0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.33 % Computer : n025.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % WCLimit : 120 0.13/0.33 % DateTime : Tue Aug 9 04:30:11 EDT 2022 0.13/0.34 % CPUTime : 0.43/1.02 ============================== Prover9 =============================== 0.43/1.02 Prover9 (32) version 2009-11A, November 2009. 0.43/1.02 Process 28189 was started by sandbox on n025.cluster.edu, 0.43/1.02 Tue Aug 9 04:30:11 2022 0.43/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_27993_n025.cluster.edu". 0.43/1.02 ============================== end of head =========================== 0.43/1.02 0.43/1.02 ============================== INPUT ================================= 0.43/1.02 0.43/1.02 % Reading from file /tmp/Prover9_27993_n025.cluster.edu 0.43/1.02 0.43/1.02 set(prolog_style_variables). 0.43/1.02 set(auto2). 0.43/1.02 % set(auto2) -> set(auto). 0.43/1.02 % set(auto) -> set(auto_inference). 0.43/1.02 % set(auto) -> set(auto_setup). 0.43/1.02 % set(auto_setup) -> set(predicate_elim). 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold). 0.43/1.02 % set(auto) -> set(auto_limits). 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000). 0.43/1.02 % set(auto) -> set(auto_denials). 0.43/1.02 % set(auto) -> set(auto_process). 0.43/1.02 % set(auto2) -> assign(new_constants, 1). 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3). 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000"). 0.43/1.02 % set(auto2) -> assign(max_hours, 1). 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.43/1.02 % set(auto2) -> assign(max_seconds, 0). 0.43/1.02 % set(auto2) -> assign(max_minutes, 5). 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.43/1.02 % set(auto2) -> set(sort_initial_sos). 0.43/1.02 % set(auto2) -> assign(sos_limit, -1). 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000). 0.43/1.02 % set(auto2) -> assign(max_megs, 400). 0.43/1.02 % set(auto2) -> assign(stats, some). 0.43/1.02 % set(auto2) -> clear(echo_input). 0.43/1.02 % set(auto2) -> set(quiet). 0.43/1.02 % set(auto2) -> clear(print_initial_clauses). 0.43/1.02 % set(auto2) -> clear(print_given). 0.43/1.02 assign(lrs_ticks,-1). 0.43/1.02 assign(sos_limit,10000). 0.43/1.02 assign(order,kbo). 0.43/1.02 set(lex_order_vars). 0.43/1.02 clear(print_given). 0.43/1.02 0.43/1.02 % formulas(sos). % not echoed (31 formulas) 0.43/1.02 0.43/1.02 ============================== end of input ========================== 0.43/1.02 0.43/1.02 % From the command line: assign(max_seconds, 960). 0.43/1.02 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.43/1.02 0.43/1.02 % Formulas that are not ordinary clauses: 0.43/1.02 1 (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]. 0.43/1.02 2 (all M1 all M2 all M3 all M4 all Dom all DomCod1 all DomCod2 all Cod (commute(M1,M2,M3,M4) & morphism(M1,Dom,DomCod1) & morphism(M2,DomCod1,Cod) & morphism(M4,DomCod2,Cod) & morphism(M3,Dom,DomCod2) -> (all ElDom (element(ElDom,Dom) -> apply(M4,apply(M3,ElDom)) = apply(M2,apply(M1,ElDom)))))) # label(commute_properties) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 3 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & surjection(Morphism) -> (all ElCod (element(ElCod,Cod) -> (exists ElDom (ElCod = apply(Morphism,ElDom) & element(ElDom,Dom))))))) # label(surjection_properties) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 4 (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]. 