%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG211+1 : TPTP v8.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n008.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 : Mon Jun 24 03:41:00 EDT 2024 % Result : Theorem 58.58s 59.10s % Output : CNFRefutation 58.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : ALG211+1 : TPTP v8.2.0. Released v3.1.0. % 0.03/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n008.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 : Wed Jun 19 15:28:09 EDT 2024 % 0.13/0.35 % CPUTime : % 0.52/0.57 start to proof:theBenchmark % 58.58/59.08 %------------------------------------------- % 58.58/59.08 % File :CSE---1.7 % 58.58/59.08 % Problem :theBenchmark % 58.58/59.08 % Transform :cnf % 58.58/59.08 % Format :tptp:raw % 58.58/59.08 % Command :java -jar mcs_scs.jar %d %s % 58.58/59.08 % 58.58/59.08 % Result :Theorem 58.000000s % 58.58/59.08 % Output :CNFRefutation 58.000000s % 58.58/59.08 %------------------------------------------- % 58.58/59.09 %------------------------------------------------------------------------------ % 58.58/59.09 % File : ALG211+1 : TPTP v8.2.0. Released v3.1.0. % 58.58/59.09 % Domain : General Algebra % 58.58/59.09 % Problem : Vector spaces and bases % 58.58/59.09 % Version : [Shu96] axioms : Especial. % 58.58/59.09 % English : % 58.58/59.09 % 58.58/59.09 % Refs : [BG80] Bishop & Goldberg (1980), Tensor Analysis on Manifolds % 58.58/59.09 % : [Shu96] Shults (1996), Email to Geoff Sutcliffe % 58.58/59.09 % Source : [Shu96] % 58.58/59.09 % Names : % 58.58/59.09 % 58.58/59.09 % Status : Theorem % 58.58/59.09 % Rating : 0.06 v8.2.0, 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 % 58.58/59.09 % Syntax : Number of formulae : 6 ( 0 unt; 0 def) % 58.58/59.09 % Number of atoms : 19 ( 0 equ) % 58.58/59.09 % Maximal formula atoms : 4 ( 3 avg) % 58.58/59.09 % Number of connectives : 13 ( 0 ~; 0 |; 6 &) % 58.58/59.09 % ( 1 <=>; 6 =>; 0 <=; 0 <~>) % 58.58/59.09 % Maximal formula depth : 7 ( 6 avg) % 58.58/59.09 % Maximal term depth : 2 ( 1 avg) % 58.58/59.09 % Number of predicates : 5 ( 5 usr; 0 prp; 1-2 aty) % 58.58/59.09 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 58.58/59.09 % Number of variables : 17 ( 13 !; 4 ?) % 58.58/59.09 % SPC : FOF_THM_RFO_NEQ % 58.58/59.09 % 58.58/59.09 % Comments : % 58.58/59.09 %------------------------------------------------------------------------------ % 58.58/59.09 %----The defintion of a basis % 58.58/59.09 fof(basis_of,axiom, % 58.58/59.09 ! [B,V] : % 58.58/59.09 ( basis_of(B,V) % 58.58/59.09 => ( lin_ind_subset(B,V) % 58.58/59.09 & a_subset_of(B,vec_to_class(V)) ) ) ). % 58.58/59.09 % 58.58/59.09 %----Proposition 2.2.5 from Bishop and Goldberg % 58.58/59.09 fof(bg_2_2_5,axiom, % 58.58/59.09 ! [S,T,V] : % 58.58/59.09 ( ( lin_ind_subset(S,V) % 58.58/59.09 & basis_of(T,V) ) % 58.58/59.09 => ? [U] : % 58.58/59.09 ( a_subset_of(U,T) % 58.58/59.09 & basis_of(union(S,U),V) ) ) ). % 58.58/59.09 % 58.58/59.09 %----The first Remark on page 63 of Bishop and Goldberg % 58.58/59.09 fof(bg_remark_63_a,axiom, % 58.58/59.09 ! [A] : % 58.58/59.09 ( a_vector_space(A) % 58.58/59.09 => ? [B] : basis_of(B,A) ) ). % 58.58/59.09 % 58.58/59.09 %----The definition of a subspace % 58.58/59.09 fof(bg_2_4_a,axiom, % 58.58/59.09 ! [A,B] : % 58.58/59.09 ( a_vector_subspace_of(A,B) % 58.58/59.09 => a_vector_space(A) ) ). % 58.58/59.09 % 58.58/59.09 %----Proposition 2.4.2 in Bishop and Goldberg % 58.58/59.09 fof(bg_2_4_2,axiom, % 58.58/59.09 ! [W,V,E] : % 58.58/59.09 ( ( a_vector_subspace_of(W,V) % 58.58/59.09 & a_subset_of(E,vec_to_class(W)) ) % 58.58/59.09 => ( lin_ind_subset(E,W) % 58.58/59.09 <=> lin_ind_subset(E,V) ) ) ). % 58.58/59.09 % 58.58/59.09 fof(bg_2_4_3,conjecture, % 58.58/59.09 ! [W,V] : % 58.58/59.09 ( ( a_vector_subspace_of(W,V) % 58.58/59.09 & a_vector_space(V) ) % 58.58/59.09 => ? [E,F] : % 58.58/59.09 ( basis_of(union(E,F),V) % 58.58/59.09 & basis_of(E,W) ) ) ). % 58.58/59.10 % 58.58/59.10 %------------------------------------------------------------------------------ % 58.58/59.10 %------------------------------------------- % 58.58/59.10 % Proof found % 58.58/59.10 % SZS status Theorem for theBenchmark % 58.58/59.10 % SZS output start Proof % 58.64/59.10 %ClaNum:11(EqnAxiom:0) % 58.64/59.10 %VarNum:50(SingletonVarNum:21) % 58.64/59.10 %MaxLitNum:4 % 58.64/59.10 %MaxfuncDepth:2 % 58.64/59.10 %SharedTerms:4 % 58.64/59.10 %goalClause: 1 2 7 % 58.64/59.10 %singleGoalClaCount:2 % 58.64/59.10 [1]P1(a1) % 58.64/59.10 [2]P3(a2,a1) % 58.64/59.10 [4]~P1(x41)+P4(f3(x41),x41) % 58.64/59.10 [3]P1(x31)+~P3(x31,x32) % 58.64/59.10 [5]~P4(x51,x52)+P5(x51,x52) % 58.64/59.10 [6]~P4(x61,x62)+P2(x61,f5(x62)) % 58.64/59.10 [7]~P4(x71,a2)+~P4(f6(x71,x72),a1) % 58.64/59.10 [10]~P4(x102,x103)+~P5(x101,x103)+P2(f4(x101,x102,x103),x102) % 58.64/59.10 [11]~P4(x112,x113)+~P5(x111,x113)+P4(f6(x111,f4(x111,x112,x113)),x113) % 58.64/59.10 [8]~P3(x82,x83)+P5(x81,x82)+~P5(x81,x83)+~P2(x81,f5(x82)) % 58.64/59.10 [9]~P3(x93,x92)+P5(x91,x92)+~P5(x91,x93)+~P2(x91,f5(x93)) % 58.64/59.10 %EqnAxiom % 58.64/59.10 % 58.64/59.10 %------------------------------------------- % 58.74/59.21 cnf(12,plain, % 58.74/59.21 (P4(f3(a2),a2)), % 58.74/59.21 inference(scs_inference,[],[2,3,4])). % 58.74/59.21 cnf(16,plain, % 58.74/59.21 (~P1(a2)+~P4(f6(f3(a2),x161),a1)), % 58.74/59.21 inference(scs_inference,[],[7,4])). % 58.74/59.21 cnf(24,plain, % 58.74/59.21 (~P4(x241,a1)+~P5(f3(a2),a1)+~P1(a2)), % 58.74/59.21 inference(scs_inference,[],[16,11])). % 58.74/59.21 cnf(40,plain, % 58.74/59.21 (~P5(f3(a2),a1)+~P1(a2)), % 58.74/59.21 inference(scs_inference,[],[1,24,4])). % 58.74/59.21 cnf(107,plain, % 58.74/59.21 (~P5(f3(a2),a1)), % 58.74/59.21 inference(scs_inference,[],[2,3,40])). % 58.74/59.21 cnf(198,plain, % 58.74/59.21 (P5(f3(a1),a1)), % 58.74/59.21 inference(scs_inference,[],[1,4,5])). % 58.74/59.21 cnf(76991,plain, % 58.74/59.21 ($false), % 58.74/59.21 inference(scs_inference,[],[1,12,2,198,107,3,6,4,5,10,9]), % 58.74/59.21 ['proof']). % 58.74/59.26 % SZS output end Proof % 58.74/59.26 % Total time :58.000000s %------------------------------------------------------------------------------