TSTP Solution File: HAL006+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HAL006+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Sat Jul 16 12:45:53 EDT 2022
% Result : Timeout 300.09s 300.35s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : HAL006+1 : TPTP v8.1.0. Released v2.6.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 7 21:13:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 20046 was started by sandbox2 on n029.cluster.edu,
% 0.43/0.99 Tue Jun 7 21:13:51 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19875_n029.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_19875_n029.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (33 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) -> (all El (element(El,Dom) -> element(apply(Morphism,El),Cod))) & apply(Morphism,zero(Dom)) = zero(Cod))) # label(morphism) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 2 (all Morphism all Dom all Cod (injection(Morphism) & morphism(Morphism,Dom,Cod) -> (all El1 all El2 (element(El1,Dom) & element(El2,Dom) & apply(Morphism,El1) = apply(Morphism,El2) -> El1 = El2)))) # label(injection_properties) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 3 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & (all El1 all El2 (element(El1,Dom) & element(El2,Dom) & apply(Morphism,El1) = apply(Morphism,El2) -> El1 = El2)) -> injection(Morphism))) # label(properties_for_injection) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (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].
% 0.43/0.99 5 (all Morphism all Dom all Cod (morphism(Morphism,Dom,Cod) & (all ElCod (element(ElCod,Cod) -> (exists ElDom (element(ElDom,Dom) & apply(Morphism,ElDom) = ElCod)))) -> surjection(Morphism))) # label(properties_for_surjection) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 6 (all Morphism1 all Morphism2 all Dom all CodDom all Cod (exact(Morphism1,Morphism2) & morphism(Morphism1,Dom,CodDom) & morphism(Morphism2,CodDom,Cod) -> (all ElCodDom (element(ElCodDom,CodDom) & apply(Morphism2,ElCodDom) = zero(Cod) <-> (exists ElDom (element(ElDom,Dom) & apply(Morphism1,ElDom) = ElCodDom)))))) # label(exact_properties) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all Morphism1 all Morphism2 all Dom all CodDom all Cod (morphism(Morphism1,Dom,CodDom) & morphism(Morphism2,CodDom,Cod) & (all ElCodDom (element(ElCodDom,CodDom) & apply(Morphism2,ElCodDom) = zero(Cod) <-> (exists ElDom (element(ElDom,Dom) & apply(Morphism1,ElDom) = ElCodDom)))) -> exact(Morphism1,Morphism2))) # label(properties_for_exact) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 (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(M3,Dom,DomCod2) & morphism(M4,DomCod2,Cod) -> (all ElDom (element(ElDom,Dom) -> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)))))) # label(commute_properties) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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) & (all ElDom (element(ElDom,Dom) -> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)))) -> commute(M1,M2,M3,M4))) # label(properties_for_commute) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 (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].
% 0.43/1.00 11 (all Dom all El (element(El,Dom) -> subtract(Dom,El,El) = zero(Dom))) # label(subtract_to_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all Dom all El1 all El2 (element(El1,Dom) & element(El2,Dom) -> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2)) # label(subtract_cancellation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 (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].
% 0.43/1.00 14 (all E (element(E,e) -> (exists R exists B1 (element(R,r) & apply(delta,E) = R & element(B1,b) & apply(h,apply(beta,B1)) = R & apply(delta,apply(g,B1)) = R)))) # label(lemma3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 15 (all E (element(E,e) -> (exists B1 exists E1 exists A (element(B1,b) & element(E1,e) & subtract(e,apply(g,B1),E) = E1 & element(A,a) & apply(gamma,apply(f,A)) = E1 & apply(g,apply(alpha,A)) = E1)))) # label(lemma8) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00 17 -injection(A) | -morphism(A,B,C) | -element(D,B) | -element(E,B) | apply(A,E) != apply(A,D) | E = D # label(injection_properties) # label(axiom). [clausify(2)].
% 0.43/1.00 18 injection(alpha) # label(alpha_injection) # label(axiom). [assumption].
