TSTP Solution File: SEU136+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU136+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n020.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 18:26:49 EDT 2022
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 9 unt; 0 def)
% Number of atoms : 260 ( 36 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 321 ( 123 ~; 136 |; 50 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 123 ( 109 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f226,plain,
$false,
inference(avatar_sat_refutation,[],[f136,f138,f189,f225]) ).
fof(f225,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f224,plain,
( $false
| ~ spl8_1
| spl8_2 ),
inference(subsumption_resolution,[],[f216,f192]) ).
fof(f192,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK6)
| ~ spl8_1 ),
inference(resolution,[],[f131,f105]) ).
fof(f105,plain,
! [X2,X1,X4] :
( in(X4,X2)
| ~ in(X4,set_difference(X2,X1)) ),
inference(equality_resolution,[],[f90]) ).
fof(f90,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_difference(X2,X1) != X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( set_difference(X2,X1) = X0
| ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2)
| ~ in(sK4(X0,X1,X2),X0) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X2) )
| in(sK4(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) )
& ( ( ~ in(X4,X1)
& in(X4,X2) )
| ~ in(X4,X0) ) )
| set_difference(X2,X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f58,f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) )
=> ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2)
| ~ in(sK4(X0,X1,X2),X0) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X2) )
| in(sK4(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( set_difference(X2,X1) = X0
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) )
& ( ( ~ in(X4,X1)
& in(X4,X2) )
| ~ in(X4,X0) ) )
| set_difference(X2,X1) != X0 ) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X1,X2,X0] :
( ( set_difference(X0,X2) = X1
| ? [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( ~ in(X3,X2)
& in(X3,X0) )
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X2)
& in(X3,X0) )
| ~ in(X3,X1) ) )
| set_difference(X0,X2) != X1 ) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X1,X2,X0] :
( ( set_difference(X0,X2) = X1
| ? [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( ~ in(X3,X2)
& in(X3,X0) )
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X2)
& in(X3,X0) )
| ~ in(X3,X1) ) )
| set_difference(X0,X2) != X1 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X1,X2,X0] :
( set_difference(X0,X2) = X1
<=> ! [X3] :
( in(X3,X1)
<=> ( ~ in(X3,X2)
& in(X3,X0) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X1] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( ( ~ in(X3,X1)
& in(X3,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f131,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5))
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl8_1
<=> in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f216,plain,
( ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK6)
| spl8_2 ),
inference(resolution,[],[f134,f99]) ).
fof(f99,plain,
! [X3,X0,X1] :
( ~ in(X3,X1)
| in(X3,set_union2(X1,X0)) ),
inference(equality_resolution,[],[f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X1)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ( ( ~ in(sK0(X0,X1,X2),X2)
| ( ~ in(sK0(X0,X1,X2),X1)
& ~ in(sK0(X0,X1,X2),X0) ) )
& ( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f39,f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X1)
| in(X4,X0) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X2)
| ( ~ in(sK0(X0,X1,X2),X1)
& ~ in(sK0(X0,X1,X2),X0) ) )
& ( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ? [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X1)
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ! [X3] :
( ( in(X3,X0)
| in(X3,X1) )
<=> in(X3,X2) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f134,plain,
( ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_union2(sK6,sK5))
| spl8_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f133,plain,
( spl8_2
<=> in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_union2(sK6,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f189,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f188,plain,
( $false
| spl8_1
| ~ spl8_2 ),
inference(subsumption_resolution,[],[f187,f139]) ).
fof(f139,plain,
~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK5),
inference(subsumption_resolution,[],[f123,f104]) ).
fof(f104,plain,
! [X2,X1,X4] :
( ~ in(X4,set_difference(X2,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f91]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| set_difference(X2,X1) != X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f123,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5))
| ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK5) ),
inference(resolution,[],[f121,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( sQ7_eqProxy(set_difference(X2,X1),X0)
| in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X1) ),
inference(equality_proxy_replacement,[],[f94,f106]) ).
fof(f106,plain,
! [X0,X1] :
( sQ7_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ7_eqProxy])]) ).
fof(f94,plain,
! [X2,X0,X1] :
( set_difference(X2,X1) = X0
| ~ in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f121,plain,
~ sQ7_eqProxy(set_difference(set_union2(sK6,sK5),sK5),set_difference(sK6,sK5)),
inference(equality_proxy_replacement,[],[f96,f106]) ).
