%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET018+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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 : n025.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 05:06:52 PM UTC 2026
% Result : Theorem 1.80s 1.90s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 28 unt; 0 def)
% Number of atoms : 155 ( 97 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 114 ( 34 ~; 64 |; 12 &)
% ( 1 <=>; 3 =>; 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 61 ( 7 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ordered_pair_determines_components2,conjecture,
! [X7,X1,X2,X5] :
( ( ordered_pair(X7,X1) = ordered_pair(X2,X5)
& member(X1,universal_class) )
=> X1 = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
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/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(unordered_pair,axiom,
! [X1,X2] : member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(null_class_defn,axiom,
! [X1] : ~ member(X1,null_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(c_0_7,negated_conjecture,
~ ! [X7,X1,X2,X5] :
( ( ordered_pair(X7,X1) = ordered_pair(X2,X5)
& member(X1,universal_class) )
=> X1 = X5 ),
inference(assume_negation,[status(cth)],[ordered_pair_determines_components2]) ).
fof(c_0_8,plain,
! [X115,X116] : ordered_pair(X115,X116) = unordered_pair(singleton(X115),unordered_pair(X115,singleton(X116))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_9,plain,
! [X114] : singleton(X114) = unordered_pair(X114,X114),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_10,plain,
! [X109,X110,X111] :
( ( member(X109,universal_class)
| ~ member(X109,unordered_pair(X110,X111)) )
& ( X109 = X110
| X109 = X111
| ~ member(X109,unordered_pair(X110,X111)) )
& ( X109 != X110
| ~ member(X109,universal_class)
| member(X109,unordered_pair(X110,X111)) )
& ( X109 != X111
| ~ member(X109,universal_class)
| member(X109,unordered_pair(X110,X111)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
fof(c_0_11,negated_conjecture,
( ordered_pair(esk8_0,esk9_0) = ordered_pair(esk10_0,esk11_0)
& member(esk9_0,universal_class)
& esk9_0 != esk11_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,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_13,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
ordered_pair(esk8_0,esk9_0) = ordered_pair(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,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_12,c_0_13]),c_0_13]) ).
fof(c_0_17,plain,
! [X112,X113] : member(unordered_pair(X112,X113),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
cnf(c_0_18,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0))) = 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_15,c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
member(unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)),unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0))
| unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( X1 = unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0))
| X1 = unordered_pair(esk8_0,esk8_0)
| ~ member(X1,unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)))) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_26,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X191] :
( ( member(esk6_1(X191),universal_class)
| X191 = null_class )
& ( member(esk6_1(X191),X191)
| X191 = null_class )
& ( disjoint(esk6_1(X191),X191)
| X191 = null_class ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[regularity])])])]) ).
cnf(c_0_28,negated_conjecture,
( unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,esk10_0)
| unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) != unordered_pair(esk10_0,esk10_0) ),
inference(ef,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0))
| unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) = unordered_pair(esk8_0,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_20])]) ).
cnf(c_0_30,negated_conjecture,
( unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,esk10_0)
| unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_20])]) ).
cnf(c_0_31,negated_conjecture,
member(unordered_pair(esk8_0,esk8_0),unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_20])]) ).
cnf(c_0_32,plain,
( member(esk6_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( member(unordered_pair(esk9_0,esk9_0),unordered_pair(esk10_0,esk10_0))
| unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) != unordered_pair(esk10_0,esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_20])]) ).
cnf(c_0_34,negated_conjecture,
( unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) = unordered_pair(esk8_0,esk8_0)
| member(unordered_pair(esk9_0,esk9_0),unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_29]),c_0_20])]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0)
| member(unordered_pair(esk9_0,esk9_0),unordered_pair(esk10_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_20])]) ).
