TSTP Solution File: LCL576+1 by Mace4---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Mace4---1109a
% Problem : LCL576+1 : TPTP v6.4.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : mace4 -t %d -f %s
% Computer : n012.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 09:58:01 EST 2017
% Result : CounterSatisfiable 30.44s
% Output : FiniteModel 30.44s
% 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 : LCL576+1 : TPTP v6.4.0. Released v3.3.0.
% 0.00/0.04 % Command : mace4 -t %d -f %s
% 0.02/0.23 % Computer : n012.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 19:23:00 CST 2017
% 0.02/0.23 % CPUTime :
% 30.44/30.69 % SZS status CounterSatisfiable
% 30.44/30.69 ============================== Mace4 =================================
% 30.44/30.69 Mace4 (32) version 2009-11A, November 2009.
% 30.44/30.69 Process 53058 was started by sandbox2 on n012.star.cs.uiowa.edu,
% 30.44/30.69 Tue Feb 7 19:23:01 2017
% 30.44/30.69 The command was "/export/starexec/sandbox2/solver/bin/mace4 -t 300 -f /tmp/Mace4_input_53025_n012.star.cs.uiowa.edu".
% 30.44/30.69 ============================== end of head ===========================
% 30.44/30.69
% 30.44/30.69 ============================== INPUT =================================
% 30.44/30.69
% 30.44/30.69 % Reading from file /tmp/Mace4_input_53025_n012.star.cs.uiowa.edu
% 30.44/30.69
% 30.44/30.69 set(prolog_style_variables).
% 30.44/30.69 set(print_models_tabular).
% 30.44/30.69 % set(print_models_tabular) -> clear(print_models).
% 30.44/30.69
% 30.44/30.69 formulas(sos).
% 30.44/30.69 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom).
% 30.44/30.69 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom).
% 30.44/30.69 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom).
% 30.44/30.69 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom).
% 30.44/30.69 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom).
% 30.44/30.69 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom).
% 30.44/30.69 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(X) & is_a_theorem(strict_implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 adjunction <-> (all X all Y (is_a_theorem(X) & is_a_theorem(Y) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom).
% 30.44/30.69 substitution_strict_equiv <-> (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> X = Y)) # label(substitution_strict_equiv) # label(axiom).
% 30.44/30.69 axiom_K <-> (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) # label(axiom_K) # label(axiom).
% 30.44/30.69 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom).
% 30.44/30.69 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom).
% 30.44/30.69 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom).
% 30.44/30.69 axiom_5 <-> (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) # label(axiom_5) # label(axiom).
% 30.44/30.69 axiom_s1 <-> (all X all Y all Z is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z))))) # label(axiom_s1) # label(axiom).
% 30.44/30.69 axiom_s2 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))) # label(axiom_s2) # label(axiom).
% 30.44/30.69 axiom_s3 <-> (all X all Y is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))) # label(axiom_s3) # label(axiom).
% 30.44/30.69 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom).
% 30.44/30.69 axiom_m1 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) # label(axiom_m1) # label(axiom).
% 30.44/30.69 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom).
% 30.44/30.69 axiom_m3 <-> (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) # label(axiom_m3) # label(axiom).
% 30.44/30.69 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom).
% 30.44/30.69 axiom_m5 <-> (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) # label(axiom_m5) # label(axiom).
% 30.44/30.69 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom).
% 30.44/30.69 axiom_m7 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),P))) # label(axiom_m7) # label(axiom).
% 30.44/30.69 axiom_m8 <-> (all P all Q is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))) # label(axiom_m8) # label(axiom).
% 30.44/30.69 axiom_m9 <-> (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) # label(axiom_m9) # label(axiom).
% 30.44/30.69 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom).
% 30.44/30.69 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom).
% 30.44/30.69 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom).
% 30.44/30.69 op_strict_implies -> (all X all Y strict_implies(X,Y) = necessarily(implies(X,Y))) # label(op_strict_implies) # label(axiom).
% 30.44/30.69 op_strict_equiv -> (all X all Y strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))) # label(op_strict_equiv) # label(axiom).
% 30.44/30.69 op_possibly # label(s1_0_op_possibly) # label(axiom).
% 30.44/30.69 op_or # label(s1_0_op_or) # label(axiom).
% 30.44/30.69 op_implies # label(s1_0_op_implies) # label(axiom).