0.43/1.02 5 (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]. 0.43/1.02 6 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) -> (all El1 all El2 (element(El1,Dom) & element(El2,Dom) -> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)))))) # label(subtract_distribution) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 7 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & (all El1 all El2 (apply(Morphism,El2) = apply(Morphism,El1) & element(El2,Dom) & element(El1,Dom) -> El2 = El1)) -> injection(Morphism))) # label(properties_for_injection) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 8 (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 (apply(Morphism1,ElDom) = ElCodDom & element(ElDom,Dom))))))) # label(exact_properties) # label(axiom) # label(non_clause). [assumption]. 0.43/1.03 9 (all Dom all El (element(El,Dom) -> subtract(Dom,El,El) = zero(Dom))) # label(subtract_to_0) # label(axiom) # label(non_clause). [assumption]. 0.43/1.03 10 (all Morphism1 all Morphism2 all Dom all CodDom all Cod (morphism(Morphism1,Dom,CodDom) & (all ElCodDom ((exists ElDom (ElCodDom = apply(Morphism1,ElDom) & element(ElDom,Dom))) <-> element(ElCodDom,CodDom) & apply(Morphism2,ElCodDom) = zero(Cod))) & morphism(Morphism2,CodDom,Cod) -> exact(Morphism1,Morphism2))) # label(properties_for_exact) # label(axiom) # label(non_clause). [assumption]. 0.43/1.03 11 (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]. 0.43/1.03 12 (all Morphism all Dom all Cod (injection(Morphism) & morphism(Morphism,Dom,Cod) -> (all El1 all El2 (element(El1,Dom) & apply(Morphism,El2) = apply(Morphism,El1) & element(El2,Dom) -> El1 = El2)))) # label(injection_properties) # label(axiom) # label(non_clause). [assumption]. 0.43/1.03 13 (all M1 all M2 all M3 all M4 all Dom all DomCod1 all DomCod2 all Cod (morphism(M2,DomCod1,Cod) & morphism(M4,DomCod2,Cod) & (all ElDom (element(ElDom,Dom) -> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)))) & morphism(M3,Dom,DomCod2) & morphism(M1,Dom,DomCod1) -> commute(M1,M2,M3,M4))) # label(properties_for_commute) # label(axiom) # label(non_clause). [assumption]. 0.43/1.03 14 -(all E (element(E,e) -> (exists R exists B1 (element(R,r) & apply(delta,E) = R & element(B1,b) & R = apply(h,apply(beta,B1)) & apply(delta,apply(g,B1)) = R)))) # label(lemma3) # label(negated_conjecture) # label(non_clause). [assumption]. 0.43/1.03 0.43/1.03 ============================== end of process non-clausal formulas === 0.43/1.03 0.43/1.03 ============================== PROCESS INITIAL CLAUSES =============== 0.43/1.03 0.43/1.03 ============================== PREDICATE ELIMINATION ================= 0.43/1.03 15 -morphism(A,B,C) | -surjection(A) | -element(D,C) | element(f1(A,B,C,D),B) # label(surjection_properties) # label(axiom). [clausify(3)]. 0.43/1.03 16 surjection(h) # label(h_surjection) # label(hypothesis). [assumption]. 