%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL456^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:34:13 AM UTC 2026
% Result : CounterSatisfiable 0.20s 0.48s
% Output : Saturation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 00:15:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.40 ---- Original DTF file ---
% 0.11/0.41 thf(spec,logic,$$dhol).
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 % File : LCL456^7 : TPTP v9.3.1. Released v5.5.0.
% 0.11/0.41 % Domain : Logic Calculi
% 0.11/0.41 % Problem : Prove Principia's r3 axiom from Hilbert's axiomatization
% 0.11/0.41 % Version : [Ben12] axioms.
% 0.11/0.41 % English :
% 0.11/0.41
% 0.11/0.41 % Refs : [HB34] Hilbert & Bernays (1934), Grundlagen der Mathematick
% 0.11/0.41 % : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.11/0.41 % : [Hal] Halleck (URL), John Halleck's Logic Systems
% 0.11/0.41 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.11/0.41 % Source : [Ben12]
% 0.11/0.41 % Names : s4-cumul-GLC456+1 [Ben12]
% 0.11/0.41
% 0.11/0.41 % Status : Theorem
% 0.11/0.41 % Rating : 1.00 v5.5.0
% 0.11/0.41 % Syntax : Number of formulae : 180 ( 38 unt; 73 typ; 32 def)
% 0.11/0.41 % Number of atoms : 999 ( 36 equ; 0 cnn)
% 0.11/0.41 % Maximal formula atoms : 36 ( 9 avg)
% 0.11/0.41 % Number of connectives : 1504 ( 5 ~; 5 |; 9 &;1475 @)
% 0.11/0.41 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.11/0.41 % Maximal formula depth : 23 ( 9 avg)
% 0.11/0.41 % Number of types : 3 ( 1 usr)
% 0.11/0.41 % Number of type conns : 222 ( 222 >; 0 *; 0 +; 0 <<)
% 0.11/0.41 % Number of symbols : 74 ( 72 usr; 1 con; 0-3 aty)
% 0.11/0.41 % Number of variables : 258 ( 203 ^; 48 !; 7 ?; 258 :)
% 0.11/0.41 % SPC : TH0_THM_EQU_NAR_NDT
% 0.11/0.41
% 0.11/0.41 % Comments : Goedel translation of LCL456+1
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 %----Include axioms for Modal logic S4 under cumulative domains
% 0.11/0.41 include('Axioms/LCL015^0.ax').
% 0.11/0.41 include('Axioms/LCL013^5.ax').
% 0.11/0.41 include('Axioms/LCL015^1.ax').
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 thf(kn1_type,type,
% 0.11/0.41 kn1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(kn2_type,type,
% 0.11/0.41 kn2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(kn3_type,type,
% 0.11/0.41 kn3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(cn1_type,type,
% 0.11/0.41 cn1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(cn2_type,type,
% 0.11/0.41 cn2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(cn3_type,type,
% 0.11/0.41 cn3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(r1_type,type,
% 0.11/0.41 r1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(r2_type,type,
% 0.11/0.41 r2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(r4_type,type,
% 0.11/0.41 r4: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(r5_type,type,
% 0.11/0.41 r5: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(op_or_type,type,
% 0.11/0.41 op_or: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(op_implies_and_type,type,
% 0.11/0.41 op_implies_and: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(modus_ponens_type,type,
% 0.11/0.41 modus_ponens: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(modus_tollens_type,type,
% 0.11/0.41 modus_tollens: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(implies_1_type,type,
% 0.11/0.41 implies_1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(implies_2_type,type,
% 0.11/0.41 implies_2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(implies_3_type,type,
% 0.11/0.41 implies_3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(and_1_type,type,
% 0.11/0.41 and_1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(and_2_type,type,
% 0.11/0.41 and_2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(and_3_type,type,
% 0.11/0.41 and_3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(or_1_type,type,
% 0.11/0.41 or_1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(or_2_type,type,
% 0.11/0.41 or_2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(or_3_type,type,
% 0.11/0.41 or_3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(equivalence_1_type,type,
% 0.11/0.41 equivalence_1: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(equivalence_2_type,type,
% 0.11/0.41 equivalence_2: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(equivalence_3_type,type,
% 0.11/0.41 equivalence_3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(substitution_of_equivalents_type,type,
% 0.11/0.41 substitution_of_equivalents: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(op_implies_or_type,type,
% 0.11/0.41 op_implies_or: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(op_and_type,type,
% 0.11/0.41 op_and: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(op_equiv_type,type,
% 0.11/0.41 op_equiv: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(r3_type,type,
% 0.11/0.41 r3: $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(is_a_theorem_type,type,
% 0.11/0.41 is_a_theorem: mu > $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(not_type,type,
% 0.11/0.41 not: mu > mu ).
