%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET108+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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 : n019.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 05:07:20 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 57 ( 38 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 67 ( 29 ~; 23 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 10 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_first_and_second,conjecture,
! [X1] :
? [X3,X4] :
( ( member(X3,universal_class)
& member(X4,universal_class)
& X1 = ordered_pair(X3,X4) )
| ( ~ ? [X2,X5] :
( member(X2,universal_class)
& member(X5,universal_class)
& X1 = ordered_pair(X2,X5) )
& X3 = X1
& X4 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_and_second) ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
? [X3,X4] :
( ( member(X3,universal_class)
& member(X4,universal_class)
& X1 = ordered_pair(X3,X4) )
| ( ~ ? [X2,X5] :
( member(X2,universal_class)
& member(X5,universal_class)
& X1 = ordered_pair(X2,X5) )
& X3 = X1
& X4 = X1 ) ),
inference(assume_negation,[status(cth)],[existence_of_first_and_second]) ).
fof(c_0_4,plain,
! [X116,X117] : ordered_pair(X116,X117) = unordered_pair(singleton(X116),unordered_pair(X116,singleton(X117))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_5,plain,
! [X115] : singleton(X115) = unordered_pair(X115,X115),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_6,negated_conjecture,
! [X199,X200] :
( ( ~ member(X199,universal_class)
| ~ member(X200,universal_class)
| esk8_0 != ordered_pair(X199,X200) )
& ( member(esk9_2(X199,X200),universal_class)
| X199 != esk8_0
| X200 != esk8_0 )
& ( member(esk10_2(X199,X200),universal_class)
| X199 != esk8_0
| X200 != esk8_0 )
& ( esk8_0 = ordered_pair(esk9_2(X199,X200),esk10_2(X199,X200))
| X199 != esk8_0
| X200 != esk8_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_7,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| esk8_0 != ordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( esk8_0 = ordered_pair(esk9_2(X1,X2),esk10_2(X1,X2))
| X1 != esk8_0
| X2 != esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( esk8_0 != unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( esk8_0 = unordered_pair(unordered_pair(esk9_2(X1,X2),esk9_2(X1,X2)),unordered_pair(esk9_2(X1,X2),unordered_pair(esk10_2(X1,X2),esk10_2(X1,X2))))
| X2 != esk8_0
| X1 != esk8_0 ),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( member(esk9_2(X1,X2),universal_class)
| X1 != esk8_0
| X2 != esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( member(esk10_2(X1,X2),universal_class)
| X1 != esk8_0
| X2 != esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( X1 != esk8_0
| X2 != esk8_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_17,negated_conjecture,
X1 != esk8_0,
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET108+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:11:14 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------