0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n019.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % DateTime : Thu Jul 2 12:15:26 EDT 2020 0.13/0.35 % CPUTime : 0.46/1.05 ============================== Prover9 =============================== 0.46/1.05 Prover9 (32) version 2009-11A, November 2009. 0.46/1.05 Process 20637 was started by sandbox2 on n019.cluster.edu, 0.46/1.05 Thu Jul 2 12:15:27 2020 0.46/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_20477_n019.cluster.edu". 0.46/1.05 ============================== end of head =========================== 0.46/1.05 0.46/1.05 ============================== INPUT ================================= 0.46/1.05 0.46/1.05 % Reading from file /tmp/Prover9_20477_n019.cluster.edu 0.46/1.05 0.46/1.05 set(prolog_style_variables). 0.46/1.05 set(auto2). 0.46/1.05 % set(auto2) -> set(auto). 0.46/1.05 % set(auto) -> set(auto_inference). 0.46/1.05 % set(auto) -> set(auto_setup). 0.46/1.05 % set(auto_setup) -> set(predicate_elim). 0.46/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.46/1.05 % set(auto) -> set(auto_limits). 0.46/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.46/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.46/1.05 % set(auto) -> set(auto_denials). 0.46/1.05 % set(auto) -> set(auto_process). 0.46/1.05 % set(auto2) -> assign(new_constants, 1). 0.46/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.46/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.46/1.05 % set(auto2) -> assign(max_hours, 1). 0.46/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.46/1.05 % set(auto2) -> assign(max_seconds, 0). 0.46/1.05 % set(auto2) -> assign(max_minutes, 5). 0.46/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.46/1.05 % set(auto2) -> set(sort_initial_sos). 0.46/1.05 % set(auto2) -> assign(sos_limit, -1). 0.46/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.46/1.05 % set(auto2) -> assign(max_megs, 400). 0.46/1.05 % set(auto2) -> assign(stats, some). 0.46/1.05 % set(auto2) -> clear(echo_input). 0.46/1.05 % set(auto2) -> set(quiet). 0.46/1.05 % set(auto2) -> clear(print_initial_clauses). 0.46/1.05 % set(auto2) -> clear(print_given). 0.46/1.05 assign(lrs_ticks,-1). 0.46/1.05 assign(sos_limit,10000). 0.46/1.05 assign(order,kbo). 0.46/1.05 set(lex_order_vars). 0.46/1.05 clear(print_given). 0.46/1.05 0.46/1.05 % formulas(sos). % not echoed (33 formulas) 0.46/1.05 0.46/1.05 ============================== end of input ========================== 0.46/1.05 0.46/1.05 % From the command line: assign(max_seconds, 960). 0.46/1.05 0.46/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.46/1.05 0.46/1.05 % Formulas that are not ordinary clauses: 0.46/1.05 1 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & (all ElCod (element(ElCod,Cod) -> (exists ElDom (ElCod = apply(Morphism,ElDom) & element(ElDom,Dom))))) -> surjection(Morphism))) # label(properties_for_surjection) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 2 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & (all El1 all El2 (element(El1,Dom) & element(El2,Dom) & apply(Morphism,El2) = apply(Morphism,El1) -> El2 = El1)) -> injection(Morphism))) # label(properties_for_injection) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 3 (all Morphism1 all Morphism2 all Dom all CodDom all Cod ((all ElCodDom (element(ElCodDom,CodDom) & apply(Morphism2,ElCodDom) = zero(Cod) <-> (exists ElDom (apply(Morphism1,ElDom) = ElCodDom & element(ElDom,Dom))))) & morphism(Morphism1,Dom,CodDom) & morphism(Morphism2,CodDom,Cod) -> exact(Morphism1,Morphism2))) # label(properties_for_exact) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 4 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) -> zero(Cod) = apply(Morphism,zero(Dom)) & (all El (element(El,Dom) -> element(apply(Morphism,El),Cod))))) # label(morphism) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 5 (all Dom all El1 all El2 (element(El1,Dom) & element(El2,Dom) -> El2 = subtract(Dom,El1,subtract(Dom,El1,El2)))) # label(subtract_cancellation) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 6 (all Morphism1 all Morphism2 all Dom all CodDom all Cod (morphism(Morphism2,CodDom,Cod) & morphism(Morphism1,Dom,CodDom) & exact(Morphism1,Morphism2) -> (all ElCodDom (zero(Cod) = apply(Morphism2,ElCodDom) & element(ElCodDom,CodDom) <-> (exists ElDom (ElCodDom = apply(Morphism1,ElDom) & element(ElDom,Dom))))))) # label(exact_properties) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 7 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & surjection(Morphism) -> (all ElCod (element(ElCod,Cod) -> (exists ElDom (element(ElDom,Dom) & ElCod = apply(Morphism,ElDom))))))) # label(surjection_properties) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 8 (all M1 all M2 all M3 all M4 all Dom all DomCod1 all DomCod2 all Cod (morphism(M2,DomCod1,Cod) & morphism(M3,Dom,DomCod2) & commute(M1,M2,M3,M4) & morphism(M4,DomCod2,Cod) & morphism(M1,Dom,DomCod1) -> (all ElDom (element(ElDom,Dom) -> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)))))) # label(commute_properties) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 9 (all Dom all El1 all El2 (element(El1,Dom) & element(El2,Dom) -> element(subtract(Dom,El1,El2),Dom))) # label(subtract_in_domain) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 10 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & injection(Morphism) -> (all El1 all El2 (element(El2,Dom) & apply(Morphism,El1) = apply(Morphism,El2) & element(El1,Dom) -> El2 = El1)))) # label(injection_properties) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 11 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) -> (all El1 all El2 (element(El1,Dom) & element(El2,Dom) -> subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) = apply(Morphism,subtract(Dom,El1,El2)))))) # label(subtract_distribution) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 12 (all M1 all M2 all M3 all M4 all Dom all DomCod1 all DomCod2 all Cod (morphism(M3,Dom,DomCod2) & morphism(M1,Dom,DomCod1) & morphism(M4,DomCod2,Cod) & (all ElDom (element(ElDom,Dom) -> apply(M4,apply(M3,ElDom)) = apply(M2,apply(M1,ElDom)))) & morphism(M2,DomCod1,Cod) -> commute(M1,M2,M3,M4))) # label(properties_for_commute) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 13 (all Dom all El (element(El,Dom) -> zero(Dom) = subtract(Dom,El,El))) # label(subtract_to_0) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 14 (all E (element(E,e) -> (exists R exists B1 (element(B1,b) & R = apply(delta,apply(g,B1)) & apply(h,apply(beta,B1)) = R & apply(delta,E) = R & element(R,r))))) # label(lemma3) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 15 (all E (element(E,e) -> (exists B1 exists E1 exists A (element(E1,e) & E1 = apply(g,apply(alpha,A)) & E1 = apply(gamma,apply(f,A)) & element(A,a) & subtract(e,apply(g,B1),E) = E1 & element(B1,b))))) # label(lemma8) # label(axiom) # label(non_clause). [assumption]. 