fof(f96,plain,
set_difference(set_union2(sK6,sK5),sK5) != set_difference(sK6,sK5),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
set_difference(set_union2(sK6,sK5),sK5) != set_difference(sK6,sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f61,f62]) ).
fof(f62,plain,
( ? [X0,X1] : set_difference(set_union2(X1,X0),X0) != set_difference(X1,X0)
=> set_difference(set_union2(sK6,sK5),sK5) != set_difference(sK6,sK5) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
? [X0,X1] : set_difference(set_union2(X1,X0),X0) != set_difference(X1,X0),
inference(rectify,[],[f29]) ).
fof(f29,plain,
? [X1,X0] : set_difference(X0,X1) != set_difference(set_union2(X0,X1),X1),
inference(ennf_transformation,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f187,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK5)
| spl8_1
| ~ spl8_2 ),
inference(subsumption_resolution,[],[f178,f176]) ).
fof(f176,plain,
( ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK6)
| spl8_1 ),
inference(subsumption_resolution,[],[f168,f139]) ).
fof(f168,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK5)
| ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK6)
| spl8_1 ),
inference(resolution,[],[f130,f103]) ).
fof(f103,plain,
! [X2,X1,X4] :
( ~ in(X4,X2)
| in(X4,X1)
| in(X4,set_difference(X2,X1)) ),
inference(equality_resolution,[],[f92]) ).
fof(f92,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_difference(X2,X1) != X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f130,plain,
( ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5))
| spl8_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f178,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK6)
| in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK5)
| ~ spl8_2 ),
inference(resolution,[],[f135,f98]) ).
fof(f98,plain,
! [X3,X0,X1] :
( in(X3,X0)
| in(X3,X1)
| ~ in(X3,set_union2(X1,X0)) ),
inference(equality_resolution,[],[f72]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f135,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_union2(sK6,sK5))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f138,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f137,f133,f129]) ).
fof(f137,plain,
( ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_union2(sK6,sK5))
| ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5)) ),
inference(subsumption_resolution,[],[f124,f104]) ).
fof(f124,plain,
( ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_union2(sK6,sK5))
| in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),sK5)
| ~ in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5)) ),
inference(resolution,[],[f121,f118]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| sQ7_eqProxy(set_difference(X2,X1),X0)
| ~ in(sK4(X0,X1,X2),X2) ),
inference(equality_proxy_replacement,[],[f95,f106]) ).
fof(f95,plain,
! [X2,X0,X1] :
( set_difference(X2,X1) = X0
| in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2)
| ~ in(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f136,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f125,f133,f129]) ).
fof(f125,plain,
( in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_union2(sK6,sK5))
| in(sK4(set_difference(sK6,sK5),sK5,set_union2(sK6,sK5)),set_difference(sK6,sK5)) ),
inference(resolution,[],[f121,f120]) ).
fof(f120,plain,
! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2)
| sQ7_eqProxy(set_difference(X2,X1),X0) ),
inference(equality_proxy_replacement,[],[f93,f106]) ).
fof(f93,plain,
! [X2,X0,X1] :
( set_difference(X2,X1) = X0
| in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU136+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % 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 : n020.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 14:43:45 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.48 % (27846)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.49 % (27838)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.21/0.49 % (27846)Instruction limit reached!
% 0.21/0.49 % (27846)------------------------------
% 0.21/0.49 % (27846)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (27846)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (27846)Termination reason: Unknown
% 0.21/0.49 % (27846)Termination phase: Unused predicate definition removal
% 0.21/0.49
% 0.21/0.49 % (27846)Memory used [KB]: 1407
% 0.21/0.49 % (27846)Time elapsed: 0.004 s
% 0.21/0.49 % (27846)Instructions burned: 2 (million)
% 0.21/0.49 % (27846)------------------------------
% 0.21/0.49 % (27846)------------------------------
% 0.21/0.49 % (27838)First to succeed.
% 0.21/0.50 % (27838)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (27838)------------------------------
% 0.21/0.50 % (27838)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50 % (27838)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50 % (27838)Termination reason: Refutation
% 0.21/0.50
% 0.21/0.50 % (27838)Memory used [KB]: 6012
% 0.21/0.50 % (27838)Time elapsed: 0.075 s
% 0.21/0.50 % (27838)Instructions burned: 4 (million)
% 0.21/0.50 % (27838)------------------------------
% 0.21/0.50 % (27838)------------------------------
% 0.21/0.50 % (27827)Success in time 0.138 s
%------------------------------------------------------------------------------