TSTP Solution File: LCL525+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL525+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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:11:33 EDT 2023
% Result : Theorem 11.53s 3.58s
% Output : Proof 73.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL525+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 07:11:24 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.18/0.67 ________ _____
% 0.18/0.67 ___ __ \_________(_)________________________________
% 0.18/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.67
% 0.18/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.67 (2023-06-19)
% 0.18/0.67
% 0.18/0.67 (c) Philipp Rümmer, 2009-2023
% 0.18/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.67 Amanda Stjerna.
% 0.18/0.67 Free software under BSD-3-Clause.
% 0.18/0.67
% 0.18/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.67
% 0.18/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.68 Running up to 7 provers in parallel.
% 0.18/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.95/1.53 Prover 4: Preprocessing ...
% 2.95/1.53 Prover 1: Preprocessing ...
% 3.59/1.59 Prover 0: Preprocessing ...
% 3.59/1.59 Prover 6: Preprocessing ...
% 3.59/1.59 Prover 3: Preprocessing ...
% 3.59/1.59 Prover 5: Preprocessing ...
% 3.59/1.59 Prover 2: Preprocessing ...
% 9.89/3.04 Prover 6: Constructing countermodel ...
% 10.12/3.08 Prover 1: Constructing countermodel ...
% 10.12/3.09 Prover 5: Proving ...
% 10.31/3.11 Prover 3: Constructing countermodel ...
% 10.45/3.22 Prover 4: Constructing countermodel ...
% 11.31/3.39 Prover 0: Proving ...
% 11.53/3.52 Prover 2: Proving ...
% 11.53/3.58 Prover 3: proved (2879ms)
% 11.53/3.58
% 11.53/3.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.53/3.58
% 11.53/3.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.86/3.61 Prover 6: stopped
% 11.86/3.63 Prover 2: stopped
% 11.86/3.63 Prover 5: stopped
% 11.86/3.63 Prover 0: stopped
% 11.86/3.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.86/3.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.86/3.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.86/3.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.82/3.71 Prover 7: Preprocessing ...
% 13.07/3.78 Prover 10: Preprocessing ...
% 13.07/3.79 Prover 8: Preprocessing ...
% 13.28/3.81 Prover 13: Preprocessing ...
% 13.28/3.83 Prover 11: Preprocessing ...
% 14.81/4.19 Prover 13: Warning: ignoring some quantifiers
% 14.81/4.25 Prover 8: Warning: ignoring some quantifiers
% 14.81/4.25 Prover 13: Constructing countermodel ...
% 14.81/4.28 Prover 8: Constructing countermodel ...
% 14.81/4.28 Prover 10: Constructing countermodel ...
% 14.81/4.28 Prover 7: Constructing countermodel ...
% 15.08/4.40 Prover 11: Constructing countermodel ...
% 40.49/9.33 Prover 13: stopped
% 41.64/9.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 41.69/9.47 Prover 16: Preprocessing ...
% 42.79/9.67 Prover 16: Warning: ignoring some quantifiers
% 43.39/9.68 Prover 16: Constructing countermodel ...
% 70.10/14.61 Prover 8: Found proof (size 81)
% 70.10/14.61 Prover 8: proved (10784ms)
% 70.10/14.61 Prover 7: stopped
% 70.10/14.61 Prover 4: stopped
% 70.10/14.62 Prover 16: stopped
% 70.10/14.62 Prover 11: stopped
% 70.47/14.64 Prover 1: stopped
% 72.41/15.04 Prover 10: stopped
% 72.41/15.04
% 72.41/15.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.41/15.04
% 72.41/15.05 % SZS output start Proof for theBenchmark
% 72.41/15.05 Assumptions after simplification:
% 72.41/15.05 ---------------------------------
% 72.41/15.06
% 72.41/15.06 (axiom_M)
% 72.49/15.10 (axiom_M & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (necessarily(v0) =