cnf(c_0_36,negated_conjecture,
( unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) = unordered_pair(esk8_0,esk8_0)
| unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_37,plain,
( esk6_1(unordered_pair(X1,X2)) = X1
| esk6_1(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk10_0
| unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) != unordered_pair(esk10_0,esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) = unordered_pair(esk8_0,esk8_0)
| unordered_pair(esk11_0,esk11_0) = unordered_pair(esk9_0,esk9_0)
| unordered_pair(esk9_0,esk9_0) = esk10_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0)
| unordered_pair(esk9_0,esk9_0) = esk10_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0)
| member(esk10_0,unordered_pair(esk8_0,esk8_0))
| ~ member(esk10_0,universal_class) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_42,plain,
( member(esk6_1(X1),universal_class)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,plain,
( esk6_1(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_37])]) ).
cnf(c_0_44,negated_conjecture,
( unordered_pair(esk11_0,esk11_0) = unordered_pair(esk9_0,esk9_0)
| unordered_pair(esk9_0,esk9_0) = esk10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0)
| esk8_0 = esk10_0
| ~ member(esk10_0,universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_46,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk10_0
| member(esk11_0,unordered_pair(esk9_0,esk9_0))
| ~ member(esk11_0,universal_class) ),
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
esk9_0 != esk11_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_49,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( unordered_pair(esk8_0,esk8_0) = unordered_pair(esk10_0,esk10_0)
| unordered_pair(esk10_0,esk10_0) = null_class
| esk8_0 = esk10_0 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_51,plain,
! [X1] : ~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[null_class_defn]) ).
cnf(c_0_52,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk10_0
| ~ member(esk11_0,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( unordered_pair(esk10_0,esk10_0) = null_class
| esk8_0 = esk10_0
| member(esk8_0,unordered_pair(esk10_0,esk10_0)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_54,plain,
! [X136] : ~ member(X136,null_class),
inference(variable_rename,[status(thm)],[c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( unordered_pair(esk11_0,esk11_0) = null_class
| unordered_pair(esk9_0,esk9_0) = esk10_0 ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( unordered_pair(esk10_0,esk10_0) = null_class
| esk8_0 = esk10_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
cnf(c_0_57,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk10_0
| unordered_pair(esk9_0,esk9_0) = null_class ),
inference(spm,[status(thm)],[c_0_44,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( esk8_0 = esk10_0
| ~ member(esk10_0,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_56]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = null_class
| member(esk10_0,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = null_class
| esk8_0 = esk10_0 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_63,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk10_0
| X1 = esk11_0
| ~ member(X1,unordered_pair(esk9_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_64,negated_conjecture,
esk8_0 = esk10_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_61]),c_0_62])]),c_0_57]) ).
cnf(c_0_65,negated_conjecture,
unordered_pair(esk9_0,esk9_0) = esk10_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_18]),c_0_62])]),c_0_48]) ).
cnf(c_0_66,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = null_class
| esk10_0 != null_class ),
inference(ef,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0)) = unordered_pair(esk10_0,esk10_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_64]),c_0_64]),c_0_64]),c_0_65])]) ).
cnf(c_0_68,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = null_class
| X1 = esk9_0
| ~ member(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
esk10_0 != null_class,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_66]),c_0_62])]),c_0_57]) ).
cnf(c_0_70,negated_conjecture,
member(unordered_pair(esk11_0,esk11_0),unordered_pair(esk10_0,esk10_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_67]),c_0_20])]) ).
cnf(c_0_71,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = null_class
| esk6_1(esk10_0) = esk9_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_32]),c_0_69]) ).
cnf(c_0_72,negated_conjecture,
unordered_pair(esk11_0,esk11_0) = esk10_0,
inference(spm,[status(thm)],[c_0_21,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
esk6_1(esk10_0) = esk9_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_71]),c_0_62])]),c_0_57]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_72]),c_0_73]),c_0_48]),c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET018+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:04:43 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.80/1.90 % Version : CSE_E---1.7
% 1.80/1.90 % Problem : theBenchmark.p
% 1.80/1.90 % SZS status Theorem for theBenchmark.p
% 1.80/1.90 % SZS output start CNFRefutation
% See solution above
% 1.90/1.90 % Total time : 1.370s
%------------------------------------------------------------------------------