TSTP Solution File: ALG211+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 : 600s
% DateTime : Thu Jul 14 17:54:01 EDT 2022
% Result : Theorem 0.77s 1.02s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 8 06:37:50 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.77/1.02 ============================== Prover9 ===============================
% 0.77/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.02 Process 11845 was started by sandbox on n022.cluster.edu,
% 0.77/1.02 Wed Jun 8 06:37:50 2022
% 0.77/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11691_n022.cluster.edu".
% 0.77/1.02 ============================== end of head ===========================
% 0.77/1.02
% 0.77/1.02 ============================== INPUT =================================
% 0.77/1.02
% 0.77/1.02 % Reading from file /tmp/Prover9_11691_n022.cluster.edu
% 0.77/1.02
% 0.77/1.02 set(prolog_style_variables).
% 0.77/1.02 set(auto2).
% 0.77/1.02 % set(auto2) -> set(auto).
% 0.77/1.02 % set(auto) -> set(auto_inference).
% 0.77/1.02 % set(auto) -> set(auto_setup).
% 0.77/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.02 % set(auto) -> set(auto_limits).
% 0.77/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.02 % set(auto) -> set(auto_denials).
% 0.77/1.02 % set(auto) -> set(auto_process).
% 0.77/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.02 % set(auto2) -> assign(stats, some).
% 0.77/1.02 % set(auto2) -> clear(echo_input).
% 0.77/1.02 % set(auto2) -> set(quiet).
% 0.77/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.02 % set(auto2) -> clear(print_given).
% 0.77/1.02 assign(lrs_ticks,-1).
% 0.77/1.02 assign(sos_limit,10000).
% 0.77/1.02 assign(order,kbo).
% 0.77/1.02 set(lex_order_vars).
% 0.77/1.02 clear(print_given).
% 0.77/1.02
% 0.77/1.02 % formulas(sos). % not echoed (6 formulas)
% 0.77/1.02
% 0.77/1.02 ============================== end of input ==========================
% 0.77/1.02
% 0.77/1.02 % From the command line: assign(max_seconds, 300).
% 0.77/1.02
% 0.77/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.02
% 0.77/1.02 % Formulas that are not ordinary clauses:
% 0.77/1.02 1 (all B all V (basis_of(B,V) -> lin_ind_subset(B,V) & a_subset_of(B,vec_to_class(V)))) # label(basis_of) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 2 (all S all T all V (lin_ind_subset(S,V) & basis_of(T,V) -> (exists U (a_subset_of(U,T) & basis_of(union(S,U),V))))) # label(bg_2_2_5) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 3 (all A (a_vector_space(A) -> (exists B basis_of(B,A)))) # label(bg_remark_63_a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 4 (all A all B (a_vector_subspace_of(A,B) -> a_vector_space(A))) # label(bg_2_4_a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 5 (all W all V all 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)))) # label(bg_2_4_2) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 6 -(all W all V (a_vector_subspace_of(W,V) & a_vector_space(V) -> (exists E exists F (basis_of(union(E,F),V) & basis_of(E,W))))) # label(bg_2_4_3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.02
% 0.77/1.02 ============================== end of process non-clausal formulas ===
% 0.77/1.02
% 0.77/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.02
% 0.77/1.02 ============================== PREDICATE ELIMINATION =================
% 0.77/1.02 7 -a_vector_space(A) | basis_of(f2(A),A) # label(bg_remark_63_a) # label(axiom). [clausify(3)].
% 0.77/1.02 8 a_vector_space(c2) # label(bg_2_4_3) # label(negated_conjecture). [clausify(6)].
% 0.77/1.02 9 -a_vector_subspace_of(A,B) | a_vector_space(A) # label(bg_2_4_a) # label(axiom). [clausify(4)].
% 0.77/1.02 Derived: basis_of(f2(c2),c2). [resolve(7,a,8,a)].
% 0.77/1.02 Derived: basis_of(f2(A),A) | -a_vector_subspace_of(A,B). [resolve(7,a,9,b)].
% 0.77/1.02 10 -a_vector_subspace_of(A,B) | -a_subset_of(C,vec_to_class(A)) | -lin_ind_subset(C,A) | lin_ind_subset(C,B) # label(bg_2_4_2) # label(axiom). [clausify(5)].
% 0.77/1.02 11 a_vector_subspace_of(c1,c2) # label(bg_2_4_3) # label(negated_conjecture). [clausify(6)].
