( ~ in(X32,X28)
| in(X32,X29)
| in(X32,X30)
| X30 != set_difference(X28,X29) )
& ( ~ in(esk2_3(X33,X34,X35),X35)
| ~ in(esk2_3(X33,X34,X35),X33)
| in(esk2_3(X33,X34,X35),X34)
| X35 = set_difference(X33,X34) )
& ( in(esk2_3(X33,X34,X35),X33)
| in(esk2_3(X33,X34,X35),X35)
| X35 = set_difference(X33,X34) )
& ( ~ in(esk2_3(X33,X34,X35),X34)
| in(esk2_3(X33,X34,X35),X35)
| X35 = set_difference(X33,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)],[c_0_3])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( in(X1,X2)
& X1 != X3 ) ),
inference(assume_negation,[status(cth)],[t64_zfmisc_1]) ).
cnf(c_0_6,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
( ( ~ in(esk5_0,set_difference(esk6_0,singleton(esk7_0)))
| ~ in(esk5_0,esk6_0)
| esk5_0 = esk7_0 )
& ( in(esk5_0,esk6_0)
| in(esk5_0,set_difference(esk6_0,singleton(esk7_0))) )
& ( esk5_0 != esk7_0
| in(esk5_0,set_difference(esk6_0,singleton(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_8,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( in(esk5_0,esk6_0)
| in(esk5_0,set_difference(esk6_0,singleton(esk7_0))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_11,plain,
! [X21,X22,X23,X24,X25,X26] :
( ( ~ in(X23,X22)
| X23 = X21
| X22 != singleton(X21) )
& ( X24 != X21
| in(X24,X22)
| X22 != singleton(X21) )
& ( ~ in(esk1_2(X25,X26),X26)
| esk1_2(X25,X26) != X25
| X26 = singleton(X25) )
& ( in(esk1_2(X25,X26),X26)
| esk1_2(X25,X26) = X25
| X26 = singleton(X25) ) ),
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_12,negated_conjecture,
( esk5_0 = esk7_0
| ~ in(esk5_0,set_difference(esk6_0,singleton(esk7_0)))
| ~ in(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
in(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk7_0 = esk5_0
| ~ in(esk5_0,set_difference(esk6_0,singleton(esk7_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_19,negated_conjecture,
( in(esk5_0,set_difference(esk6_0,X1))
| in(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( in(esk5_0,set_difference(esk6_0,singleton(esk7_0)))
| esk5_0 != esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
esk7_0 = esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_25,plain,
~ in(X1,set_difference(X2,singleton(X1))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET921+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n013.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:39:11 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------