0.43/1.03 17 surjection(f) # label(f_surjection) # label(hypothesis). [assumption]. 0.43/1.03 18 surjection(delta) # label(delta_surjection) # label(axiom). [assumption]. 0.43/1.03 19 surjection(beta) # label(beta_surjection) # label(axiom). [assumption]. 0.43/1.03 20 -morphism(A,B,C) | element(f2(A,B,C),C) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(5)]. 0.43/1.03 Derived: -morphism(h,A,B) | -element(C,B) | element(f1(h,A,B,C),A). [resolve(15,b,16,a)]. 0.43/1.03 Derived: -morphism(f,A,B) | -element(C,B) | element(f1(f,A,B,C),A). [resolve(15,b,17,a)]. 0.43/1.03 Derived: -morphism(delta,A,B) | -element(C,B) | element(f1(delta,A,B,C),A). [resolve(15,b,18,a)]. 0.43/1.03 Derived: -morphism(beta,A,B) | -element(C,B) | element(f1(beta,A,B,C),A). [resolve(15,b,19,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,C) | element(f1(A,B,C,D),B) | -morphism(A,E,F) | element(f2(A,E,F),F). [resolve(15,b,20,c)]. 0.43/1.03 21 -morphism(A,B,C) | apply(A,D) != f2(A,B,C) | -element(D,B) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(5)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,D) != f2(A,B,C) | -element(D,B) | -morphism(A,E,F) | -element(V6,F) | element(f1(A,E,F,V6),E). [resolve(21,d,15,b)]. 0.43/1.03 22 -morphism(A,B,C) | -surjection(A) | -element(D,C) | apply(A,f1(A,B,C,D)) = D # label(surjection_properties) # label(axiom). [clausify(3)]. 0.43/1.03 Derived: -morphism(h,A,B) | -element(C,B) | apply(h,f1(h,A,B,C)) = C. [resolve(22,b,16,a)]. 0.43/1.03 Derived: -morphism(f,A,B) | -element(C,B) | apply(f,f1(f,A,B,C)) = C. [resolve(22,b,17,a)]. 0.43/1.03 Derived: -morphism(delta,A,B) | -element(C,B) | apply(delta,f1(delta,A,B,C)) = C. [resolve(22,b,18,a)]. 0.43/1.03 Derived: -morphism(beta,A,B) | -element(C,B) | apply(beta,f1(beta,A,B,C)) = C. [resolve(22,b,19,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,C) | apply(A,f1(A,B,C,D)) = D | -morphism(A,E,F) | element(f2(A,E,F),F). [resolve(22,b,20,c)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,C) | apply(A,f1(A,B,C,D)) = D | -morphism(A,E,F) | apply(A,V6) != f2(A,E,F) | -element(V6,E). [resolve(22,b,21,d)]. 0.43/1.03 23 -injection(A) | -morphism(A,B,C) | -element(D,B) | apply(A,E) != apply(A,D) | -element(E,B) | E = D # label(injection_properties) # label(axiom). [clausify(12)]. 0.43/1.03 24 injection(gamma) # label(gamma_injection) # label(axiom). [assumption]. 0.43/1.03 25 injection(alpha) # label(alpha_injection) # label(axiom). [assumption]. 0.43/1.03 26 -morphism(A,B,C) | element(f4(A,B,C),B) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(7)]. 0.43/1.03 27 -morphism(A,B,C) | element(f3(A,B,C),B) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(7)]. 0.43/1.03 28 -morphism(A,B,C) | f4(A,B,C) != f3(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(7)]. 0.43/1.03 29 -morphism(A,B,C) | apply(A,f4(A,B,C)) = apply(A,f3(A,B,C)) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(7)]. 0.43/1.03 Derived: -morphism(gamma,A,B) | -element(C,A) | apply(gamma,D) != apply(gamma,C) | -element(D,A) | D = C. [resolve(23,a,24,a)]. 