0.46/1.05 16 -(all E (element(E,e) -> (exists B1 exists B2 (apply(g,subtract(b,B1,B2)) = E & element(B2,b) & element(B1,b))))) # label(lemma12) # label(negated_conjecture) # label(non_clause). [assumption]. 0.46/1.05 0.46/1.05 ============================== end of process non-clausal formulas === 0.46/1.05 0.46/1.05 ============================== PROCESS INITIAL CLAUSES =============== 0.46/1.05 0.46/1.05 ============================== PREDICATE ELIMINATION ================= 0.46/1.05 17 -morphism(A,B,C) | -surjection(A) | -element(D,C) | element(f7(A,B,C,D),B) # label(surjection_properties) # label(axiom). [clausify(7)]. 0.46/1.05 18 surjection(delta) # label(delta_surjection) # label(axiom). [assumption]. 0.46/1.05 19 surjection(h) # label(h_surjection) # label(hypothesis). [assumption]. 0.46/1.05 20 surjection(f) # label(f_surjection) # label(hypothesis). [assumption]. 0.46/1.05 21 surjection(beta) # label(beta_surjection) # label(axiom). [assumption]. 0.46/1.05 22 -morphism(A,B,C) | element(f1(A,B,C),C) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(1)]. 0.46/1.05 Derived: -morphism(delta,A,B) | -element(C,B) | element(f7(delta,A,B,C),A). [resolve(17,b,18,a)]. 0.46/1.05 Derived: -morphism(h,A,B) | -element(C,B) | element(f7(h,A,B,C),A). [resolve(17,b,19,a)]. 0.46/1.05 Derived: -morphism(f,A,B) | -element(C,B) | element(f7(f,A,B,C),A). [resolve(17,b,20,a)]. 0.46/1.05 Derived: -morphism(beta,A,B) | -element(C,B) | element(f7(beta,A,B,C),A). [resolve(17,b,21,a)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,C) | element(f7(A,B,C,D),B) | -morphism(A,E,F) | element(f1(A,E,F),F). [resolve(17,b,22,c)]. 0.46/1.05 23 -morphism(A,B,C) | apply(A,D) != f1(A,B,C) | -element(D,B) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(1)]. 0.46/1.05 Derived: -morphism(A,B,C) | apply(A,D) != f1(A,B,C) | -element(D,B) | -morphism(A,E,F) | -element(V6,F) | element(f7(A,E,F,V6),E). [resolve(23,d,17,b)]. 0.46/1.05 24 -morphism(A,B,C) | -surjection(A) | -element(D,C) | apply(A,f7(A,B,C,D)) = D # label(surjection_properties) # label(axiom). [clausify(7)]. 0.46/1.05 Derived: -morphism(delta,A,B) | -element(C,B) | apply(delta,f7(delta,A,B,C)) = C. [resolve(24,b,18,a)]. 0.46/1.05 Derived: -morphism(h,A,B) | -element(C,B) | apply(h,f7(h,A,B,C)) = C. [resolve(24,b,19,a)]. 0.46/1.05 Derived: -morphism(f,A,B) | -element(C,B) | apply(f,f7(f,A,B,C)) = C. [resolve(24,b,20,a)]. 0.46/1.05 Derived: -morphism(beta,A,B) | -element(C,B) | apply(beta,f7(beta,A,B,C)) = C. [resolve(24,b,21,a)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,C) | apply(A,f7(A,B,C,D)) = D | -morphism(A,E,F) | element(f1(A,E,F),F). [resolve(24,b,22,c)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,C) | apply(A,f7(A,B,C,D)) = D | -morphism(A,E,F) | apply(A,V6) != f1(A,E,F) | -element(V6,E). [resolve(24,b,23,d)]. 0.46/1.05 25 -morphism(A,B,C) | -injection(A) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E # label(injection_properties) # label(axiom). [clausify(10)]. 0.46/1.05 26 injection(gamma) # label(gamma_injection) # label(axiom). [assumption]. 0.46/1.05 27 injection(alpha) # label(alpha_injection) # label(axiom). [assumption]. 0.46/1.05 28 -morphism(A,B,C) | element(f2(A,B,C),B) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.46/1.05 29 -morphism(A,B,C) | element(f3(A,B,C),B) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.46/1.05 30 -morphism(A,B,C) | f3(A,B,C) != f2(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.46/1.05 31 -morphism(A,B,C) | apply(A,f3(A,B,C)) = apply(A,f2(A,B,C)) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.46/1.05 Derived: -morphism(gamma,A,B) | -element(C,A) | apply(gamma,C) != apply(gamma,D) | -element(D,A) | C = D. [resolve(25,b,26,a)]. 