TSTP Solution File: ALG211+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 : Fri May 3 02:04:17 EDT 2024
% Result : Theorem 1.87s 1.19s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 6 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 177 ( 70 ~; 58 |; 30 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 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 : 122 ( 5 sgn 79 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( 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(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) ).
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(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(f5,axiom,
! [X6,X1,X7] :
( ( a_subset_of(X7,vec_to_class(X6))
& a_vector_subspace_of(X6,X1) )
=> ( lin_ind_subset(X7,X6)
<=> lin_ind_subset(X7,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(f6,conjecture,
! [X6,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X6,X1) )
=> ? [X7,X8] :
( basis_of(X7,X6)
& basis_of(union(X7,X8),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(f7,negated_conjecture,
~ ! [X6,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X6,X1) )
=> ? [X7,X8] :
( basis_of(X7,X6)
& basis_of(union(X7,X8),X1) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ( 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(f9,plain,
! [X0] :
( a_vector_space(X0)
=> ? [X1] : basis_of(X1,X0) ),
inference(rectify,[],[f3]) ).
fof(f10,plain,
! [X0,X1] :
( a_vector_subspace_of(X0,X1)
=> a_vector_space(X0) ),
inference(rectify,[],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( a_subset_of(X2,vec_to_class(X0))
& a_vector_subspace_of(X0,X1) )
=> ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f12,plain,
~ ! [X0,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X0,X1) )
=> ? [X2,X3] :
( basis_of(X2,X0)
& basis_of(union(X2,X3),X1) ) ),
inference(rectify,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) )
| ~ basis_of(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
| ~ a_vector_space(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) )
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) )
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_space(X1)
& a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_space(X1)
& a_vector_subspace_of(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
=> ( basis_of(union(X0,sK0(X0,X1,X2)),X2)
& a_subset_of(sK0(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( basis_of(union(X0,sK0(X0,X1,X2)),X2)
& a_subset_of(sK0(X0,X1,X2),X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f22]) ).
fof(f24,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
=> basis_of(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0] :
( basis_of(sK1(X0),X0)
| ~ a_vector_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ( lin_ind_subset(X2,X0)
| ~ lin_ind_subset(X2,X1) )
& ( lin_ind_subset(X2,X1)
| ~ lin_ind_subset(X2,X0) ) )
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(nnf_transformation,[],[f19]) ).
fof(f27,plain,
( ? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_space(X1)
& a_vector_subspace_of(X0,X1) )
=> ( ! [X3,X2] :
( ~ basis_of(X2,sK2)
| ~ basis_of(union(X2,X3),sK3) )
& a_vector_space(sK3)
& a_vector_subspace_of(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ! [X2,X3] :
( ~ basis_of(X2,sK2)
| ~ basis_of(union(X2,X3),sK3) )
& a_vector_space(sK3)
& a_vector_subspace_of(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f21,f27]) ).
fof(f29,plain,
! [X0,X1] :
( lin_ind_subset(X0,X1)
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0,X1] :
( a_subset_of(X0,vec_to_class(X1))
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
! [X2,X0,X1] :
( basis_of(union(X0,sK0(X0,X1,X2)),X2)
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0] :
( basis_of(sK1(X0),X0)
| ~ a_vector_space(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X2,X0,X1] :
( lin_ind_subset(X2,X1)
| ~ lin_ind_subset(X2,X0)
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
a_vector_subspace_of(sK2,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f38,plain,
a_vector_space(sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f39,plain,
! [X2,X3] :
( ~ basis_of(X2,sK2)
| ~ basis_of(union(X2,X3),sK3) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_49,plain,
( ~ basis_of(X0,X1)
| a_subset_of(X0,vec_to_class(X1)) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_50,plain,
( ~ basis_of(X0,X1)
| lin_ind_subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_51,plain,
( ~ basis_of(X0,X1)
| ~ lin_ind_subset(X2,X1)
| basis_of(union(X2,sK0(X2,X0,X1)),X1) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_53,plain,
( ~ a_vector_space(X0)
| basis_of(sK1(X0),X0) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_54,plain,
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_56,plain,
( ~ a_subset_of(X0,vec_to_class(X1))
| ~ lin_ind_subset(X0,X1)
| ~ a_vector_subspace_of(X1,X2)
| lin_ind_subset(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_57,negated_conjecture,
( ~ basis_of(union(X0,X1),sK3)
| ~ basis_of(X0,sK2) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_58,negated_conjecture,
a_vector_space(sK3),
inference(cnf_transformation,[],[f38]) ).