% 0.43/1.00 19 injection(gamma) # label(gamma_injection) # label(axiom). [assumption].
% 0.43/1.00 20 -morphism(A,B,C) | element(f1(A,B,C),B) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(3)].
% 0.43/1.00 21 -morphism(A,B,C) | element(f2(A,B,C),B) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(3)].
% 0.43/1.00 22 -morphism(A,B,C) | f2(A,B,C) != f1(A,B,C) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(3)].
% 0.43/1.00 23 -morphism(A,B,C) | apply(A,f2(A,B,C)) = apply(A,f1(A,B,C)) | injection(A) # label(properties_for_injection) # label(axiom). [clausify(3)].
% 0.43/1.00 Derived: -morphism(alpha,A,B) | -element(C,A) | -element(D,A) | apply(alpha,D) != apply(alpha,C) | D = C. [resolve(17,a,18,a)].
% 0.43/1.00 Derived: -morphism(gamma,A,B) | -element(C,A) | -element(D,A) | apply(gamma,D) != apply(gamma,C) | D = C. [resolve(17,a,19,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -element(D,B) | -element(E,B) | apply(A,E) != apply(A,D) | E = D | -morphism(A,F,V6) | element(f1(A,F,V6),F). [resolve(17,a,20,c)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -element(D,B) | -element(E,B) | apply(A,E) != apply(A,D) | E = D | -morphism(A,F,V6) | element(f2(A,F,V6),F). [resolve(17,a,21,c)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -element(D,B) | -element(E,B) | apply(A,E) != apply(A,D) | E = D | -morphism(A,F,V6) | f2(A,F,V6) != f1(A,F,V6). [resolve(17,a,22,c)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -element(D,B) | -element(E,B) | apply(A,E) != apply(A,D) | E = D | -morphism(A,F,V6) | apply(A,f2(A,F,V6)) = apply(A,f1(A,F,V6)). [resolve(17,a,23,c)].
% 0.43/1.00 24 -surjection(A) | -morphism(A,B,C) | -element(D,C) | element(f3(A,B,C,D),B) # label(surjection_properties) # label(axiom). [clausify(4)].
% 0.43/1.00 25 surjection(beta) # label(beta_surjection) # label(axiom). [assumption].
% 0.43/1.00 26 surjection(delta) # label(delta_surjection) # label(axiom). [assumption].
% 0.43/1.00 27 surjection(f) # label(f_surjection) # label(hypothesis). [assumption].
% 0.43/1.00 28 surjection(h) # label(h_surjection) # label(hypothesis). [assumption].
% 0.43/1.00 29 -morphism(A,B,C) | element(f4(A,B,C),C) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(5)].
% 0.43/1.00 Derived: -morphism(beta,A,B) | -element(C,B) | element(f3(beta,A,B,C),A). [resolve(24,a,25,a)].
% 0.43/1.00 Derived: -morphism(delta,A,B) | -element(C,B) | element(f3(delta,A,B,C),A). [resolve(24,a,26,a)].
% 0.43/1.00 Derived: -morphism(f,A,B) | -element(C,B) | element(f3(f,A,B,C),A). [resolve(24,a,27,a)].
% 0.43/1.00 Derived: -morphism(h,A,B) | -element(C,B) | element(f3(h,A,B,C),A). [resolve(24,a,28,a)].
% 0.43/1.00 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(24,a,29,c)].
% 0.43/1.00 30 -morphism(A,B,C) | -element(D,B) | apply(A,D) != f4(A,B,C) | surjection(A) # label(properties_for_surjection) # label(axiom). [clausify(5)].
% 0.43/1.00 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(30,d,24,a)].
% 0.43/1.00 31 -surjection(A) | -morphism(A,B,C) | -element(D,C) | apply(A,f3(A,B,C,D)) = D # label(surjection_properties) # label(axiom). [clausify(4)].
% 0.43/1.00 Derived: -morphism(beta,A,B) | -element(C,B) | apply(beta,f3(beta,A,B,C)) = C. [resolve(31,a,25,a)].