% 72.49/15.10 v1) | ~ (implies(v1, v0) = v2) | ~ $i(v0) | is_a_theorem(v2) = 0)) | (
% 72.49/15.10 ~ axiom_M & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3
% 72.49/15.10 = 0) & necessarily(v0) = v1 & implies(v1, v0) = v2 & is_a_theorem(v2) =
% 72.49/15.10 v3 & $i(v2) & $i(v1) & $i(v0)))
% 72.49/15.10
% 72.49/15.10 (axiom_m4)
% 72.49/15.11 (axiom_m4 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (strict_implies(v0,
% 72.49/15.11 v1) = v2) | ~ (and(v0, v0) = v1) | ~ $i(v0) | is_a_theorem(v2) = 0))
% 72.49/15.11 | ( ~ axiom_m4 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~
% 72.49/15.11 (v3 = 0) & strict_implies(v0, v1) = v2 & and(v0, v0) = v1 &
% 72.49/15.11 is_a_theorem(v2) = v3 & $i(v2) & $i(v1) & $i(v0)))
% 72.49/15.11
% 72.49/15.11 (hilbert_modus_ponens)
% 72.49/15.11 modus_ponens
% 72.49/15.11
% 72.49/15.11 (km5_axiom_M)
% 72.49/15.11 axiom_M
% 72.49/15.11
% 72.49/15.11 (modus_ponens)
% 72.49/15.11 (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 72.49/15.11 (is_a_theorem(v1) = v2) | ~ (is_a_theorem(v0) = 0) | ~ $i(v1) | ~
% 72.49/15.11 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & implies(v0, v1) = v3
% 72.49/15.11 & is_a_theorem(v3) = v4 & $i(v3)))) | ( ~ modus_ponens & ? [v0: $i] :
% 72.49/15.11 ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & implies(v0, v1) =
% 72.49/15.11 v2 & is_a_theorem(v2) = 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 &
% 72.49/15.11 $i(v2) & $i(v1) & $i(v0)))
% 72.49/15.11
% 72.49/15.11 (modus_ponens_strict_implies)
% 72.49/15.12 (modus_ponens_strict_implies & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 72.49/15.12 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 72.49/15.12 [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5
% 72.49/15.12 & is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))) | ( ~
% 72.49/15.12 modus_ponens_strict_implies & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 72.49/15.12 [v3: int] : ( ~ (v3 = 0) & strict_implies(v0, v1) = v2 & is_a_theorem(v2) =
% 72.49/15.12 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & $i(v2) & $i(v1) &
% 72.49/15.12 $i(v0)))
% 72.49/15.12
% 72.49/15.12 (op_strict_implies)
% 72.49/15.12 ~ op_strict_implies | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 72.49/15.12 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 72.49/15.12 (necessarily(v3) = v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2)))
% 72.49/15.12
% 72.49/15.12 (s1_0_modus_ponens_strict_implies)
% 72.49/15.12 ~ modus_ponens_strict_implies
% 72.49/15.12
% 72.49/15.12 (s1_0_op_strict_implies)
% 72.49/15.12 op_strict_implies
% 72.49/15.12
% 72.49/15.12 (function-axioms)
% 72.49/15.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 72.49/15.14 (strict_equiv(v3, v2) = v1) | ~ (strict_equiv(v3, v2) = v0)) & ! [v0: $i]
% 72.49/15.14 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (strict_implies(v3,
% 72.49/15.14 v2) = v1) | ~ (strict_implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 72.49/15.14 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~
% 72.49/15.14 (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 72.49/15.14 (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0)) & ! [v0: $i] : !
% 72.49/15.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~
% 72.49/15.14 (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 72.49/15.14 $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) & !
% 72.49/15.14 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (possibly(v2) = v1) | ~
% 72.49/15.14 (possibly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 72.49/15.14 ~ (necessarily(v2) = v1) | ~ (necessarily(v2) = v0)) & ! [v0: $i] : !
