TSTP Solution File: KLE180+1 by Mace4---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Mace4---1109a
% Problem : KLE180+1 : TPTP v6.4.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : mace4 -t %d -f %s
% Computer : n136.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.75MB
% OS : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Feb 8 09:56:14 EST 2017
% Result : Satisfiable 0.07s
% Output : FiniteModel 0.07s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE180+1 : TPTP v6.4.0. Released v6.4.0.
% 0.00/0.04 % Command : mace4 -t %d -f %s
% 0.02/0.23 % Computer : n136.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.75MB
% 0.02/0.23 % OS : Linux 3.10.0-327.36.3.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Tue Feb 7 19:39:00 CST 2017
% 0.02/0.24 % CPUTime :
% 0.07/0.45 % SZS status Satisfiable
% 0.07/0.45 ============================== Mace4 =================================
% 0.07/0.45 Mace4 (32) version 2009-11A, November 2009.
% 0.07/0.45 Process 35316 was started by sandbox2 on n136.star.cs.uiowa.edu,
% 0.07/0.45 Tue Feb 7 19:39:01 2017
% 0.07/0.45 The command was "/export/starexec/sandbox2/solver/bin/mace4 -t 300 -f /tmp/Mace4_input_35283_n136.star.cs.uiowa.edu".
% 0.07/0.45 ============================== end of head ===========================
% 0.07/0.45
% 0.07/0.45 ============================== INPUT =================================
% 0.07/0.45
% 0.07/0.45 % Reading from file /tmp/Mace4_input_35283_n136.star.cs.uiowa.edu
% 0.07/0.45
% 0.07/0.45 set(prolog_style_variables).
% 0.07/0.45 set(print_models_tabular).
% 0.07/0.45 % set(print_models_tabular) -> clear(print_models).
% 0.07/0.45
% 0.07/0.45 formulas(sos).
% 0.07/0.45 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom).
% 0.07/0.45 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom).
% 0.07/0.45 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom).
% 0.07/0.45 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom).
% 0.07/0.45 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom).
% 0.07/0.45 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom).
% 0.07/0.45 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom).
% 0.07/0.45 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom).
% 0.07/0.45 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom).
% 0.07/0.45 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom).
% 0.07/0.45 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom).
% 0.07/0.45 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom).
% 0.07/0.45 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom).
% 0.07/0.45 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom).
% 0.07/0.45 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom).
% 0.07/0.45 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom).
% 0.07/0.45 (all A multiplication(A,omega(A)) = omega(A)) # label(omega_unfold) # label(axiom).
% 0.07/0.45 (all A all B all C (leq(A,addition(multiplication(B,A),C)) -> leq(A,addition(omega(B),multiplication(star(B),C))))) # label(omega_co_induction) # label(axiom).
% 0.07/0.45 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom).
% 0.07/0.45 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom).
% 0.07/0.45 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom).
% 0.07/0.45 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom).
% 0.07/0.45 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom).
% 0.07/0.45 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom).
% 0.07/0.45 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom).
% 0.07/0.45 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom).
% 0.07/0.45 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom).
% 0.07/0.45 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom).
% 0.07/0.45 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom).
% 0.07/0.45 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom).
% 0.07/0.45 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom).
% 0.07/0.45 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom).
% 0.07/0.45 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom).
% 0.07/0.45 (all X0 all X1 all X2 (addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2)) -> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))))) # label(divergence2) # label(axiom).
% 0.07/0.45 end_of_list.
% 0.07/0.45
% 0.07/0.45 % From the command line: assign(max_seconds, 300).
% 0.07/0.45
% 0.07/0.45 ============================== end of input ==========================
% 0.07/0.45
% 0.07/0.45 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.07/0.45
% 0.07/0.45 % Formulas that are not ordinary clauses:
% 0.07/0.45 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 17 (all A multiplication(A,omega(A)) = omega(A)) # label(omega_unfold) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 18 (all A all B all C (leq(A,addition(multiplication(B,A),C)) -> leq(A,addition(omega(B),multiplication(star(B),C))))) # label(omega_co_induction) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 19 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 20 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 21 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 22 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 23 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 24 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 25 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 26 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 27 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 28 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 29 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 30 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 31 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 32 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 33 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45 34 (all X0 all X1 all X2 (addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2)) -> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))))) # label(divergence2) # label(axiom) # label(non_clause). [assumption].
% 0.07/0.45
% 0.07/0.45 ============================== end of process non-clausal formulas ===
% 0.07/0.45
% 0.07/0.45 ============================== CLAUSES FOR SEARCH ====================
% 0.07/0.45
% 0.07/0.45 formulas(mace4_clauses).
% 0.07/0.45 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).
% 0.07/0.45 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).
% 0.07/0.45 addition(A,zero) = A # label(additive_identity) # label(axiom).
