%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET882+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 : n029.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 63 ( 39 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 26 |; 9 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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_4,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
inference(assume_negation,[status(cth)],[t23_zfmisc_1]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
( esk4_0 != esk5_0
& set_difference(unordered_pair(esk4_0,esk5_0),singleton(esk5_0)) != singleton(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X20,X21] : unordered_pair(X20,X21) = unordered_pair(X21,X20),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_8,plain,
! [X29,X30,X31] :
( ( ~ in(X29,X31)
| set_difference(unordered_pair(X29,X30),X31) != singleton(X29) )
& ( in(X30,X31)
| X29 = X30
| set_difference(unordered_pair(X29,X30),X31) != singleton(X29) )
& ( ~ in(X30,X31)
| in(X29,X31)
| set_difference(unordered_pair(X29,X30),X31) = singleton(X29) )
& ( X29 != X30
| in(X29,X31)
| set_difference(unordered_pair(X29,X30),X31) = singleton(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X22,X23,X24,X25,X26,X27] :
( ( ~ in(X24,X23)
| X24 = X22
| X23 != singleton(X22) )
& ( X25 != X22
| in(X25,X23)
| X23 != singleton(X22) )
& ( ~ in(esk1_2(X26,X27),X27)
| esk1_2(X26,X27) != X26
| X27 = singleton(X26) )
& ( in(esk1_2(X26,X27),X27)
| esk1_2(X26,X27) = X26
| X27 = singleton(X26) ) ),
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_10,negated_conjecture,
set_difference(unordered_pair(esk4_0,esk5_0),singleton(esk5_0)) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( in(X3,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
set_difference(unordered_pair(esk5_0,esk4_0),singleton(esk5_0)) != singleton(esk4_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X2)
| in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_17,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
in(esk4_0,singleton(esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET882+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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:38:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------