cnf(c_59,negated_conjecture,
a_vector_subspace_of(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
cnf(c_60,plain,
( ~ a_vector_space(sK3)
| basis_of(sK1(sK3),sK3) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_118,plain,
( ~ a_vector_subspace_of(X0,X1)
| basis_of(sK1(X0),X0) ),
inference(resolution,[status(thm)],[c_54,c_53]) ).
cnf(c_133,plain,
basis_of(sK1(sK2),sK2),
inference(resolution,[status(thm)],[c_118,c_59]) ).
cnf(c_137,plain,
( ~ a_subset_of(X0,vec_to_class(sK2))
| ~ lin_ind_subset(X0,sK2)
| lin_ind_subset(X0,sK3) ),
inference(resolution,[status(thm)],[c_56,c_59]) ).
cnf(c_307,negated_conjecture,
( ~ basis_of(union(X0,X1),sK3)
| ~ basis_of(X0,sK2) ),
inference(demodulation,[status(thm)],[c_57]) ).
cnf(c_308,plain,
( ~ basis_of(union(sK1(sK2),X0),sK3)
| ~ basis_of(sK1(sK2),sK2) ),
inference(instantiation,[status(thm)],[c_307]) ).
cnf(c_311,plain,
( ~ basis_of(sK1(sK2),sK2)
| a_subset_of(sK1(sK2),vec_to_class(sK2)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_313,plain,
( ~ basis_of(sK1(sK2),sK2)
| lin_ind_subset(sK1(sK2),sK2) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_318,plain,
( ~ basis_of(sK1(sK3),sK3)
| ~ lin_ind_subset(X0,sK3)
| basis_of(union(X0,sK0(X0,sK1(sK3),sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_323,plain,
( ~ a_subset_of(sK1(sK2),vec_to_class(sK2))
| ~ lin_ind_subset(sK1(sK2),sK2)
| lin_ind_subset(sK1(sK2),sK3) ),
inference(instantiation,[status(thm)],[c_137]) ).
cnf(c_328,plain,
( ~ basis_of(sK1(sK3),sK3)
| ~ lin_ind_subset(sK1(sK2),sK3)
| basis_of(union(sK1(sK2),sK0(sK1(sK2),sK1(sK3),sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_318]) ).
cnf(c_354,plain,
( ~ basis_of(union(sK1(sK2),sK0(sK1(sK2),sK1(sK3),sK3)),sK3)
| ~ basis_of(sK1(sK2),sK2) ),
inference(instantiation,[status(thm)],[c_308]) ).
cnf(c_355,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_354,c_328,c_323,c_313,c_311,c_133,c_60,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n007.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 : Thu May 2 22:36:50 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.87/1.19 % SZS status Started for theBenchmark.p
% 1.87/1.19 % SZS status Theorem for theBenchmark.p
% 1.87/1.19
% 1.87/1.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.87/1.19
% 1.87/1.19 ------ iProver source info
% 1.87/1.19
% 1.87/1.19 git: date: 2024-05-02 19:28:25 +0000
% 1.87/1.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.87/1.19 git: non_committed_changes: false
% 1.87/1.19
% 1.87/1.19 ------ Parsing...
% 1.87/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.87/1.19
% 1.87/1.19 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 1.87/1.19
% 1.87/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.87/1.19 ------ Proving...
% 1.87/1.19 ------ Problem Properties
% 1.87/1.19
% 1.87/1.19
% 1.87/1.19 clauses 9
% 1.87/1.19 conjectures 1
% 1.87/1.19 EPR 1
% 1.87/1.19 Horn 9
% 1.87/1.19 unary 2
% 1.87/1.19 binary 3
% 1.87/1.19 lits 20
% 1.87/1.19 lits eq 0
% 1.87/1.19 fd_pure 0
% 1.87/1.19 fd_pseudo 0
% 1.87/1.19 fd_cond 0
% 1.87/1.19 fd_pseudo_cond 0
% 1.87/1.19 AC symbols 0
% 1.87/1.19
% 1.87/1.19 ------ Schedule dynamic 5 is on
% 1.87/1.19
% 1.87/1.19 ------ no equalities: superposition off
% 1.87/1.19
% 1.87/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.87/1.19
% 1.87/1.19
% 1.87/1.19 ------
% 1.87/1.19 Current options:
% 1.87/1.19 ------
% 1.87/1.19
% 1.87/1.19
% 1.87/1.19
% 1.87/1.19
% 1.87/1.19 ------ Proving...
% 1.87/1.19
% 1.87/1.19
% 1.87/1.19 % SZS status Theorem for theBenchmark.p
% 1.87/1.19
% 1.87/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.19
% 1.87/1.19
%------------------------------------------------------------------------------