%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET016+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n028.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 05:06:51 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 75 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 24 ~; 27 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI50a,conjecture,
! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> X1 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50a) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> X1 = X6 ),
inference(assume_negation,[status(cth)],[thI50a]) ).
fof(c_0_6,plain,
! [X46,X47] :
( ( subset(X46,X47)
| ~ equal_set(X46,X47) )
& ( subset(X47,X46)
| ~ equal_set(X46,X47) )
& ( ~ subset(X46,X47)
| ~ subset(X47,X46)
| equal_set(X46,X47) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
fof(c_0_7,negated_conjecture,
( equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)))
& esk4_0 != esk6_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X40,X41,X42,X43,X44] :
( ( ~ subset(X40,X41)
| ~ member(X42,X40)
| member(X42,X41) )
& ( member(esk1_2(X43,X44),X43)
| subset(X43,X44) )
& ( ~ member(esk1_2(X43,X44),X44)
| subset(X43,X44) ) ),
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)],[subset])])])])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X62,X63,X64] :
( ( ~ member(X62,unordered_pair(X63,X64))
| X62 = X63
| X62 = X64 )
& ( X62 != X63
| member(X62,unordered_pair(X63,X64)) )
& ( X62 != X64
| member(X62,unordered_pair(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).
cnf(c_0_12,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X60,X61] :
( ( ~ member(X60,singleton(X61))
| X60 = X61 )
& ( X60 != X61
| member(X60,singleton(X61)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_16,negated_conjecture,
( member(X1,unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)))
| ~ member(X1,unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
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_11]) ).
cnf(c_0_20,negated_conjecture,
member(singleton(esk6_0),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( singleton(esk6_0) = unordered_pair(esk4_0,esk5_0)
| singleton(esk6_0) = singleton(esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( singleton(esk6_0) = unordered_pair(esk4_0,esk5_0)
| member(esk6_0,singleton(esk4_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
esk4_0 != esk6_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
singleton(esk6_0) = unordered_pair(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
member(esk6_0,unordered_pair(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
esk5_0 = esk6_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_27]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
singleton(esk6_0) = unordered_pair(esk4_0,esk6_0),
inference(rw,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( X1 = esk6_0
| ~ member(X1,unordered_pair(esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET016+4 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:05:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------