% 0.43/1.00 Derived: -morphism(delta,A,B) | -element(C,B) | apply(delta,f3(delta,A,B,C)) = C. [resolve(31,a,26,a)].
% 0.43/1.00 Derived: -morphism(f,A,B) | -element(C,B) | apply(f,f3(f,A,B,C)) = C. [resolve(31,a,27,a)].
% 0.43/1.00 Derived: -morphism(h,A,B) | -element(C,B) | apply(h,f3(h,A,B,C)) = C. [resolve(31,a,28,a)].
% 0.43/1.00 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(31,a,29,c)].
% 0.43/1.00 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(31,a,30,d)].
% 0.43/1.00 32 -exact(A,B) | -morphism(A,C,D) | -morphism(B,D,E) | element(F,D) | -element(V6,C) | apply(A,V6) != F # label(exact_properties) # label(axiom). [clausify(6)].
% 0.43/1.00 33 exact(alpha,beta) # label(alpha_beta_exact) # label(axiom). [assumption].
% 0.43/1.00 34 exact(gammma,delta) # label(gamma_delta_exact) # label(axiom). [assumption].
% 0.43/1.00 Derived: -morphism(alpha,A,B) | -morphism(beta,B,C) | element(D,B) | -element(E,A) | apply(alpha,E) != D. [resolve(32,a,33,a)].
% 0.43/1.00 Derived: -morphism(gammma,A,B) | -morphism(delta,B,C) | element(D,B) | -element(E,A) | apply(gammma,E) != D. [resolve(32,a,34,a)].
% 0.43/1.00 35 -exact(A,B) | -morphism(A,C,D) | -morphism(B,D,E) | zero(E) = apply(B,F) | -element(V6,C) | apply(A,V6) != F # label(exact_properties) # label(axiom). [clausify(6)].
% 0.43/1.00 Derived: -morphism(alpha,A,B) | -morphism(beta,B,C) | zero(C) = apply(beta,D) | -element(E,A) | apply(alpha,E) != D. [resolve(35,a,33,a)].
% 0.43/1.00 Derived: -morphism(gammma,A,B) | -morphism(delta,B,C) | zero(C) = apply(delta,D) | -element(E,A) | apply(gammma,E) != D. [resolve(35,a,34,a)].
% 0.43/1.00 36 -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | element(f7(A,D,B,C,E),B) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(7)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | element(f7(A,D,B,C,E),B) | -morphism(A,F,V6) | -morphism(D,V6,V7) | element(V8,V6) | -element(V9,F) | apply(A,V9) != V8. [resolve(36,e,32,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | element(f7(A,D,B,C,E),B) | -morphism(A,F,V6) | -morphism(D,V6,V7) | zero(V7) = apply(D,V8) | -element(V9,F) | apply(A,V9) != V8. [resolve(36,e,35,a)].
% 0.43/1.00 37 -exact(A,B) | -morphism(A,C,D) | -morphism(B,D,E) | -element(F,D) | zero(E) != apply(B,F) | element(f5(A,B,C,D,E,F),C) # label(exact_properties) # label(axiom). [clausify(6)].
% 0.43/1.00 Derived: -morphism(alpha,A,B) | -morphism(beta,B,C) | -element(D,B) | zero(C) != apply(beta,D) | element(f5(alpha,beta,A,B,C,D),A). [resolve(37,a,33,a)].
% 0.43/1.00 Derived: -morphism(gammma,A,B) | -morphism(delta,B,C) | -element(D,B) | zero(C) != apply(delta,D) | element(f5(gammma,delta,A,B,C,D),A). [resolve(37,a,34,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(F,C) | zero(E) != apply(D,F) | element(f5(A,D,B,C,E,F),B) | -morphism(A,V6,V7) | -morphism(D,V7,V8) | element(f6(A,D,V6,V7,V8),V7) | element(f7(A,D,V6,V7,V8),V6). [resolve(37,a,36,e)].
