TSTP Solution File: SET902+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET902+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 18:22:42 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 133 ( 94 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 159 ( 73 ~; 44 |; 36 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 35 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f134,plain,
$false,
inference(avatar_sat_refutation,[],[f58,f62,f66,f98,f118,f133]) ).
fof(f133,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f126,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(unit_resulting_resolution,[],[f45,f123]) ).
fof(f123,plain,
( empty_set = singleton(sK2)
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_demodulation,[],[f121,f38]) ).
fof(f38,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f121,plain,
( singleton(sK2) = set_union2(empty_set,empty_set)
| ~ spl5_1
| ~ spl5_4 ),
inference(backward_demodulation,[],[f101,f116]) ).
fof(f116,plain,
( empty_set = sK3
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl5_1
<=> empty_set = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f101,plain,
( set_union2(empty_set,sK3) = singleton(sK2)
| ~ spl5_4 ),
inference(backward_demodulation,[],[f49,f97]) ).
fof(f97,plain,
( empty_set = sK4
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl5_4
<=> empty_set = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f49,plain,
singleton(sK2) = set_union2(sK4,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( singleton(sK2) = set_union2(sK4,sK3)
& ( empty_set != sK4
| singleton(sK2) != sK3 )
& ( sK4 != singleton(sK2)
| empty_set != sK3 )
& ( sK4 != singleton(sK2)
| singleton(sK2) != sK3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f20,f31]) ).
fof(f31,plain,
( ? [X0,X1,X2] :
( singleton(X0) = set_union2(X2,X1)
& ( empty_set != X2
| singleton(X0) != X1 )
& ( singleton(X0) != X2
| empty_set != X1 )
& ( singleton(X0) != X2
| singleton(X0) != X1 ) )
=> ( singleton(sK2) = set_union2(sK4,sK3)
& ( empty_set != sK4
| singleton(sK2) != sK3 )
& ( sK4 != singleton(sK2)
| empty_set != sK3 )
& ( sK4 != singleton(sK2)
| singleton(sK2) != sK3 ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2] :
( singleton(X0) = set_union2(X2,X1)
& ( empty_set != X2
| singleton(X0) != X1 )
& ( singleton(X0) != X2
| empty_set != X1 )
& ( singleton(X0) != X2
| singleton(X0) != X1 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X1,X2,X0] :
~ ( ~ ( singleton(X0) = X1
& singleton(X0) = X2 )
& singleton(X0) = set_union2(X2,X1)
& ~ ( singleton(X0) = X2
& empty_set = X1 )
& ~ ( empty_set = X2
& singleton(X0) = X1 ) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X2,X1] :
~ ( ~ ( singleton(X0) = X1
& singleton(X0) = X2 )
& ~ ( empty_set = X1
& singleton(X0) = X2 )
& ~ ( empty_set = X2
& singleton(X0) = X1 )
& singleton(X0) = set_union2(X1,X2) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X2,X1] :
~ ( ~ ( singleton(X0) = X1
& singleton(X0) = X2 )
& ~ ( empty_set = X1
& singleton(X0) = X2 )
& ~ ( empty_set = X2
& singleton(X0) = X1 )
& singleton(X0) = set_union2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f45,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : empty_set != singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f118,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f115,f60,f53]) ).
fof(f60,plain,
( spl5_3
<=> singleton(sK2) = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f115,plain,
( singleton(sK2) = sK3
| empty_set = sK3 ),
inference(resolution,[],[f92,f42]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X1,singleton(X0))
| empty_set = X1
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(X1,singleton(X0))
| ( empty_set != X1
& singleton(X0) != X1 ) )
& ( empty_set = X1
| singleton(X0) = X1
| ~ subset(X1,singleton(X0)) ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( empty_set = X0
| singleton(X1) = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( empty_set = X0
| singleton(X1) = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( subset(X0,singleton(X1))
<=> ( empty_set = X0
| singleton(X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f92,plain,
subset(sK3,singleton(sK2)),
inference(superposition,[],[f37,f80]) ).
fof(f80,plain,
singleton(sK2) = set_union2(sK3,sK4),
inference(superposition,[],[f39,f49]) ).
fof(f39,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f37,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f98,plain,
( spl5_2
| spl5_4 ),
inference(avatar_split_clause,[],[f95,f64,f56]) ).
fof(f56,plain,
( spl5_2
<=> sK4 = singleton(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f95,plain,
( empty_set = sK4
| sK4 = singleton(sK2) ),
inference(resolution,[],[f42,f67]) ).
fof(f67,plain,
subset(sK4,singleton(sK2)),
inference(superposition,[],[f37,f49]) ).
fof(f66,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f48,f64,f60]) ).
fof(f48,plain,
( empty_set != sK4
| singleton(sK2) != sK3 ),
inference(cnf_transformation,[],[f32]) ).
fof(f62,plain,
( ~ spl5_3
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f46,f56,f60]) ).
fof(f46,plain,
( sK4 != singleton(sK2)
| singleton(sK2) != sK3 ),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f47,f56,f53]) ).
fof(f47,plain,
( sK4 != singleton(sK2)
| empty_set != sK3 ),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET902+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
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 14:30:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.50 % (15491)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.50 % (15482)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)
% 0.20/0.50 % (15495)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.51 % (15495)First to succeed.
% 0.20/0.51 % (15495)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (15495)------------------------------
% 0.20/0.51 % (15495)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (15495)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (15495)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (15495)Memory used [KB]: 6012
% 0.20/0.51 % (15495)Time elapsed: 0.113 s
% 0.20/0.51 % (15495)Instructions burned: 4 (million)
% 0.20/0.51 % (15495)------------------------------
% 0.20/0.51 % (15495)------------------------------
% 0.20/0.51 % (15462)Success in time 0.153 s
%------------------------------------------------------------------------------