% 72.49/15.14 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) &
% 72.49/15.14 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 72.49/15.14 v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) & ? [v0: $i]
% 72.49/15.14 : ? [v1: $i] : ? [v2: $i] : (strict_equiv(v1, v0) = v2 & $i(v2)) & ? [v0:
% 72.49/15.14 $i] : ? [v1: $i] : ? [v2: $i] : (strict_implies(v1, v0) = v2 & $i(v2)) &
% 72.49/15.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (or(v1, v0) = v2 & $i(v2)) & ? [v0:
% 72.49/15.14 $i] : ? [v1: $i] : ? [v2: $i] : (and(v1, v0) = v2 & $i(v2)) & ? [v0: $i]
% 72.49/15.14 : ? [v1: $i] : ? [v2: $i] : (equiv(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 72.49/15.14 [v1: $i] : ? [v2: $i] : (implies(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 72.49/15.14 [v1: MultipleValueBool] : (is_a_theorem(v0) = v1) & ? [v0: $i] : ? [v1: $i]
% 72.49/15.14 : (possibly(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (necessarily(v0)
% 72.49/15.14 = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (not(v0) = v1 & $i(v1))
% 72.49/15.14
% 72.49/15.14 Further assumptions not needed in the proof:
% 72.49/15.14 --------------------------------------------
% 72.49/15.14 adjunction, and_1, and_2, and_3, axiom_4, axiom_5, axiom_B, axiom_K, axiom_m1,
% 72.49/15.14 axiom_m10, axiom_m2, axiom_m3, axiom_m5, axiom_m6, axiom_m7, axiom_m8, axiom_m9,
% 72.49/15.14 axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1,
% 72.49/15.14 equivalence_2, equivalence_3, hilbert_and_1, hilbert_and_2, hilbert_and_3,
% 72.49/15.14 hilbert_equivalence_1, hilbert_equivalence_2, hilbert_equivalence_3,
% 72.49/15.14 hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, hilbert_modus_tollens,
% 72.49/15.14 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, hilbert_or_1,
% 72.49/15.14 hilbert_or_2, hilbert_or_3, implies_1, implies_2, implies_3, km5_axiom_5,
% 72.49/15.14 km5_axiom_K, km5_necessitation, km5_op_possibly, kn1, kn2, kn3, modus_tollens,
% 72.49/15.14 necessitation, op_and, op_equiv, op_implies_and, op_implies_or, op_necessarily,
% 72.49/15.14 op_or, op_possibly, op_strict_equiv, or_1, or_2, or_3, r1, r2, r3, r4, r5,
% 72.49/15.14 s1_0_op_equiv, s1_0_op_implies, s1_0_op_or, s1_0_op_possibly,
% 72.49/15.14 s1_0_op_strict_equiv, substitution_of_equivalents, substitution_strict_equiv
% 72.49/15.14
% 72.49/15.14 Those formulas are unsatisfiable:
% 72.85/15.14 ---------------------------------
% 72.85/15.14
% 72.85/15.14 Begin of proof
% 72.85/15.14 |
% 72.85/15.14 | ALPHA: (function-axioms) implies:
% 72.85/15.15 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 72.85/15.15 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 72.85/15.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 72.85/15.15 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 72.85/15.15 |
% 72.85/15.15 | BETA: splitting (op_strict_implies) gives:
% 72.85/15.15 |
% 72.85/15.15 | Case 1:
% 72.85/15.15 | |
% 72.85/15.15 | | (3) ~ op_strict_implies
% 72.85/15.15 | |
% 72.85/15.15 | | PRED_UNIFY: (3), (s1_0_op_strict_implies) imply:
% 72.85/15.15 | | (4) $false
% 72.85/15.15 | |
% 72.85/15.15 | | CLOSE: (4) is inconsistent.
% 72.85/15.15 | |
% 72.85/15.15 | Case 2:
% 72.85/15.15 | |
% 72.85/15.15 | | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (strict_implies(v0, v1)
% 72.85/15.15 | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (necessarily(v3) =
% 72.85/15.15 | | v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2)))
% 72.85/15.15 | |
% 72.85/15.15 | | BETA: splitting (axiom_M) gives:
% 72.85/15.15 | |
% 72.85/15.15 | | Case 1:
% 72.85/15.15 | | |
% 72.85/15.15 | | | (6) axiom_M & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 72.85/15.15 | | | (necessarily(v0) = v1) | ~ (implies(v1, v0) = v2) | ~ $i(v0) |
% 72.85/15.15 | | | is_a_theorem(v2) = 0)
% 72.85/15.15 | | |
% 72.85/15.15 | | | ALPHA: (6) implies:
% 72.85/15.16 | | | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (necessarily(v0) =
% 72.85/15.16 | | | v1) | ~ (implies(v1, v0) = v2) | ~ $i(v0) | is_a_theorem(v2)
% 72.85/15.16 | | | = 0)
% 72.85/15.16 | | |
% 72.85/15.16 | | | BETA: splitting (modus_ponens) gives:
% 72.85/15.16 | | |
% 72.85/15.16 | | | Case 1:
% 72.85/15.16 | | | |
% 72.85/15.16 | | | | (8) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0
% 72.85/15.16 | | | | | ~ (is_a_theorem(v1) = v2) | ~ (is_a_theorem(v0) = 0) | ~
% 72.85/15.16 | | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 72.85/15.16 | | | | & implies(v0, v1) = v3 & is_a_theorem(v3) = v4 & $i(v3)))
% 72.85/15.16 | | | |
% 72.85/15.16 | | | | ALPHA: (8) implies:
% 72.85/15.16 | | | | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 72.85/15.16 | | | | (is_a_theorem(v1) = v2) | ~ (is_a_theorem(v0) = 0) | ~ $i(v1)
% 72.85/15.16 | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 72.85/15.16 | | | | implies(v0, v1) = v3 & is_a_theorem(v3) = v4 & $i(v3)))
% 72.85/15.16 | | | |
% 72.85/15.16 | | | | BETA: splitting (modus_ponens_strict_implies) gives:
% 72.85/15.16 | | | |
% 72.85/15.16 | | | | Case 1:
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | (10) modus_ponens_strict_implies & ! [v0: $i] : ! [v1: $i] : !