% 30.44/30.69 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom).
% 30.44/30.69 op_equiv # label(s1_0_op_equiv) # label(axiom).
% 30.44/30.69 op_strict_equiv # label(s1_0_op_strict_equiv) # label(axiom).
% 30.44/30.69 modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 substitution_strict_equiv # label(s1_0_substitution_strict_equiv) # label(axiom).
% 30.44/30.69 adjunction # label(s1_0_adjunction) # label(axiom).
% 30.44/30.69 axiom_m1 # label(s1_0_axiom_m1) # label(axiom).
% 30.44/30.69 axiom_m2 # label(s1_0_axiom_m2) # label(axiom).
% 30.44/30.69 axiom_m3 # label(s1_0_axiom_m3) # label(axiom).
% 30.44/30.69 axiom_m4 # label(s1_0_axiom_m4) # label(axiom).
% 30.44/30.69 axiom_m5 # label(s1_0_axiom_m5) # label(axiom).
% 30.44/30.69 axiom_m10 # label(s1_0_m10_axiom_m10) # label(axiom).
% 30.44/30.69 -axiom_m6 # label(s1_0_m6s3m9b_axiom_m6) # label(negated_conjecture).
% 30.44/30.69 end_of_list.
% 30.44/30.69
% 30.44/30.69 % From the command line: assign(max_seconds, 300).
% 30.44/30.69
% 30.44/30.69 ============================== end of input ==========================
% 30.44/30.69
% 30.44/30.69 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 30.44/30.69
% 30.44/30.69 % Formulas that are not ordinary clauses:
% 30.44/30.69 1 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 2 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 3 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 4 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 5 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 6 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 7 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(X) & is_a_theorem(strict_implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 8 adjunction <-> (all X all Y (is_a_theorem(X) & is_a_theorem(Y) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 9 substitution_strict_equiv <-> (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> X = Y)) # label(substitution_strict_equiv) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 10 axiom_K <-> (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) # label(axiom_K) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 11 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 12 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 13 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 14 axiom_5 <-> (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 15 axiom_s1 <-> (all X all Y all Z is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z))))) # label(axiom_s1) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 16 axiom_s2 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))) # label(axiom_s2) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 17 axiom_s3 <-> (all X all Y is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))) # label(axiom_s3) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 18 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 19 axiom_m1 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) # label(axiom_m1) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 20 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 21 axiom_m3 <-> (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) # label(axiom_m3) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 22 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 23 axiom_m5 <-> (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) # label(axiom_m5) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 24 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 25 axiom_m7 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),P))) # label(axiom_m7) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 26 axiom_m8 <-> (all P all Q is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))) # label(axiom_m8) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 27 axiom_m9 <-> (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) # label(axiom_m9) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 28 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 29 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 30 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 31 op_strict_implies -> (all X all Y strict_implies(X,Y) = necessarily(implies(X,Y))) # label(op_strict_implies) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69 32 op_strict_equiv -> (all X all Y strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))) # label(op_strict_equiv) # label(axiom) # label(non_clause). [assumption].
% 30.44/30.69
% 30.44/30.69 ============================== end of process non-clausal formulas ===
% 30.44/30.69
% 30.44/30.69 ============================== CLAUSES FOR SEARCH ====================
% 30.44/30.69
% 30.44/30.69 formulas(mace4_clauses).
% 30.44/30.69 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom).
% 30.44/30.69 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom).
% 30.44/30.69 -op_implies_and | implies(A,B) = not(and(A,not(B))) # label(op_implies_and) # label(axiom).
% 30.44/30.69 -op_implies_or | implies(A,B) = or(not(A),B) # label(op_implies_or) # label(axiom).
% 30.44/30.69 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom).
% 30.44/30.69 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom).
% 30.44/30.69 necessitation | is_a_theorem(c1) # label(necessitation) # label(axiom).
% 30.44/30.69 necessitation | -is_a_theorem(necessarily(c1)) # label(necessitation) # label(axiom).
% 30.44/30.69 -modus_ponens_strict_implies | -is_a_theorem(A) | -is_a_theorem(strict_implies(A,B)) | is_a_theorem(B) # label(modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 modus_ponens_strict_implies | is_a_theorem(c2) # label(modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 modus_ponens_strict_implies | is_a_theorem(strict_implies(c2,c3)) # label(modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 modus_ponens_strict_implies | -is_a_theorem(c3) # label(modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 -adjunction | -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(A,B)) # label(adjunction) # label(axiom).