0.46/1.05 Derived: -morphism(alpha,A,B) | -element(C,A) | apply(alpha,C) != apply(alpha,D) | -element(D,A) | C = D. [resolve(25,b,27,a)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | -morphism(A,F,V6) | element(f2(A,F,V6),F). [resolve(25,b,28,c)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | -morphism(A,F,V6) | element(f3(A,F,V6),F). [resolve(25,b,29,c)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | -morphism(A,F,V6) | f3(A,F,V6) != f2(A,F,V6). [resolve(25,b,30,c)]. 0.46/1.05 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | -morphism(A,F,V6) | apply(A,f3(A,F,V6)) = apply(A,f2(A,F,V6)). [resolve(25,b,31,c)]. 0.46/1.05 32 -morphism(A,B,C) | -morphism(D,E,B) | -exact(D,A) | element(F,B) | apply(D,V6) != F | -element(V6,E) # label(exact_properties) # label(axiom). [clausify(6)]. 0.46/1.05 33 exact(gammma,delta) # label(gamma_delta_exact) # label(axiom). [assumption]. 0.46/1.05 34 exact(alpha,beta) # label(alpha_beta_exact) # label(axiom). [assumption]. 0.46/1.05 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | element(D,A) | apply(gammma,E) != D | -element(E,C). [resolve(32,c,33,a)]. 0.46/1.05 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | element(D,A) | apply(alpha,E) != D | -element(E,C). [resolve(32,c,34,a)]. 0.46/1.05 35 -morphism(A,B,C) | -morphism(D,E,B) | -exact(D,A) | zero(C) = apply(A,F) | apply(D,V6) != F | -element(V6,E) # label(exact_properties) # label(axiom). [clausify(6)]. 0.46/1.05 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) = apply(delta,D) | apply(gammma,E) != D | -element(E,C). [resolve(35,c,33,a)]. 0.46/1.05 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) = apply(beta,D) | apply(alpha,E) != D | -element(E,C). [resolve(35,c,34,a)]. 0.46/1.05 36 element(f4(A,B,C,D,E),D) | element(f5(A,B,C,D,E),C) | -morphism(A,C,D) | -morphism(B,D,E) | exact(A,B) # label(properties_for_exact) # label(axiom). [clausify(3)]. 0.46/1.05 Derived: element(f4(A,B,C,D,E),D) | element(f5(A,B,C,D,E),C) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,F,V6) | -morphism(A,V7,F) | element(V8,F) | apply(A,V9) != V8 | -element(V9,V7). [resolve(36,e,32,c)]. 0.46/1.05 Derived: element(f4(A,B,C,D,E),D) | element(f5(A,B,C,D,E),C) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(B,V8) | apply(A,V9) != V8 | -element(V9,V7). [resolve(36,e,35,c)]. 0.46/1.06 37 -morphism(A,B,C) | -morphism(D,E,B) | -exact(D,A) | zero(C) != apply(A,F) | -element(F,B) | element(f6(D,A,E,B,C,F),E) # label(exact_properties) # label(axiom). [clausify(6)]. 0.46/1.06 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) != apply(delta,D) | -element(D,A) | element(f6(gammma,delta,C,A,B,D),C). [resolve(37,c,33,a)]. 0.46/1.06 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) != apply(beta,D) | -element(D,A) | element(f6(alpha,beta,C,A,B,D),C). [resolve(37,c,34,a)]. 0.46/1.06 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | element(f6(D,A,E,B,C,F),E) | element(f4(D,A,V6,V7,V8),V7) | element(f5(D,A,V6,V7,V8),V6) | -morphism(D,V6,V7) | -morphism(A,V7,V8). [resolve(37,c,36,e)]. 