TSTP Solution File: ALG211+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n025.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 30 15:59:05 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 03:41:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.000000s
% 0.19/0.62 % Output :CNFRefutation 0.000000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 % File : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.19/0.63 % Domain : General Algebra
% 0.19/0.63 % Problem : Vector spaces and bases
% 0.19/0.63 % Version : [Shu96] axioms : Especial.
% 0.19/0.63 % English :
% 0.19/0.63
% 0.19/0.63 % Refs : [BG80] Bishop & Goldberg (1980), Tensor Analysis on Manifolds
% 0.19/0.63 % : [Shu96] Shults (1996), Email to Geoff Sutcliffe
% 0.19/0.63 % Source : [Shu96]
% 0.19/0.63 % Names :
% 0.19/0.63
% 0.19/0.63 % Status : Theorem
% 0.19/0.63 % Rating : 0.07 v7.5.0, 0.05 v7.4.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.50 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.22 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.00 v3.1.0
% 0.19/0.63 % Syntax : Number of formulae : 6 ( 0 unt; 0 def)
% 0.19/0.63 % Number of atoms : 19 ( 0 equ)
% 0.19/0.63 % Maximal formula atoms : 4 ( 3 avg)
% 0.19/0.63 % Number of connectives : 13 ( 0 ~; 0 |; 6 &)
% 0.19/0.63 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.63 % Maximal formula depth : 7 ( 6 avg)
% 0.19/0.63 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.63 % Number of predicates : 5 ( 5 usr; 0 prp; 1-2 aty)
% 0.19/0.63 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.63 % Number of variables : 17 ( 13 !; 4 ?)
% 0.19/0.63 % SPC : FOF_THM_RFO_NEQ
% 0.19/0.63
% 0.19/0.63 % Comments :
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 %----The defintion of a basis
% 0.19/0.63 fof(basis_of,axiom,
% 0.19/0.63 ! [B,V] :
% 0.19/0.63 ( basis_of(B,V)
% 0.19/0.63 => ( lin_ind_subset(B,V)
% 0.19/0.63 & a_subset_of(B,vec_to_class(V)) ) ) ).
% 0.19/0.63
% 0.19/0.63 %----Proposition 2.2.5 from Bishop and Goldberg
% 0.19/0.63 fof(bg_2_2_5,axiom,
% 0.19/0.63 ! [S,T,V] :
% 0.19/0.63 ( ( lin_ind_subset(S,V)
% 0.19/0.63 & basis_of(T,V) )
% 0.19/0.63 => ? [U] :
% 0.19/0.63 ( a_subset_of(U,T)
% 0.19/0.63 & basis_of(union(S,U),V) ) ) ).
% 0.19/0.63
% 0.19/0.63 %----The first Remark on page 63 of Bishop and Goldberg
% 0.19/0.63 fof(bg_remark_63_a,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( a_vector_space(A)
% 0.19/0.63 => ? [B] : basis_of(B,A) ) ).
% 0.19/0.63
% 0.19/0.63 %----The definition of a subspace
% 0.19/0.63 fof(bg_2_4_a,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( a_vector_subspace_of(A,B)
% 0.19/0.63 => a_vector_space(A) ) ).
% 0.19/0.63
% 0.19/0.63 %----Proposition 2.4.2 in Bishop and Goldberg
% 0.19/0.63 fof(bg_2_4_2,axiom,
% 0.19/0.63 ! [W,V,E] :
% 0.19/0.63 ( ( a_vector_subspace_of(W,V)
% 0.19/0.63 & a_subset_of(E,vec_to_class(W)) )
% 0.19/0.63 => ( lin_ind_subset(E,W)
% 0.19/0.63 <=> lin_ind_subset(E,V) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(bg_2_4_3,conjecture,
% 0.19/0.63 ! [W,V] :
% 0.19/0.63 ( ( a_vector_subspace_of(W,V)
% 0.19/0.63 & a_vector_space(V) )
% 0.19/0.63 => ? [E,F] :
% 0.19/0.63 ( basis_of(union(E,F),V)
% 0.19/0.63 & basis_of(E,W) ) ) ).
% 0.19/0.63
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:11(EqnAxiom:0)
% 0.19/0.63 %VarNum:50(SingletonVarNum:21)
% 0.19/0.63 %MaxLitNum:4
% 0.19/0.63 %MaxfuncDepth:2
% 0.19/0.63 %SharedTerms:4
% 0.19/0.63 %goalClause: 1 2 7
% 0.19/0.63 %singleGoalClaCount:2
% 0.19/0.63 [1]P1(a1)
% 0.19/0.63 [2]P3(a2,a1)
% 0.19/0.63 [4]~P1(x41)+P4(f3(x41),x41)
% 0.19/0.63 [3]P1(x31)+~P3(x31,x32)
% 0.19/0.63 [5]~P4(x51,x52)+P5(x51,x52)
% 0.19/0.63 [6]~P4(x61,x62)+P2(x61,f5(x62))
% 0.19/0.63 [7]~P4(x71,a2)+~P4(f6(x71,x72),a1)
% 0.19/0.63 [10]~P4(x102,x103)+~P5(x101,x103)+P2(f4(x101,x102,x103),x102)
% 0.19/0.63 [11]~P4(x112,x113)+~P5(x111,x113)+P4(f6(x111,f4(x111,x112,x113)),x113)
% 0.19/0.63 [8]~P3(x82,x83)+P5(x81,x82)+~P5(x81,x83)+~P2(x81,f5(x82))
% 0.19/0.63 [9]~P3(x93,x92)+P5(x91,x92)+~P5(x91,x93)+~P2(x91,f5(x93))
% 0.19/0.63 %EqnAxiom
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(12,plain,
% 0.19/0.63 (P1(a2)),
% 0.19/0.63 inference(scs_inference,[],[2,3])).
% 0.19/0.63 cnf(13,plain,
% 0.19/0.63 (P4(f3(a1),a1)),
% 0.19/0.63 inference(scs_inference,[],[1,2,3,4])).
% 0.19/0.63 cnf(31,plain,
% 0.19/0.63 (P4(f3(a2),a2)),
% 0.19/0.63 inference(scs_inference,[],[12,4])).
% 0.19/0.63 cnf(33,plain,
% 0.19/0.63 (P5(f3(a2),a2)),
% 0.19/0.63 inference(scs_inference,[],[12,4,5])).
% 0.19/0.63 cnf(37,plain,
% 0.19/0.63 (~P4(f6(f3(a2),x371),a1)),
% 0.19/0.63 inference(scs_inference,[],[12,7,4])).
% 0.19/0.63 cnf(45,plain,
% 0.19/0.63 ($false),
% 0.19/0.63 inference(scs_inference,[],[13,31,37,33,2,11,9,5,6]),
% 0.19/0.63 ['proof']).
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------