TSTP Solution File: ALG211+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : ALG211+1 : TPTP v8.1.0. Released 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 15:40:40 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 9 unt; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 182 ( 72 ~; 54 |; 35 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 121 ( 97 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116,plain,
$false,
inference(avatar_sat_refutation,[],[f58,f67,f115]) ).
fof(f115,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f114]) ).
fof(f114,plain,
( $false
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f107,f79]) ).
fof(f79,plain,
a_subset_of(sK0(sK3),vec_to_class(sK3)),
inference(unit_resulting_resolution,[],[f59,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ basis_of(X1,X0)
| a_subset_of(X1,vec_to_class(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( lin_ind_subset(X1,X0)
& a_subset_of(X1,vec_to_class(X0)) )
| ~ basis_of(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ( lin_ind_subset(X0,X1)
& a_subset_of(X0,vec_to_class(X1)) )
| ~ basis_of(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( basis_of(X0,X1)
=> ( lin_ind_subset(X0,X1)
& a_subset_of(X0,vec_to_class(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
fof(f59,plain,
basis_of(sK0(sK3),sK3),
inference(unit_resulting_resolution,[],[f47,f34]) ).
fof(f34,plain,
! [X0] :
( basis_of(sK0(X0),X0)
| ~ a_vector_space(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(sK0(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f22]) ).
fof(f22,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
=> basis_of(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
( ~ a_vector_space(X0)
| ? [X1] : basis_of(X1,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] :
( a_vector_space(X0)
=> ? [X1] : basis_of(X1,X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X5] :
( a_vector_space(X5)
=> ? [X0] : basis_of(X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(f47,plain,
a_vector_space(sK3),
inference(unit_resulting_resolution,[],[f43,f35]) ).
fof(f35,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X1,X0)
| a_vector_space(X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( a_vector_space(X1)
| ~ a_vector_subspace_of(X1,X0) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
! [X1,X0] :
( a_vector_subspace_of(X0,X1)
=> a_vector_space(X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X5,X0] :
( a_vector_subspace_of(X5,X0)
=> a_vector_space(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(f43,plain,
a_vector_subspace_of(sK3,sK2),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
( a_vector_space(sK2)
& a_vector_subspace_of(sK3,sK2)
& ! [X2,X3] :
( ~ basis_of(union(X2,X3),sK2)
| ~ basis_of(X2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f31,f32]) ).
fof(f32,plain,
( ? [X0,X1] :
( a_vector_space(X0)
& a_vector_subspace_of(X1,X0)
& ! [X2,X3] :
( ~ basis_of(union(X2,X3),X0)
| ~ basis_of(X2,X1) ) )
=> ( a_vector_space(sK2)
& a_vector_subspace_of(sK3,sK2)
& ! [X3,X2] :
( ~ basis_of(union(X2,X3),sK2)
| ~ basis_of(X2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0,X1] :
( a_vector_space(X0)
& a_vector_subspace_of(X1,X0)
& ! [X2,X3] :
( ~ basis_of(union(X2,X3),X0)
| ~ basis_of(X2,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
? [X1,X0] :
( a_vector_space(X1)
& a_vector_subspace_of(X0,X1)
& ! [X2,X3] :
( ~ basis_of(union(X2,X3),X1)
| ~ basis_of(X2,X0) ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(union(X2,X3),X1)
| ~ basis_of(X2,X0) )
& a_vector_subspace_of(X0,X1)
& a_vector_space(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,plain,
~ ! [X0,X1] :
( ( a_vector_subspace_of(X0,X1)
& a_vector_space(X1) )
=> ? [X3,X2] :
( basis_of(X2,X0)
& basis_of(union(X2,X3),X1) ) ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X6,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X6,X1) )
=> ? [X7,X8] :
( basis_of(union(X7,X8),X1)
& basis_of(X7,X6) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X6,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X6,X1) )
=> ? [X7,X8] :
( basis_of(union(X7,X8),X1)
& basis_of(X7,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(f107,plain,
( ~ a_subset_of(sK0(sK3),vec_to_class(sK3))
| ~ spl4_1 ),
inference(unit_resulting_resolution,[],[f43,f77,f83,f39]) ).
fof(f39,plain,
! [X2,X0,X1] :
( lin_ind_subset(X2,X1)
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1)
| ~ lin_ind_subset(X2,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1)
| ( ( lin_ind_subset(X2,X1)
| ~ lin_ind_subset(X2,X0) )
& ( lin_ind_subset(X2,X0)
| ~ lin_ind_subset(X2,X1) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ a_subset_of(X1,vec_to_class(X2))
| ~ a_vector_subspace_of(X2,X0)
| ( ( lin_ind_subset(X1,X0)
| ~ lin_ind_subset(X1,X2) )
& ( lin_ind_subset(X1,X2)
| ~ lin_ind_subset(X1,X0) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ a_subset_of(X1,vec_to_class(X2))
| ~ a_vector_subspace_of(X2,X0)
| ( lin_ind_subset(X1,X0)
<=> lin_ind_subset(X1,X2) ) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X1,X0)
<=> lin_ind_subset(X1,X2) )
| ~ a_vector_subspace_of(X2,X0)
| ~ a_subset_of(X1,vec_to_class(X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( a_vector_subspace_of(X2,X0)
& a_subset_of(X1,vec_to_class(X2)) )
=> ( lin_ind_subset(X1,X0)
<=> lin_ind_subset(X1,X2) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X7,X6] :
( ( a_subset_of(X7,vec_to_class(X6))
& a_vector_subspace_of(X6,X1) )
=> ( lin_ind_subset(X7,X1)
<=> lin_ind_subset(X7,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(f83,plain,
lin_ind_subset(sK0(sK3),sK3),
inference(resolution,[],[f59,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ basis_of(X1,X0)
| lin_ind_subset(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f77,plain,
( ~ lin_ind_subset(sK0(sK3),sK2)
| ~ spl4_1 ),
inference(unit_resulting_resolution,[],[f59,f54]) ).