0.46/1.06 38 zero(A) = apply(B,f4(C,B,D,E,A)) | element(f5(C,B,D,E,A),D) | -morphism(C,D,E) | -morphism(B,E,A) | exact(C,B) # label(properties_for_exact) # label(axiom). [clausify(3)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | element(f5(C,B,D,E,A),D) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | element(V8,F) | apply(C,V9) != V8 | -element(V9,V7). [resolve(38,e,32,c)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | element(f5(C,B,D,E,A),D) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) = apply(B,V8) | apply(C,V9) != V8 | -element(V9,V7). [resolve(38,e,35,c)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | element(f5(C,B,D,E,A),D) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | element(f6(C,B,V7,F,V6,V8),V7). [resolve(38,e,37,c)]. 0.46/1.06 39 -morphism(A,B,C) | -morphism(D,E,B) | -exact(D,A) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f6(D,A,E,B,C,F)) = F # label(exact_properties) # label(axiom). [clausify(6)]. 0.46/1.06 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) != apply(delta,D) | -element(D,A) | apply(gammma,f6(gammma,delta,C,A,B,D)) = D. [resolve(39,c,33,a)]. 0.46/1.06 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) != apply(beta,D) | -element(D,A) | apply(alpha,f6(alpha,beta,C,A,B,D)) = D. [resolve(39,c,34,a)]. 0.46/1.06 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f6(D,A,E,B,C,F)) = F | element(f4(D,A,V6,V7,V8),V7) | element(f5(D,A,V6,V7,V8),V6) | -morphism(D,V6,V7) | -morphism(A,V7,V8). [resolve(39,c,36,e)]. 0.46/1.06 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f6(D,A,E,B,C,F)) = F | zero(V6) = apply(A,f4(D,A,V7,V8,V6)) | element(f5(D,A,V7,V8,V6),V7) | -morphism(D,V7,V8) | -morphism(A,V8,V6). [resolve(39,c,38,e)]. 0.46/1.06 40 element(f4(A,B,C,D,E),D) | apply(A,f5(A,B,C,D,E)) = f4(A,B,C,D,E) | -morphism(A,C,D) | -morphism(B,D,E) | exact(A,B) # label(properties_for_exact) # label(axiom). [clausify(3)]. 0.46/1.06 Derived: element(f4(A,B,C,D,E),D) | apply(A,f5(A,B,C,D,E)) = f4(A,B,C,D,E) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,F,V6) | -morphism(A,V7,F) | element(V8,F) | apply(A,V9) != V8 | -element(V9,V7). [resolve(40,e,32,c)]. 0.46/1.06 Derived: element(f4(A,B,C,D,E),D) | apply(A,f5(A,B,C,D,E)) = f4(A,B,C,D,E) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(B,V8) | apply(A,V9) != V8 | -element(V9,V7). [resolve(40,e,35,c)]. 0.46/1.06 Derived: element(f4(A,B,C,D,E),D) | apply(A,f5(A,B,C,D,E)) = f4(A,B,C,D,E) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | element(f6(A,B,V7,F,V6,V8),V7). [resolve(40,e,37,c)]. 0.46/1.06 Derived: element(f4(A,B,C,D,E),D) | apply(A,f5(A,B,C,D,E)) = f4(A,B,C,D,E) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | apply(A,f6(A,B,V7,F,V6,V8)) = V8. [resolve(40,e,39,c)]. 0.46/1.06 41 zero(A) = apply(B,f4(C,B,D,E,A)) | apply(C,f5(C,B,D,E,A)) = f4(C,B,D,E,A) | -morphism(C,D,E) | -morphism(B,E,A) | exact(C,B) # label(properties_for_exact) # label(axiom). [clausify(3)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | apply(C,f5(C,B,D,E,A)) = f4(C,B,D,E,A) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | element(V8,F) | apply(C,V9) != V8 | -element(V9,V7). [resolve(41,e,32,c)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | apply(C,f5(C,B,D,E,A)) = f4(C,B,D,E,A) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) = apply(B,V8) | apply(C,V9) != V8 | -element(V9,V7). [resolve(41,e,35,c)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | apply(C,f5(C,B,D,E,A)) = f4(C,B,D,E,A) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | element(f6(C,B,V7,F,V6,V8),V7). [resolve(41,e,37,c)]. 