% 0.43/1.00 38 -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | element(f7(A,D,B,C,E),B) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(7)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | element(f7(A,D,B,C,E),B) | -morphism(A,F,V6) | -morphism(D,V6,V7) | element(V8,V6) | -element(V9,F) | apply(A,V9) != V8. [resolve(38,e,32,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | element(f7(A,D,B,C,E),B) | -morphism(A,F,V6) | -morphism(D,V6,V7) | zero(V7) = apply(D,V8) | -element(V9,F) | apply(A,V9) != V8. [resolve(38,e,35,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | element(f7(A,D,B,C,E),B) | -morphism(A,F,V6) | -morphism(D,V6,V7) | -element(V8,V6) | zero(V7) != apply(D,V8) | element(f5(A,D,F,V6,V7,V8),F). [resolve(38,e,37,a)].
% 0.43/1.00 39 -exact(A,B) | -morphism(A,C,D) | -morphism(B,D,E) | -element(F,D) | zero(E) != apply(B,F) | apply(A,f5(A,B,C,D,E,F)) = F # label(exact_properties) # label(axiom). [clausify(6)].
% 0.43/1.00 Derived: -morphism(alpha,A,B) | -morphism(beta,B,C) | -element(D,B) | zero(C) != apply(beta,D) | apply(alpha,f5(alpha,beta,A,B,C,D)) = D. [resolve(39,a,33,a)].
% 0.43/1.00 Derived: -morphism(gammma,A,B) | -morphism(delta,B,C) | -element(D,B) | zero(C) != apply(delta,D) | apply(gammma,f5(gammma,delta,A,B,C,D)) = D. [resolve(39,a,34,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(F,C) | zero(E) != apply(D,F) | apply(A,f5(A,D,B,C,E,F)) = F | -morphism(A,V6,V7) | -morphism(D,V7,V8) | element(f6(A,D,V6,V7,V8),V7) | element(f7(A,D,V6,V7,V8),V6). [resolve(39,a,36,e)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(F,C) | zero(E) != apply(D,F) | apply(A,f5(A,D,B,C,E,F)) = F | -morphism(A,V6,V7) | -morphism(D,V7,V8) | zero(V8) = apply(D,f6(A,D,V6,V7,V8)) | element(f7(A,D,V6,V7,V8),V6). [resolve(39,a,38,e)].
% 0.43/1.00 40 -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(7)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | element(V8,V6) | -element(V9,F) | apply(A,V9) != V8. [resolve(40,e,32,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | zero(V7) = apply(D,V8) | -element(V9,F) | apply(A,V9) != V8. [resolve(40,e,35,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | -element(V8,V6) | zero(V7) != apply(D,V8) | element(f5(A,D,F,V6,V7,V8),F). [resolve(40,e,37,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | element(f6(A,D,B,C,E),C) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | -element(V8,V6) | zero(V7) != apply(D,V8) | apply(A,f5(A,D,F,V6,V7,V8)) = V8. [resolve(40,e,39,a)].
% 0.43/1.00 41 -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(7)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | element(V8,V6) | -element(V9,F) | apply(A,V9) != V8. [resolve(41,e,32,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | zero(V7) = apply(D,V8) | -element(V9,F) | apply(A,V9) != V8. [resolve(41,e,35,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | -element(V8,V6) | zero(V7) != apply(D,V8) | element(f5(A,D,F,V6,V7,V8),F). [resolve(41,e,37,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | zero(E) = apply(D,f6(A,D,B,C,E)) | apply(A,f7(A,D,B,C,E)) = f6(A,D,B,C,E) | -morphism(A,F,V6) | -morphism(D,V6,V7) | -element(V8,V6) | zero(V7) != apply(D,V8) | apply(A,f5(A,D,F,V6,V7,V8)) = V8. [resolve(41,e,39,a)].
