TSTP Solution File: ALG211+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n010.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 15:43:39 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 4 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 193 ( 79 ~; 59 |; 35 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 124 ( 100 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73,plain,
$false,
inference(resolution,[],[f72,f39]) ).
fof(f39,plain,
a_vector_space(sK0),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( a_vector_space(sK0)
& a_vector_subspace_of(sK1,sK0)
& ! [X2,X3] :
( ~ basis_of(X3,sK1)
| ~ basis_of(union(X3,X2),sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f25,f26]) ).
fof(f26,plain,
( ? [X0,X1] :
( a_vector_space(X0)
& a_vector_subspace_of(X1,X0)
& ! [X2,X3] :
( ~ basis_of(X3,X1)
| ~ basis_of(union(X3,X2),X0) ) )
=> ( a_vector_space(sK0)
& a_vector_subspace_of(sK1,sK0)
& ! [X3,X2] :
( ~ basis_of(X3,sK1)
| ~ basis_of(union(X3,X2),sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0,X1] :
( a_vector_space(X0)
& a_vector_subspace_of(X1,X0)
& ! [X2,X3] :
( ~ basis_of(X3,X1)
| ~ basis_of(union(X3,X2),X0) ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
? [X1,X0] :
( a_vector_space(X1)
& a_vector_subspace_of(X0,X1)
& ! [X3,X2] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) ) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
? [X1,X0] :
( ! [X3,X2] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_subspace_of(X0,X1)
& a_vector_space(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X1,X0] :
( ( 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_subspace_of(X6,X1)
& a_vector_space(X1) )
=> ? [X7,X8] :
( basis_of(union(X7,X8),X1)
& basis_of(X7,X6) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X6,X1] :
( ( a_vector_subspace_of(X6,X1)
& a_vector_space(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(f72,plain,
~ a_vector_space(sK0),
inference(resolution,[],[f71,f38]) ).
fof(f38,plain,
a_vector_subspace_of(sK1,sK0),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
! [X0] :
( ~ a_vector_subspace_of(sK1,X0)
| ~ a_vector_space(sK0) ),
inference(resolution,[],[f69,f43]) ).
fof(f43,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
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(f69,plain,
( ~ a_vector_space(sK1)
| ~ a_vector_space(sK0) ),
inference(resolution,[],[f68,f42]) ).
fof(f42,plain,
! [X0] :
( basis_of(sK3(X0),X0)
| ~ a_vector_space(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(sK3(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f31]) ).
fof(f31,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
=> basis_of(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
( ~ a_vector_space(X0)
| ? [X1] : basis_of(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,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(f68,plain,
! [X4] :
( ~ basis_of(X4,sK1)
| ~ a_vector_space(sK0) ),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f67,plain,
! [X4] :
( ~ basis_of(X4,sK1)
| ~ a_vector_space(sK0)
| ~ basis_of(X4,sK1) ),
inference(resolution,[],[f63,f35]) ).
fof(f35,plain,
! [X0,X1] :
( lin_ind_subset(X0,X1)
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) )
| ~ basis_of(X0,X1) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ( a_subset_of(X1,vec_to_class(X0))
& lin_ind_subset(X1,X0) )
| ~ basis_of(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0] :
( basis_of(X1,X0)
=> ( a_subset_of(X1,vec_to_class(X0))
& lin_ind_subset(X1,X0) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( basis_of(X0,X1)
=> ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
fof(f63,plain,
! [X0] :
( ~ lin_ind_subset(X0,sK1)
| ~ basis_of(X0,sK1)
| ~ a_vector_space(sK0) ),
inference(duplicate_literal_removal,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ basis_of(X0,sK1)
| ~ a_vector_space(sK0)
| ~ lin_ind_subset(X0,sK1)
| ~ basis_of(X0,sK1) ),
inference(resolution,[],[f57,f38]) ).
fof(f57,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X1,sK0)
| ~ lin_ind_subset(X0,X1)
| ~ basis_of(X0,sK1)
| ~ basis_of(X0,X1)
| ~ a_vector_space(sK0) ),
inference(resolution,[],[f54,f36]) ).