% 30.44/30.69 adjunction | is_a_theorem(c4) # label(adjunction) # label(axiom).
% 30.44/30.69 adjunction | is_a_theorem(c5) # label(adjunction) # label(axiom).
% 30.44/30.69 adjunction | -is_a_theorem(and(c4,c5)) # label(adjunction) # label(axiom).
% 30.44/30.69 -substitution_strict_equiv | -is_a_theorem(strict_equiv(A,B)) | B = A # label(substitution_strict_equiv) # label(axiom).
% 30.44/30.69 substitution_strict_equiv | is_a_theorem(strict_equiv(c6,c7)) # label(substitution_strict_equiv) # label(axiom).
% 30.44/30.69 substitution_strict_equiv | c7 != c6 # label(substitution_strict_equiv) # label(axiom).
% 30.44/30.69 -axiom_K | is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))) # label(axiom_K) # label(axiom).
% 30.44/30.69 axiom_K | -is_a_theorem(implies(necessarily(implies(c8,c9)),implies(necessarily(c8),necessarily(c9)))) # label(axiom_K) # label(axiom).
% 30.44/30.69 -axiom_M | is_a_theorem(implies(necessarily(A),A)) # label(axiom_M) # label(axiom).
% 30.44/30.69 axiom_M | -is_a_theorem(implies(necessarily(c10),c10)) # label(axiom_M) # label(axiom).
% 30.44/30.69 -axiom_4 | is_a_theorem(implies(necessarily(A),necessarily(necessarily(A)))) # label(axiom_4) # label(axiom).
% 30.44/30.69 axiom_4 | -is_a_theorem(implies(necessarily(c11),necessarily(necessarily(c11)))) # label(axiom_4) # label(axiom).
% 30.44/30.69 -axiom_B | is_a_theorem(implies(A,necessarily(possibly(A)))) # label(axiom_B) # label(axiom).
% 30.44/30.69 axiom_B | -is_a_theorem(implies(c12,necessarily(possibly(c12)))) # label(axiom_B) # label(axiom).
% 30.44/30.69 -axiom_5 | is_a_theorem(implies(possibly(A),necessarily(possibly(A)))) # label(axiom_5) # label(axiom).
% 30.44/30.69 axiom_5 | -is_a_theorem(implies(possibly(c13),necessarily(possibly(c13)))) # label(axiom_5) # label(axiom).
% 30.44/30.69 -axiom_s1 | is_a_theorem(implies(and(necessarily(implies(A,B)),necessarily(implies(B,C))),necessarily(implies(A,C)))) # label(axiom_s1) # label(axiom).
% 30.44/30.69 axiom_s1 | -is_a_theorem(implies(and(necessarily(implies(c14,c15)),necessarily(implies(c15,c16))),necessarily(implies(c14,c16)))) # label(axiom_s1) # label(axiom).
% 30.44/30.69 -axiom_s2 | is_a_theorem(strict_implies(possibly(and(A,B)),and(possibly(A),possibly(B)))) # label(axiom_s2) # label(axiom).
% 30.44/30.69 axiom_s2 | -is_a_theorem(strict_implies(possibly(and(c17,c18)),and(possibly(c17),possibly(c18)))) # label(axiom_s2) # label(axiom).
% 30.44/30.69 -axiom_s3 | is_a_theorem(strict_implies(strict_implies(A,B),strict_implies(not(possibly(B)),not(possibly(A))))) # label(axiom_s3) # label(axiom).
% 30.44/30.69 axiom_s3 | -is_a_theorem(strict_implies(strict_implies(c19,c20),strict_implies(not(possibly(c20)),not(possibly(c19))))) # label(axiom_s3) # label(axiom).
% 30.44/30.69 -axiom_s4 | is_a_theorem(strict_implies(necessarily(A),necessarily(necessarily(A)))) # label(axiom_s4) # label(axiom).
% 30.44/30.69 axiom_s4 | -is_a_theorem(strict_implies(necessarily(c21),necessarily(necessarily(c21)))) # label(axiom_s4) # label(axiom).
% 30.44/30.69 -axiom_m1 | is_a_theorem(strict_implies(and(A,B),and(B,A))) # label(axiom_m1) # label(axiom).
