0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n002.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1200 0.12/0.33 % DateTime : Tue Jul 13 15:12:18 EDT 2021 0.12/0.34 % CPUTime : 0.40/1.01 ============================== Prover9 =============================== 0.40/1.01 Prover9 (32) version 2009-11A, November 2009. 0.40/1.01 Process 5165 was started by sandbox on n002.cluster.edu, 0.40/1.01 Tue Jul 13 15:12:18 2021 0.40/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_5004_n002.cluster.edu". 0.40/1.01 ============================== end of head =========================== 0.40/1.01 0.40/1.01 ============================== INPUT ================================= 0.40/1.01 0.40/1.01 % Reading from file /tmp/Prover9_5004_n002.cluster.edu 0.40/1.01 0.40/1.01 set(prolog_style_variables). 0.40/1.01 set(auto2). 0.40/1.01 % set(auto2) -> set(auto). 0.40/1.01 % set(auto) -> set(auto_inference). 0.40/1.01 % set(auto) -> set(auto_setup). 0.40/1.01 % set(auto_setup) -> set(predicate_elim). 0.40/1.01 % set(auto_setup) -> assign(eq_defs, unfold). 0.40/1.01 % set(auto) -> set(auto_limits). 0.40/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). 0.40/1.01 % set(auto_limits) -> assign(sos_limit, 20000). 0.40/1.01 % set(auto) -> set(auto_denials). 0.40/1.01 % set(auto) -> set(auto_process). 0.40/1.01 % set(auto2) -> assign(new_constants, 1). 0.40/1.01 % set(auto2) -> assign(fold_denial_max, 3). 0.40/1.01 % set(auto2) -> assign(max_weight, "200.000"). 0.40/1.01 % set(auto2) -> assign(max_hours, 1). 0.40/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.40/1.01 % set(auto2) -> assign(max_seconds, 0). 0.40/1.01 % set(auto2) -> assign(max_minutes, 5). 0.40/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.40/1.01 % set(auto2) -> set(sort_initial_sos). 0.40/1.01 % set(auto2) -> assign(sos_limit, -1). 0.40/1.01 % set(auto2) -> assign(lrs_ticks, 3000). 0.40/1.01 % set(auto2) -> assign(max_megs, 400). 0.40/1.01 % set(auto2) -> assign(stats, some). 0.40/1.01 % set(auto2) -> clear(echo_input). 0.40/1.01 % set(auto2) -> set(quiet). 0.40/1.01 % set(auto2) -> clear(print_initial_clauses). 0.40/1.01 % set(auto2) -> clear(print_given). 0.40/1.01 assign(lrs_ticks,-1). 0.40/1.01 assign(sos_limit,10000). 0.40/1.01 assign(order,kbo). 0.40/1.01 set(lex_order_vars). 0.40/1.01 clear(print_given). 0.40/1.01 0.40/1.01 % formulas(sos). % not echoed (33 formulas) 0.40/1.01 0.40/1.01 ============================== end of input ========================== 0.40/1.01 0.40/1.01 % From the command line: assign(max_seconds, 1200). 0.40/1.01 0.40/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.40/1.01 0.40/1.01 % Formulas that are not ordinary clauses: 0.40/1.01 1 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) -> (all El (element(El,Dom) -> element(apply(Morphism,El),Cod))) & zero(Cod) = apply(Morphism,zero(Dom)))) # label(morphism) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 2 (all Morphism all Dom all Cod ((all El1 all El2 (apply(Morphism,El1) = apply(Morphism,El2) & element(El2,Dom) & element(El1,Dom) -> El1 = El2)) & morphism(Morphism,Dom,Cod) -> injection(Morphism))) # label(properties_for_injection) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 3 (all Morphism all Dom all Cod (surjection(Morphism) & morphism(Morphism,Dom,Cod) -> (all ElCod (element(ElCod,Cod) -> (exists ElDom (element(ElDom,Dom) & apply(Morphism,ElDom) = ElCod)))))) # label(surjection_properties) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 4 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) -> (all El1 all El2 (element(El2,Dom) & element(El1,Dom) -> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)))))) # label(subtract_distribution) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 5 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & (all ElCod (element(ElCod,Cod) -> (exists ElDom (element(ElDom,Dom) & ElCod = apply(Morphism,ElDom))))) -> surjection(Morphism))) # label(properties_for_surjection) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 6 (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]. 0.40/1.01 7 (all M1 all M2 all M3 all M4 all Dom all DomCod1 all DomCod2 all Cod (morphism(M3,Dom,DomCod2) & (all ElDom (element(ElDom,Dom) -> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)))) & morphism(M4,DomCod2,Cod) & morphism(M2,DomCod1,Cod) & morphism(M1,Dom,DomCod1) -> commute(M1,M2,M3,M4))) # label(properties_for_commute) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 8 (all Dom all El1 all El2 (element(El2,Dom) & element(El1,Dom) -> element(subtract(Dom,El1,El2),Dom))) # label(subtract_in_domain) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 9 (all M1 all M2 all M3 all M4 all Dom all DomCod1 all DomCod2 all Cod (morphism(M1,Dom,DomCod1) & morphism(M2,DomCod1,Cod) & morphism(M3,Dom,DomCod2) & morphism(M4,DomCod2,Cod) & commute(M1,M2,M3,M4) -> (all ElDom (element(ElDom,Dom) -> apply(M4,apply(M3,ElDom)) = apply(M2,apply(M1,ElDom)))))) # label(commute_properties) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 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) -> El1 = El2)))) # label(injection_properties) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 11 (all Morphism1 all Morphism2 all Dom all CodDom all Cod ((all ElCodDom (element(ElCodDom,CodDom) & zero(Cod) = apply(Morphism2,ElCodDom) <-> (exists ElDom (apply(Morphism1,ElDom) = ElCodDom & element(ElDom,Dom))))) & morphism(Morphism2,CodDom,Cod) & morphism(Morphism1,Dom,CodDom) -> exact(Morphism1,Morphism2))) # label(properties_for_exact) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 12 (all Morphism1 all Morphism2 all Dom all CodDom all Cod (exact(Morphism1,Morphism2) & morphism(Morphism2,CodDom,Cod) & morphism(Morphism1,Dom,CodDom) -> (all ElCodDom (zero(Cod) = apply(Morphism2,ElCodDom) & element(ElCodDom,CodDom) <-> (exists ElDom (element(ElDom,Dom) & ElCodDom = apply(Morphism1,ElDom))))))) # label(exact_properties) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 13 (all Dom all El (element(El,Dom) -> zero(Dom) = subtract(Dom,El,El))) # label(subtract_to_0) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 14 (all E (element(E,e) -> (exists R exists B1 (R = apply(delta,apply(g,B1)) & R = apply(h,apply(beta,B1)) & element(B1,b) & R = apply(delta,E) & element(R,r))))) # label(lemma3) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 15 (all E (element(E,e) -> (exists B1 exists E1 exists A (element(E1,e) & E1 = apply(g,apply(alpha,A)) & apply(gamma,apply(f,A)) = E1 & element(A,a) & E1 = subtract(e,apply(g,B1),E) & element(B1,b))))) # label(lemma8) # label(axiom) # label(non_clause). [assumption]. 0.40/1.01 16 -(all E (element(E,e) -> (exists B1 exists B2 (element(B1,b) & element(B2,b) & apply(g,subtract(b,B1,B2)) = E)))) # label(lemma12) # label(negated_conjecture) # label(non_clause). [assumption]. 