%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET103+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 : n010.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 05:07:19 PM UTC 2026
% Result : Theorem 1.92s 1.91s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 58 ( 32 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 48 ( 14 ~; 23 |; 9 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 18 !; 1 ?)
% 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(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(property_1_of_ordered_pair,conjecture,
! [X1,X2] :
( unordered_pair(singleton(X1),unordered_pair(X1,null_class)) = ordered_pair(X1,X2)
| member(X2,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).
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_5,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_6,plain,
! [X189] :
( ( member(esk6_1(X189),universal_class)
| X189 = null_class )
& ( member(esk6_1(X189),X189)
| X189 = null_class )
& ( disjoint(esk6_1(X189),X189)
| X189 = null_class ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[regularity])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( unordered_pair(singleton(X1),unordered_pair(X1,null_class)) = ordered_pair(X1,X2)
| member(X2,universal_class) ),
inference(assume_negation,[status(cth)],[property_1_of_ordered_pair]) ).
fof(c_0_8,plain,
! [X113,X114] : ordered_pair(X113,X114) = unordered_pair(singleton(X113),unordered_pair(X113,singleton(X114))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_9,plain,
! [X112] : singleton(X112) = unordered_pair(X112,X112),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_10,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( member(esk6_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( unordered_pair(singleton(esk8_0),unordered_pair(esk8_0,null_class)) != ordered_pair(esk8_0,esk9_0)
& ~ member(esk9_0,universal_class) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk6_1(X1),universal_class)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( esk6_1(unordered_pair(X1,X2)) = X2
| esk6_1(unordered_pair(X1,X2)) = X1
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
unordered_pair(singleton(esk8_0),unordered_pair(esk8_0,null_class)) != ordered_pair(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,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_13,c_0_14]),c_0_14]) ).
cnf(c_0_19,plain,
( esk6_1(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,null_class)) != unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_14]),c_0_18]) ).
cnf(c_0_21,plain,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET103+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
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:10:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.92/1.91 % Version : CSE_E---1.7
% 1.92/1.91 % Problem : theBenchmark.p
% 1.92/1.91 % SZS status Theorem for theBenchmark.p
% 1.92/1.91 % SZS output start CNFRefutation
% See solution above
% 1.92/1.91 % Total time : 1.370s
%------------------------------------------------------------------------------