TSTP Solution File: ALG211+1 by PyRes---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.5
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n027.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 : Thu May 9 17:14:55 EDT 2024
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.34 % Computer : n027.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 : Thu May 9 00:28:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.53 % Version: 1.5
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 % SZS output start CNFRefutation
% 0.19/0.53 fof(bg_2_4_3,conjecture,(![W]:(![V]:((a_vector_subspace_of(W,V)&a_vector_space(V))=>(?[E]:(?[F]:(basis_of(union(E,F),V)&basis_of(E,W))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bg_2_4_3)).
% 0.19/0.53 fof(c0,negated_conjecture,(~(![W]:(![V]:((a_vector_subspace_of(W,V)&a_vector_space(V))=>(?[E]:(?[F]:(basis_of(union(E,F),V)&basis_of(E,W)))))))),inference(assume_negation,[status(cth)],[bg_2_4_3])).
% 0.19/0.53 fof(c1,negated_conjecture,(?[W]:(?[V]:((a_vector_subspace_of(W,V)&a_vector_space(V))&(![E]:(![F]:(~basis_of(union(E,F),V)|~basis_of(E,W))))))),inference(fof_nnf,[status(thm)],[c0])).
% 0.19/0.53 fof(c2,negated_conjecture,(?[W]:(?[V]:((a_vector_subspace_of(W,V)&a_vector_space(V))&(![E]:((![F]:~basis_of(union(E,F),V))|~basis_of(E,W)))))),inference(shift_quantors,[status(thm)],[c1])).
% 0.19/0.53 fof(c3,negated_conjecture,(?[X2]:(?[X3]:((a_vector_subspace_of(X2,X3)&a_vector_space(X3))&(![X4]:((![X5]:~basis_of(union(X4,X5),X3))|~basis_of(X4,X2)))))),inference(variable_rename,[status(thm)],[c2])).
% 0.19/0.53 fof(c5,negated_conjecture,(![X4]:(![X5]:((a_vector_subspace_of(skolem0001,skolem0002)&a_vector_space(skolem0002))&(~basis_of(union(X4,X5),skolem0002)|~basis_of(X4,skolem0001))))),inference(shift_quantors,[status(thm)],[fof(c4,negated_conjecture,((a_vector_subspace_of(skolem0001,skolem0002)&a_vector_space(skolem0002))&(![X4]:((![X5]:~basis_of(union(X4,X5),skolem0002))|~basis_of(X4,skolem0001)))),inference(skolemize,[status(esa)],[c3])).])).
% 0.19/0.53 cnf(c6,negated_conjecture,a_vector_subspace_of(skolem0001,skolem0002),inference(split_conjunct,[status(thm)],[c5])).
% 0.19/0.53 fof(bg_2_4_a,axiom,(![A]:(![B]:(a_vector_subspace_of(A,B)=>a_vector_space(A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bg_2_4_a)).
% 0.19/0.53 fof(c14,plain,(![A]:(![B]:(~a_vector_subspace_of(A,B)|a_vector_space(A)))),inference(fof_nnf,[status(thm)],[bg_2_4_a])).
% 0.19/0.53 fof(c15,plain,(![A]:((![B]:~a_vector_subspace_of(A,B))|a_vector_space(A))),inference(shift_quantors,[status(thm)],[c14])).
% 0.19/0.53 fof(c17,plain,(![X9]:(![X10]:(~a_vector_subspace_of(X9,X10)|a_vector_space(X9)))),inference(shift_quantors,[status(thm)],[fof(c16,plain,(![X9]:((![X10]:~a_vector_subspace_of(X9,X10))|a_vector_space(X9))),inference(variable_rename,[status(thm)],[c15])).])).
% 0.19/0.53 cnf(c18,plain,~a_vector_subspace_of(X20,X19)|a_vector_space(X20),inference(split_conjunct,[status(thm)],[c17])).
% 0.19/0.53 cnf(c34,plain,a_vector_space(skolem0001),inference(resolution,[status(thm)],[c18, c6])).
% 0.19/0.53 fof(bg_remark_63_a,axiom,(![A]:(a_vector_space(A)=>(?[B]:basis_of(B,A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bg_remark_63_a)).
% 0.19/0.53 fof(c19,plain,(![A]:(~a_vector_space(A)|(?[B]:basis_of(B,A)))),inference(fof_nnf,[status(thm)],[bg_remark_63_a])).
% 0.19/0.53 fof(c20,plain,(![X11]:(~a_vector_space(X11)|(?[X12]:basis_of(X12,X11)))),inference(variable_rename,[status(thm)],[c19])).
