%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET016+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 : n002.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 05:06:50 PM UTC 2026
% Result : Theorem 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 60 ( 31 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 47 ( 17 ~; 19 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 6 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ordered_pair_determines_components1,conjecture,
! [X7,X1,X2,X5] :
( ( ordered_pair(X7,X1) = ordered_pair(X2,X5)
& member(X7,universal_class) )
=> X7 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
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(c_0_5,negated_conjecture,
~ ! [X7,X1,X2,X5] :
( ( ordered_pair(X7,X1) = ordered_pair(X2,X5)
& member(X7,universal_class) )
=> X7 = X2 ),
inference(assume_negation,[status(cth)],[ordered_pair_determines_components1]) ).
fof(c_0_6,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_7,plain,
! [X114] : singleton(X114) = unordered_pair(X114,X114),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_8,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_9,negated_conjecture,
( ordered_pair(esk8_0,esk9_0) = ordered_pair(esk10_0,esk11_0)
& member(esk8_0,universal_class)
& esk8_0 != esk10_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
ordered_pair(esk8_0,esk9_0) = ordered_pair(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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_10,c_0_11]),c_0_11]) ).
fof(c_0_15,plain,
! [X112,X113] : member(unordered_pair(X112,X113),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
cnf(c_0_16,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,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_13,c_0_14]),c_0_14]) ).
cnf(c_0_18,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
member(unordered_pair(esk10_0,esk10_0),unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
( unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,esk10_0)
| unordered_pair(esk10_0,esk10_0) = unordered_pair(esk8_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
( unordered_pair(esk10_0,esk10_0) = unordered_pair(esk8_0,esk8_0)
| member(esk8_0,unordered_pair(esk10_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_22])]) ).
cnf(c_0_24,negated_conjecture,
esk8_0 != esk10_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
unordered_pair(esk10_0,esk10_0) = unordered_pair(esk8_0,esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_24]) ).
cnf(c_0_26,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( X1 = esk10_0
| ~ member(X1,unordered_pair(esk8_0,esk8_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_28,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET016+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
% 0.17/0.33 % Computer : n002.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:05:46 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------