% 72.85/15.16 | | | | | [v2: $i] : ( ~ (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~
% 72.85/15.16 | | | | | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 72.85/15.16 | | | | | (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 &
% 72.85/15.16 | | | | | is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 72.85/15.16 | | | | | 0)))
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | ALPHA: (10) implies:
% 72.85/15.16 | | | | | (11) modus_ponens_strict_implies
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | PRED_UNIFY: (11), (s1_0_modus_ponens_strict_implies) imply:
% 72.85/15.16 | | | | | (12) $false
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | CLOSE: (12) is inconsistent.
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | Case 2:
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | (13) ~ modus_ponens_strict_implies & ? [v0: $i] : ? [v1: $i] :
% 72.85/15.16 | | | | | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & strict_implies(v0,
% 72.85/15.16 | | | | | v1) = v2 & is_a_theorem(v2) = 0 & is_a_theorem(v1) = v3 &
% 72.85/15.16 | | | | | is_a_theorem(v0) = 0 & $i(v2) & $i(v1) & $i(v0))
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | ALPHA: (13) implies:
% 72.85/15.16 | | | | | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~
% 72.85/15.16 | | | | | (v3 = 0) & strict_implies(v0, v1) = v2 & is_a_theorem(v2) =
% 72.85/15.16 | | | | | 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & $i(v2) &
% 72.85/15.16 | | | | | $i(v1) & $i(v0))
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | DELTA: instantiating (14) with fresh symbols all_125_0, all_125_1,
% 72.85/15.16 | | | | | all_125_2, all_125_3 gives:
% 72.85/15.16 | | | | | (15) ~ (all_125_0 = 0) & strict_implies(all_125_3, all_125_2) =
% 72.85/15.16 | | | | | all_125_1 & is_a_theorem(all_125_1) = 0 &
% 72.85/15.16 | | | | | is_a_theorem(all_125_2) = all_125_0 & is_a_theorem(all_125_3)
% 72.85/15.16 | | | | | = 0 & $i(all_125_1) & $i(all_125_2) & $i(all_125_3)
% 72.85/15.16 | | | | |
% 72.85/15.16 | | | | | ALPHA: (15) implies:
% 72.85/15.16 | | | | | (16) ~ (all_125_0 = 0)
% 72.85/15.17 | | | | | (17) $i(all_125_3)
% 72.85/15.17 | | | | | (18) $i(all_125_2)
% 72.85/15.17 | | | | | (19) $i(all_125_1)
% 72.85/15.17 | | | | | (20) is_a_theorem(all_125_3) = 0
% 72.85/15.17 | | | | | (21) is_a_theorem(all_125_2) = all_125_0
% 72.85/15.17 | | | | | (22) is_a_theorem(all_125_1) = 0
% 72.85/15.17 | | | | | (23) strict_implies(all_125_3, all_125_2) = all_125_1
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | GROUND_INST: instantiating (9) with all_125_3, all_125_2, all_125_0,
% 72.85/15.17 | | | | | simplifying with (17), (18), (20), (21) gives:
% 72.85/15.17 | | | | | (24) all_125_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 72.85/15.17 | | | | | implies(all_125_3, all_125_2) = v0 & is_a_theorem(v0) = v1 &
% 72.85/15.17 | | | | | $i(v0))
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | GROUND_INST: instantiating (9) with all_125_1, all_125_2, all_125_0,
% 72.85/15.17 | | | | | simplifying with (18), (19), (21), (22) gives:
% 72.85/15.17 | | | | | (25) all_125_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 72.85/15.17 | | | | | implies(all_125_1, all_125_2) = v0 & is_a_theorem(v0) = v1 &
% 72.85/15.17 | | | | | $i(v0))
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | GROUND_INST: instantiating (5) with all_125_3, all_125_2, all_125_1,
% 72.85/15.17 | | | | | simplifying with (17), (18), (23) gives:
% 72.85/15.17 | | | | | (26) ? [v0: $i] : (necessarily(v0) = all_125_1 &
% 72.85/15.17 | | | | | implies(all_125_3, all_125_2) = v0 & $i(v0) & $i(all_125_1))
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | DELTA: instantiating (26) with fresh symbol all_132_0 gives:
% 72.85/15.17 | | | | | (27) necessarily(all_132_0) = all_125_1 & implies(all_125_3,
% 72.85/15.17 | | | | | all_125_2) = all_132_0 & $i(all_132_0) & $i(all_125_1)
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | ALPHA: (27) implies:
% 72.85/15.17 | | | | | (28) implies(all_125_3, all_125_2) = all_132_0
% 72.85/15.17 | | | | | (29) necessarily(all_132_0) = all_125_1
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | BETA: splitting (24) gives:
% 72.85/15.17 | | | | |
% 72.85/15.17 | | | | | Case 1:
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | (30) all_125_0 = 0
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | REDUCE: (16), (30) imply:
% 72.85/15.17 | | | | | | (31) $false
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | CLOSE: (31) is inconsistent.
