TSTP Solution File: LCL536+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL536+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 : 300s
% DateTime : Thu Aug 31 08:11:35 EDT 2023
% Result : Theorem 12.26s 2.54s
% Output : Proof 30.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL536+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.35 % Computer : n026.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 06:26:17 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.93/1.35 Prover 4: Preprocessing ...
% 3.93/1.35 Prover 1: Preprocessing ...
% 3.93/1.39 Prover 3: Preprocessing ...
% 3.93/1.39 Prover 2: Preprocessing ...
% 3.93/1.39 Prover 6: Preprocessing ...
% 3.93/1.39 Prover 5: Preprocessing ...
% 4.44/1.40 Prover 0: Preprocessing ...
% 10.01/2.29 Prover 5: Proving ...
% 10.01/2.30 Prover 1: Constructing countermodel ...
% 10.01/2.32 Prover 6: Constructing countermodel ...
% 10.01/2.35 Prover 4: Constructing countermodel ...
% 11.54/2.39 Prover 3: Constructing countermodel ...
% 11.85/2.45 Prover 0: Proving ...
% 12.26/2.51 Prover 2: Proving ...
% 12.26/2.53 Prover 3: proved (1883ms)
% 12.26/2.54
% 12.26/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.26/2.54
% 12.26/2.54 Prover 5: stopped
% 12.26/2.54 Prover 0: stopped
% 12.26/2.54 Prover 2: stopped
% 12.26/2.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.26/2.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.81/2.56 Prover 6: stopped
% 12.81/2.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.81/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.81/2.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.51/2.67 Prover 10: Preprocessing ...
% 13.51/2.68 Prover 7: Preprocessing ...
% 13.51/2.70 Prover 11: Preprocessing ...
% 13.51/2.70 Prover 13: Preprocessing ...
% 13.51/2.72 Prover 8: Preprocessing ...
% 15.28/3.03 Prover 13: Warning: ignoring some quantifiers
% 15.28/3.04 Prover 7: Constructing countermodel ...
% 15.28/3.07 Prover 13: Constructing countermodel ...
% 15.28/3.09 Prover 8: Warning: ignoring some quantifiers
% 15.28/3.12 Prover 8: Constructing countermodel ...
% 15.28/3.13 Prover 10: Constructing countermodel ...
% 17.47/3.19 Prover 11: Constructing countermodel ...
% 27.62/4.60 Prover 8: Found proof (size 41)
% 27.62/4.60 Prover 8: proved (2048ms)
% 27.62/4.60 Prover 7: stopped
% 27.62/4.60 Prover 11: stopped
% 27.62/4.60 Prover 1: stopped
% 27.62/4.60 Prover 4: stopped
% 28.43/4.69 Prover 10: stopped
% 29.97/5.04 Prover 13: stopped
% 29.97/5.04
% 29.97/5.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.97/5.04
% 29.97/5.05 % SZS output start Proof for theBenchmark
% 29.97/5.05 Assumptions after simplification:
% 29.97/5.05 ---------------------------------
% 29.97/5.05
% 29.97/5.06 (axiom_5)
% 30.20/5.11 (axiom_5 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 30.20/5.11 (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v1, v2) =
% 30.20/5.11 v3) | ~ $i(v0) | is_a_theorem(v3) = 0)) | ( ~ axiom_5 & ? [v0: $i] :
% 30.20/5.11 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 30.20/5.11 possibly(v0) = v1 & necessarily(v1) = v2 & implies(v1, v2) = v3 &
% 30.20/5.11 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)))
% 30.20/5.11
% 30.20/5.11 (axiom_m10)
% 30.20/5.12 (axiom_m10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 30.20/5.12 (possibly(v0) = v1) | ~ (strict_implies(v1, v2) = v3) | ~
% 30.20/5.12 (necessarily(v1) = v2) | ~ $i(v0) | is_a_theorem(v3) = 0)) | ( ~
% 30.20/5.12 axiom_m10 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 30.20/5.12 int] : ( ~ (v4 = 0) & possibly(v0) = v1 & strict_implies(v1, v2) = v3 &
% 30.20/5.12 necessarily(v1) = v2 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) &
% 30.20/5.12 $i(v0)))
% 30.20/5.12
% 30.20/5.12 (km5_axiom_5)
