TSTP Solution File: SET927+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET927+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_sat --cores 0 -t %d %s
% Computer : n019.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 18:26:07 EDT 2022
% Result : Theorem 0.20s 0.57s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 1 unt; 0 def)
% Number of atoms : 183 ( 66 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 208 ( 77 ~; 95 |; 26 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 33 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f105,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f49,f54,f55,f60,f85,f100,f104]) ).
fof(f104,plain,
( spl5_1
| spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f103,plain,
( $false
| spl5_1
| spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f101,f63]) ).
fof(f63,plain,
( set_difference(unordered_pair(sK2,sK2),sK4) = singleton(sK2)
| spl5_1 ),
inference(resolution,[],[f35,f38]) ).
fof(f38,plain,
( ~ in(sK2,sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f37,plain,
( spl5_1
<=> in(sK2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f35,plain,
! [X2,X1] :
( in(X1,X2)
| singleton(X1) = set_difference(unordered_pair(X1,X1),X2) ),
inference(equality_resolution,[],[f31]) ).
fof(f31,plain,
! [X2,X0,X1] :
( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| in(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ( ~ in(X1,X2)
& ( in(X0,X2)
| X0 = X1 ) )
| singleton(X1) != set_difference(unordered_pair(X1,X0),X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| in(X1,X2)
| ( ~ in(X0,X2)
& X0 != X1 ) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ( ~ in(X1,X2)
& ( in(X0,X2)
| X0 = X1 ) )
| singleton(X1) != set_difference(unordered_pair(X1,X0),X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| in(X1,X2)
| ( ~ in(X0,X2)
& X0 != X1 ) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ( ~ in(X1,X2)
& ( in(X0,X2)
| X0 = X1 ) )
<=> singleton(X1) = set_difference(unordered_pair(X1,X0),X2) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0,X2] :
( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
<=> set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f101,plain,
( set_difference(unordered_pair(sK2,sK2),sK4) != singleton(sK2)
| spl5_2
| ~ spl5_4 ),
inference(backward_demodulation,[],[f43,f53]) ).
fof(f53,plain,
( sK2 = sK3
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f51,plain,
( spl5_4
<=> sK2 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f43,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f41,plain,
( spl5_2
<=> set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f100,plain,
( spl5_1
| spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f99]) ).
fof(f99,plain,
( $false
| spl5_1
| spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f95,f43]) ).
fof(f95,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f87,f38]) ).
fof(f87,plain,
( ! [X0] :
( in(X0,sK4)
| singleton(X0) = set_difference(unordered_pair(X0,sK3),sK4) )
| ~ spl5_3 ),
inference(resolution,[],[f46,f32]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| in(X1,X2)
| singleton(X1) = set_difference(unordered_pair(X1,X0),X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
( in(sK3,sK4)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f45,plain,
( spl5_3
<=> in(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f85,plain,
( ~ spl5_2
| spl5_3
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f84,plain,
( $false
| ~ spl5_2
| spl5_3
| spl5_4 ),
inference(subsumption_resolution,[],[f83,f52]) ).
fof(f52,plain,
( sK2 != sK3
| spl5_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f83,plain,
( sK2 = sK3
| ~ spl5_2
| spl5_3 ),
inference(subsumption_resolution,[],[f82,f47]) ).
fof(f47,plain,
( ~ in(sK3,sK4)
| spl5_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f82,plain,
( in(sK3,sK4)
| sK2 = sK3
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f79]) ).
fof(f79,plain,
( in(sK3,sK4)
| sK2 = sK3
| singleton(sK2) != singleton(sK2)
| ~ spl5_2 ),
inference(superposition,[],[f33,f42]) ).
fof(f42,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f33,plain,
! [X2,X0,X1] :
( singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
| X0 = X1
| in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f60,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f59,f41,f37]) ).
fof(f59,plain,
( ~ in(sK2,sK4)
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f58]) ).
fof(f58,plain,
( singleton(sK2) != singleton(sK2)
| ~ in(sK2,sK4)
| ~ spl5_2 ),
inference(superposition,[],[f34,f42]) ).
fof(f34,plain,
! [X2,X0,X1] :
( singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f29,f51,f41,f37]) ).
fof(f29,plain,
( sK2 != sK3
| set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| in(sK2,sK4)
| ( ~ in(sK3,sK4)
& sK2 != sK3 ) )
& ( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| ( ~ in(sK2,sK4)
& ( in(sK3,sK4)
| sK2 = sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ) )
=> ( ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| in(sK2,sK4)
| ( ~ in(sK3,sK4)
& sK2 != sK3 ) )
& ( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| ( ~ in(sK2,sK4)
& ( in(sK3,sK4)
| sK2 = sK3 ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
<~> set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,negated_conjecture,
~ ! [X1,X2,X0] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
! [X1,X2,X0] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(f54,plain,
( spl5_3
| spl5_2
| spl5_4 ),
inference(avatar_split_clause,[],[f27,f51,f41,f45]) ).
fof(f27,plain,
( sK2 = sK3
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| in(sK3,sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
( spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f28,f37,f41]) ).
fof(f28,plain,
( ~ in(sK2,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f30,f45,f41,f37]) ).
fof(f30,plain,
( ~ in(sK3,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 14:34:05 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.20/0.55 % (10890)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/176Mi)
% 0.20/0.55 % (10893)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.20/0.56 % (10890)First to succeed.
% 0.20/0.57 % (10877)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 0.20/0.57 % (10874)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.57 % (10890)Refutation found. Thanks to Tanya!
% 0.20/0.57 % SZS status Theorem for theBenchmark
% 0.20/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.57 % (10890)------------------------------
% 0.20/0.57 % (10890)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57 % (10890)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.57 % (10890)Termination reason: Refutation
% 0.20/0.57
% 0.20/0.57 % (10890)Memory used [KB]: 5500
% 0.20/0.57 % (10890)Time elapsed: 0.087 s
% 0.20/0.57 % (10890)Instructions burned: 4 (million)
% 0.20/0.57 % (10890)------------------------------
% 0.20/0.57 % (10890)------------------------------
% 0.20/0.57 % (10869)Success in time 0.217 s
%------------------------------------------------------------------------------