TSTP Solution File: SET882+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n012.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 : Wed Aug 31 18:22:39 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 109 ( 63 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 137 ( 56 ~; 47 |; 26 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 47 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,plain,
$false,
inference(subsumption_resolution,[],[f55,f29]) ).
fof(f29,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( set_difference(unordered_pair(sK0,sK1),singleton(sK1)) != singleton(sK0)
& sK0 != sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f17]) ).
fof(f17,plain,
( ? [X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
& X0 != X1 )
=> ( set_difference(unordered_pair(sK0,sK1),singleton(sK1)) != singleton(sK0)
& sK0 != sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
? [X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
& X0 != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X1,X0] :
( X0 != X1
=> singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X1,X0] :
( X0 != X1
=> singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(f55,plain,
sK0 = sK1,
inference(resolution,[],[f54,f38]) ).
fof(f38,plain,
! [X3,X1] :
( ~ in(X3,singleton(X1))
| X1 = X3 ),
inference(equality_resolution,[],[f31]) ).
fof(f31,plain,
! [X3,X0,X1] :
( X1 = X3
| ~ in(X3,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) )
=> ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f54,plain,
in(sK0,singleton(sK1)),
inference(subsumption_resolution,[],[f52,f37]) ).
fof(f37,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X3,X0] :
( in(X3,X0)
| singleton(X3) != X0 ),
inference(equality_resolution,[],[f32]) ).
fof(f32,plain,
! [X3,X0,X1] :
( in(X3,X0)
| X1 != X3
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f52,plain,
( in(sK0,singleton(sK1))
| ~ in(sK1,singleton(sK1)) ),
inference(trivial_inequality_removal,[],[f49]) ).
fof(f49,plain,
( ~ in(sK1,singleton(sK1))
| in(sK0,singleton(sK1))
| singleton(sK0) != singleton(sK0) ),
inference(superposition,[],[f30,f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
| ~ in(X2,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ( ~ in(X0,X1)
& ( in(X2,X1)
| X0 = X2 ) )
| singleton(X0) != set_difference(unordered_pair(X0,X2),X1) )
& ( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
| in(X0,X1)
| ( ~ in(X2,X1)
& X0 != X2 ) ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
! [X2,X1,X0] :
( ( ( ~ in(X2,X1)
& ( in(X0,X1)
| X0 = X2 ) )
| set_difference(unordered_pair(X2,X0),X1) != singleton(X2) )
& ( set_difference(unordered_pair(X2,X0),X1) = singleton(X2)
| in(X2,X1)
| ( ~ in(X0,X1)
& X0 != X2 ) ) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X2,X1,X0] :
( ( ( ~ in(X2,X1)
& ( in(X0,X1)
| X0 = X2 ) )
| set_difference(unordered_pair(X2,X0),X1) != singleton(X2) )
& ( set_difference(unordered_pair(X2,X0),X1) = singleton(X2)
| in(X2,X1)
| ( ~ in(X0,X1)
& X0 != X2 ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X2,X1,X0] :
( ( ~ in(X2,X1)
& ( in(X0,X1)
| X0 = X2 ) )
<=> set_difference(unordered_pair(X2,X0),X1) = singleton(X2) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X0] :
( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
<=> singleton(X0) = set_difference(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f30,plain,
set_difference(unordered_pair(sK0,sK1),singleton(sK1)) != singleton(sK0),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:27:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44 % (28720)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.44 % (28720)First to succeed.
% 0.19/0.46 % (28720)Refutation found. Thanks to Tanya!
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46 % (28720)------------------------------
% 0.19/0.46 % (28720)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.46 % (28720)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.46 % (28720)Termination reason: Refutation
% 0.19/0.46
% 0.19/0.46 % (28720)Memory used [KB]: 6012
% 0.19/0.46 % (28720)Time elapsed: 0.066 s
% 0.19/0.46 % (28720)Instructions burned: 3 (million)
% 0.19/0.46 % (28720)------------------------------
% 0.19/0.46 % (28720)------------------------------
% 0.19/0.46 % (28709)Success in time 0.117 s
%------------------------------------------------------------------------------