% 0.19/0.53 fof(c21,plain,(![X11]:(~a_vector_space(X11)|basis_of(skolem0003(X11),X11))),inference(skolemize,[status(esa)],[c20])).
% 0.19/0.53 cnf(c22,plain,~a_vector_space(X25)|basis_of(skolem0003(X25),X25),inference(split_conjunct,[status(thm)],[c21])).
% 0.19/0.53 cnf(c36,plain,basis_of(skolem0003(skolem0001),skolem0001),inference(resolution,[status(thm)],[c22, c34])).
% 0.19/0.53 cnf(c8,negated_conjecture,~basis_of(union(X24,X23),skolem0002)|~basis_of(X24,skolem0001),inference(split_conjunct,[status(thm)],[c5])).
% 0.19/0.53 fof(basis_of,axiom,(![B]:(![V]:(basis_of(B,V)=>(lin_ind_subset(B,V)&a_subset_of(B,vec_to_class(V)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p', basis_of)).
% 0.19/0.53 fof(c29,plain,(![B]:(![V]:(~basis_of(B,V)|(lin_ind_subset(B,V)&a_subset_of(B,vec_to_class(V)))))),inference(fof_nnf,[status(thm)],[basis_of])).
% 0.19/0.53 fof(c30,plain,(![X17]:(![X18]:(~basis_of(X17,X18)|(lin_ind_subset(X17,X18)&a_subset_of(X17,vec_to_class(X18)))))),inference(variable_rename,[status(thm)],[c29])).
% 0.19/0.53 fof(c31,plain,(![X17]:(![X18]:((~basis_of(X17,X18)|lin_ind_subset(X17,X18))&(~basis_of(X17,X18)|a_subset_of(X17,vec_to_class(X18)))))),inference(distribute,[status(thm)],[c30])).
% 0.19/0.53 cnf(c32,plain,~basis_of(X22,X21)|lin_ind_subset(X22,X21),inference(split_conjunct,[status(thm)],[c31])).
% 0.19/0.53 cnf(c38,plain,lin_ind_subset(skolem0003(skolem0001),skolem0001),inference(resolution,[status(thm)],[c36, c32])).
% 0.19/0.53 fof(bg_2_4_2,axiom,(![W]:(![V]:(![E]:((a_vector_subspace_of(W,V)&a_subset_of(E,vec_to_class(W)))=>(lin_ind_subset(E,W)<=>lin_ind_subset(E,V)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bg_2_4_2)).
% 0.19/0.53 fof(c9,plain,(![W]:(![V]:(![E]:((~a_vector_subspace_of(W,V)|~a_subset_of(E,vec_to_class(W)))|((~lin_ind_subset(E,W)|lin_ind_subset(E,V))&(~lin_ind_subset(E,V)|lin_ind_subset(E,W))))))),inference(fof_nnf,[status(thm)],[bg_2_4_2])).
% 0.19/0.53 fof(c10,plain,(![X6]:(![X7]:(![X8]:((~a_vector_subspace_of(X6,X7)|~a_subset_of(X8,vec_to_class(X6)))|((~lin_ind_subset(X8,X6)|lin_ind_subset(X8,X7))&(~lin_ind_subset(X8,X7)|lin_ind_subset(X8,X6))))))),inference(variable_rename,[status(thm)],[c9])).
% 0.19/0.53 fof(c11,plain,(![X6]:(![X7]:(![X8]:(((~a_vector_subspace_of(X6,X7)|~a_subset_of(X8,vec_to_class(X6)))|(~lin_ind_subset(X8,X6)|lin_ind_subset(X8,X7)))&((~a_vector_subspace_of(X6,X7)|~a_subset_of(X8,vec_to_class(X6)))|(~lin_ind_subset(X8,X7)|lin_ind_subset(X8,X6))))))),inference(distribute,[status(thm)],[c10])).
% 0.19/0.53 cnf(c12,plain,~a_vector_subspace_of(X27,X26)|~a_subset_of(X28,vec_to_class(X27))|~lin_ind_subset(X28,X27)|lin_ind_subset(X28,X26),inference(split_conjunct,[status(thm)],[c11])).
% 0.19/0.53 cnf(c33,plain,~basis_of(X30,X29)|a_subset_of(X30,vec_to_class(X29)),inference(split_conjunct,[status(thm)],[c31])).
% 0.19/0.53 cnf(c39,plain,a_subset_of(skolem0003(skolem0001),vec_to_class(skolem0001)),inference(resolution,[status(thm)],[c33, c36])).