fof(f54,plain,
( ! [X0] :
( ~ lin_ind_subset(X0,sK2)
| ~ basis_of(X0,sK3) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl4_1
<=> ! [X0] :
( ~ lin_ind_subset(X0,sK2)
| ~ basis_of(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f67,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f66]) ).
fof(f66,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f61,f44]) ).
fof(f44,plain,
a_vector_space(sK2),
inference(cnf_transformation,[],[f33]) ).
fof(f61,plain,
( ~ a_vector_space(sK2)
| ~ spl4_2 ),
inference(unit_resulting_resolution,[],[f57,f34]) ).
fof(f57,plain,
( ! [X1] : ~ basis_of(X1,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f56,plain,
( spl4_2
<=> ! [X1] : ~ basis_of(X1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f58,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f51,f56,f53]) ).
fof(f51,plain,
! [X0,X1] :
( ~ basis_of(X1,sK2)
| ~ lin_ind_subset(X0,sK2)
| ~ basis_of(X0,sK3) ),
inference(resolution,[],[f42,f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2)
| basis_of(union(X0,sK1(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( a_subset_of(sK1(X0,X1,X2),X1)
& basis_of(union(X0,sK1(X0,X1,X2)),X2) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X3] :
( a_subset_of(X3,X1)
& basis_of(union(X0,X3),X2) )
=> ( a_subset_of(sK1(X0,X1,X2),X1)
& basis_of(union(X0,sK1(X0,X1,X2)),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ? [X3] :
( a_subset_of(X3,X1)
& basis_of(union(X0,X3),X2) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X2,X0] :
( ? [X3] :
( a_subset_of(X3,X2)
& basis_of(union(X1,X3),X0) )
| ~ basis_of(X2,X0)
| ~ lin_ind_subset(X1,X0) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ? [X3] :
( a_subset_of(X3,X2)
& basis_of(union(X1,X3),X0) )
| ~ lin_ind_subset(X1,X0)
| ~ basis_of(X2,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X2,X0,X1] :
( ( lin_ind_subset(X1,X0)
& basis_of(X2,X0) )
=> ? [X3] :
( a_subset_of(X3,X2)
& basis_of(union(X1,X3),X0) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X3] :
( ( lin_ind_subset(X2,X1)
& basis_of(X3,X1) )
=> ? [X4] :
( basis_of(union(X2,X4),X1)
& a_subset_of(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(f42,plain,
! [X2,X3] :
( ~ basis_of(union(X2,X3),sK2)
| ~ basis_of(X2,sK3) ),
inference(cnf_transformation,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 14:55:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (32581)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)
% 0.19/0.51 % (32582)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)
% 0.19/0.51 % (32580)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)
% 0.19/0.51 % (32581)Refutation not found, incomplete strategy% (32581)------------------------------
% 0.19/0.51 % (32581)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (32581)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (32581)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51
% 0.19/0.51 % (32581)Memory used [KB]: 1407
% 0.19/0.51 % (32581)Time elapsed: 0.112 s
% 0.19/0.51 % (32581)Instructions burned: 2 (million)
% 0.19/0.51 % (32581)------------------------------
% 0.19/0.51 % (32581)------------------------------
% 0.19/0.51 % (32580)Refutation not found, incomplete strategy% (32580)------------------------------
% 0.19/0.51 % (32580)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (32580)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (32580)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51
% 0.19/0.51 % (32580)Memory used [KB]: 5884
% 0.19/0.51 % (32580)Time elapsed: 0.116 s
% 0.19/0.51 % (32580)Instructions burned: 2 (million)
% 0.19/0.51 % (32580)------------------------------
% 0.19/0.51 % (32580)------------------------------
% 0.19/0.51 % (32602)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51 % (32583)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51 % (32594)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)
% 0.19/0.51 % (32594)Instruction limit reached!
% 0.19/0.51 % (32594)------------------------------
% 0.19/0.51 % (32594)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (32583)First to succeed.
% 0.19/0.51 % (32594)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (32594)Termination reason: Unknown
% 0.19/0.51 % (32594)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (32594)Memory used [KB]: 5884
% 0.19/0.51 % (32594)Time elapsed: 0.003 s
% 0.19/0.51 % (32594)Instructions burned: 2 (million)
% 0.19/0.51 % (32594)------------------------------
% 0.19/0.51 % (32594)------------------------------
% 0.19/0.51 % (32602)Also succeeded, but the first one will report.
% 0.19/0.52 % (32583)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (32583)------------------------------
% 0.19/0.52 % (32583)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (32583)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (32583)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (32583)Memory used [KB]: 6012
% 0.19/0.52 % (32583)Time elapsed: 0.079 s
% 0.19/0.52 % (32583)Instructions burned: 3 (million)
% 0.19/0.52 % (32583)------------------------------
% 0.19/0.52 % (32583)------------------------------
% 0.19/0.52 % (32574)Success in time 0.167 s
%------------------------------------------------------------------------------