% 30.20/5.12 axiom_5
% 30.20/5.12
% 30.20/5.12 (km5_necessitation)
% 30.20/5.12 necessitation
% 30.20/5.12
% 30.20/5.12 (necessitation)
% 30.20/5.12 (necessitation & ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) = v1) | ~
% 30.20/5.12 $i(v0) | ? [v2: any] : ? [v3: any] : (is_a_theorem(v1) = v3 &
% 30.20/5.12 is_a_theorem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))) | ( ~ necessitation &
% 30.20/5.12 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & necessarily(v0) =
% 30.20/5.12 v1 & is_a_theorem(v1) = v2 & is_a_theorem(v0) = 0 & $i(v1) & $i(v0)))
% 30.20/5.12
% 30.20/5.12 (op_strict_implies)
% 30.20/5.13 ~ op_strict_implies | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 30.20/5.13 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 30.20/5.13 (necessarily(v3) = v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2)))
% 30.20/5.13
% 30.20/5.13 (s1_0_m10_axiom_m10)
% 30.20/5.13 ~ axiom_m10
% 30.20/5.13
% 30.20/5.13 (s1_0_op_strict_implies)
% 30.20/5.13 op_strict_implies
% 30.20/5.13
% 30.20/5.13 (function-axioms)
% 30.20/5.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 30.20/5.15 (strict_equiv(v3, v2) = v1) | ~ (strict_equiv(v3, v2) = v0)) & ! [v0: $i]
% 30.20/5.15 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (strict_implies(v3,
% 30.20/5.15 v2) = v1) | ~ (strict_implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 30.20/5.15 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~
% 30.20/5.15 (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 30.20/5.15 (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0)) & ! [v0: $i] : !
% 30.20/5.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~
% 30.20/5.15 (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 30.20/5.15 $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) & !
% 30.20/5.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (possibly(v2) = v1) | ~
% 30.20/5.15 (possibly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 30.20/5.15 ~ (necessarily(v2) = v1) | ~ (necessarily(v2) = v0)) & ! [v0: $i] : !
% 30.20/5.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) &
% 30.20/5.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 30.20/5.15 v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) & ? [v0: $i]
% 30.20/5.15 : ? [v1: $i] : ? [v2: $i] : (strict_equiv(v1, v0) = v2 & $i(v2)) & ? [v0:
% 30.20/5.15 $i] : ? [v1: $i] : ? [v2: $i] : (strict_implies(v1, v0) = v2 & $i(v2)) &
% 30.20/5.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (or(v1, v0) = v2 & $i(v2)) & ? [v0:
% 30.20/5.15 $i] : ? [v1: $i] : ? [v2: $i] : (and(v1, v0) = v2 & $i(v2)) & ? [v0: $i]
% 30.20/5.15 : ? [v1: $i] : ? [v2: $i] : (equiv(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 30.20/5.15 [v1: $i] : ? [v2: $i] : (implies(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 30.20/5.15 [v1: MultipleValueBool] : (is_a_theorem(v0) = v1) & ? [v0: $i] : ? [v1: $i]
% 30.20/5.15 : (possibly(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (necessarily(v0)
% 30.20/5.15 = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (not(v0) = v1 & $i(v1))
% 30.20/5.15
% 30.20/5.15 Further assumptions not needed in the proof:
% 30.20/5.15 --------------------------------------------
% 30.20/5.15 adjunction, and_1, and_2, and_3, axiom_4, axiom_B, axiom_K, axiom_M, axiom_m1,
% 30.20/5.15 axiom_m2, axiom_m3, axiom_m4, axiom_m5, axiom_m6, axiom_m7, axiom_m8, axiom_m9,
% 30.20/5.15 axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1,
% 30.20/5.15 equivalence_2, equivalence_3, hilbert_and_1, hilbert_and_2, hilbert_and_3,
% 30.20/5.15 hilbert_equivalence_1, hilbert_equivalence_2, hilbert_equivalence_3,
% 30.20/5.15 hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, hilbert_modus_ponens,