0.43/1.03 Derived: -morphism(alpha,A,B) | -element(C,A) | apply(alpha,D) != apply(alpha,C) | -element(D,A) | D = C. [resolve(23,a,25,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,E) != apply(A,D) | -element(E,B) | E = D | -morphism(A,F,V6) | element(f4(A,F,V6),F). [resolve(23,a,26,c)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,E) != apply(A,D) | -element(E,B) | E = D | -morphism(A,F,V6) | element(f3(A,F,V6),F). [resolve(23,a,27,c)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,E) != apply(A,D) | -element(E,B) | E = D | -morphism(A,F,V6) | f4(A,F,V6) != f3(A,F,V6). [resolve(23,a,28,c)]. 0.43/1.03 Derived: -morphism(A,B,C) | -element(D,B) | apply(A,E) != apply(A,D) | -element(E,B) | E = D | -morphism(A,F,V6) | apply(A,f4(A,F,V6)) = apply(A,f3(A,F,V6)). [resolve(23,a,29,c)]. 0.43/1.03 30 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | element(F,C) | apply(A,V6) != F | -element(V6,E) # label(exact_properties) # label(axiom). [clausify(8)]. 0.43/1.03 31 exact(alpha,beta) # label(alpha_beta_exact) # label(axiom). [assumption]. 0.43/1.03 32 exact(gammma,delta) # label(gamma_delta_exact) # label(axiom). [assumption]. 0.43/1.03 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | element(D,A) | apply(alpha,E) != D | -element(E,C). [resolve(30,a,31,a)]. 0.43/1.03 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | element(D,A) | apply(gammma,E) != D | -element(E,C). [resolve(30,a,32,a)]. 0.43/1.03 33 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | zero(D) = apply(B,F) | apply(A,V6) != F | -element(V6,E) # label(exact_properties) # label(axiom). [clausify(8)]. 0.43/1.03 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) = apply(beta,D) | apply(alpha,E) != D | -element(E,C). [resolve(33,a,31,a)]. 0.43/1.03 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) = apply(delta,D) | apply(gammma,E) != D | -element(E,C). [resolve(33,a,32,a)]. 0.43/1.03 34 -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(10)]. 0.43/1.03 Derived: -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | element(V8,F) | apply(A,V9) != V8 | -element(V9,V7). [resolve(34,e,30,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(D,V8) | apply(A,V9) != V8 | -element(V9,V7). [resolve(34,e,33,a)]. 0.43/1.03 35 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | zero(D) != apply(B,F) | -element(F,C) | element(f5(A,B,E,C,D,F),E) # label(exact_properties) # label(axiom). [clausify(8)]. 0.43/1.03 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) != apply(beta,D) | -element(D,A) | element(f5(alpha,beta,C,A,B,D),C). [resolve(35,a,31,a)]. 0.43/1.03 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) != apply(delta,D) | -element(D,A) | element(f5(gammma,delta,C,A,B,D),C). [resolve(35,a,32,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | element(f5(D,A,E,B,C,F),E) | -morphism(D,V6,V7) | element(f7(D,A,V6,V7,V8),V6) | element(f6(D,A,V6,V7,V8),V7) | -morphism(A,V7,V8). [resolve(35,a,34,e)]. 0.43/1.03 36 -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(10)]. 0.43/1.03 Derived: -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | element(V8,F) | apply(A,V9) != V8 | -element(V9,V7). [resolve(36,e,30,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(D,V8) | apply(A,V9) != V8 | -element(V9,V7). [resolve(36,e,33,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | element(f7(A,D,B,C,E),B) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(D,V8) | -element(V8,F) | element(f5(A,D,V7,F,V6,V8),V7). [resolve(36,e,35,a)]. 