% 0.43/1.00 42 -morphism(A,B,C) | -morphism(D,C,E) | -element(f6(A,D,B,C,E),C) | zero(E) != apply(D,f6(A,D,B,C,E)) | -element(F,B) | apply(A,F) != f6(A,D,B,C,E) | exact(A,D) # label(properties_for_exact) # label(axiom). [clausify(7)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(f6(A,D,B,C,E),C) | zero(E) != apply(D,f6(A,D,B,C,E)) | -element(F,B) | apply(A,F) != f6(A,D,B,C,E) | -morphism(A,V6,V7) | -morphism(D,V7,V8) | element(V9,V7) | -element(V10,V6) | apply(A,V10) != V9. [resolve(42,g,32,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(f6(A,D,B,C,E),C) | zero(E) != apply(D,f6(A,D,B,C,E)) | -element(F,B) | apply(A,F) != f6(A,D,B,C,E) | -morphism(A,V6,V7) | -morphism(D,V7,V8) | zero(V8) = apply(D,V9) | -element(V10,V6) | apply(A,V10) != V9. [resolve(42,g,35,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(f6(A,D,B,C,E),C) | zero(E) != apply(D,f6(A,D,B,C,E)) | -element(F,B) | apply(A,F) != f6(A,D,B,C,E) | -morphism(A,V6,V7) | -morphism(D,V7,V8) | -element(V9,V7) | zero(V8) != apply(D,V9) | element(f5(A,D,V6,V7,V8,V9),V6). [resolve(42,g,37,a)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -element(f6(A,D,B,C,E),C) | zero(E) != apply(D,f6(A,D,B,C,E)) | -element(F,B) | apply(A,F) != f6(A,D,B,C,E) | -morphism(A,V6,V7) | -morphism(D,V7,V8) | -element(V9,V7) | zero(V8) != apply(D,V9) | apply(A,f5(A,D,V6,V7,V8,V9)) = V9. [resolve(42,g,39,a)].
% 0.43/1.00 43 -commute(A,B,C,D) | -morphism(A,E,F) | -morphism(B,F,V6) | -morphism(C,E,V7) | -morphism(D,V7,V6) | -element(V8,E) | apply(D,apply(C,V8)) = apply(B,apply(A,V8)) # label(commute_properties) # label(axiom). [clausify(8)].
% 0.43/1.00 44 commute(alpha,g,f,gamma) # label(alpha_g_f_gamma_commute) # label(axiom). [assumption].
% 0.43/1.00 45 commute(beta,h,g,delta) # label(beta_h_g_delta_commute) # label(axiom). [assumption].
% 0.43/1.00 46 -morphism(A,B,C) | -morphism(D,C,E) | -morphism(F,B,V6) | -morphism(V7,V6,E) | element(f8(A,D,F,V7,B,C,V6,E),B) | commute(A,D,F,V7) # label(properties_for_commute) # label(axiom). [clausify(9)].
% 0.43/1.00 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,a,44,a)].
% 0.43/1.00 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,a,45,a)].
% 0.43/1.00 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(A,V9,V10) | -morphism(D,V10,V11) | -morphism(F,V9,V12) | -morphism(V7,V12,V11) | element(f8(A,D,F,V7,V9,V10,V12,V11),V9). [resolve(43,a,46,f)].
% 0.43/1.00 47 -morphism(A,B,C) | -morphism(D,C,E) | -morphism(F,B,V6) | -morphism(V7,V6,E) | apply(V7,apply(F,f8(A,D,F,V7,B,C,V6,E))) != apply(D,apply(A,f8(A,D,F,V7,B,C,V6,E))) | commute(A,D,F,V7) # label(properties_for_commute) # label(axiom). [clausify(9)].
% 0.43/1.00 Derived: -morphism(A,B,C) | -morphism(D,C,E) | -morphism(F,B,V6) | -morphism(V7,V6,E) | apply(V7,apply(F,f8(A,D,F,V7,B,C,V6,E))) != apply(D,apply(A,f8(A,D,F,V7,B,C,V6,E))) | -morpCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------