0.40/1.01 0.40/1.01 ============================== end of process non-clausal formulas === 0.40/1.01 0.40/1.01 ============================== PROCESS INITIAL CLAUSES =============== 0.40/1.01 0.40/1.01 ============================== PREDICATE ELIMINATION ================= 0.40/1.01 17 -surjection(A) | -morphism(A,B,C) | -element(D,C) | element(f3(A,B,C,D),B) # label(surjection_properties) # label(axiom). [clausify(3)]. 0.40/1.01 18 surjection(beta) # label(beta_surjection) # label(axiom). [assumption]. 0.40/1.01 19 surjection(delta) # label(delta_surjection) # label(axiom). [assumption]. 0.40/1.01 20 surjection(f) # label(f_surjection) # label(hypothesis). [assumption]. 0.40/1.01 21 surjection(h) # label(h_surjection) # label(hypothesis). [assumption]. 0.40/1.01 22 -morphism(A,B,C) | element(f4(A,B,C),C) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(5)]. 0.40/1.01 Derived: -morphism(beta,A,B) | -element(C,B) | element(f3(beta,A,B,C),A). [resolve(17,a,18,a)]. 0.40/1.01 Derived: -morphism(delta,A,B) | -element(C,B) | element(f3(delta,A,B,C),A). [resolve(17,a,19,a)]. 0.40/1.01 Derived: -morphism(f,A,B) | -element(C,B) | element(f3(f,A,B,C),A). [resolve(17,a,20,a)]. 0.40/1.01 Derived: -morphism(h,A,B) | -element(C,B) | element(f3(h,A,B,C),A). [resolve(17,a,21,a)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,C) | element(f3(A,B,C,D),B) | -morphism(A,E,F) | element(f4(A,E,F),F). [resolve(17,a,22,c)]. 0.40/1.01 23 -morphism(A,B,C) | -element(D,B) | apply(A,D) != f4(A,B,C) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(5)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != f4(A,B,C) | -morphism(A,E,F) | -element(V6,F) | element(f3(A,E,F,V6),E). [resolve(23,d,17,a)]. 0.40/1.01 24 -surjection(A) | -morphism(A,B,C) | -element(D,C) | apply(A,f3(A,B,C,D)) = D # label(surjection_properties) # label(axiom). [clausify(3)]. 0.40/1.01 Derived: -morphism(beta,A,B) | -element(C,B) | apply(beta,f3(beta,A,B,C)) = C. [resolve(24,a,18,a)]. 0.40/1.01 Derived: -morphism(delta,A,B) | -element(C,B) | apply(delta,f3(delta,A,B,C)) = C. [resolve(24,a,19,a)]. 0.40/1.01 Derived: -morphism(f,A,B) | -element(C,B) | apply(f,f3(f,A,B,C)) = C. [resolve(24,a,20,a)]. 0.40/1.01 Derived: -morphism(h,A,B) | -element(C,B) | apply(h,f3(h,A,B,C)) = C. [resolve(24,a,21,a)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,C) | apply(A,f3(A,B,C,D)) = D | -morphism(A,E,F) | element(f4(A,E,F),F). [resolve(24,a,22,c)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,C) | apply(A,f3(A,B,C,D)) = D | -morphism(A,E,F) | -element(V6,E) | apply(A,V6) != f4(A,E,F). [resolve(24,a,23,d)]. 0.40/1.01 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)]. 0.40/1.01 26 injection(gamma) # label(gamma_injection) # label(axiom). [assumption]. 0.40/1.01 27 injection(alpha) # label(alpha_injection) # label(axiom). [assumption]. 0.40/1.01 28 element(f2(A,B,C),B) | -morphism(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.40/1.01 29 element(f1(A,B,C),B) | -morphism(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.40/1.01 30 f2(A,B,C) != f1(A,B,C) | -morphism(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.40/1.01 31 apply(A,f2(A,B,C)) = apply(A,f1(A,B,C)) | -morphism(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(2)]. 0.40/1.01 Derived: -morphism(gamma,A,B) | -element(C,A) | apply(gamma,C) != apply(gamma,D) | -element(D,A) | C = D. [resolve(25,b,26,a)]. 