TSTP Solution File: LCL469+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL469+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 08:11:24 EDT 2023
% Result : Theorem 9.70s 2.15s
% Output : Proof 29.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL469+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Fri Aug 25 04:11:32 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.14/1.16 Prover 4: Preprocessing ...
% 3.14/1.16 Prover 1: Preprocessing ...
% 3.52/1.21 Prover 5: Preprocessing ...
% 3.52/1.21 Prover 6: Preprocessing ...
% 3.52/1.21 Prover 0: Preprocessing ...
% 3.52/1.21 Prover 3: Preprocessing ...
% 3.52/1.21 Prover 2: Preprocessing ...
% 7.52/1.83 Prover 5: Proving ...
% 7.88/1.83 Prover 6: Constructing countermodel ...
% 7.96/1.86 Prover 1: Constructing countermodel ...
% 7.96/1.86 Prover 3: Constructing countermodel ...
% 7.96/1.90 Prover 0: Proving ...
% 8.45/1.92 Prover 4: Constructing countermodel ...
% 8.45/1.95 Prover 2: Proving ...
% 9.70/2.15 Prover 5: proved (1514ms)
% 9.70/2.15
% 9.70/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.70/2.15
% 9.70/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.70/2.15 Prover 3: stopped
% 9.70/2.16 Prover 2: stopped
% 9.70/2.18 Prover 0: stopped
% 9.70/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.70/2.19 Prover 6: stopped
% 9.70/2.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.70/2.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.70/2.20 Prover 7: Preprocessing ...
% 9.70/2.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.70/2.24 Prover 8: Preprocessing ...
% 9.70/2.25 Prover 10: Preprocessing ...
% 9.70/2.28 Prover 13: Preprocessing ...
% 9.70/2.29 Prover 11: Preprocessing ...
% 11.82/2.42 Prover 7: Constructing countermodel ...
% 11.82/2.42 Prover 8: Warning: ignoring some quantifiers
% 11.82/2.44 Prover 13: Warning: ignoring some quantifiers
% 11.82/2.44 Prover 8: Constructing countermodel ...
% 11.82/2.44 Prover 10: Constructing countermodel ...
% 12.42/2.47 Prover 13: Constructing countermodel ...
% 12.69/2.52 Prover 11: Constructing countermodel ...
% 14.70/2.79 Prover 1: gave up
% 14.70/2.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 14.70/2.82 Prover 10: gave up
% 14.70/2.83 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 14.70/2.87 Prover 16: Preprocessing ...
% 14.70/2.92 Prover 19: Preprocessing ...
% 14.70/2.93 Prover 13: gave up
% 16.04/2.97 Prover 16: Warning: ignoring some quantifiers
% 16.04/3.00 Prover 16: Constructing countermodel ...
% 16.04/3.04 Prover 19: Warning: ignoring some quantifiers
% 16.04/3.05 Prover 19: Constructing countermodel ...
% 17.00/3.13 Prover 8: gave up
% 17.97/3.28 Prover 19: gave up
% 23.34/4.01 Prover 16: gave up
% 28.38/4.99 Prover 11: Found proof (size 105)
% 28.38/4.99 Prover 11: proved (2791ms)
% 28.38/4.99 Prover 4: stopped
% 28.38/4.99 Prover 7: stopped
% 28.38/4.99
% 28.38/4.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.38/4.99
% 28.38/5.00 % SZS output start Proof for theBenchmark
% 28.38/5.00 Assumptions after simplification:
% 28.38/5.00 ---------------------------------
% 28.38/5.00
% 28.38/5.00 (cn1)
% 28.38/5.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 28.38/5.03 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ($i(v2) & $i(v1) & $i(v0) &
% 28.38/5.03 (( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 & implies(v1,
% 28.38/5.03 v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) = v3 &
% 28.38/5.03 is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ~
% 28.38/5.03 cn1) | (cn1 & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 28.38/5.03 ! [v13: $i] : ! [v14: $i] : ( ~ (implies(v12, v13) = v14) | ~
% 28.38/5.03 (implies(v10, v11) = v12) | ~ (implies(v9, v11) = v13) | ~ $i(v11) |
% 28.38/5.03 ~ $i(v10) | ~ $i(v9) | ? [v15: $i] : ? [v16: $i] : (implies(v15,
% 28.38/5.03 v14) = v16 & implies(v9, v10) = v15 & is_a_theorem(v16) = 0 &
% 28.38/5.03 $i(v16) & $i(v15))))))
% 28.38/5.03
% 28.38/5.03 (cn2)
% 28.38/5.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 28.38/5.04 int] : ($i(v1) & $i(v0) & (( ~ (v5 = 0) & not(v0) = v2 & implies(v2, v1) =
% 28.38/5.04 v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = v5 & $i(v4) & $i(v3) &
% 28.38/5.04 $i(v2) & ~ cn2) | (cn2 & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : !
% 28.38/5.04 [v9: $i] : ( ~ (not(v6) = v8) | ~ (implies(v8, v7) = v9) | ~ $i(v7) |
% 28.38/5.04 ~ $i(v6) | ? [v10: $i] : (implies(v6, v9) = v10 & is_a_theorem(v10) =
% 28.38/5.04 0 & $i(v10))))))
% 28.38/5.04
% 28.38/5.04 (hilbert_op_equiv)
% 28.38/5.04 op_equiv
% 28.38/5.04
% 28.38/5.04 (hilbert_op_implies_and)
% 28.38/5.04 op_implies_and
% 28.38/5.04
% 28.38/5.04 (hilbert_op_or)
% 28.38/5.04 op_or
% 28.38/5.04
% 28.38/5.04 (hilbert_or_1)
% 28.38/5.04 ~ or_1
% 28.38/5.04
% 28.38/5.04 (kn2)
% 28.38/5.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ($i(v1)
% 28.38/5.04 & $i(v0) & (( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3 &
% 28.38/5.04 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & ~ kn2) | (kn2 & ! [v5: $i] :
% 28.38/5.04 ! [v6: $i] : ! [v7: $i] : ( ~ (and(v5, v6) = v7) | ~ $i(v6) | ~
% 28.38/5.04 $i(v5) | ? [v8: $i] : (implies(v7, v5) = v8 & is_a_theorem(v8) = 0 &
% 28.38/5.04 $i(v8))))))
% 28.38/5.04
% 28.38/5.04 (luka_cn1)
% 28.38/5.04 cn1
% 28.38/5.04
% 28.38/5.04 (luka_cn2)
% 28.38/5.04 cn2
% 28.38/5.04
% 28.38/5.04 (luka_modus_ponens)
% 28.38/5.04 modus_ponens
% 28.38/5.04
% 28.38/5.04 (luka_op_equiv)
% 28.38/5.04 op_equiv
% 28.38/5.04
% 28.38/5.04 (luka_op_or)
% 28.38/5.04 op_or
% 28.38/5.04
% 28.38/5.04 (modus_ponens)
% 28.38/5.04 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ?
% 28.38/5.04 [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v2 = 0 & ~ (v5 = 0) & implies(v0,
% 28.38/5.04 v1) = v3 & is_a_theorem(v3) = 0 & is_a_theorem(v1) = v5 &
% 28.38/5.04 is_a_theorem(v0) = 0 & $i(v3) & ~ modus_ponens) | (modus_ponens & !
% 28.38/5.04 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~
% 28.38/5.04 $i(v7) | ~ $i(v6) | ? [v9: int] : ? [v10: int] : ? [v11: int] :
% 28.38/5.04 ((v11 = 0 & is_a_theorem(v7) = 0) | ( ~ (v10 = 0) & is_a_theorem(v8) =
% 28.38/5.04 v10) | ( ~ (v9 = 0) & is_a_theorem(v6) = v9))))))
% 28.38/5.04
% 28.38/5.04 (op_equiv)
% 28.38/5.05 ~ op_equiv | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) =
% 28.38/5.05 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (and(v3, v4) =
% 28.38/5.05 v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3 & $i(v4) & $i(v3) &
% 28.38/5.05 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1,
% 28.38/5.05 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 28.38/5.05 (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4 & $i(v4) &
% 28.38/5.05 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0,
% 28.38/5.05 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 28.38/5.05 (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4 & $i(v4) &
% 28.38/5.05 $i(v3))))
% 28.38/5.05
% 28.38/5.05 (op_implies_and)
% 28.38/5.05 ~ op_implies_and | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 28.38/5.05 ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 28.38/5.05 $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : !
% 28.38/5.05 [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 28.38/5.05 | ? [v3: $i] : ? [v4: $i] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) =
% 28.38/5.05 v3 & $i(v4) & $i(v3) & $i(v2))))
% 28.38/5.05
% 28.38/5.05 (op_or)
% 28.38/5.05 ~ op_or | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 28.38/5.05 $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ~
% 28.38/5.05 $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = v5 & not(v4) = v5 &
% 28.38/5.05 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) =
% 28.38/5.05 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 28.38/5.05 (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3 & $i(v5) &
% 28.38/5.05 $i(v4) & $i(v3) & $i(v2))))
% 28.38/5.05
% 28.38/5.05 (or_1)
% 28.38/5.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ($i(v1)
% 28.38/5.05 & $i(v0) & (( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v0, v2) = v3 &
% 28.38/5.05 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & ~ or_1) | (or_1 & ! [v5: $i]
% 28.38/5.05 : ! [v6: $i] : ! [v7: $i] : ( ~ (or(v5, v6) = v7) | ~ $i(v6) | ~
% 28.38/5.05 $i(v5) | ? [v8: $i] : (implies(v5, v7) = v8 & is_a_theorem(v8) = 0 &
% 28.38/5.05 $i(v8))))))
% 28.38/5.05
% 28.38/5.05 (function-axioms)
% 28.38/5.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3,
% 28.38/5.05 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 28.38/5.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) =
% 28.38/5.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 28.38/5.05 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 28.38/5.05 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~
% 28.38/5.05 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 28.38/5.05 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 28.38/5.05 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1)
% 28.38/5.05 | ~ (is_a_theorem(v2) = v0))
% 28.38/5.05
% 28.38/5.05 Further assumptions not needed in the proof:
% 28.38/5.05 --------------------------------------------
% 28.38/5.06 and_1, and_2, and_3, cn3, equivalence_1, equivalence_2, equivalence_3,
% 28.38/5.06 implies_1, implies_2, implies_3, kn1, kn3, luka_cn3, luka_op_implies,
% 28.38/5.06 modus_tollens, op_and, op_implies_or, or_2, or_3, r1, r2, r3, r4, r5,
% 28.38/5.06 substitution_of_equivalents
% 28.38/5.06
% 28.38/5.06 Those formulas are unsatisfiable:
% 28.38/5.06 ---------------------------------
% 28.38/5.06
% 28.38/5.06 Begin of proof
% 28.38/5.06 |
% 28.38/5.06 | ALPHA: (function-axioms) implies:
% 28.38/5.06 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 28.38/5.06 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 28.38/5.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1)
% 28.38/5.06 | | ~ (not(v2) = v0))
% 28.38/5.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 28.38/5.06 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 28.38/5.06 |
% 28.38/5.06 | DELTA: instantiating (kn2) with fresh symbols all_14_0, all_14_1, all_14_2,
% 28.38/5.06 | all_14_3, all_14_4 gives:
% 28.38/5.06 | (4) $i(all_14_3) & $i(all_14_4) & (( ~ (all_14_0 = 0) & and(all_14_4,
% 28.38/5.06 | all_14_3) = all_14_2 & implies(all_14_2, all_14_4) = all_14_1 &
% 28.38/5.06 | is_a_theorem(all_14_1) = all_14_0 & $i(all_14_1) & $i(all_14_2) &
