%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET076+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 : n017.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 05:07:11 PM UTC 2026
% Result : Theorem 4.13s 3.29s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 54 ( 11 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 54 ( 17 ~; 22 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(unordered_pair_is_subset,conjecture,
! [X1,X2,X5] :
( ( member(X1,X5)
& member(X2,X5) )
=> subclass(unordered_pair(X1,X2),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(c_0_3,plain,
! [X108,X109,X110] :
( ( member(X108,universal_class)
| ~ member(X108,unordered_pair(X109,X110)) )
& ( X108 = X109
| X108 = X110
| ~ member(X108,unordered_pair(X109,X110)) )
& ( X108 != X109
| ~ member(X108,universal_class)
| member(X108,unordered_pair(X109,X110)) )
& ( X108 != X110
| ~ member(X108,universal_class)
| member(X108,unordered_pair(X109,X110)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
fof(c_0_4,plain,
! [X99,X100,X101,X102,X103] :
( ( ~ subclass(X99,X100)
| ~ member(X101,X99)
| member(X101,X100) )
& ( member(esk1_2(X102,X103),X102)
| subclass(X102,X103) )
& ( ~ member(esk1_2(X102,X103),X103)
| subclass(X102,X103) ) ),
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)],[subclass_defn])])])])])]) ).
cnf(c_0_5,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X5] :
( ( member(X1,X5)
& member(X2,X5) )
=> subclass(unordered_pair(X1,X2),X5) ),
inference(assume_negation,[status(cth)],[unordered_pair_is_subset]) ).
cnf(c_0_8,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X1
| esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
fof(c_0_10,negated_conjecture,
( member(esk8_0,esk10_0)
& member(esk9_0,esk10_0)
& ~ subclass(unordered_pair(esk8_0,esk9_0),esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
~ subclass(unordered_pair(esk8_0,esk9_0),esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( subclass(unordered_pair(X1,X2),X3)
| ~ member(X1,X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
member(esk8_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
member(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET076+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n017.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 02:09:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.13/3.29 % Version : CSE_E---1.7
% 4.13/3.29 % Problem : theBenchmark.p
% 4.13/3.29 % SZS status Theorem for theBenchmark.p
% 4.13/3.29 % SZS output start CNFRefutation
% See solution above
% 4.24/3.30 % Total time : 2.369s
%------------------------------------------------------------------------------