% 0.19/0.53 cnf(c41,plain,~a_vector_subspace_of(skolem0001,X40)|~lin_ind_subset(skolem0003(skolem0001),skolem0001)|lin_ind_subset(skolem0003(skolem0001),X40),inference(resolution,[status(thm)],[c39, c12])).
% 0.19/0.53 cnf(c49,plain,~a_vector_subspace_of(skolem0001,X41)|lin_ind_subset(skolem0003(skolem0001),X41),inference(resolution,[status(thm)],[c41, c38])).
% 0.19/0.53 cnf(c50,plain,lin_ind_subset(skolem0003(skolem0001),skolem0002),inference(resolution,[status(thm)],[c49, c6])).
% 0.19/0.53 cnf(c7,negated_conjecture,a_vector_space(skolem0002),inference(split_conjunct,[status(thm)],[c5])).
% 0.19/0.53 cnf(c35,plain,basis_of(skolem0003(skolem0002),skolem0002),inference(resolution,[status(thm)],[c22, c7])).
% 0.19/0.53 fof(bg_2_2_5,axiom,(![S]:(![T]:(![V]:((lin_ind_subset(S,V)&basis_of(T,V))=>(?[U]:(a_subset_of(U,T)&basis_of(union(S,U),V))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bg_2_2_5)).
% 0.19/0.53 fof(c23,plain,(![S]:(![T]:(![V]:((~lin_ind_subset(S,V)|~basis_of(T,V))|(?[U]:(a_subset_of(U,T)&basis_of(union(S,U),V))))))),inference(fof_nnf,[status(thm)],[bg_2_2_5])).
% 0.19/0.53 fof(c24,plain,(![X13]:(![X14]:(![X15]:((~lin_ind_subset(X13,X15)|~basis_of(X14,X15))|(?[X16]:(a_subset_of(X16,X14)&basis_of(union(X13,X16),X15))))))),inference(variable_rename,[status(thm)],[c23])).
% 0.19/0.53 fof(c25,plain,(![X13]:(![X14]:(![X15]:((~lin_ind_subset(X13,X15)|~basis_of(X14,X15))|(a_subset_of(skolem0004(X13,X14,X15),X14)&basis_of(union(X13,skolem0004(X13,X14,X15)),X15)))))),inference(skolemize,[status(esa)],[c24])).
% 0.19/0.53 fof(c26,plain,(![X13]:(![X14]:(![X15]:(((~lin_ind_subset(X13,X15)|~basis_of(X14,X15))|a_subset_of(skolem0004(X13,X14,X15),X14))&((~lin_ind_subset(X13,X15)|~basis_of(X14,X15))|basis_of(union(X13,skolem0004(X13,X14,X15)),X15)))))),inference(distribute,[status(thm)],[c25])).
% 0.19/0.53 cnf(c28,plain,~lin_ind_subset(X39,X37)|~basis_of(X38,X37)|basis_of(union(X39,skolem0004(X39,X38,X37)),X37),inference(split_conjunct,[status(thm)],[c26])).
% 0.19/0.53 cnf(c48,plain,~lin_ind_subset(X49,skolem0002)|basis_of(union(X49,skolem0004(X49,skolem0003(skolem0002),skolem0002)),skolem0002),inference(resolution,[status(thm)],[c28, c35])).
% 0.19/0.53 cnf(c57,plain,basis_of(union(skolem0003(skolem0001),skolem0004(skolem0003(skolem0001),skolem0003(skolem0002),skolem0002)),skolem0002),inference(resolution,[status(thm)],[c48, c50])).
% 0.19/0.53 cnf(c68,plain,~basis_of(skolem0003(skolem0001),skolem0001),inference(resolution,[status(thm)],[c57, c8])).
% 0.19/0.53 cnf(c72,plain,$false,inference(resolution,[status(thm)],[c68, c36])).
% 0.19/0.53 % SZS output end CNFRefutation
% 0.19/0.53
% 0.19/0.53 % Initial clauses : 11
% 0.19/0.53 % Processed clauses : 35
% 0.19/0.53 % Factors computed : 0
% 0.19/0.53 % Resolvents computed: 39
% 0.19/0.53 % Tautologies deleted: 0
% 0.19/0.53 % Forward subsumed : 2
% 0.19/0.53 % Backward subsumed : 2
% 0.19/0.53 % -------- CPU Time ---------
% 0.19/0.53 % User time : 0.175 s
% 0.19/0.53 % System time : 0.015 s
% 0.19/0.53 % Total time : 0.191 s
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