TSTP Solution File: SYN551+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 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 : n021.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 19:27:43 EDT 2022
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 1 unt; 0 def)
% Number of atoms : 323 ( 182 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 422 ( 188 ~; 177 |; 31 &)
% ( 15 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 70 ( 50 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f181,plain,
$false,
inference(avatar_sat_refutation,[],[f27,f34,f38,f42,f50,f51,f52,f53,f69,f94,f104,f114,f136,f165,f172,f180]) ).
fof(f180,plain,
( spl4_13
| ~ spl4_2
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f178,f40,f24,f142]) ).
fof(f142,plain,
( spl4_13
<=> sK0(sK2) = f(g(sK0(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f24,plain,
( spl4_2
<=> sK2 = f(g(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f40,plain,
( spl4_6
<=> ! [X0] :
( f(g(sK0(X0))) = sK0(X0)
| f(g(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f178,plain,
( sK0(sK2) = f(g(sK0(sK2)))
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f176]) ).
fof(f176,plain,
( sK2 != sK2
| sK0(sK2) = f(g(sK0(sK2)))
| ~ spl4_2
| ~ spl4_6 ),
inference(superposition,[],[f41,f26]) ).
fof(f26,plain,
( sK2 = f(g(sK2))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f41,plain,
( ! [X0] :
( f(g(X0)) != X0
| f(g(sK0(X0))) = sK0(X0) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f172,plain,
( ~ spl4_4
| ~ spl4_13
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f171]) ).
fof(f171,plain,
( $false
| ~ spl4_4
| ~ spl4_13
| ~ spl4_14 ),
inference(subsumption_resolution,[],[f168,f148]) ).
fof(f148,plain,
( sK0(sK2) = sK2
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f147,plain,
( spl4_14
<=> sK0(sK2) = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f168,plain,
( sK0(sK2) != sK2
| ~ spl4_4
| ~ spl4_13
| ~ spl4_14 ),
inference(backward_demodulation,[],[f159,f148]) ).
fof(f159,plain,
( sK0(sK0(sK2)) != sK0(sK2)
| ~ spl4_4
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f157]) ).
fof(f157,plain,
( sK0(sK2) != sK0(sK2)
| sK0(sK0(sK2)) != sK0(sK2)
| ~ spl4_4
| ~ spl4_13 ),
inference(superposition,[],[f33,f144]) ).
fof(f144,plain,
( sK0(sK2) = f(g(sK0(sK2)))
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f33,plain,
( ! [X0] :
( f(g(X0)) != X0
| sK0(X0) != X0 )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f32,plain,
( spl4_4
<=> ! [X0] :
( f(g(X0)) != X0
| sK0(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f165,plain,
( spl4_14
| ~ spl4_7
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f162,f142,f44,f147]) ).
fof(f44,plain,
( spl4_7
<=> ! [X5] :
( sK2 = X5
| f(g(X5)) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f162,plain,
( sK0(sK2) = sK2
| ~ spl4_7
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f161]) ).
fof(f161,plain,
( sK0(sK2) = sK2
| sK0(sK2) != sK0(sK2)
| ~ spl4_7
| ~ spl4_13 ),
inference(superposition,[],[f45,f144]) ).
fof(f45,plain,
( ! [X5] :
( f(g(X5)) != X5
| sK2 = X5 )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f136,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f135]) ).
fof(f135,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(subsumption_resolution,[],[f132,f118]) ).
fof(f118,plain,
( sK0(f(sK3)) != f(sK3)
| ~ spl4_4
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f117]) ).
fof(f117,plain,
( f(sK3) != f(sK3)
| sK0(f(sK3)) != f(sK3)
| ~ spl4_4
| ~ spl4_8 ),
inference(superposition,[],[f33,f49]) ).
fof(f49,plain,
( sK3 = g(f(sK3))
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f47,plain,
( spl4_8
<=> sK3 = g(f(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f132,plain,
( sK0(f(sK3)) = f(sK3)
| ~ spl4_1
| ~ spl4_6
| ~ spl4_8 ),
inference(backward_demodulation,[],[f123,f131]) ).
fof(f131,plain,
( sK3 = g(sK0(f(sK3)))
| ~ spl4_1
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f126]) ).
fof(f126,plain,
( sK3 = g(sK0(f(sK3)))
| g(sK0(f(sK3))) != g(sK0(f(sK3)))
| ~ spl4_1
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f22,f123]) ).
fof(f22,plain,
( ! [X7] :
( g(f(X7)) != X7
| sK3 = X7 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f21,plain,
( spl4_1
<=> ! [X7] :
( g(f(X7)) != X7
| sK3 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f123,plain,
( sK0(f(sK3)) = f(g(sK0(f(sK3))))
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f122]) ).
fof(f122,plain,
( f(sK3) != f(sK3)
| sK0(f(sK3)) = f(g(sK0(f(sK3))))
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f41,f49]) ).
fof(f114,plain,
( spl4_10
| ~ spl4_1
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f111,f89,f21,f84]) ).