0.40/1.01 Derived: -morphism(alpha,A,B) | -element(C,A) | apply(alpha,C) != apply(alpha,D) | -element(D,A) | C = D. [resolve(25,b,27,a)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | element(f2(A,F,V6),F) | -morphism(A,F,V6). [resolve(25,b,28,c)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | element(f1(A,F,V6),F) | -morphism(A,F,V6). [resolve(25,b,29,c)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | f2(A,F,V6) != f1(A,F,V6) | -morphism(A,F,V6). [resolve(25,b,30,c)]. 0.40/1.01 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,D) != apply(A,E) | -element(E,B) | D = E | apply(A,f2(A,F,V6)) = apply(A,f1(A,F,V6)) | -morphism(A,F,V6). [resolve(25,b,31,c)]. 0.40/1.01 32 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | element(F,C) | -element(V6,E) | apply(A,V6) != F # label(exact_properties) # label(axiom). [clausify(12)]. 0.40/1.01 33 exact(alpha,beta) # label(alpha_beta_exact) # label(axiom). [assumption]. 0.40/1.01 34 exact(gammma,delta) # label(gamma_delta_exact) # label(axiom). [assumption]. 0.40/1.01 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | element(D,A) | -element(E,C) | apply(alpha,E) != D. [resolve(32,a,33,a)]. 0.40/1.01 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | element(D,A) | -element(E,C) | apply(gammma,E) != D. [resolve(32,a,34,a)]. 0.40/1.01 35 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | zero(D) = apply(B,F) | -element(V6,E) | apply(A,V6) != F # label(exact_properties) # label(axiom). [clausify(12)]. 0.40/1.01 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) = apply(beta,D) | -element(E,C) | apply(alpha,E) != D. [resolve(35,a,33,a)]. 0.40/1.01 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) = apply(delta,D) | -element(E,C) | apply(gammma,E) != D. [resolve(35,a,34,a)]. 0.40/1.01 36 element(f6(A,B,C,D,E),D) | element(f7(A,B,C,D,E),C) | -morphism(B,D,E) | -morphism(A,C,D) | exact(A,B) # label(properties_for_exact) # label(axiom). [clausify(11)]. 0.40/1.01 Derived: element(f6(A,B,C,D,E),D) | element(f7(A,B,C,D,E),C) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,F,V6) | -morphism(A,V7,F) | element(V8,F) | -element(V9,V7) | apply(A,V9) != V8. [resolve(36,e,32,a)]. 0.40/1.01 Derived: element(f6(A,B,C,D,E),D) | element(f7(A,B,C,D,E),C) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(B,V8) | -element(V9,V7) | apply(A,V9) != V8. [resolve(36,e,35,a)]. 0.40/1.01 37 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | zero(D) != apply(B,F) | -element(F,C) | element(f8(A,B,E,C,D,F),E) # label(exact_properties) # label(axiom). [clausify(12)]. 0.40/1.01 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) != apply(beta,D) | -element(D,A) | element(f8(alpha,beta,C,A,B,D),C). [resolve(37,a,33,a)]. 0.40/1.01 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) != apply(delta,D) | -element(D,A) | element(f8(gammma,delta,C,A,B,D),C). [resolve(37,a,34,a)]. 0.40/1.01 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | element(f8(D,A,E,B,C,F),E) | element(f6(D,A,V6,V7,V8),V7) | element(f7(D,A,V6,V7,V8),V6) | -morphism(A,V7,V8) | -morphism(D,V6,V7). [resolve(37,a,36,e)]. 