% 0.07/0.45 addition(A,A) = A # label(additive_idempotence) # label(axiom).
% 0.07/0.45 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).
% 0.07/0.45 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).
% 0.07/0.45 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).
% 0.07/0.45 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).
% 0.07/0.45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).
% 0.07/0.45 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).
% 0.07/0.45 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).
% 0.07/0.45 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).
% 0.07/0.45 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).
% 0.07/0.45 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom).
% 0.07/0.45 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom).
% 0.07/0.45 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom).
% 0.07/0.45 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom).
% 0.07/0.45 omega(A) = multiplication(A,omega(A)) # label(omega_unfold) # label(axiom).
% 0.07/0.45 -leq(A,addition(multiplication(B,A),C)) | leq(A,addition(omega(B),multiplication(star(B),C))) # label(omega_co_induction) # label(axiom).
% 0.07/0.45 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom).
% 0.07/0.45 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom).
% 0.07/0.45 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom).
% 0.07/0.45 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom).
% 0.07/0.45 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom).
% 0.07/0.45 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom).
% 0.07/0.45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom).
% 0.07/0.45 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom).
% 0.07/0.45 c(A) = antidomain(domain(A)) # label(complement) # label(axiom).
% 0.07/0.45 domain_difference(A,B) = multiplication(domain(A),antidomain(B)) # label(domain_difference) # label(axiom).
% 0.07/0.45 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom).
% 0.07/0.45 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom).
% 0.07/0.45 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom).
% 0.07/0.45 backward_box(A,B) = c(backward_diamond(A,c(B))) # label(backward_box) # label(axiom).
% 0.07/0.45 divergence(A) = forward_diamond(A,divergence(A)) # label(divergence1) # label(axiom).
% 0.07/0.45 addition(forward_diamond(A,domain(B)),domain(C)) != addition(domain(B),addition(forward_diamond(A,domain(B)),domain(C))) | addition(divergence(A),forward_diamond(star(A),domain(C))) = addition(domain(B),addition(divergence(A),forward_diamond(star(A),domain(C)))) # label(divergence2) # label(axiom).
% 0.07/0.45 end_of_list.
% 0.07/0.45
% 0.07/0.45 ============================== end of clauses for search =============
% 0.07/0.45 % SZS output start FiniteModel
% 0.07/0.45
% 0.07/0.45 % There are no natural numbers in the input.
% 0.07/0.45
% 0.07/0.45 one : 0
% 0.07/0.45
% 0.07/0.45 zero : 1
% 0.07/0.45
% 0.07/0.45 antidomain :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 1 0
% 0.07/0.45
% 0.07/0.45 c :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 1 0
% 0.07/0.45
% 0.07/0.45 coantidomain :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 1 0
% 0.07/0.45
% 0.07/0.45 codomain :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 0 1
% 0.07/0.45
% 0.07/0.45 divergence :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 0 1
% 0.07/0.45
% 0.07/0.45 domain :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 0 1
% 0.07/0.45
% 0.07/0.45 omega :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 0 1
% 0.07/0.45
% 0.07/0.45 star :
% 0.07/0.45 0 1
% 0.07/0.45 -------
% 0.07/0.45 0 0
% 0.07/0.45
% 0.07/0.45 addition :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 0 0
% 0.07/0.45 1 | 0 1
% 0.07/0.45
% 0.07/0.45 backward_box :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 0 1
% 0.07/0.45 1 | 0 0
% 0.07/0.45
% 0.07/0.45 backward_diamond :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 0 1
% 0.07/0.45 1 | 1 1
% 0.07/0.45
% 0.07/0.45 domain_difference :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 1 0
% 0.07/0.45 1 | 1 1
% 0.07/0.45
% 0.07/0.45 forward_box :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 0 1
% 0.07/0.45 1 | 0 0
% 0.07/0.45
% 0.07/0.45 forward_diamond :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 0 1
% 0.07/0.45 1 | 1 1
% 0.07/0.45
% 0.07/0.45 multiplication :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 0 1
% 0.07/0.45 1 | 1 1
% 0.07/0.45
% 0.07/0.45 leq :
% 0.07/0.45 | 0 1
% 0.07/0.45 --+----
% 0.07/0.45 0 | 1 0
% 0.07/0.45 1 | 1 1
% 0.07/0.45
% 0.07/0.45 % SZS output end FiniteModel
% 0.07/0.45 ------ process 35316 exit (max_models) ------
% 0.07/0.45
% 0.07/0.45 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.07/0.45
% 0.07/0.45 Exiting with 1 model.
% 0.07/0.45
% 0.07/0.45 Process 35316 exit (max_models) Tue Feb 7 19:39:01 2017
% 0.07/0.45 The process finished Tue Feb 7 19:39:01 2017
% 0.07/0.45 Mace4 ended
%------------------------------------------------------------------------------