fof(f84,plain,
( spl4_10
<=> sK1(sK3) = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f89,plain,
( spl4_11
<=> g(f(sK1(sK3))) = sK1(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f111,plain,
( sK1(sK3) = sK3
| ~ spl4_1
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f110]) ).
fof(f110,plain,
( sK1(sK3) != sK1(sK3)
| sK1(sK3) = sK3
| ~ spl4_1
| ~ spl4_11 ),
inference(superposition,[],[f22,f91]) ).
fof(f91,plain,
( g(f(sK1(sK3))) = sK1(sK3)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f104,plain,
( spl4_11
| ~ spl4_5
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f74,f47,f36,f89]) ).
fof(f36,plain,
( spl4_5
<=> ! [X2] :
( g(f(X2)) != X2
| g(f(sK1(X2))) = sK1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f74,plain,
( g(f(sK1(sK3))) = sK1(sK3)
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f70]) ).
fof(f70,plain,
( sK3 != sK3
| g(f(sK1(sK3))) = sK1(sK3)
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f37,f49]) ).
fof(f37,plain,
( ! [X2] :
( g(f(X2)) != X2
| g(f(sK1(X2))) = sK1(X2) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f94,plain,
( ~ spl4_10
| ~ spl4_3
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f75,f47,f29,f84]) ).
fof(f29,plain,
( spl4_3
<=> ! [X2] :
( sK1(X2) != X2
| g(f(X2)) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f75,plain,
( sK1(sK3) != sK3
| ~ spl4_3
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f71]) ).
fof(f71,plain,
( sK3 != sK3
| sK1(sK3) != sK3
| ~ spl4_3
| ~ spl4_8 ),
inference(superposition,[],[f30,f49]) ).
fof(f30,plain,
( ! [X2] :
( g(f(X2)) != X2
| sK1(X2) != X2 )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f69,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f68,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f65,f56]) ).
fof(f56,plain,
( sK1(g(sK2)) != g(sK2)
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f55]) ).
fof(f55,plain,
( sK1(g(sK2)) != g(sK2)
| g(sK2) != g(sK2)
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[],[f30,f26]) ).
fof(f65,plain,
( sK1(g(sK2)) = g(sK2)
| ~ spl4_2
| ~ spl4_5
| ~ spl4_7 ),
inference(backward_demodulation,[],[f58,f62]) ).
fof(f62,plain,
( f(sK1(g(sK2))) = sK2
| ~ spl4_2
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f61]) ).
fof(f61,plain,
( f(sK1(g(sK2))) != f(sK1(g(sK2)))
| f(sK1(g(sK2))) = sK2
| ~ spl4_2
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f45,f58]) ).
fof(f58,plain,
( sK1(g(sK2)) = g(f(sK1(g(sK2))))
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f57]) ).
fof(f57,plain,
( g(sK2) != g(sK2)
| sK1(g(sK2)) = g(f(sK1(g(sK2))))
| ~ spl4_2
| ~ spl4_5 ),
inference(superposition,[],[f37,f26]) ).
fof(f53,plain,
( spl4_2
| spl4_8 ),
inference(avatar_split_clause,[],[f13,f47,f24]) ).
fof(f13,plain,
( sK3 = g(f(sK3))
| sK2 = f(g(sK2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
( ( ! [X0] :
( ( f(g(sK0(X0))) = sK0(X0)
& sK0(X0) != X0 )
| f(g(X0)) != X0 )
| ! [X2] :
( g(f(X2)) != X2
| ( sK1(X2) != X2
& g(f(sK1(X2))) = sK1(X2) ) ) )
& ( ( ! [X5] :
( f(g(X5)) != X5
| sK2 = X5 )
& sK2 = f(g(sK2)) )
| ( sK3 = g(f(sK3))
& ! [X7] :
( sK3 = X7
| g(f(X7)) != X7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f10,f9,f8,f7]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( f(g(X1)) = X1
& X0 != X1 )
=> ( f(g(sK0(X0))) = sK0(X0)
& sK0(X0) != X0 ) ),
introduced(choice_axiom,[]) ).
fof(f8,plain,
! [X2] :
( ? [X3] :
( X2 != X3
& g(f(X3)) = X3 )
=> ( sK1(X2) != X2
& g(f(sK1(X2))) = sK1(X2) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
( ? [X4] :
( ! [X5] :
( f(g(X5)) != X5
| X4 = X5 )
& f(g(X4)) = X4 )
=> ( ! [X5] :
( f(g(X5)) != X5
| sK2 = X5 )
& sK2 = f(g(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ? [X6] :
( g(f(X6)) = X6
& ! [X7] :
( X6 = X7
| g(f(X7)) != X7 ) )
=> ( sK3 = g(f(sK3))
& ! [X7] :
( sK3 = X7
| g(f(X7)) != X7 ) ) ),
introduced(choice_axiom,[]) ).