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | Case 2:
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 72.85/15.17 | | | | | | implies(all_125_3, all_125_2) = v0 & is_a_theorem(v0) = v1
% 72.85/15.17 | | | | | | & $i(v0))
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | DELTA: instantiating (32) with fresh symbols all_138_0, all_138_1
% 72.85/15.17 | | | | | | gives:
% 72.85/15.17 | | | | | | (33) ~ (all_138_0 = 0) & implies(all_125_3, all_125_2) =
% 72.85/15.17 | | | | | | all_138_1 & is_a_theorem(all_138_1) = all_138_0 &
% 72.85/15.17 | | | | | | $i(all_138_1)
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | ALPHA: (33) implies:
% 72.85/15.17 | | | | | | (34) ~ (all_138_0 = 0)
% 72.85/15.17 | | | | | | (35) $i(all_138_1)
% 72.85/15.17 | | | | | | (36) is_a_theorem(all_138_1) = all_138_0
% 72.85/15.17 | | | | | | (37) implies(all_125_3, all_125_2) = all_138_1
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | BETA: splitting (25) gives:
% 72.85/15.17 | | | | | |
% 72.85/15.17 | | | | | | Case 1:
% 72.85/15.17 | | | | | | |
% 72.85/15.17 | | | | | | | (38) all_125_0 = 0
% 72.85/15.17 | | | | | | |
% 72.85/15.17 | | | | | | | REDUCE: (16), (38) imply:
% 72.85/15.17 | | | | | | | (39) $false
% 72.85/15.17 | | | | | | |
% 72.85/15.17 | | | | | | | CLOSE: (39) is inconsistent.
% 72.85/15.17 | | | | | | |
% 72.85/15.17 | | | | | | Case 2:
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 72.85/15.18 | | | | | | | implies(all_125_1, all_125_2) = v0 & is_a_theorem(v0) =
% 72.85/15.18 | | | | | | | v1 & $i(v0))
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | DELTA: instantiating (40) with fresh symbols all_143_0, all_143_1
% 72.85/15.18 | | | | | | | gives:
% 72.85/15.18 | | | | | | | (41) ~ (all_143_0 = 0) & implies(all_125_1, all_125_2) =
% 72.85/15.18 | | | | | | | all_143_1 & is_a_theorem(all_143_1) = all_143_0 &
% 72.85/15.18 | | | | | | | $i(all_143_1)
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | ALPHA: (41) implies:
% 72.85/15.18 | | | | | | | (42) ~ (all_143_0 = 0)
% 72.85/15.18 | | | | | | | (43) $i(all_143_1)
% 72.85/15.18 | | | | | | | (44) is_a_theorem(all_143_1) = all_143_0
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | GROUND_INST: instantiating (2) with all_132_0, all_138_1,
% 72.85/15.18 | | | | | | | all_125_2, all_125_3, simplifying with (28), (37)
% 72.85/15.18 | | | | | | | gives:
% 72.85/15.18 | | | | | | | (45) all_138_1 = all_132_0
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | REDUCE: (36), (45) imply:
% 72.85/15.18 | | | | | | | (46) is_a_theorem(all_132_0) = all_138_0
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | REDUCE: (35), (45) imply:
% 72.85/15.18 | | | | | | | (47) $i(all_132_0)
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | BETA: splitting (axiom_m4) gives:
% 72.85/15.18 | | | | | | |
% 72.85/15.18 | | | | | | | Case 1:
% 72.85/15.18 | | | | | | | |
% 72.85/15.18 | | | | | | | |
% 73.03/15.18 | | | | | | | | GROUND_INST: instantiating (9) with all_125_1, all_132_0,
% 73.03/15.18 | | | | | | | | all_138_0, simplifying with (19), (22), (46), (47)
% 73.03/15.18 | | | | | | | | gives:
% 73.03/15.18 | | | | | | | | (48) all_138_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 =