% 30.20/5.15 hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or,
% 30.20/5.15 hilbert_or_1, hilbert_or_2, hilbert_or_3, implies_1, implies_2, implies_3,
% 30.20/5.15 km5_axiom_K, km5_axiom_M, km5_op_possibly, kn1, kn2, kn3, modus_ponens,
% 30.20/5.15 modus_ponens_strict_implies, modus_tollens, op_and, op_equiv, op_implies_and,
% 30.20/5.15 op_implies_or, op_necessarily, op_or, op_possibly, op_strict_equiv, or_1, or_2,
% 30.20/5.15 or_3, r1, r2, r3, r4, r5, s1_0_op_equiv, s1_0_op_implies, s1_0_op_or,
% 30.20/5.15 s1_0_op_possibly, s1_0_op_strict_equiv, substitution_of_equivalents,
% 30.20/5.15 substitution_strict_equiv
% 30.20/5.15
% 30.20/5.15 Those formulas are unsatisfiable:
% 30.20/5.15 ---------------------------------
% 30.20/5.15
% 30.20/5.15 Begin of proof
% 30.20/5.15 |
% 30.20/5.15 | ALPHA: (function-axioms) implies:
% 30.20/5.15 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 30.20/5.15 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 30.20/5.15 |
% 30.20/5.15 | BETA: splitting (op_strict_implies) gives:
% 30.20/5.15 |
% 30.20/5.15 | Case 1:
% 30.20/5.15 | |
% 30.20/5.15 | | (2) ~ op_strict_implies
% 30.20/5.15 | |
% 30.20/5.15 | | PRED_UNIFY: (2), (s1_0_op_strict_implies) imply:
% 30.20/5.15 | | (3) $false
% 30.20/5.15 | |
% 30.20/5.15 | | CLOSE: (3) is inconsistent.
% 30.20/5.15 | |
% 30.20/5.15 | Case 2:
% 30.20/5.15 | |
% 30.20/5.15 | | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (strict_implies(v0, v1)
% 30.20/5.15 | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (necessarily(v3) =
% 30.20/5.15 | | v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2)))
% 30.20/5.15 | |
% 30.20/5.15 | | BETA: splitting (axiom_5) gives:
% 30.20/5.15 | |
% 30.20/5.15 | | Case 1:
% 30.20/5.15 | | |
% 30.20/5.16 | | | (5) axiom_5 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 30.20/5.16 | | | ~ (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~
% 30.20/5.16 | | | (implies(v1, v2) = v3) | ~ $i(v0) | is_a_theorem(v3) = 0)
% 30.20/5.16 | | |
% 30.20/5.16 | | | ALPHA: (5) implies:
% 30.20/5.16 | | | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 30.20/5.16 | | | (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v1,
% 30.20/5.16 | | | v2) = v3) | ~ $i(v0) | is_a_theorem(v3) = 0)
% 30.20/5.16 | | |
% 30.20/5.16 | | | BETA: splitting (necessitation) gives:
% 30.20/5.16 | | |
% 30.20/5.16 | | | Case 1:
% 30.20/5.16 | | | |
% 30.20/5.16 | | | | (7) necessitation & ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0)
% 30.20/5.16 | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 30.20/5.16 | | | | (is_a_theorem(v1) = v3 & is_a_theorem(v0) = v2 & ( ~ (v2 = 0) |
% 30.20/5.16 | | | | v3 = 0)))
% 30.20/5.16 | | | |
% 30.20/5.16 | | | | ALPHA: (7) implies:
% 30.20/5.16 | | | | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) = v1) | ~
% 30.20/5.16 | | | | $i(v0) | ? [v2: any] : ? [v3: any] : (is_a_theorem(v1) = v3 &
% 30.20/5.16 | | | | is_a_theorem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.20/5.16 | | | |
% 30.20/5.16 | | | | BETA: splitting (axiom_m10) gives:
% 30.20/5.16 | | | |
% 30.20/5.16 | | | | Case 1:
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | (9) axiom_m10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 30.20/5.16 | | | | | $i] : ( ~ (possibly(v0) = v1) | ~ (strict_implies(v1, v2) =
% 30.20/5.16 | | | | | v3) | ~ (necessarily(v1) = v2) | ~ $i(v0) |
% 30.20/5.16 | | | | | is_a_theorem(v3) = 0)
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | ALPHA: (9) implies:
% 30.20/5.16 | | | | | (10) axiom_m10
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | PRED_UNIFY: (10), (s1_0_m10_axiom_m10) imply:
% 30.20/5.16 | | | | | (11) $false
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | CLOSE: (11) is inconsistent.