fof(f6,plain,
( ( ! [X0] :
( ? [X1] :
( f(g(X1)) = X1
& X0 != X1 )
| f(g(X0)) != X0 )
| ! [X2] :
( g(f(X2)) != X2
| ? [X3] :
( X2 != X3
& g(f(X3)) = X3 ) ) )
& ( ? [X4] :
( ! [X5] :
( f(g(X5)) != X5
| X4 = X5 )
& f(g(X4)) = X4 )
| ? [X6] :
( g(f(X6)) = X6
& ! [X7] :
( X6 = X7
| g(f(X7)) != X7 ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,plain,
( ( ! [X0] :
( ? [X1] :
( f(g(X1)) = X1
& X0 != X1 )
| f(g(X0)) != X0 )
| ! [X2] :
( g(f(X2)) != X2
| ? [X3] :
( X2 != X3
& g(f(X3)) = X3 ) ) )
& ( ? [X0] :
( ! [X1] :
( f(g(X1)) != X1
| X0 = X1 )
& f(g(X0)) = X0 )
| ? [X2] :
( g(f(X2)) = X2
& ! [X3] :
( X2 = X3
| g(f(X3)) != X3 ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,plain,
( ? [X2] :
( g(f(X2)) = X2
& ! [X3] :
( X2 = X3
| g(f(X3)) != X3 ) )
<~> ? [X0] :
( ! [X1] :
( f(g(X1)) != X1
| X0 = X1 )
& f(g(X0)) = X0 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ? [X2] :
( g(f(X2)) = X2
& ! [X3] :
( g(f(X3)) = X3
=> X2 = X3 ) )
<=> ? [X0] :
( f(g(X0)) = X0
& ! [X1] :
( f(g(X1)) = X1
=> X0 = X1 ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( f(g(X0)) = X0
& ! [X1] :
( f(g(X1)) = X1
=> X0 = X1 ) )
<=> ? [X0] :
( ! [X1] :
( g(f(X1)) = X1
=> X0 = X1 )
& g(f(X0)) = X0 ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ? [X0] :
( f(g(X0)) = X0
& ! [X1] :
( f(g(X1)) = X1
=> X0 = X1 ) )
<=> ? [X0] :
( ! [X1] :
( g(f(X1)) = X1
=> X0 = X1 )
& g(f(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(f52,plain,
( spl4_7
| spl4_1 ),
inference(avatar_split_clause,[],[f14,f21,f44]) ).
fof(f14,plain,
! [X7,X5] :
( g(f(X7)) != X7
| sK2 = X5
| f(g(X5)) != X5
| sK3 = X7 ),
inference(cnf_transformation,[],[f11]) ).
fof(f51,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f18,f40,f36]) ).
fof(f18,plain,
! [X2,X0] :
( f(g(sK0(X0))) = sK0(X0)
| f(g(X0)) != X0
| g(f(sK1(X2))) = sK1(X2)
| g(f(X2)) != X2 ),
inference(cnf_transformation,[],[f11]) ).
fof(f50,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f15,f47,f44]) ).
fof(f15,plain,
! [X5] :
( sK3 = g(f(sK3))
| sK2 = X5
| f(g(X5)) != X5 ),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
( spl4_3
| spl4_6 ),
inference(avatar_split_clause,[],[f19,f40,f29]) ).
fof(f19,plain,
! [X2,X0] :
( f(g(sK0(X0))) = sK0(X0)
| f(g(X0)) != X0
| g(f(X2)) != X2
| sK1(X2) != X2 ),
inference(cnf_transformation,[],[f11]) ).
fof(f38,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f16,f32,f36]) ).
fof(f16,plain,
! [X2,X0] :
( f(g(X0)) != X0
| sK0(X0) != X0
| g(f(X2)) != X2
| g(f(sK1(X2))) = sK1(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f34,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f17,f32,f29]) ).
fof(f17,plain,
! [X2,X0] :
( f(g(X0)) != X0
| sK1(X2) != X2
| sK0(X0) != X0
| g(f(X2)) != X2 ),
inference(cnf_transformation,[],[f11]) ).
fof(f27,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f12,f24,f21]) ).
fof(f12,plain,
! [X7] :
( sK2 = f(g(sK2))
| g(f(X7)) != X7
| sK3 = X7 ),
inference(cnf_transformation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.09/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 30 22:03:56 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.45 % (13701)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)
% 0.16/0.47 % (13717)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.16/0.47 % (13701)First to succeed.
% 0.16/0.48 % (13709)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.48 % (13701)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (13701)------------------------------
% 0.16/0.48 % (13701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48 % (13701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.48 % (13701)Termination reason: Refutation
% 0.16/0.48
% 0.16/0.48 % (13701)Memory used [KB]: 6012
% 0.16/0.48 % (13701)Time elapsed: 0.109 s
% 0.16/0.48 % (13701)Instructions burned: 6 (million)
% 0.16/0.48 % (13701)------------------------------
% 0.16/0.48 % (13701)------------------------------
% 0.16/0.48 % (13694)Success in time 0.16 s
%------------------------------------------------------------------------------