%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET067+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 : n006.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 05:07:08 PM UTC 2026
% Result : Theorem 2.13s 2.01s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 67 ( 13 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 31 |; 6 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 5 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(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(pair_contains_other,conjecture,
! [X1,X2] : subclass(unordered_pair(X1,X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pair_contains_other) ).
fof(c_0_4,plain,
! [X107,X108,X109] :
( ( member(X107,universal_class)
| ~ member(X107,unordered_pair(X108,X109)) )
& ( X107 = X108
| X107 = X109
| ~ member(X107,unordered_pair(X108,X109)) )
& ( X107 != X108
| ~ member(X107,universal_class)
| member(X107,unordered_pair(X108,X109)) )
& ( X107 != X109
| ~ member(X107,universal_class)
| member(X107,unordered_pair(X108,X109)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
fof(c_0_5,plain,
! [X98,X99,X100,X101,X102] :
( ( ~ subclass(X98,X99)
| ~ member(X100,X98)
| member(X100,X99) )
& ( member(esk1_2(X101,X102),X101)
| subclass(X101,X102) )
& ( ~ member(esk1_2(X101,X102),X102)
| subclass(X101,X102) ) ),
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_6,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X104] : subclass(X104,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] : subclass(unordered_pair(X1,X1),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[pair_contains_other]) ).
cnf(c_0_10,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X2
| esk1_2(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,negated_conjecture,
~ subclass(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk9_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ subclass(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( subclass(unordered_pair(X1,X2),X3)
| ~ member(X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_19,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,plain,
( member(esk1_2(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_7]) ).
cnf(c_0_21,plain,
( esk1_2(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_11])]) ).
cnf(c_0_22,negated_conjecture,
~ member(esk8_0,unordered_pair(esk8_0,esk9_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( member(X1,universal_class)
| subclass(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
~ member(esk8_0,universal_class),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET067+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
% 0.15/0.32 % Computer : n006.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 02:09:01 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 2.13/2.01 % Version : CSE_E---1.7
% 2.13/2.01 % Problem : theBenchmark.p
% 2.13/2.01 % SZS status Theorem for theBenchmark.p
% 2.13/2.01 % SZS output start CNFRefutation
% See solution above
% 2.13/2.01 % Total time : 1.371s
%------------------------------------------------------------------------------