0.40/1.01 38 zero(A) = apply(B,f6(C,B,D,E,A)) | element(f7(C,B,D,E,A),D) | -morphism(B,E,A) | -morphism(C,D,E) | exact(C,B) # label(properties_for_exact) # label(axiom). [clausify(11)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | element(f7(C,B,D,E,A),D) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | element(V8,F) | -element(V9,V7) | apply(C,V9) != V8. [resolve(38,e,32,a)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | element(f7(C,B,D,E,A),D) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) = apply(B,V8) | -element(V9,V7) | apply(C,V9) != V8. [resolve(38,e,35,a)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | element(f7(C,B,D,E,A),D) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | element(f8(C,B,V7,F,V6,V8),V7). [resolve(38,e,37,a)]. 0.40/1.01 39 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | zero(D) != apply(B,F) | -element(F,C) | apply(A,f8(A,B,E,C,D,F)) = F # label(exact_properties) # label(axiom). [clausify(12)]. 0.40/1.01 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) != apply(beta,D) | -element(D,A) | apply(alpha,f8(alpha,beta,C,A,B,D)) = D. [resolve(39,a,33,a)]. 0.40/1.01 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) != apply(delta,D) | -element(D,A) | apply(gammma,f8(gammma,delta,C,A,B,D)) = D. [resolve(39,a,34,a)]. 0.40/1.01 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f8(D,A,E,B,C,F)) = F | element(f6(D,A,V6,V7,V8),V7) | element(f7(D,A,V6,V7,V8),V6) | -morphism(A,V7,V8) | -morphism(D,V6,V7). [resolve(39,a,36,e)]. 0.40/1.01 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f8(D,A,E,B,C,F)) = F | zero(V6) = apply(A,f6(D,A,V7,V8,V6)) | element(f7(D,A,V7,V8,V6),V7) | -morphism(A,V8,V6) | -morphism(D,V7,V8). [resolve(39,a,38,e)]. 0.40/1.01 40 element(f6(A,B,C,D,E),D) | apply(A,f7(A,B,C,D,E)) = f6(A,B,C,D,E) | -morphism(B,D,E) | -morphism(A,C,D) | exact(A,B) # label(properties_for_exact) # label(axiom). [clausify(11)]. 0.40/1.01 Derived: element(f6(A,B,C,D,E),D) | apply(A,f7(A,B,C,D,E)) = f6(A,B,C,D,E) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,F,V6) | -morphism(A,V7,F) | element(V8,F) | -element(V9,V7) | apply(A,V9) != V8. [resolve(40,e,32,a)]. 0.40/1.01 Derived: element(f6(A,B,C,D,E),D) | apply(A,f7(A,B,C,D,E)) = f6(A,B,C,D,E) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(B,V8) | -element(V9,V7) | apply(A,V9) != V8. [resolve(40,e,35,a)]. 0.40/1.01 Derived: element(f6(A,B,C,D,E),D) | apply(A,f7(A,B,C,D,E)) = f6(A,B,C,D,E) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | element(f8(A,B,V7,F,V6,V8),V7). [resolve(40,e,37,a)]. 0.40/1.01 Derived: element(f6(A,B,C,D,E),D) | apply(A,f7(A,B,C,D,E)) = f6(A,B,C,D,E) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | apply(A,f8(A,B,V7,F,V6,V8)) = V8. [resolve(40,e,39,a)]. 0.40/1.01 41 zero(A) = apply(B,f6(C,B,D,E,A)) | apply(C,f7(C,B,D,E,A)) = f6(C,B,D,E,A) | -morphism(B,E,A) | -morphism(C,D,E) | exact(C,B) # label(properties_for_exact) # label(axiom). [clausify(11)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | apply(C,f7(C,B,D,E,A)) = f6(C,B,D,E,A) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | element(V8,F) | -element(V9,V7) | apply(C,V9) != V8. [resolve(41,e,32,a)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | apply(C,f7(C,B,D,E,A)) = f6(C,B,D,E,A) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) = apply(B,V8) | -element(V9,V7) | apply(C,V9) != V8. [resolve(41,e,35,a)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | apply(C,f7(C,B,D,E,A)) = f6(C,B,D,E,A) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | element(f8(C,B,V7,F,V6,V8),V7). [resolve(41,e,37,a)]. 