% 73.03/15.18 | | | | | | | | 0) & implies(all_125_1, all_132_0) = v0 &
% 73.03/15.18 | | | | | | | | is_a_theorem(v0) = v1 & $i(v0))
% 73.03/15.18 | | | | | | | |
% 73.03/15.18 | | | | | | | | GROUND_INST: instantiating (9) with all_125_1, all_143_1,
% 73.03/15.18 | | | | | | | | all_143_0, simplifying with (19), (22), (43), (44)
% 73.03/15.18 | | | | | | | | gives:
% 73.03/15.18 | | | | | | | | (49) all_143_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 =
% 73.03/15.18 | | | | | | | | 0) & implies(all_125_1, all_143_1) = v0 &
% 73.03/15.18 | | | | | | | | is_a_theorem(v0) = v1 & $i(v0))
% 73.03/15.18 | | | | | | | |
% 73.03/15.18 | | | | | | | | BETA: splitting (48) gives:
% 73.03/15.18 | | | | | | | |
% 73.03/15.18 | | | | | | | | Case 1:
% 73.03/15.18 | | | | | | | | |
% 73.03/15.18 | | | | | | | | | (50) all_138_0 = 0
% 73.03/15.18 | | | | | | | | |
% 73.03/15.18 | | | | | | | | | REDUCE: (34), (50) imply:
% 73.03/15.18 | | | | | | | | | (51) $false
% 73.03/15.18 | | | | | | | | |
% 73.03/15.18 | | | | | | | | | CLOSE: (51) is inconsistent.
% 73.03/15.18 | | | | | | | | |
% 73.03/15.18 | | | | | | | | Case 2:
% 73.03/15.18 | | | | | | | | |
% 73.03/15.18 | | | | | | | | | (52) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 73.03/15.18 | | | | | | | | | implies(all_125_1, all_132_0) = v0 &
% 73.03/15.18 | | | | | | | | | is_a_theorem(v0) = v1 & $i(v0))
% 73.03/15.18 | | | | | | | | |
% 73.03/15.18 | | | | | | | | | DELTA: instantiating (52) with fresh symbols all_529_0,
% 73.03/15.18 | | | | | | | | | all_529_1 gives:
% 73.03/15.19 | | | | | | | | | (53) ~ (all_529_0 = 0) & implies(all_125_1, all_132_0) =
% 73.03/15.19 | | | | | | | | | all_529_1 & is_a_theorem(all_529_1) = all_529_0 &
% 73.03/15.19 | | | | | | | | | $i(all_529_1)
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | | ALPHA: (53) implies:
% 73.03/15.19 | | | | | | | | | (54) ~ (all_529_0 = 0)
% 73.03/15.19 | | | | | | | | | (55) is_a_theorem(all_529_1) = all_529_0
% 73.03/15.19 | | | | | | | | | (56) implies(all_125_1, all_132_0) = all_529_1
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | | BETA: splitting (49) gives:
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | | Case 1:
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | (57) all_143_0 = 0
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | REDUCE: (42), (57) imply:
% 73.03/15.19 | | | | | | | | | | (58) $false
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | CLOSE: (58) is inconsistent.
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | Case 2:
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | GROUND_INST: instantiating (7) with all_132_0, all_125_1,
% 73.03/15.19 | | | | | | | | | | all_529_1, simplifying with (29), (47), (56)
% 73.03/15.19 | | | | | | | | | | gives:
% 73.03/15.19 | | | | | | | | | | (59) is_a_theorem(all_529_1) = 0
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | GROUND_INST: instantiating (1) with all_529_0, 0, all_529_1,
% 73.03/15.19 | | | | | | | | | | simplifying with (55), (59) gives:
% 73.03/15.19 | | | | | | | | | | (60) all_529_0 = 0
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | REDUCE: (54), (60) imply:
% 73.03/15.19 | | | | | | | | | | (61) $false
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | | CLOSE: (61) is inconsistent.