% 0.77/1.02 Derived: -a_subset_of(A,vec_to_class(c1)) | -lin_ind_subset(A,c1) | lin_ind_subset(A,c2). [resolve(10,a,11,a)].
% 0.77/1.02 12 -a_vector_subspace_of(A,B) | -a_subset_of(C,vec_to_class(A)) | lin_ind_subset(C,A) | -lin_ind_subset(C,B) # label(bg_2_4_2) # label(axiom). [clausify(5)].
% 0.77/1.02 Derived: -a_subset_of(A,vec_to_class(c1)) | lin_ind_subset(A,c1) | -lin_ind_subset(A,c2). [resolve(12,a,11,a)].
% 0.77/1.02 13 basis_of(f2(A),A) | -a_vector_subspace_of(A,B). [resolve(7,a,9,b)].
% 0.77/1.02 Derived: basis_of(f2(c1),c1). [resolve(13,b,11,a)].
% 0.77/1.02 14 -a_subset_of(A,vec_to_class(c1)) | -lin_ind_subset(A,c1) | lin_ind_subset(A,c2). [resolve(10,a,11,a)].
% 0.77/1.02 15 -basis_of(A,B) | a_subset_of(A,vec_to_class(B)) # label(basis_of) # label(axiom). [clausify(1)].
% 0.77/1.02 16 -lin_ind_subset(A,B) | -basis_of(C,B) | a_subset_of(f1(A,C,B),C) # label(bg_2_2_5) # label(axiom). [clausify(2)].
% 0.77/1.02 Derived: -lin_ind_subset(A,c1) | lin_ind_subset(A,c2) | -basis_of(A,c1). [resolve(14,a,15,b)].
% 0.77/1.02 Derived: -lin_ind_subset(f1(A,vec_to_class(c1),B),c1) | lin_ind_subset(f1(A,vec_to_class(c1),B),c2) | -lin_ind_subset(A,B) | -basis_of(vec_to_class(c1),B). [resolve(14,a,16,c)].
% 0.77/1.02 17 -a_subset_of(A,vec_to_class(c1)) | lin_ind_subset(A,c1) | -lin_ind_subset(A,c2). [resolve(12,a,11,a)].
% 0.77/1.02 Derived: lin_ind_subset(A,c1) | -lin_ind_subset(A,c2) | -basis_of(A,c1). [resolve(17,a,15,b)].
% 0.77/1.02 Derived: lin_ind_subset(f1(A,vec_to_class(c1),B),c1) | -lin_ind_subset(f1(A,vec_to_class(c1),B),c2) | -lin_ind_subset(A,B) | -basis_of(vec_to_class(c1),B). [resolve(17,a,16,c)].
% 0.77/1.02
% 0.77/1.02 ============================== end predicate elimination =============
% 0.77/1.02
% 0.77/1.02 Auto_denials:
% 0.77/1.02 % copying label bg_2_4_3 to answer in negative clause
% 0.77/1.02
% 0.77/1.02 Term ordering decisions:
% 0.77/1.02 Function symbol KB weights: c1=1. c2=1. union=1. vec_to_class=1. f2=1. f1=1.
% 0.77/1.02
% 0.77/1.02 ============================== end of process initial clauses ========
% 0.77/1.02
% 0.77/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.02
% 0.77/1.02 ============================== end of clauses for search =============
% 0.77/1.02
% 0.77/1.02 ============================== SEARCH ================================
% 0.77/1.02
% 0.77/1.02 % Starting search at 0.01 seconds.
% 0.77/1.02
% 0.77/1.02 ============================== PROOF =================================
% 0.77/1.02 % SZS status Theorem
% 0.77/1.02 % SZS output start Refutation
% 0.77/1.02
% 0.77/1.02 % Proof 1 at 0.01 (+ 0.00) seconds: bg_2_4_3.
% 0.77/1.02 % Length of proof is 24.
% 0.77/1.02 % Level of proof is 6.
% 0.77/1.02 % Maximum clause weight is 14.000.
% 0.77/1.02 % Given clauses 11.