% 0.11/0.41
% 0.11/0.41 thf(existence_of_not_ax,axiom,
% 0.11/0.41 ! [V: $i,V1: mu] : ( exists_in_world @ ( not @ V1 ) @ V ) ).
% 0.11/0.41
% 0.11/0.41 thf(or_type,type,
% 0.11/0.41 or: mu > mu > mu ).
% 0.11/0.41
% 0.11/0.41 thf(existence_of_or_ax,axiom,
% 0.11/0.41 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( or @ V2 @ V1 ) @ V ) ).
% 0.11/0.41
% 0.11/0.41 thf(implies_type,type,
% 0.11/0.41 implies: mu > mu > mu ).
% 0.11/0.41
% 0.11/0.41 thf(existence_of_implies_ax,axiom,
% 0.11/0.41 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( implies @ V2 @ V1 ) @ V ) ).
% 0.11/0.41
% 0.11/0.41 thf(and_type,type,
% 0.11/0.41 and: mu > mu > mu ).
% 0.11/0.41
% 0.11/0.41 thf(existence_of_and_ax,axiom,
% 0.11/0.41 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( and @ V2 @ V1 ) @ V ) ).
% 0.11/0.41
% 0.11/0.41 thf(equiv_type,type,
% 0.11/0.41 equiv: mu > mu > mu ).
% 0.11/0.41
% 0.11/0.41 thf(existence_of_equiv_ax,axiom,
% 0.11/0.41 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( equiv @ V2 @ V1 ) @ V ) ).
% 0.11/0.41
% 0.11/0.41 thf(reflexivity,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(symmetry,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(transitivity,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(and_substitution_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( and @ A @ C ) @ ( and @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(and_substitution_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( and @ C @ A ) @ ( and @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(equiv_substitution_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( equiv @ A @ C ) @ ( equiv @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(equiv_substitution_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( equiv @ C @ A ) @ ( equiv @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(implies_substitution_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( implies @ A @ C ) @ ( implies @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(implies_substitution_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(not_substitution_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(or_substitution_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( or @ A @ C ) @ ( or @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(or_substitution_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(is_a_theorem_substitution_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [A: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( is_a_theorem @ A ) ) ) @ ( mbox_s4 @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(modus_ponens,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ modus_ponens )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( is_a_theorem @ X ) ) @ ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ Y ) ) ) ) @ ( mbox_s4 @ ( is_a_theorem @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( is_a_theorem @ X ) ) @ ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ Y ) ) ) ) @ ( mbox_s4 @ ( is_a_theorem @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ modus_ponens ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(substitution_of_equivalents,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ substitution_of_equivalents )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( is_a_theorem @ ( equiv @ X @ Y ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( is_a_theorem @ ( equiv @ X @ Y ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ substitution_of_equivalents ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(modus_tollens,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ modus_tollens )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ modus_tollens ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(implies_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ implies_1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ implies_1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(implies_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ implies_2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ implies_2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(implies_3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ implies_3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Z: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Z: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ implies_3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(and_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ and_1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ and_1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(and_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ and_2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ and_2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(and_3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ and_3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ and_3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(or_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ or_1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ or_1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(or_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ or_2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ or_2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(or_3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ or_3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Z: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Z: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ or_3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(equivalence_1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ equivalence_1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ equivalence_1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(equivalence_2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ equivalence_2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ equivalence_2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(equivalence_3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ equivalence_3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ equivalence_3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(kn1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ kn1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ kn1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(kn2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ kn2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ kn2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(kn3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ kn3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ kn3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(cn1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ cn1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ cn1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(cn2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ cn2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ cn2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(cn3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ cn3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ cn3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(r1,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ r1 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ r1 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(r2,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ r2 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ r2 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(r3,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ r3 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ r3 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(r4,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ r4 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ r4 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(r5,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mand
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ r5 )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [P: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Q: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) )
% 0.11/0.41 @ ( mbox_s4 @ r5 ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(op_or,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ op_or )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( qmltpeq @ ( or @ X @ Y ) @ ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(op_and,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ op_and )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( qmltpeq @ ( and @ X @ Y ) @ ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(op_implies_and,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ op_implies_and )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( qmltpeq @ ( implies @ X @ Y ) @ ( not @ ( and @ X @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(op_implies_or,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ op_implies_or )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( qmltpeq @ ( implies @ X @ Y ) @ ( or @ ( not @ X ) @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(op_equiv,axiom,
% 0.11/0.41 ( mvalid
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mimplies @ ( mbox_s4 @ op_equiv )
% 0.11/0.41 @ ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [X: mu] :
% 0.11/0.41 ( mbox_s4
% 0.11/0.41 @ ( mforall_ind
% 0.11/0.41 @ ^ [Y: mu] : ( mbox_s4 @ ( qmltpeq @ ( equiv @ X @ Y ) @ ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_op_or,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ op_or ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_op_implies_and,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ op_implies_and ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_op_equiv,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ op_equiv ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_modus_ponens,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ modus_ponens ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_modus_tollens,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ modus_tollens ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_implies_1,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ implies_1 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_implies_2,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ implies_2 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_implies_3,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ implies_3 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_and_1,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ and_1 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_and_2,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ and_2 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_and_3,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ and_3 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_or_1,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ or_1 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_or_2,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ or_2 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_or_3,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ or_3 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_equivalence_1,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ equivalence_1 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_equivalence_2,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ equivalence_2 ) ).
