%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET878+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 : n002.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 05:08:53 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 44 ( 30 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 46 ( 19 ~; 19 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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; 0-3 aty)
% Number of variables : 34 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t19_zfmisc_1,conjecture,
! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(l32_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_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,negated_conjecture,
~ ! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
inference(assume_negation,[status(cth)],[t19_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
set_intersection2(singleton(esk4_0),unordered_pair(esk4_0,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_6,plain,
! [X27,X28] : set_intersection2(X27,X28) = set_intersection2(X28,X27),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_7,negated_conjecture,
set_intersection2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X39,X40] :
( ~ in(X39,X40)
| set_intersection2(X40,singleton(X39)) = singleton(X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_zfmisc_1])]) ).
fof(c_0_10,plain,
! [X29,X30,X31,X32,X33,X34,X35,X36] :
( ( ~ in(X32,X31)
| X32 = X29
| X32 = X30
| X31 != unordered_pair(X29,X30) )
& ( X33 != X29
| in(X33,X31)
| X31 != unordered_pair(X29,X30) )
& ( X33 != X30
| in(X33,X31)
| X31 != unordered_pair(X29,X30) )
& ( esk1_3(X34,X35,X36) != X34
| ~ in(esk1_3(X34,X35,X36),X36)
| X36 = unordered_pair(X34,X35) )
& ( esk1_3(X34,X35,X36) != X35
| ~ in(esk1_3(X34,X35,X36),X36)
| X36 = unordered_pair(X34,X35) )
& ( in(esk1_3(X34,X35,X36),X36)
| esk1_3(X34,X35,X36) = X34
| esk1_3(X34,X35,X36) = X35
| X36 = unordered_pair(X34,X35) ) ),
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])])])])])]) ).
cnf(c_0_11,negated_conjecture,
set_intersection2(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)) != singleton(esk4_0),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( set_intersection2(X2,singleton(X1)) = singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ in(esk4_0,unordered_pair(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET878+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n002.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:39:01 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.368s
%------------------------------------------------------------------------------