0.40/1.01 Derived: zero(A) = apply(B,f6(C,B,D,E,A)) | apply(C,f7(C,B,D,E,A)) = f6(C,B,D,E,A) | -morphism(B,E,A) | -morphism(C,D,E) | -morphism(B,F,V6) | -morphism(C,V7,F) | zero(V6) != apply(B,V8) | -element(V8,F) | apply(C,f8(C,B,V7,F,V6,V8)) = V8. [resolve(41,e,39,a)]. 0.40/1.01 42 -element(f6(A,B,C,D,E),D) | zero(E) != apply(B,f6(A,B,C,D,E)) | apply(A,F) != f6(A,B,C,D,E) | -element(F,C) | -morphism(B,D,E) | -morphism(A,C,D) | exact(A,B) # label(properties_for_exact) # label(axiom). [clausify(11)]. 0.40/1.01 Derived: -element(f6(A,B,C,D,E),D) | zero(E) != apply(B,f6(A,B,C,D,E)) | apply(A,F) != f6(A,B,C,D,E) | -element(F,C) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | element(V9,V6) | -element(V10,V8) | apply(A,V10) != V9. [resolve(42,g,32,a)]. 0.40/1.01 Derived: -element(f6(A,B,C,D,E),D) | zero(E) != apply(B,f6(A,B,C,D,E)) | apply(A,F) != f6(A,B,C,D,E) | -element(F,C) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | zero(V7) = apply(B,V9) | -element(V10,V8) | apply(A,V10) != V9. [resolve(42,g,35,a)]. 0.40/1.01 Derived: -element(f6(A,B,C,D,E),D) | zero(E) != apply(B,f6(A,B,C,D,E)) | apply(A,F) != f6(A,B,C,D,E) | -element(F,C) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | zero(V7) != apply(B,V9) | -element(V9,V6) | element(f8(A,B,V8,V6,V7,V9),V8). [resolve(42,g,37,a)]. 0.40/1.01 Derived: -element(f6(A,B,C,D,E),D) | zero(E) != apply(B,f6(A,B,C,D,E)) | apply(A,F) != f6(A,B,C,D,E) | -element(F,C) | -morphism(B,D,E) | -morphism(A,C,D) | -morphism(B,V6,V7) | -morphism(A,V8,V6) | zero(V7) != apply(B,V9) | -element(V9,V6) | apply(A,f8(A,B,V8,V6,V7,V9)) = V9. [resolve(42,g,39,a)]. 0.40/1.01 43 -morphism(A,B,C) | -morphism(D,C,E) | -morphism(F,B,V6) | -morphism(V7,V6,E) | -commute(A,D,F,V7) | -element(V8,B) | apply(V7,apply(F,V8)) = apply(D,apply(A,V8)) # label(commute_properties) # label(axiom). [clausify(9)]. 0.40/1.01 44 commute(beta,h,g,delta) # label(beta_h_g_delta_commute) # label(axiom). [assumption]. 0.40/1.01 45 commute(alpha,g,f,gamma) # label(alpha_g_f_gamma_commute) # label(axiom). [assumption]. 0.40/1.01 46 -morphism(A,B,C) | element(f5(D,E,A,F,B,V6,C,V7),B) | -morphism(F,C,V7) | -morphism(E,V6,V7) | -morphism(D,B,V6) | commute(D,E,A,F) # label(properties_for_commute) # label(axiom). [clausify(7)]. 0.40/1.01 Derived: -morphism(beta,A,B) | -morphism(h,B,C) | -morphism(g,A,D) | -morphism(delta,D,C) | -element(E,A) | apply(delta,apply(g,E)) = apply(h,apply(beta,E)). [resolve(43,e,44,a)]. 0.40/1.01 Derived: -morphism(alpha,A,B) | -morphism(g,B,C) | -morphism(f,A,D) | -morphism(gamma,D,C) | -element(E,A) | apply(gamma,apply(f,E)) = apply(g,apply(alpha,E)). [resolve(43,e,45,a)]. 0.40/1.01 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -morphism(F,B,V6) | -morphism(V7,V6,E) | -element(V8,B) | apply(V7,apply(F,V8)) = apply(D,apply(A,V8)) | -morphism(F,V9,V10) | element(f5(A,D,F,V7,V9,V11,V10,V12),V9) | -morphism(V7,V10,V12) | -morphism(D,V11,V12) | -morphism(A,V9,V11). [resolve(43,e,46,f)]. 0.40/1.01 47 -morphism(A,B,C) | apply(D,apply(A,f5(E,F,A,D,B,V6,C,V7))) != apply(F,apply(E,f5(E,F,A,D,B,V6,C,V7))) | -morphism(D,C,V7) | -morphism(F,V6,V7) | -morphism(E,B,V6) | commute(E,F,A,D) # label(properties_for_commute) # label(axiom). [clausify(7)]. 0.40/1.01 Derived: -morphism(A,B,C) | apply(D,apply(A,f5(E,F,A,D,B,V6,C,V7))) != apply(F,apply(E,f5(E,F,A,D,B,V6,C,V7))) | -morphism(D,C,V7) | -morphism(F,V6,V7) | -morphism(E,B,V6) | -morphismAlarm clock 119.55/120.04 Prover9 interrupted 119.55/120.04 EOF