% 30.44/30.69 axiom_m1 | -is_a_theorem(strict_implies(and(c22,c23),and(c23,c22))) # label(axiom_m1) # label(axiom).
% 30.44/30.69 -axiom_m2 | is_a_theorem(strict_implies(and(A,B),A)) # label(axiom_m2) # label(axiom).
% 30.44/30.69 axiom_m2 | -is_a_theorem(strict_implies(and(c24,c25),c24)) # label(axiom_m2) # label(axiom).
% 30.44/30.69 -axiom_m3 | is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))) # label(axiom_m3) # label(axiom).
% 30.44/30.69 axiom_m3 | -is_a_theorem(strict_implies(and(and(c26,c27),c28),and(c26,and(c27,c28)))) # label(axiom_m3) # label(axiom).
% 30.44/30.69 -axiom_m4 | is_a_theorem(strict_implies(A,and(A,A))) # label(axiom_m4) # label(axiom).
% 30.44/30.69 axiom_m4 | -is_a_theorem(strict_implies(c29,and(c29,c29))) # label(axiom_m4) # label(axiom).
% 30.44/30.69 -axiom_m5 | is_a_theorem(strict_implies(and(strict_implies(A,B),strict_implies(B,C)),strict_implies(A,C))) # label(axiom_m5) # label(axiom).
% 30.44/30.69 axiom_m5 | -is_a_theorem(strict_implies(and(strict_implies(c30,c31),strict_implies(c31,c32)),strict_implies(c30,c32))) # label(axiom_m5) # label(axiom).
% 30.44/30.69 -axiom_m6 | is_a_theorem(strict_implies(A,possibly(A))) # label(axiom_m6) # label(axiom).
% 30.44/30.69 axiom_m6 | -is_a_theorem(strict_implies(c33,possibly(c33))) # label(axiom_m6) # label(axiom).
% 30.44/30.69 -axiom_m7 | is_a_theorem(strict_implies(possibly(and(A,B)),A)) # label(axiom_m7) # label(axiom).
% 30.44/30.69 axiom_m7 | -is_a_theorem(strict_implies(possibly(and(c34,c35)),c34)) # label(axiom_m7) # label(axiom).
% 30.44/30.69 -axiom_m8 | is_a_theorem(strict_implies(strict_implies(A,B),strict_implies(possibly(A),possibly(B)))) # label(axiom_m8) # label(axiom).
% 30.44/30.69 axiom_m8 | -is_a_theorem(strict_implies(strict_implies(c36,c37),strict_implies(possibly(c36),possibly(c37)))) # label(axiom_m8) # label(axiom).
% 30.44/30.69 -axiom_m9 | is_a_theorem(strict_implies(possibly(possibly(A)),possibly(A))) # label(axiom_m9) # label(axiom).
% 30.44/30.69 axiom_m9 | -is_a_theorem(strict_implies(possibly(possibly(c38)),possibly(c38))) # label(axiom_m9) # label(axiom).
% 30.44/30.69 -axiom_m10 | is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A)))) # label(axiom_m10) # label(axiom).
% 30.44/30.69 axiom_m10 | -is_a_theorem(strict_implies(possibly(c39),necessarily(possibly(c39)))) # label(axiom_m10) # label(axiom).
% 30.44/30.69 -op_possibly | possibly(A) = not(necessarily(not(A))) # label(op_possibly) # label(axiom).
% 30.44/30.69 -op_necessarily | necessarily(A) = not(possibly(not(A))) # label(op_necessarily) # label(axiom).
% 30.44/30.69 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom).
% 30.44/30.69 -op_strict_equiv | strict_equiv(A,B) = and(strict_implies(A,B),strict_implies(B,A)) # label(op_strict_equiv) # label(axiom).
% 30.44/30.69 op_possibly # label(s1_0_op_possibly) # label(axiom).
% 30.44/30.69 op_or # label(s1_0_op_or) # label(axiom).
% 30.44/30.69 op_implies # label(s1_0_op_implies) # label(axiom).
% 30.44/30.69 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom).
% 30.44/30.69 op_equiv # label(s1_0_op_equiv) # label(axiom).
% 30.44/30.69 op_strict_equiv # label(s1_0_op_strict_equiv) # label(axiom).