0.43/1.03 37 -exact(A,B) | -morphism(B,C,D) | -morphism(A,E,C) | zero(D) != apply(B,F) | -element(F,C) | apply(A,f5(A,B,E,C,D,F)) = F # label(exact_properties) # label(axiom). [clausify(8)]. 0.43/1.03 Derived: -morphism(beta,A,B) | -morphism(alpha,C,A) | zero(B) != apply(beta,D) | -element(D,A) | apply(alpha,f5(alpha,beta,C,A,B,D)) = D. [resolve(37,a,31,a)]. 0.43/1.03 Derived: -morphism(delta,A,B) | -morphism(gammma,C,A) | zero(B) != apply(delta,D) | -element(D,A) | apply(gammma,f5(gammma,delta,C,A,B,D)) = D. [resolve(37,a,32,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f5(D,A,E,B,C,F)) = F | -morphism(D,V6,V7) | element(f7(D,A,V6,V7,V8),V6) | element(f6(D,A,V6,V7,V8),V7) | -morphism(A,V7,V8). [resolve(37,a,34,e)]. 0.43/1.03 Derived: -morphism(A,B,C) | -morphism(D,E,B) | zero(C) != apply(A,F) | -element(F,B) | apply(D,f5(D,A,E,B,C,F)) = F | -morphism(D,V6,V7) | element(f7(D,A,V6,V7,V8),V6) | zero(V8) = apply(A,f6(D,A,V6,V7,V8)) | -morphism(A,V7,V8). [resolve(37,a,36,e)]. 0.43/1.03 38 -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(10)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | element(V8,F) | apply(A,V9) != V8 | -element(V9,V7). [resolve(38,e,30,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(D,V8) | apply(A,V9) != V8 | -element(V9,V7). [resolve(38,e,33,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(D,V8) | -element(V8,F) | element(f5(A,D,V7,F,V6,V8),V7). [resolve(38,e,35,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | element(f6(A,D,B,C,E),C) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(D,V8) | -element(V8,F) | apply(A,f5(A,D,V7,F,V6,V8)) = V8. [resolve(38,e,37,a)]. 0.43/1.03 39 -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(10)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | element(V8,F) | apply(A,V9) != V8 | -element(V9,V7). [resolve(39,e,30,a)]. 0.43/1.03 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) = apply(D,V8) | apply(A,V9) != V8 | -element(V9,V7). [resolve(39,e,33,a)]. 4.56/4.85 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(D,V8) | -element(V8,F) | element(f5(A,D,V7,F,V6,V8),V7). [resolve(39,e,35,a)]. 4.56/4.85 Derived: -morphism(A,B,C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | -morphism(D,C,E) | -morphism(D,F,V6) | -morphism(A,V7,F) | zero(V6) != apply(D,V8) | -element(V8,F) | apply(A,f5(A,D,V7,F,V6,V8)) = V8. [resolve(39,e,37,a)]. 4.56/4.85 40 -morphism(A,B,C) | apply(A,D) != f6(A,E,B,C,F) | -element(D,B) | -element(f6(A,E,B,C,F),C) | zero(F) != apply(E,f6(A,E,B,C,F)) | -morphism(E,C,F) | exact(A,E) # label(properties_for_exact) # label(axiom). [clausify(10)]. 4.56/4.85 Derived: -morphism(A,B,C) | apply(A,D) != f6(A,E,B,C,F) | -element(D,B) | -element(f6(A,E,B,C,F),C) | zero(F) != apply(E,f6(A,E,B,C,F)) | -morphism(E,C,F) | -morphism(E,V6,V7) | -morphism(A,V8,V6) | element(V9,V6) | apply(A,V10) != V9 | -element(V10,V8). [resolve(40,g,30,a)]. 