%------------------------------------------------------------------------------
% File : PyRes---1.5
% Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 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 : Thu May 9 17:40:18 EDT 2024
% Result : Theorem 3.34s 3.51s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 68 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 19 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 1 sgn 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t27_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
fof(c6,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(assume_negation,[status(cth)],[t27_zfmisc_1]) ).
fof(c7,negated_conjecture,
? [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
& unordered_pair(A,B) != singleton(C) ),
inference(fof_nnf,[status(thm)],[c6]) ).
fof(c8,negated_conjecture,
? [X3,X4,X5] :
( subset(unordered_pair(X3,X4),singleton(X5))
& unordered_pair(X3,X4) != singleton(X5) ),
inference(variable_rename,[status(thm)],[c7]) ).
fof(c9,negated_conjecture,
( subset(unordered_pair(skolem0001,skolem0002),singleton(skolem0003))
& unordered_pair(skolem0001,skolem0002) != singleton(skolem0003) ),
inference(skolemize,[status(esa)],[c8]) ).
cnf(c11,negated_conjecture,
unordered_pair(skolem0001,skolem0002) != singleton(skolem0003),
inference(split_conjunct,[status(thm)],[c9]) ).
cnf(transitivity,axiom,
( X19 != X18
| X18 != X20
| X19 = X20 ),
theory(equality) ).
cnf(symmetry,axiom,
( X17 != X16
| X16 = X17 ),
theory(equality) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(c4,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c5,plain,
unordered_pair(X25,X25) = singleton(X25),
inference(split_conjunct,[status(thm)],[c4]) ).
cnf(c30,plain,
singleton(X26) = unordered_pair(X26,X26),
inference(resolution,[status(thm)],[c5,symmetry]) ).
cnf(c33,plain,
( X67 != singleton(X66)
| X67 = unordered_pair(X66,X66) ),
inference(resolution,[status(thm)],[c30,transitivity]) ).
cnf(c1,axiom,
( X39 != X40
| singleton(X39) = singleton(X40) ),
theory(equality) ).
cnf(c10,negated_conjecture,
subset(unordered_pair(skolem0001,skolem0002),singleton(skolem0003)),
inference(split_conjunct,[status(thm)],[c9]) ).
fof(t26_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(c12,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
inference(fof_nnf,[status(thm)],[t26_zfmisc_1]) ).
fof(c13,plain,
! [X6,X7,X8] :
( ~ subset(unordered_pair(X6,X7),singleton(X8))
| X6 = X8 ),
inference(variable_rename,[status(thm)],[c12]) ).
cnf(c14,plain,
( ~ subset(unordered_pair(X60,X59),singleton(X58))
| X60 = X58 ),
inference(split_conjunct,[status(thm)],[c13]) ).
cnf(c60,plain,
skolem0001 = skolem0003,
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(c66,plain,
skolem0003 = skolem0001,
inference(resolution,[status(thm)],[c60,symmetry]) ).
cnf(c73,plain,
singleton(skolem0003) = singleton(skolem0001),
inference(resolution,[status(thm)],[c66,c1]) ).
cnf(c131,plain,
singleton(skolem0003) = unordered_pair(skolem0001,skolem0001),
inference(resolution,[status(thm)],[c73,c33]) ).
cnf(c177,plain,
unordered_pair(skolem0001,skolem0001) = singleton(skolem0003),
inference(resolution,[status(thm)],[c131,symmetry]) ).
cnf(c264,plain,
( X463 != unordered_pair(skolem0001,skolem0001)
| X463 = singleton(skolem0003) ),
inference(resolution,[status(thm)],[c177,transitivity]) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c25,plain,
! [X12,X13] : unordered_pair(X12,X13) = unordered_pair(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c26,plain,
unordered_pair(X36,X35) = unordered_pair(X35,X36),
inference(split_conjunct,[status(thm)],[c25]) ).
cnf(c44,plain,
( X99 != unordered_pair(X98,X97)
| X99 = unordered_pair(X97,X98) ),
inference(resolution,[status(thm)],[c26,transitivity]) ).
cnf(reflexivity,axiom,
X14 = X14,
theory(equality) ).
cnf(c0,axiom,
( X27 != X30
| X29 != X28
| unordered_pair(X27,X29) = unordered_pair(X30,X28) ),
theory(equality) ).
cnf(c37,plain,
( X89 != X87
| unordered_pair(X89,X88) = unordered_pair(X87,X88) ),
inference(resolution,[status(thm)],[c0,reflexivity]) ).
cnf(c3,axiom,
( X44 != X47
| X46 != X45
| ~ subset(X44,X46)
| subset(X47,X45) ),
theory(equality) ).
cnf(c49,plain,
( unordered_pair(skolem0001,skolem0002) != X116
| singleton(skolem0003) != X115
| subset(X116,X115) ),
inference(resolution,[status(thm)],[c3,c10]) ).
cnf(c311,plain,
( singleton(skolem0003) != X512
| subset(unordered_pair(skolem0002,skolem0001),X512) ),
inference(resolution,[status(thm)],[c49,c26]) ).
cnf(c3585,plain,
subset(unordered_pair(skolem0002,skolem0001),singleton(skolem0001)),
inference(resolution,[status(thm)],[c311,c73]) ).
cnf(c3597,plain,
skolem0002 = skolem0001,
inference(resolution,[status(thm)],[c3585,c14]) ).
cnf(c3609,plain,
skolem0001 = skolem0002,
inference(resolution,[status(thm)],[c3597,symmetry]) ).
cnf(c3637,plain,
unordered_pair(skolem0001,X549) = unordered_pair(skolem0002,X549),
inference(resolution,[status(thm)],[c3609,c37]) ).
cnf(c4380,plain,
unordered_pair(skolem0001,X584) = unordered_pair(X584,skolem0002),
inference(resolution,[status(thm)],[c3637,c44]) ).
cnf(c5096,plain,
unordered_pair(X639,skolem0002) = unordered_pair(skolem0001,X639),
inference(resolution,[status(thm)],[c4380,symmetry]) ).
cnf(c6563,plain,
unordered_pair(skolem0001,skolem0002) = singleton(skolem0003),
inference(resolution,[status(thm)],[c5096,c264]) ).
cnf(c7781,plain,
$false,
inference(resolution,[status(thm)],[c6563,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.13 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed May 8 19:38:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 3.34/3.51 % Version: 1.5
% 3.34/3.51 % SZS status Theorem
% 3.34/3.51 % SZS output start CNFRefutation
% See solution above
% 3.34/3.51
% 3.34/3.51 % Initial clauses : 15
% 3.34/3.51 % Processed clauses : 458
% 3.34/3.51 % Factors computed : 4
% 3.34/3.51 % Resolvents computed: 7790
% 3.34/3.51 % Tautologies deleted: 3
% 3.34/3.51 % Forward subsumed : 589
% 3.34/3.51 % Backward subsumed : 9
% 3.34/3.51 % -------- CPU Time ---------
% 3.34/3.51 % User time : 3.124 s
% 3.34/3.51 % System time : 0.028 s
% 3.34/3.51 % Total time : 3.152 s
%------------------------------------------------------------------------------