fof(f36,plain,
! [X0,X1] :
( a_subset_of(X0,vec_to_class(X1))
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f54,plain,
! [X0,X1] :
( ~ a_subset_of(X0,vec_to_class(X1))
| ~ lin_ind_subset(X0,X1)
| ~ basis_of(X0,sK1)
| ~ a_vector_subspace_of(X1,sK0)
| ~ a_vector_space(sK0) ),
inference(resolution,[],[f45,f34]) ).
fof(f34,plain,
! [X2,X0,X1] :
( lin_ind_subset(X1,X0)
| ~ a_vector_subspace_of(X2,X0)
| ~ lin_ind_subset(X1,X2)
| ~ a_subset_of(X1,vec_to_class(X2)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ 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,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ 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,[],[f17]) ).
fof(f17,plain,
! [X1,X2,X0] :
( ( 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,[],[f8]) ).
fof(f8,plain,
! [X1,X2,X0] :
( ( 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_vector_subspace_of(X6,X1)
& a_subset_of(X7,vec_to_class(X6)) )
=> ( lin_ind_subset(X7,X6)
<=> lin_ind_subset(X7,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(f45,plain,
! [X0] :
( ~ lin_ind_subset(X0,sK0)
| ~ basis_of(X0,sK1)
| ~ a_vector_space(sK0) ),
inference(resolution,[],[f44,f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ basis_of(X1,sK0)
| ~ lin_ind_subset(X0,sK0)
| ~ basis_of(X0,sK1) ),
inference(resolution,[],[f41,f37]) ).
fof(f37,plain,
! [X2,X3] :
( ~ basis_of(union(X3,X2),sK0)
| ~ basis_of(X3,sK1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X2,X0,X1] :
( basis_of(union(X1,sK2(X0,X1,X2)),X2)
| ~ lin_ind_subset(X1,X2)
| ~ basis_of(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ lin_ind_subset(X1,X2)
| ~ basis_of(X0,X2)
| ( basis_of(union(X1,sK2(X0,X1,X2)),X2)
& a_subset_of(sK2(X0,X1,X2),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X1,X3),X2)
& a_subset_of(X3,X0) )
=> ( basis_of(union(X1,sK2(X0,X1,X2)),X2)
& a_subset_of(sK2(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ lin_ind_subset(X1,X2)
| ~ basis_of(X0,X2)
| ? [X3] :
( basis_of(union(X1,X3),X2)
& a_subset_of(X3,X0) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0,X2] :
( ~ lin_ind_subset(X0,X2)
| ~ basis_of(X1,X2)
| ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X2,X1] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0,X2,X1] :
( ( basis_of(X1,X2)
& lin_ind_subset(X0,X2) )
=> ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X3,X1] :
( ( basis_of(X3,X1)
& lin_ind_subset(X2,X1) )
=> ? [X4] :
( basis_of(union(X2,X4),X1)
& a_subset_of(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n010.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 14:51:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.49 % (13754)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.50 % (13762)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (13754)Refutation not found, incomplete strategy% (13754)------------------------------
% 0.21/0.51 % (13754)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (13754)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (13754)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51 % (13754)Memory used [KB]: 5373
% 0.21/0.51 % (13754)Time elapsed: 0.100 s
% 0.21/0.51 % (13754)Instructions burned: 2 (million)
% 0.21/0.51 % (13754)------------------------------
% 0.21/0.51 % (13754)------------------------------
% 0.21/0.51 % (13762)First to succeed.
% 0.21/0.51 % (13774)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.51 % (13762)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (13762)------------------------------
% 0.21/0.51 % (13762)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (13762)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (13762)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (13762)Memory used [KB]: 895
% 0.21/0.51 % (13762)Time elapsed: 0.101 s
% 0.21/0.51 % (13762)Instructions burned: 2 (million)
% 0.21/0.51 % (13762)------------------------------
% 0.21/0.51 % (13762)------------------------------
% 0.21/0.51 % (13752)Success in time 0.166 s
%------------------------------------------------------------------------------