4.56/4.85 Derived: -morphism(A,B,C) | apply(A,D) != f6(A,E,B,C,F) | -element(D,B) | -element(f6(A,E,B,C,F),C) | zero(F) != apply(E,f6(A,E,B,C,F)) | -morphism(E,C,F) | -morphism(E,V6,V7) | -morphism(A,V8,V6) | zero(V7) = apply(E,V9) | apply(A,V10) != V9 | -element(V10,V8). [resolve(40,g,33,a)]. 4.56/4.85 Derived: -morphism(A,B,C) | apply(A,D) != f6(A,E,B,C,F) | -element(D,B) | -element(f6(A,E,B,C,F),C) | zero(F) != apply(E,f6(A,E,B,C,F)) | -morphism(E,C,F) | -morphism(E,V6,V7) | -morphism(A,V8,V6) | zero(V7) != apply(E,V9) | -element(V9,V6) | element(f5(A,E,V8,V6,V7,V9),V8). [resolve(40,g,35,a)]. 4.56/4.85 Derived: -morphism(A,B,C) | apply(A,D) != f6(A,E,B,C,F) | -element(D,B) | -element(f6(A,E,B,C,F),C) | zero(F) != apply(E,f6(A,E,B,C,F)) | -morphism(E,C,F) | -morphism(E,V6,V7) | -morphism(A,V8,V6) | zero(V7) != apply(E,V9) | -element(V9,V6) | apply(A,f5(A,E,V8,V6,V7,V9)) = V9. [resolve(40,g,37,a)]. 4.56/4.85 41 -commute(A,B,C,D) | -morphism(A,E,F) | -morphism(B,F,V6) | -morphism(D,V7,V6) | -morphism(C,E,V7) | -element(V8,E) | apply(D,apply(C,V8)) = apply(B,apply(A,V8)) # label(commute_properties) # label(axiom). [clausify(2)]. 4.56/4.85 42 commute(alpha,g,f,gamma) # label(alpha_g_f_gamma_commute) # label(axiom). [assumption]. 4.56/4.85 43 commute(beta,h,g,delta) # label(beta_h_g_delta_commute) # label(axiom). [assumption]. 4.56/4.85 44 -morphism(A,B,C) | -morphism(D,E,C) | element(f8(F,A,V6,D,V7,B,E,C),V7) | -morphism(V6,V7,E) | -morphism(F,V7,B) | commute(F,A,V6,D) # label(properties_for_commute) # label(axiom). [clausify(13)]. 4.56/4.85 Derived: -morphism(alpha,A,B) | -morphism(g,B,C) | -morphism(gamma,D,C) | -morphism(f,A,D) | -element(E,A) | apply(gamma,apply(f,E)) = apply(g,apply(alpha,E)). [resolve(41,a,42,a)]. 4.56/4.85 Derived: -morphism(beta,A,B) | -morphism(h,B,C) | -morphism(delta,D,C) | -morphism(g,A,D) | -element(E,A) | apply(delta,apply(g,E)) = apply(h,apply(beta,E)). [resolve(41,a,43,a)]. 4.56/4.85 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -morphism(F,V6,E) | -morphism(V7,B,V6) | -element(V8,B) | apply(F,apply(V7,V8)) = apply(D,apply(A,V8)) | -morphism(D,V9,V10) | -morphism(F,V11,V10) | element(f8(A,D,V7,F,V12,V9,V11,V10),V12) | -morphism(V7,V12,V11) | -morphism(A,V12,V9). [resolve(41,a,44,f)]. 4.56/4.85 45 -morphism(A,B,C) | -morphism(D,E,C) | apply(D,apply(F,f8(V6,A,F,D,V7,B,E,C))) != apply(A,apply(V6,f8(V6,A,F,D,V7,B,E,C))) | -morphism(F,V7,E) | -morphism(V6,V7,B) | commute(V6,A,F,D) # label(properties_for_commute) # label(axiom). [clausify(13)]. 4.56/4.85 Derived: -morphism(A,B,C) | -morphism(D,E,C) | apply(D,apply(F,f8(V6,A,F,D,V7,B,E,C))) != apply(A,apply(V6,f8(V6,A,F,D,V7,B,E,C))) | -morphism(F,V7,E) | -morphism(V6,V7,B) | -morphism(V6,V8,V9) | -morphism(A,V9,V10) | -morphism(D,V11,V10) | -morphism(F,V8,V11) | -element(V12,V8) | apply(D,apply(F,V12)) = apply(A,apply(V6,V12)). [resolve(45,f,41,a)]. 4.56/4.85 4.56/4.85 ============================== end predicate elimination ============= 4.56/4.85 4.56/4.85 Auto_denials: (non-Horn, no changes). 4.56/4.85 4.56/4.85 Term ordering decisions: 4.56/4.85 4.56/4.85 % Assigning unary symbol zero kb_weight 0 and highest precedence (29). 4.56/4.85 Function symbol KB weights: beta=1. delta=1. alpha=1. gammma=1. f=1. h=Alarm clock 119.51/120.02 Prover9 interrupted 119.51/120.03 EOF