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | Case 2:
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | (12) ~ axiom_m10 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 30.20/5.16 | | | | | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & possibly(v0) = v1 &
% 30.20/5.16 | | | | | strict_implies(v1, v2) = v3 & necessarily(v1) = v2 &
% 30.20/5.16 | | | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | ALPHA: (12) implies:
% 30.20/5.16 | | | | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 30.20/5.16 | | | | | [v4: int] : ( ~ (v4 = 0) & possibly(v0) = v1 &
% 30.20/5.16 | | | | | strict_implies(v1, v2) = v3 & necessarily(v1) = v2 &
% 30.20/5.16 | | | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | DELTA: instantiating (13) with fresh symbols all_125_0, all_125_1,
% 30.20/5.16 | | | | | all_125_2, all_125_3, all_125_4 gives:
% 30.20/5.16 | | | | | (14) ~ (all_125_0 = 0) & possibly(all_125_4) = all_125_3 &
% 30.20/5.16 | | | | | strict_implies(all_125_3, all_125_2) = all_125_1 &
% 30.20/5.16 | | | | | necessarily(all_125_3) = all_125_2 & is_a_theorem(all_125_1) =
% 30.20/5.16 | | | | | all_125_0 & $i(all_125_1) & $i(all_125_2) & $i(all_125_3) &
% 30.20/5.16 | | | | | $i(all_125_4)
% 30.20/5.16 | | | | |
% 30.20/5.16 | | | | | ALPHA: (14) implies:
% 30.20/5.16 | | | | | (15) ~ (all_125_0 = 0)
% 30.20/5.17 | | | | | (16) $i(all_125_4)
% 30.20/5.17 | | | | | (17) $i(all_125_3)
% 30.20/5.17 | | | | | (18) $i(all_125_2)
% 30.20/5.17 | | | | | (19) is_a_theorem(all_125_1) = all_125_0
% 30.20/5.17 | | | | | (20) necessarily(all_125_3) = all_125_2
% 30.20/5.17 | | | | | (21) strict_implies(all_125_3, all_125_2) = all_125_1
% 30.20/5.17 | | | | | (22) possibly(all_125_4) = all_125_3
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | GROUND_INST: instantiating (4) with all_125_3, all_125_2, all_125_1,
% 30.20/5.17 | | | | | simplifying with (17), (18), (21) gives:
% 30.20/5.17 | | | | | (23) ? [v0: $i] : (necessarily(v0) = all_125_1 &
% 30.20/5.17 | | | | | implies(all_125_3, all_125_2) = v0 & $i(v0) & $i(all_125_1))
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | DELTA: instantiating (23) with fresh symbol all_132_0 gives:
% 30.20/5.17 | | | | | (24) necessarily(all_132_0) = all_125_1 & implies(all_125_3,
% 30.20/5.17 | | | | | all_125_2) = all_132_0 & $i(all_132_0) & $i(all_125_1)
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | ALPHA: (24) implies:
% 30.20/5.17 | | | | | (25) $i(all_132_0)
% 30.20/5.17 | | | | | (26) implies(all_125_3, all_125_2) = all_132_0
% 30.20/5.17 | | | | | (27) necessarily(all_132_0) = all_125_1
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | GROUND_INST: instantiating (6) with all_125_4, all_125_3, all_125_2,
% 30.20/5.17 | | | | | all_132_0, simplifying with (16), (20), (22), (26) gives:
% 30.20/5.17 | | | | | (28) is_a_theorem(all_132_0) = 0
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | GROUND_INST: instantiating (8) with all_132_0, all_125_1, simplifying
% 30.20/5.17 | | | | | with (25), (27) gives:
% 30.20/5.17 | | | | | (29) ? [v0: any] : ? [v1: any] : (is_a_theorem(all_132_0) = v0 &
% 30.20/5.17 | | | | | is_a_theorem(all_125_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | DELTA: instantiating (29) with fresh symbols all_397_0, all_397_1
% 30.20/5.17 | | | | | gives:
% 30.20/5.17 | | | | | (30) is_a_theorem(all_132_0) = all_397_1 & is_a_theorem(all_125_1)
% 30.20/5.17 | | | | | = all_397_0 & ( ~ (all_397_1 = 0) | all_397_0 = 0)
