%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU142+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n001.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 05:10:45 PM UTC 2026
% Result : Theorem 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 75 ( 54 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 82 ( 28 ~; 42 |; 8 &)
% ( 4 <=>; 0 =>; 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 : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 54 ( 4 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t69_enumset1,conjecture,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(c_0_3,plain,
! [X31,X32,X33,X34,X35,X36,X37,X38] :
( ( ~ in(X34,X33)
| X34 = X31
| X34 = X32
| X33 != unordered_pair(X31,X32) )
& ( X35 != X31
| in(X35,X33)
| X33 != unordered_pair(X31,X32) )
& ( X35 != X32
| in(X35,X33)
| X33 != unordered_pair(X31,X32) )
& ( esk2_3(X36,X37,X38) != X36
| ~ in(esk2_3(X36,X37,X38),X38)
| X38 = unordered_pair(X36,X37) )
& ( esk2_3(X36,X37,X38) != X37
| ~ in(esk2_3(X36,X37,X38),X38)
| X38 = unordered_pair(X36,X37) )
& ( in(esk2_3(X36,X37,X38),X38)
| esk2_3(X36,X37,X38) = X36
| esk2_3(X36,X37,X38) = X37
| X38 = unordered_pair(X36,X37) ) ),
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_4,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X24,X25,X26,X27,X28,X29] :
( ( ~ in(X26,X25)
| X26 = X24
| X25 != singleton(X24) )
& ( X27 != X24
| in(X27,X25)
| X25 != singleton(X24) )
& ( ~ in(esk1_2(X28,X29),X29)
| esk1_2(X28,X29) != X28
| X29 = singleton(X28) )
& ( in(esk1_2(X28,X29),X29)
| esk1_2(X28,X29) = X28
| X29 = singleton(X28) ) ),
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_6,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( esk1_2(X1,unordered_pair(X2,X3)) = X1
| esk1_2(X1,unordered_pair(X2,X3)) = X3
| esk1_2(X1,unordered_pair(X2,X3)) = X2
| unordered_pair(X2,X3) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] : unordered_pair(X1,X1) = singleton(X1),
inference(assume_negation,[status(cth)],[t69_enumset1]) ).
cnf(c_0_11,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( esk1_2(X1,unordered_pair(X2,X1)) = X2
| esk1_2(X1,unordered_pair(X2,X1)) = X1
| unordered_pair(X2,X1) = singleton(X1) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_8])]) ).
cnf(c_0_13,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_14,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_15,negated_conjecture,
unordered_pair(esk4_0,esk4_0) != singleton(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_16,plain,
( esk1_2(X1,unordered_pair(X2,X1)) = X2
| unordered_pair(X2,X1) = singleton(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_17,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
unordered_pair(esk4_0,esk4_0) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_16]),c_0_17])])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU142+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.32 % Computer : n001.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 02:45:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------