TSTP Solution File: SET873+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET873+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 : n014.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 18:22:38 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 91 ( 54 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 89 ( 35 ~; 31 |; 16 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 44 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f119,plain,
$false,
inference(subsumption_resolution,[],[f117,f49]) ).
fof(f49,plain,
sK4 != sK3,
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
( sK4 != sK3
& set_union2(singleton(sK4),singleton(sK3)) = singleton(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f32,f33]) ).
fof(f33,plain,
( ? [X0,X1] :
( X0 != X1
& singleton(X1) = set_union2(singleton(X1),singleton(X0)) )
=> ( sK4 != sK3
& set_union2(singleton(sK4),singleton(sK3)) = singleton(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
? [X0,X1] :
( X0 != X1
& singleton(X1) = set_union2(singleton(X1),singleton(X0)) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
? [X1,X0] :
( X0 != X1
& singleton(X0) = set_union2(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X1,X0] :
( singleton(X0) = set_union2(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X1,X0] :
( singleton(X0) = set_union2(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(f117,plain,
sK4 = sK3,
inference(resolution,[],[f116,f84]) ).
fof(f84,plain,
! [X0] :
( ~ in(X0,sF5)
| sK4 = X0 ),
inference(superposition,[],[f51,f54]) ).
fof(f54,plain,
singleton(sK4) = sF5,
introduced(function_definition,[]) ).
fof(f51,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( ~ in(sK2(X0,X1),X1)
| sK2(X0,X1) != X0 )
& ( in(sK2(X0,X1),X1)
| sK2(X0,X1) = X0 ) ) )
& ( ! [X3] :
( ( X0 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| X0 != X3 ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) )
=> ( ( ~ in(sK2(X0,X1),X1)
| sK2(X0,X1) != X0 )
& ( in(sK2(X0,X1),X1)
| sK2(X0,X1) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) ) )
& ( ! [X3] :
( ( X0 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| X0 != X3 ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) ) )
& ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( X0 = X2
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f116,plain,
in(sK3,sF5),
inference(subsumption_resolution,[],[f115,f38]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f115,plain,
( in(sK3,sF5)
| ~ subset(sF5,sF5) ),
inference(superposition,[],[f107,f60]) ).
fof(f60,plain,
sF5 = set_union2(sF5,sF6),
inference(forward_demodulation,[],[f56,f57]) ).
fof(f57,plain,
sF7 = sF5,
inference(definition_folding,[],[f48,f54,f56,f55,f54]) ).
fof(f55,plain,
singleton(sK3) = sF6,
introduced(function_definition,[]) ).
fof(f48,plain,
set_union2(singleton(sK4),singleton(sK3)) = singleton(sK4),
inference(cnf_transformation,[],[f34]) ).
fof(f56,plain,
sF7 = set_union2(sF5,sF6),
introduced(function_definition,[]) ).
fof(f107,plain,
! [X0] :
( ~ subset(set_union2(X0,sF6),X0)
| in(sK3,X0) ),
inference(superposition,[],[f89,f50]) ).
fof(f50,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f89,plain,
! [X1] :
( ~ subset(set_union2(sF6,X1),X1)
| in(sK3,X1) ),
inference(superposition,[],[f40,f55]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n014.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 : Tue Aug 30 14:28:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.51 % (9692)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.51 % (9692)First to succeed.
% 0.19/0.52 % (9693)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53 % (9707)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53 % (9692)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (9692)------------------------------
% 0.19/0.53 % (9692)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (9692)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (9692)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (9692)Memory used [KB]: 6012
% 0.19/0.53 % (9692)Time elapsed: 0.093 s
% 0.19/0.53 % (9692)Instructions burned: 4 (million)
% 0.19/0.53 % (9692)------------------------------
% 0.19/0.53 % (9692)------------------------------
% 0.19/0.53 % (9691)Success in time 0.174 s
%------------------------------------------------------------------------------