TSTP Solution File: SET893+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET893+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 : n022.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 18:22:41 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 2 unt; 0 def)
% Number of atoms : 210 ( 75 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 251 ( 98 ~; 103 |; 35 &)
% ( 12 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 72 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f85,plain,
$false,
inference(avatar_sat_refutation,[],[f51,f56,f57,f64,f75,f84]) ).
fof(f84,plain,
( ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f83]) ).
fof(f83,plain,
( $false
| ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f82,f41]) ).
fof(f41,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( in(X2,X1)
| X0 != X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> X1 = X2 )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( X0 = X2
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f82,plain,
( ~ in(sK0,singleton(sK0))
| ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f80,f41]) ).
fof(f80,plain,
( ~ in(sK1,singleton(sK1))
| ~ in(sK0,singleton(sK0))
| ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f38,f77]) ).
fof(f77,plain,
( ~ in(ordered_pair(sK1,sK0),cartesian_product2(singleton(sK1),singleton(sK0)))
| ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(forward_demodulation,[],[f76,f54]) ).
fof(f54,plain,
( sK1 = sK2
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl5_3
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f76,plain,
( ~ in(ordered_pair(sK2,sK0),cartesian_product2(singleton(sK1),singleton(sK0)))
| ~ spl5_1
| spl5_2 ),
inference(forward_demodulation,[],[f49,f46]) ).
fof(f46,plain,
( sK3 = sK0
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f44,plain,
( spl5_1
<=> sK3 = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f49,plain,
( ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
| spl5_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl5_2
<=> in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
| ~ in(X1,X3)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
| ~ in(X1,X3)
| ~ in(X2,X0) )
& ( ( in(X1,X3)
& in(X2,X0) )
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X0)) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X2,X1,X3,X0] :
( ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
| ~ in(X1,X0)
| ~ in(X3,X2) )
& ( ( in(X1,X0)
& in(X3,X2) )
| ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2)) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X2,X1,X3,X0] :
( ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
| ~ in(X1,X0)
| ~ in(X3,X2) )
& ( ( in(X1,X0)
& in(X3,X2) )
| ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X2,X1,X3,X0] :
( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
<=> ( in(X1,X0)
& in(X3,X2) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X3,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f75,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f74]) ).
fof(f74,plain,
( $false
| ~ spl5_1
| ~ spl5_2
| spl5_3 ),
inference(subsumption_resolution,[],[f72,f55]) ).
fof(f55,plain,
( sK1 != sK2
| spl5_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f72,plain,
( sK1 = sK2
| ~ spl5_1
| ~ spl5_2 ),
inference(resolution,[],[f71,f42]) ).
fof(f42,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f71,plain,
( in(sK2,singleton(sK1))
| ~ spl5_1
| ~ spl5_2 ),
inference(resolution,[],[f37,f68]) ).
fof(f68,plain,
( in(ordered_pair(sK2,sK0),cartesian_product2(singleton(sK1),singleton(sK0)))
| ~ spl5_1
| ~ spl5_2 ),
inference(backward_demodulation,[],[f50,f46]) ).
fof(f50,plain,
( in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
| in(X1,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f64,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f62,f48,f44]) ).
fof(f62,plain,
( sK3 = sK0
| ~ spl5_2 ),
inference(resolution,[],[f61,f42]) ).
fof(f61,plain,
( in(sK3,singleton(sK0))
| ~ spl5_2 ),
inference(resolution,[],[f36,f50]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f57,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f30,f48,f53]) ).
fof(f30,plain,
( in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
| sK1 = sK2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ( sK1 != sK2
| sK3 != sK0
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) )
& ( ( sK1 = sK2
& sK3 = sK0 )
| in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2,X3] :
( ( X1 != X2
| X0 != X3
| ~ in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) )
& ( ( X1 = X2
& X0 = X3 )
| in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) ) )
=> ( ( sK1 != sK2
| sK3 != sK0
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) )
& ( ( sK1 = sK2
& sK3 = sK0 )
| in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( ( X1 != X2
| X0 != X3
| ~ in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) )
& ( ( X1 = X2
& X0 = X3 )
| in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
? [X0,X2,X1,X3] :
( ( X1 != X2
| X0 != X3
| ~ in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) )
& ( ( X1 = X2
& X0 = X3 )
| in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X2,X1,X3] :
( ( X1 != X2
| X0 != X3
| ~ in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) )
& ( ( X1 = X2
& X0 = X3 )
| in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
? [X0,X2,X1,X3] :
( in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0)))
<~> ( X1 = X2
& X0 = X3 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X2,X1,X0,X3] :
( ( X1 = X2
& X0 = X3 )
<=> in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X3,X0,X2,X1] :
( ( X1 = X3
& X0 = X2 )
<=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X3,X0,X2,X1] :
( ( X1 = X3
& X0 = X2 )
<=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).
fof(f56,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f31,f44,f53,f48]) ).
fof(f31,plain,
( sK3 != sK0
| sK1 != sK2
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ),
inference(cnf_transformation,[],[f20]) ).
fof(f51,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f29,f48,f44]) ).
fof(f29,plain,
( in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
| sK3 = sK0 ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:29:56 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50 % (11053)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.50 % (11045)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)
% 0.20/0.50 % (11063)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.50 % (11054)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)
% 0.20/0.50 % (11054)Refutation not found, incomplete strategy% (11054)------------------------------
% 0.20/0.50 % (11054)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (11054)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (11054)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50
% 0.20/0.50 % (11054)Memory used [KB]: 5884
% 0.20/0.50 % (11054)Time elapsed: 0.106 s
% 0.20/0.50 % (11054)Instructions burned: 2 (million)
% 0.20/0.50 % (11054)------------------------------
% 0.20/0.50 % (11054)------------------------------
% 0.20/0.51 % (11049)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.51 % (11058)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)
% 0.20/0.51 % (11056)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.51 % (11048)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.51 % (11048)First to succeed.
% 0.20/0.51 % (11048)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
% 0.20/0.52 % (11048)------------------------------
% 0.20/0.52 % (11048)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (11048)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (11048)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (11048)Memory used [KB]: 6012
% 0.20/0.52 % (11048)Time elapsed: 0.119 s
% 0.20/0.52 % (11048)Instructions burned: 2 (million)
% 0.20/0.52 % (11048)------------------------------
% 0.20/0.52 % (11048)------------------------------
% 0.20/0.52 % (11043)Success in time 0.167 s
%------------------------------------------------------------------------------