% 0.11/0.41
% 0.11/0.41 thf(hilbert_equivalence_3,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ equivalence_3 ) ).
% 0.11/0.41
% 0.11/0.41 thf(substitution_of_equivalents_001,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ substitution_of_equivalents ) ).
% 0.11/0.41
% 0.11/0.41 thf(principia_op_implies_or,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ op_implies_or ) ).
% 0.11/0.41
% 0.11/0.41 thf(principia_op_and,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ op_and ) ).
% 0.11/0.41
% 0.11/0.41 thf(principia_op_equiv,axiom,
% 0.11/0.41 mvalid @ ( mbox_s4 @ op_equiv ) ).
% 0.11/0.41
% 0.11/0.41 thf(principia_r3,conjecture,
% 0.11/0.41 mvalid @ ( mbox_s4 @ r3 ) ).
% 0.11/0.41
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 ------------------------
% 0.11/0.41 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.11/0.41 ---- Embedded in THF ---
% 0.11/0.41 ------------------------
% 0.11/0.44 ---- Cleaned THF ---
% 0.11/0.44 ------------------------
% 0.20/0.48 % (1599608)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/183Mi)
% 0.20/0.48 % (1599610)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/27Mi)
% 0.20/0.48 % (1599609)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/4Mi)
% 0.20/0.48 % (1599611)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/2Mi)
% 0.20/0.48 % (1599612)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/2Mi)
% 0.20/0.48 % (1599610)Refutation not found, incomplete strategy
% 0.20/0.48 % (1599610)------------------------------
% 0.20/0.48 % (1599610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/0.48 % (1599610)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 % (1599610)Memory used [KB]: 5373
% 0.20/0.48 % (1599608)First to succeed.
% 0.20/0.48 % (1599610)Time elapsed: 0.002 s
% 0.20/0.48 % (1599610)------------------------------
% 0.20/0.48 % (1599610)------------------------------
% 0.20/0.48 % (1599613)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/275Mi)
% 0.20/0.48 % (1599612)Refutation not found, incomplete strategy
% 0.20/0.48 % (1599612)------------------------------
% 0.20/0.48 % (1599612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/0.48 % (1599612)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 % (1599612)Memory used [KB]: 5373
% 0.20/0.48 % (1599612)Time elapsed: 0.002 s
% 0.20/0.48 % (1599612)------------------------------
% 0.20/0.48 % (1599612)------------------------------
% 0.20/0.48 % (1599611)Also succeeded, but the first one will report.
% 0.20/0.48 % (1599614)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1599592 for (3000ds/18Mi)
% 0.20/0.48 % (1599613)Refutation not found, incomplete strategy
% 0.20/0.48 % (1599613)------------------------------
% 0.20/0.48 % (1599613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/0.48 % (1599613)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 % (1599613)Memory used [KB]: 5373
% 0.20/0.48 % (1599613)Time elapsed: 0.002 s
% 0.20/0.48 % (1599613)------------------------------
% 0.20/0.48 % (1599613)------------------------------
% 0.20/0.48 % SZS status Satisfiable for DTF2THF_1599592
% 0.20/0.48 % (1599608)# SZS output start Saturation.
% 0.20/0.48 % (1599608)# SZS output end Saturation.
% 0.20/0.48 % (1599608)------------------------------
% 0.20/0.48 % (1599608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/0.48 % (1599608)Termination reason: Satisfiable
% 0.20/0.48
% 0.20/0.48 % (1599608)Memory used [KB]: 5373
% 0.20/0.48 % (1599608)Time elapsed: 0.003 s
% 0.20/0.48 % (1599608)Instructions burned: 1 (million)
% 0.20/0.48 % (1599608)------------------------------
% 0.20/0.48 % (1599608)------------------------------
% 0.20/0.48 % (1599607)Success in time 0.018 s
%------------------------------------------------------------------------------