% 30.44/30.69 modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(axiom).
% 30.44/30.69 substitution_strict_equiv # label(s1_0_substitution_strict_equiv) # label(axiom).
% 30.44/30.69 adjunction # label(s1_0_adjunction) # label(axiom).
% 30.44/30.69 axiom_m1 # label(s1_0_axiom_m1) # label(axiom).
% 30.44/30.69 axiom_m2 # label(s1_0_axiom_m2) # label(axiom).
% 30.44/30.69 axiom_m3 # label(s1_0_axiom_m3) # label(axiom).
% 30.44/30.69 axiom_m4 # label(s1_0_axiom_m4) # label(axiom).
% 30.44/30.69 axiom_m5 # label(s1_0_axiom_m5) # label(axiom).
% 30.44/30.69 axiom_m10 # label(s1_0_m10_axiom_m10) # label(axiom).
% 30.44/30.69 -axiom_m6 # label(s1_0_m6s3m9b_axiom_m6) # label(negated_conjecture).
% 30.44/30.69 end_of_list.
% 30.44/30.69
% 30.44/30.69 ============================== end of clauses for search =============
% 30.44/30.69 % SZS output start FiniteModel
% 30.44/30.69
% 30.44/30.69 % There are no natural numbers in the input.
% 30.44/30.69
% 30.44/30.69 c1 : 0
% 30.44/30.69
% 30.44/30.69 c2 : 0
% 30.44/30.69
% 30.44/30.69 c3 : 0
% 30.44/30.69
% 30.44/30.69 c4 : 0
% 30.44/30.69
% 30.44/30.69 c5 : 0
% 30.44/30.69
% 30.44/30.69 c6 : 0
% 30.44/30.69
% 30.44/30.69 c7 : 0
% 30.44/30.69
% 30.44/30.69 c8 : 0
% 30.44/30.69
% 30.44/30.69 c9 : 0
% 30.44/30.69
% 30.44/30.69 c10 : 0
% 30.44/30.69
% 30.44/30.69 c11 : 0
% 30.44/30.69
% 30.44/30.69 c12 : 0
% 30.44/30.69
% 30.44/30.69 c13 : 0
% 30.44/30.69
% 30.44/30.69 c14 : 0
% 30.44/30.69
% 30.44/30.69 c15 : 0
% 30.44/30.69
% 30.44/30.69 c16 : 0
% 30.44/30.69
% 30.44/30.69 c17 : 0
% 30.44/30.69
% 30.44/30.69 c18 : 0
% 30.44/30.69
% 30.44/30.69 c19 : 0
% 30.44/30.69
% 30.44/30.69 c20 : 0
% 30.44/30.69
% 30.44/30.69 c21 : 0
% 30.44/30.69
% 30.44/30.69 c22 : 0
% 30.44/30.69
% 30.44/30.69 c23 : 0
% 30.44/30.69
% 30.44/30.69 c24 : 0
% 30.44/30.69
% 30.44/30.69 c25 : 0
% 30.44/30.69
% 30.44/30.69 c26 : 0
% 30.44/30.69
% 30.44/30.69 c27 : 0
% 30.44/30.69
% 30.44/30.69 c28 : 0
% 30.44/30.69
% 30.44/30.69 c29 : 0
% 30.44/30.69
% 30.44/30.69 c30 : 0
% 30.44/30.69
% 30.44/30.69 c31 : 0
% 30.44/30.69
% 30.44/30.69 c32 : 0
% 30.44/30.69
% 30.44/30.69 c33 : 0
% 30.44/30.69
% 30.44/30.69 c34 : 0
% 30.44/30.69
% 30.44/30.69 c35 : 0
% 30.44/30.69
% 30.44/30.69 c36 : 0
% 30.44/30.69
% 30.44/30.69 c37 : 0
% 30.44/30.69
% 30.44/30.69 c38 : 0
% 30.44/30.69
% 30.44/30.69 c39 : 0
% 30.44/30.69
% 30.44/30.69 necessarily :
% 30.44/30.69 0 1
% 30.44/30.69 -------
% 30.44/30.69 0 1
% 30.44/30.69
% 30.44/30.69 not :
% 30.44/30.69 0 1
% 30.44/30.69 -------
% 30.44/30.69 1 1
% 30.44/30.69
% 30.44/30.69 possibly :
% 30.44/30.69 0 1
% 30.44/30.69 -------
% 30.44/30.69 1 1
% 30.44/30.69
% 30.44/30.69 and :
% 30.44/30.69 | 0 1
% 30.44/30.69 --+----
% 30.44/30.69 0 | 0 1
% 30.44/30.69 1 | 1 1