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | ALPHA: (30) implies:
% 30.20/5.17 | | | | | (31) is_a_theorem(all_125_1) = all_397_0
% 30.20/5.17 | | | | | (32) is_a_theorem(all_132_0) = all_397_1
% 30.20/5.17 | | | | | (33) ~ (all_397_1 = 0) | all_397_0 = 0
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | GROUND_INST: instantiating (1) with all_125_0, all_397_0, all_125_1,
% 30.20/5.17 | | | | | simplifying with (19), (31) gives:
% 30.20/5.17 | | | | | (34) all_397_0 = all_125_0
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | GROUND_INST: instantiating (1) with 0, all_397_1, all_132_0,
% 30.20/5.17 | | | | | simplifying with (28), (32) gives:
% 30.20/5.17 | | | | | (35) all_397_1 = 0
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | BETA: splitting (33) gives:
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | | Case 1:
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | (36) ~ (all_397_1 = 0)
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | REDUCE: (35), (36) imply:
% 30.20/5.17 | | | | | | (37) $false
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | CLOSE: (37) is inconsistent.
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | Case 2:
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | (38) all_397_0 = 0
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | COMBINE_EQS: (34), (38) imply:
% 30.20/5.17 | | | | | | (39) all_125_0 = 0
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | SIMP: (39) implies:
% 30.20/5.17 | | | | | | (40) all_125_0 = 0
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | REDUCE: (15), (40) imply:
% 30.20/5.17 | | | | | | (41) $false
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | | CLOSE: (41) is inconsistent.
% 30.20/5.17 | | | | | |
% 30.20/5.17 | | | | | End of split
% 30.20/5.17 | | | | |
% 30.20/5.17 | | | | End of split
% 30.20/5.17 | | | |
% 30.20/5.17 | | | Case 2:
% 30.20/5.17 | | | |
% 30.20/5.17 | | | | (42) ~ necessitation & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : (
% 30.20/5.17 | | | | ~ (v2 = 0) & necessarily(v0) = v1 & is_a_theorem(v1) = v2 &
% 30.20/5.17 | | | | is_a_theorem(v0) = 0 & $i(v1) & $i(v0))
% 30.20/5.17 | | | |
% 30.20/5.17 | | | | ALPHA: (42) implies:
% 30.20/5.17 | | | | (43) ~ necessitation
% 30.20/5.17 | | | |
% 30.20/5.17 | | | | PRED_UNIFY: (43), (km5_necessitation) imply:
% 30.20/5.17 | | | | (44) $false
% 30.20/5.17 | | | |
% 30.20/5.17 | | | | CLOSE: (44) is inconsistent.
% 30.20/5.17 | | | |
% 30.20/5.17 | | | End of split
% 30.20/5.17 | | |
% 30.20/5.17 | | Case 2:
% 30.20/5.17 | | |
% 30.20/5.18 | | | (45) ~ axiom_5 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 30.20/5.18 | | | : ? [v4: int] : ( ~ (v4 = 0) & possibly(v0) = v1 &
% 30.20/5.18 | | | necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) =
% 30.20/5.18 | | | v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 30.20/5.18 | | |
% 30.20/5.18 | | | ALPHA: (45) implies:
% 30.20/5.18 | | | (46) ~ axiom_5
% 30.20/5.18 | | |
% 30.20/5.18 | | | PRED_UNIFY: (46), (km5_axiom_5) imply:
% 30.20/5.18 | | | (47) $false
% 30.20/5.18 | | |
% 30.20/5.18 | | | CLOSE: (47) is inconsistent.
% 30.20/5.18 | | |
% 30.20/5.18 | | End of split
% 30.20/5.18 | |
% 30.20/5.18 | End of split
% 30.20/5.18 |
% 30.20/5.18 End of proof
% 30.20/5.18 % SZS output end Proof for theBenchmark
% 30.20/5.18
% 30.20/5.18 4548ms
%------------------------------------------------------------------------------