% 0.77/1.02
% 0.77/1.02 1 (all B all V (basis_of(B,V) -> lin_ind_subset(B,V) & a_subset_of(B,vec_to_class(V)))) # label(basis_of) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 2 (all S all T all V (lin_ind_subset(S,V) & basis_of(T,V) -> (exists U (a_subset_of(U,T) & basis_of(union(S,U),V))))) # label(bg_2_2_5) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 3 (all A (a_vector_space(A) -> (exists B basis_of(B,A)))) # label(bg_remark_63_a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 4 (all A all B (a_vector_subspace_of(A,B) -> a_vector_space(A))) # label(bg_2_4_a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 5 (all W all V all 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)))) # label(bg_2_4_2) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 6 -(all W all V (a_vector_subspace_of(W,V) & a_vector_space(V) -> (exists E exists F (basis_of(union(E,F),V) & basis_of(E,W))))) # label(bg_2_4_3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.02 7 -a_vector_space(A) | basis_of(f2(A),A) # label(bg_remark_63_a) # label(axiom). [clausify(3)].
% 0.77/1.02 8 a_vector_space(c2) # label(bg_2_4_3) # label(negated_conjecture). [clausify(6)].
% 0.77/1.02 9 -a_vector_subspace_of(A,B) | a_vector_space(A) # label(bg_2_4_a) # label(axiom). [clausify(4)].
% 0.77/1.02 10 -a_vector_subspace_of(A,B) | -a_subset_of(C,vec_to_class(A)) | -lin_ind_subset(C,A) | lin_ind_subset(C,B) # label(bg_2_4_2) # label(axiom). [clausify(5)].
% 0.77/1.02 11 a_vector_subspace_of(c1,c2) # label(bg_2_4_3) # label(negated_conjecture). [clausify(6)].
% 0.77/1.02 13 basis_of(f2(A),A) | -a_vector_subspace_of(A,B). [resolve(7,a,9,b)].
% 0.77/1.02 14 -a_subset_of(A,vec_to_class(c1)) | -lin_ind_subset(A,c1) | lin_ind_subset(A,c2). [resolve(10,a,11,a)].
% 0.77/1.02 15 -basis_of(A,B) | a_subset_of(A,vec_to_class(B)) # label(basis_of) # label(axiom). [clausify(1)].
% 0.77/1.02 18 -basis_of(union(A,B),c2) | -basis_of(A,c1) # label(bg_2_4_3) # label(negated_conjecture) # answer(bg_2_4_3). [clausify(6)].
% 0.77/1.02 19 -basis_of(A,B) | lin_ind_subset(A,B) # label(basis_of) # label(axiom). [clausify(1)].
% 0.77/1.02 20 -lin_ind_subset(A,B) | -basis_of(C,B) | basis_of(union(A,f1(A,C,B)),B) # label(bg_2_2_5) # label(axiom). [clausify(2)].
% 0.77/1.02 21 basis_of(f2(c2),c2). [resolve(7,a,8,a)].
% 0.77/1.02 22 basis_of(f2(c1),c1). [resolve(13,b,11,a)].
% 0.77/1.02 23 -lin_ind_subset(A,c1) | lin_ind_subset(A,c2) | -basis_of(A,c1). [resolve(14,a,15,b)].
% 0.77/1.02 29 -basis_of(union(f2(c1),A),c2) # answer(bg_2_4_3). [resolve(22,a,18,b)].
% 0.77/1.02 30 lin_ind_subset(f2(c1),c1). [ur(19,a,22,a)].
% 0.77/1.02 37 -lin_ind_subset(f2(c1),c2) # answer(bg_2_4_3). [ur(20,b,21,a,c,29,a)].
% 0.77/1.02 38 $F # answer(bg_2_4_3). [resolve(37,a,23,b),unit_del(a,30),unit_del(b,22)].
% 0.77/1.02
% 0.77/1.02 % SZS output end Refutation
% 0.77/1.02 ============================== end of proof ==========================
% 0.77/1.02
% 0.77/1.02 ============================== STATISTICS ============================
% 0.77/1.02
% 0.77/1.02 Given=11. Generated=23. Kept=20. proofs=1.
% 0.77/1.02 Usable=11. Sos=8. Demods=0. Limbo=0, Disabled=21. Hints=0.
% 0.77/1.02 Megabytes=0.06.
% 0.77/1.02 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.77/1.02
% 0.77/1.02 ============================== end of statistics =====================
% 0.77/1.02
% 0.77/1.02 ============================== end of search =========================
% 0.77/1.02
% 0.77/1.02 THEOREM PROVED
% 0.77/1.02 % SZS status Theorem
% 0.77/1.02
% 0.77/1.02 Exiting with 1 proof.
% 0.77/1.02
% 0.77/1.02 Process 11845 exit (max_proofs) Wed Jun 8 06:37:50 2022
% 0.77/1.02 Prover9 interrupted
%------------------------------------------------------------------------------