% 30.44/30.69
% 30.44/30.69 equiv :
% 30.44/30.69 | 0 1
% 30.44/30.69 --+----
% 30.44/30.69 0 | 0 1
% 30.44/30.69 1 | 1 0
% 30.44/30.69
% 30.44/30.69 implies :
% 30.44/30.69 | 0 1
% 30.44/30.69 --+----
% 30.44/30.69 0 | 0 1
% 30.44/30.69 1 | 0 0
% 30.44/30.69
% 30.44/30.69 or :
% 30.44/30.69 | 0 1
% 30.44/30.69 --+----
% 30.44/30.69 0 | 1 1
% 30.44/30.69 1 | 1 1
% 30.44/30.69
% 30.44/30.69 strict_equiv :
% 30.44/30.69 | 0 1
% 30.44/30.69 --+----
% 30.44/30.69 0 | 0 1
% 30.44/30.69 1 | 1 0
% 30.44/30.69
% 30.44/30.69 strict_implies :
% 30.44/30.69 | 0 1
% 30.44/30.69 --+----
% 30.44/30.69 0 | 0 1
% 30.44/30.69 1 | 0 0
% 30.44/30.69
% 30.44/30.69 adjunction : 1
% 30.44/30.69
% 30.44/30.69 axiom_4 : 1
% 30.44/30.69
% 30.44/30.69 axiom_5 : 1
% 30.44/30.69
% 30.44/30.69 axiom_B : 0
% 30.44/30.69
% 30.44/30.69 axiom_K : 1
% 30.44/30.69
% 30.44/30.69 axiom_M : 1
% 30.44/30.69
% 30.44/30.69 axiom_m1 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m10 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m2 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m3 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m4 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m5 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m6 : 0
% 30.44/30.69
% 30.44/30.69 axiom_m7 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m8 : 1
% 30.44/30.69
% 30.44/30.69 axiom_m9 : 1
% 30.44/30.69
% 30.44/30.69 axiom_s1 : 1
% 30.44/30.69
% 30.44/30.69 axiom_s2 : 1
% 30.44/30.69
% 30.44/30.69 axiom_s3 : 1
% 30.44/30.69
% 30.44/30.69 axiom_s4 : 1
% 30.44/30.69
% 30.44/30.69 modus_ponens_strict_implies : 1
% 30.44/30.69
% 30.44/30.69 necessitation : 1
% 30.44/30.69
% 30.44/30.69 op_and : 0
% 30.44/30.69
% 30.44/30.69 op_equiv : 1
% 30.44/30.69
% 30.44/30.69 op_implies : 1
% 30.44/30.69
% 30.44/30.69 op_implies_and : 0
% 30.44/30.69
% 30.44/30.69 op_implies_or : 0
% 30.44/30.69
% 30.44/30.69 op_necessarily : 0
% 30.44/30.69
% 30.44/30.69 op_or : 1
% 30.44/30.69
% 30.44/30.69 op_possibly : 1
% 30.44/30.69
% 30.44/30.69 op_strict_equiv : 1
% 30.44/30.69
% 30.44/30.69 op_strict_implies : 1
% 30.44/30.69
% 30.44/30.69 substitution_strict_equiv : 1
% 30.44/30.69
% 30.44/30.69 is_a_theorem :
% 30.44/30.69 0 1
% 30.44/30.69 -------
% 30.44/30.69 1 0
% 30.44/30.69
% 30.44/30.69 % SZS output end FiniteModel
% 30.44/30.69 ------ process 53058 exit (max_models) ------
% 30.44/30.69
% 30.44/30.69 User_CPU=29.19, System_CPU=1.06, Wall_clock=30.
% 30.44/30.69
% 30.44/30.69 Exiting with 1 model.
% 30.44/30.69
% 30.44/30.69 Process 53058 exit (max_models) Tue Feb 7 19:23:31 2017
% 30.44/30.69 The process finished Tue Feb 7 19:23:31 2017
% 30.44/30.69 Mace4 ended
%------------------------------------------------------------------------------