% 73.03/15.19 | | | | | | | | | |
% 73.03/15.19 | | | | | | | | | End of split
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | End of split
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | Case 2:
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | (62) ~ axiom_m4 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 73.03/15.19 | | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & strict_implies(v0, v1) = v2
% 73.03/15.19 | | | | | | | | & and(v0, v0) = v1 & is_a_theorem(v2) = v3 & $i(v2) &
% 73.03/15.19 | | | | | | | | $i(v1) & $i(v0))
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | ALPHA: (62) implies:
% 73.03/15.19 | | | | | | | | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] :
% 73.03/15.19 | | | | | | | | ( ~ (v3 = 0) & strict_implies(v0, v1) = v2 & and(v0, v0)
% 73.03/15.19 | | | | | | | | = v1 & is_a_theorem(v2) = v3 & $i(v2) & $i(v1) &
% 73.03/15.19 | | | | | | | | $i(v0))
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | DELTA: instantiating (63) with fresh symbols all_363_0,
% 73.03/15.19 | | | | | | | | all_363_1, all_363_2, all_363_3 gives:
% 73.03/15.19 | | | | | | | | (64) ~ (all_363_0 = 0) & strict_implies(all_363_3,
% 73.03/15.19 | | | | | | | | all_363_2) = all_363_1 & and(all_363_3, all_363_3) =
% 73.03/15.19 | | | | | | | | all_363_2 & is_a_theorem(all_363_1) = all_363_0 &
% 73.03/15.19 | | | | | | | | $i(all_363_1) & $i(all_363_2) & $i(all_363_3)
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | ALPHA: (64) implies:
% 73.03/15.19 | | | | | | | | (65) ~ (all_363_0 = 0)
% 73.03/15.19 | | | | | | | | (66) $i(all_363_1)
% 73.03/15.19 | | | | | | | | (67) is_a_theorem(all_363_1) = all_363_0
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | GROUND_INST: instantiating (9) with all_125_1, all_132_0,
% 73.03/15.19 | | | | | | | | all_138_0, simplifying with (19), (22), (46), (47)
% 73.03/15.19 | | | | | | | | gives:
% 73.03/15.19 | | | | | | | | (68) all_138_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 =
% 73.03/15.19 | | | | | | | | 0) & implies(all_125_1, all_132_0) = v0 &
% 73.03/15.19 | | | | | | | | is_a_theorem(v0) = v1 & $i(v0))
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | GROUND_INST: instantiating (9) with all_125_1, all_363_1,
% 73.03/15.19 | | | | | | | | all_363_0, simplifying with (19), (22), (66), (67)
% 73.03/15.19 | | | | | | | | gives:
% 73.03/15.19 | | | | | | | | (69) all_363_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 =
% 73.03/15.19 | | | | | | | | 0) & implies(all_125_1, all_363_1) = v0 &
% 73.03/15.19 | | | | | | | | is_a_theorem(v0) = v1 & $i(v0))
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | BETA: splitting (68) gives:
% 73.03/15.19 | | | | | | | |
% 73.03/15.19 | | | | | | | | Case 1:
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | | (70) all_138_0 = 0
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | | REDUCE: (34), (70) imply:
% 73.03/15.19 | | | | | | | | | (71) $false
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | | CLOSE: (71) is inconsistent.
% 73.03/15.19 | | | | | | | | |
% 73.03/15.19 | | | | | | | | Case 2:
% 73.03/15.19 | | | | | | | | |
% 73.03/15.20 | | | | | | | | | (72) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 73.03/15.20 | | | | | | | | | implies(all_125_1, all_132_0) = v0 &
% 73.03/15.20 | | | | | | | | | is_a_theorem(v0) = v1 & $i(v0))
% 73.03/15.20 | | | | | | | | |
% 73.03/15.20 | | | | | | | | | DELTA: instantiating (72) with fresh symbols all_509_0,
% 73.03/15.20 | | | | | | | | | all_509_1 gives:
% 73.03/15.20 | | | | | | | | | (73) ~ (all_509_0 = 0) & implies(all_125_1, all_132_0) =
% 73.03/15.20 | | | | | | | | | all_509_1 & is_a_theorem(all_509_1) = all_509_0 &
% 73.03/15.20 | | | | | | | | | $i(all_509_1)
% 73.03/15.20 | | | | | | | | |
% 73.03/15.20 | | | | | | | | | ALPHA: (73) implies:
% 73.03/15.20 | | | | | | | | | (74) ~ (all_509_0 = 0)
% 73.03/15.20 | | | | | | | | | (75) is_a_theorem(all_509_1) = all_509_0
% 73.03/15.20 | | | | | | | | | (76) implies(all_125_1, all_132_0) = all_509_1
% 73.03/15.20 | | | | | | | | |
% 73.03/15.20 | | | | | | | | | BETA: splitting (69) gives:
% 73.03/15.20 | | | | | | | | |
% 73.03/15.20 | | | | | | | | | Case 1:
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | (77) all_363_0 = 0
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | REDUCE: (65), (77) imply:
% 73.03/15.20 | | | | | | | | | | (78) $false
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | CLOSE: (78) is inconsistent.
