%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET918+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n025.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 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 106 ( 57 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 124 ( 47 ~; 51 |; 20 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 2 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t59_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
& in(X2,X3)
& X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
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(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
& in(X2,X3)
& X1 != X2 ),
inference(assume_negation,[status(cth)],[t59_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( set_intersection2(unordered_pair(esk6_0,esk7_0),esk8_0) = singleton(esk6_0)
& in(esk7_0,esk8_0)
& esk6_0 != esk7_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X31,X32] : unordered_pair(X31,X32) = unordered_pair(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_9,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58] :
( ( in(X54,X51)
| ~ in(X54,X53)
| X53 != set_intersection2(X51,X52) )
& ( in(X54,X52)
| ~ in(X54,X53)
| X53 != set_intersection2(X51,X52) )
& ( ~ in(X55,X51)
| ~ in(X55,X52)
| in(X55,X53)
| X53 != set_intersection2(X51,X52) )
& ( ~ in(esk3_3(X56,X57,X58),X58)
| ~ in(esk3_3(X56,X57,X58),X56)
| ~ in(esk3_3(X56,X57,X58),X57)
| X58 = set_intersection2(X56,X57) )
& ( in(esk3_3(X56,X57,X58),X56)
| in(esk3_3(X56,X57,X58),X58)
| X58 = set_intersection2(X56,X57) )
& ( in(esk3_3(X56,X57,X58),X57)
| in(esk3_3(X56,X57,X58),X58)
| X58 = set_intersection2(X56,X57) ) ),
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_xboole_0])])])])])]) ).
cnf(c_0_10,negated_conjecture,
set_intersection2(unordered_pair(esk6_0,esk7_0),esk8_0) = singleton(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X33,X34] : set_intersection2(X33,X34) = set_intersection2(X34,X33),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_13,plain,
! [X35,X36,X37,X38,X39,X40] :
( ( ~ in(X37,X36)
| X37 = X35
| X36 != singleton(X35) )
& ( X38 != X35
| in(X38,X36)
| X36 != singleton(X35) )
& ( ~ in(esk1_2(X39,X40),X40)
| esk1_2(X39,X40) != X39
| X40 = singleton(X39) )
& ( in(esk1_2(X39,X40),X40)
| esk1_2(X39,X40) = X39
| X40 = singleton(X39) ) ),
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_14,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
set_intersection2(unordered_pair(esk7_0,esk6_0),esk8_0) = singleton(esk6_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
set_intersection2(esk8_0,unordered_pair(esk7_0,esk6_0)) = singleton(esk6_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49] :
( ( ~ in(X45,X44)
| X45 = X42
| X45 = X43
| X44 != unordered_pair(X42,X43) )
& ( X46 != X42
| in(X46,X44)
| X44 != unordered_pair(X42,X43) )
& ( X46 != X43
| in(X46,X44)
| X44 != unordered_pair(X42,X43) )
& ( esk2_3(X47,X48,X49) != X47
| ~ in(esk2_3(X47,X48,X49),X49)
| X49 = unordered_pair(X47,X48) )
& ( esk2_3(X47,X48,X49) != X48
| ~ in(esk2_3(X47,X48,X49),X49)
| X49 = unordered_pair(X47,X48) )
& ( in(esk2_3(X47,X48,X49),X49)
| esk2_3(X47,X48,X49) = X47
| esk2_3(X47,X48,X49) = X48
| X49 = unordered_pair(X47,X48) ) ),
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_21,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( in(X1,singleton(esk6_0))
| ~ in(X1,unordered_pair(esk7_0,esk6_0))
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( X1 = esk6_0
| ~ in(X1,unordered_pair(esk7_0,esk6_0))
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
in(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
esk6_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET918+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:39:28 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Theorem for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------