0.46/1.06 Derived: zero(A) = apply(B,f4(C,B,D,E,A)) | apply(C,f5(C,B,D,E,A)) = f4(C,B,D,E,A) | -morphism(C,D,E) | -morphism(B,E,A) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | apply(C,f6(C,B,V7,F,V6,V8)) = V8. [resolve(41,e,39,c)]. 0.46/1.06 42 -element(f4(A,B,C,D,E),D) | zero(E) != apply(B,f4(A,B,C,D,E)) | apply(A,F) != f4(A,B,C,D,E) | -element(F,C) | -morphism(A,C,D) | -morphism(B,D,E) | exact(A,B) # label(properties_for_exact) # label(axiom). [clausify(3)]. 0.46/1.06 Derived: -element(f4(A,B,C,D,E),D) | zero(E) != apply(B,f4(A,B,C,D,E)) | apply(A,F) != f4(A,B,C,D,E) | -element(F,C) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | element(V9,V6) | apply(A,V10) != V9 | -element(V10,V8). [resolve(42,g,32,c)]. 0.46/1.06 Derived: -element(f4(A,B,C,D,E),D) | zero(E) != apply(B,f4(A,B,C,D,E)) | apply(A,F) != f4(A,B,C,D,E) | -element(F,C) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | zero(V7) = apply(B,V9) | apply(A,V10) != V9 | -element(V10,V8). [resolve(42,g,35,c)]. 0.46/1.06 Derived: -element(f4(A,B,C,D,E),D) | zero(E) != apply(B,f4(A,B,C,D,E)) | apply(A,F) != f4(A,B,C,D,E) | -element(F,C) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | zero(V7) != apply(B,V9) | -element(V9,V6) | element(f6(A,B,V8,V6,V7,V9),V8). [resolve(42,g,37,c)]. 0.46/1.06 Derived: -element(f4(A,B,C,D,E),D) | zero(E) != apply(B,f4(A,B,C,D,E)) | apply(A,F) != f4(A,B,C,D,E) | -element(F,C) | -morphism(A,C,D) | -morphism(B,D,E) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | zero(V7) != apply(B,V9) | -element(V9,V6) | apply(A,f6(A,B,V8,V6,V7,V9)) = V9. [resolve(42,g,39,c)]. 0.46/1.06 43 -morphism(A,B,C) | -morphism(D,E,F) | -commute(V6,A,D,V7) | -morphism(V7,F,C) | -morphism(V6,E,B) | -element(V8,E) | apply(V7,apply(D,V8)) = apply(A,apply(V6,V8)) # label(commute_properties) # label(axiom). [clausify(8)]. 0.46/1.06 44 commute(beta,h,g,delta) # label(beta_h_g_delta_commute) # label(axiom). [assumption]. 0.46/1.06 45 commute(alpha,g,f,gamma) # label(alpha_g_f_gamma_commute) # label(axiom). [assumption]. 0.46/1.06 46 -morphism(A,B,C) | -morphism(D,B,E) | -morphism(F,C,V6) | element(f8(D,V7,A,F,B,E,C,V6),B) | -morphism(V7,E,V6) | commute(D,V7,A,F) # label(properties_for_commute) # label(axiom). [clausify(12)]. 0.46/1.06 Derived: -morphism(h,A,B) | -morphism(g,C,D) | -morphism(delta,D,B) | -morphism(beta,C,A) | -element(E,C) | apply(delta,apply(g,E)) = apply(h,apply(beta,E)). [resolve(43,c,44,a)]. 0.46/1.06 Derived: -morphism(g,A,B) | -morphism(f,C,D) | -morphism(gamma,D,B) | -morphism(alpha,C,A) | -element(E,C) | apply(gamma,apply(f,E)) = apply(g,apply(alpha,E)). [resolve(43,c,45,a)]. 0.46/1.06 Derived: -morphism(A,B,C) | -morphism(D,E,F) | -morphism(V6,F,C) | -morphism(V7,E,B) | -element(V8,E) | apply(V6,apply(D,V8)) = apply(A,apply(V7,V8)) | -morphism(D,V9,V10) | -morphism(V7,V9,V11) | -morphism(V6,V10,V12) | element(f8(V7,A,D,V6,V9,V11,V10,V12),V9) | -morphism(A,V11,V12). [resolve(43,c,46,f)]. 0.46/1.06 47 -morphism(A,B,C) | -morphism(D,B,E) | -morphism(F,C,V6) | apply(F,apply(A,f8(D,V7,A,F,B,E,C,V6))) != apply(V7,apply(D,f8(D,V7,A,F,B,E,C,V6))) | -morphism(V7,E,V6) | commute(D,V7,A,F) # label(properties_for_commute) # label(axiom). [clausify(12)]. 0.46/1.06 Derived: -morphism(A,B,C) | -morphism(D,B,E) | -morphism(F,C,V6) | apply(F,apply(A,f8(D,V7,A,F,B,E,C,V6))) != apply(V7,apply(D,f8(D,V7,A,F,B,E,C,V6))) | -morphism(V7,E,V6) | -morphismAlarm clock 119.78/120.04 Prover9 interrupted 119.78/120.04 EOF