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | Case 2:
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | GROUND_INST: instantiating (7) with all_132_0, all_125_1,
% 73.03/15.20 | | | | | | | | | | all_509_1, simplifying with (29), (47), (76)
% 73.03/15.20 | | | | | | | | | | gives:
% 73.03/15.20 | | | | | | | | | | (79) is_a_theorem(all_509_1) = 0
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | GROUND_INST: instantiating (1) with all_509_0, 0, all_509_1,
% 73.03/15.20 | | | | | | | | | | simplifying with (75), (79) gives:
% 73.03/15.20 | | | | | | | | | | (80) all_509_0 = 0
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | REDUCE: (74), (80) imply:
% 73.03/15.20 | | | | | | | | | | (81) $false
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | | CLOSE: (81) is inconsistent.
% 73.03/15.20 | | | | | | | | | |
% 73.03/15.20 | | | | | | | | | End of split
% 73.03/15.20 | | | | | | | | |
% 73.03/15.20 | | | | | | | | End of split
% 73.03/15.20 | | | | | | | |
% 73.03/15.20 | | | | | | | End of split
% 73.03/15.20 | | | | | | |
% 73.03/15.20 | | | | | | End of split
% 73.03/15.20 | | | | | |
% 73.03/15.20 | | | | | End of split
% 73.03/15.20 | | | | |
% 73.03/15.20 | | | | End of split
% 73.03/15.20 | | | |
% 73.03/15.20 | | | Case 2:
% 73.03/15.20 | | | |
% 73.03/15.20 | | | | (82) ~ modus_ponens & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 73.03/15.20 | | | | [v3: int] : ( ~ (v3 = 0) & implies(v0, v1) = v2 &
% 73.03/15.20 | | | | is_a_theorem(v2) = 0 & is_a_theorem(v1) = v3 &
% 73.03/15.20 | | | | is_a_theorem(v0) = 0 & $i(v2) & $i(v1) & $i(v0))
% 73.03/15.20 | | | |
% 73.03/15.20 | | | | ALPHA: (82) implies:
% 73.03/15.20 | | | | (83) ~ modus_ponens
% 73.03/15.20 | | | |
% 73.03/15.20 | | | | PRED_UNIFY: (83), (hilbert_modus_ponens) imply:
% 73.03/15.20 | | | | (84) $false
% 73.03/15.20 | | | |
% 73.03/15.20 | | | | CLOSE: (84) is inconsistent.
% 73.03/15.20 | | | |
% 73.03/15.20 | | | End of split
% 73.03/15.20 | | |
% 73.03/15.20 | | Case 2:
% 73.03/15.20 | | |
% 73.03/15.20 | | | (85) ~ axiom_M & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 73.03/15.20 | | | int] : ( ~ (v3 = 0) & necessarily(v0) = v1 & implies(v1, v0) =
% 73.03/15.20 | | | v2 & is_a_theorem(v2) = v3 & $i(v2) & $i(v1) & $i(v0))
% 73.03/15.20 | | |
% 73.03/15.20 | | | ALPHA: (85) implies:
% 73.03/15.20 | | | (86) ~ axiom_M
% 73.03/15.20 | | |
% 73.03/15.20 | | | PRED_UNIFY: (86), (km5_axiom_M) imply:
% 73.03/15.20 | | | (87) $false
% 73.03/15.20 | | |
% 73.03/15.20 | | | CLOSE: (87) is inconsistent.
% 73.03/15.20 | | |
% 73.03/15.20 | | End of split
% 73.03/15.20 | |
% 73.03/15.20 | End of split
% 73.03/15.20 |
% 73.03/15.20 End of proof
% 73.03/15.20 % SZS output end Proof for theBenchmark
% 73.03/15.20
% 73.03/15.20 14533ms
%------------------------------------------------------------------------------