% 28.38/5.06 | ~ kn2) | (kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 28.38/5.06 | (and(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 28.38/5.06 | (implies(v2, v0) = v3 & is_a_theorem(v3) = 0 & $i(v3)))))
% 28.38/5.06 |
% 28.38/5.06 | ALPHA: (4) implies:
% 28.38/5.06 | (5) ( ~ (all_14_0 = 0) & and(all_14_4, all_14_3) = all_14_2 &
% 28.38/5.06 | implies(all_14_2, all_14_4) = all_14_1 & is_a_theorem(all_14_1) =
% 28.38/5.06 | all_14_0 & $i(all_14_1) & $i(all_14_2) & ~ kn2) | (kn2 & ! [v0: $i]
% 28.38/5.06 | : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~
% 28.38/5.06 | $i(v0) | ? [v3: $i] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0
% 28.38/5.06 | & $i(v3))))
% 28.38/5.06 |
% 28.38/5.06 | DELTA: instantiating (or_1) with fresh symbols all_18_0, all_18_1, all_18_2,
% 28.38/5.06 | all_18_3, all_18_4 gives:
% 28.38/5.06 | (6) $i(all_18_3) & $i(all_18_4) & (( ~ (all_18_0 = 0) & or(all_18_4,
% 28.38/5.06 | all_18_3) = all_18_2 & implies(all_18_4, all_18_2) = all_18_1 &
% 28.38/5.06 | is_a_theorem(all_18_1) = all_18_0 & $i(all_18_1) & $i(all_18_2) &
% 28.38/5.06 | ~ or_1) | (or_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 28.38/5.06 | (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 28.38/5.07 | (implies(v0, v2) = v3 & is_a_theorem(v3) = 0 & $i(v3)))))
% 28.38/5.07 |
% 28.38/5.07 | ALPHA: (6) implies:
% 28.38/5.07 | (7) $i(all_18_4)
% 28.38/5.07 | (8) $i(all_18_3)
% 28.38/5.07 | (9) ( ~ (all_18_0 = 0) & or(all_18_4, all_18_3) = all_18_2 &
% 28.38/5.07 | implies(all_18_4, all_18_2) = all_18_1 & is_a_theorem(all_18_1) =
% 28.38/5.07 | all_18_0 & $i(all_18_1) & $i(all_18_2) & ~ or_1) | (or_1 & ! [v0:
% 28.38/5.07 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1)
% 28.38/5.07 | | ~ $i(v0) | ? [v3: $i] : (implies(v0, v2) = v3 &
% 28.38/5.07 | is_a_theorem(v3) = 0 & $i(v3))))
% 28.38/5.07 |
% 28.38/5.07 | DELTA: instantiating (cn2) with fresh symbols all_24_0, all_24_1, all_24_2,
% 28.38/5.07 | all_24_3, all_24_4, all_24_5 gives:
% 28.38/5.07 | (10) $i(all_24_4) & $i(all_24_5) & (( ~ (all_24_0 = 0) & not(all_24_5) =
% 28.38/5.07 | all_24_3 & implies(all_24_3, all_24_4) = all_24_2 &
% 28.38/5.07 | implies(all_24_5, all_24_2) = all_24_1 & is_a_theorem(all_24_1) =
% 28.38/5.07 | all_24_0 & $i(all_24_1) & $i(all_24_2) & $i(all_24_3) & ~ cn2) |
% 28.38/5.07 | (cn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 28.38/5.07 | (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ $i(v1) | ~
% 28.38/5.07 | $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 & is_a_theorem(v4)
% 28.38/5.07 | = 0 & $i(v4)))))
% 28.38/5.07 |
% 28.38/5.07 | ALPHA: (10) implies:
% 28.38/5.07 | (11) ( ~ (all_24_0 = 0) & not(all_24_5) = all_24_3 & implies(all_24_3,
% 28.38/5.07 | all_24_4) = all_24_2 & implies(all_24_5, all_24_2) = all_24_1 &
% 28.38/5.07 | is_a_theorem(all_24_1) = all_24_0 & $i(all_24_1) & $i(all_24_2) &
% 28.38/5.07 | $i(all_24_3) & ~ cn2) | (cn2 & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 28.38/5.07 | $i] : ! [v3: $i] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3)
% 28.38/5.07 | | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 &
% 28.38/5.07 | is_a_theorem(v4) = 0 & $i(v4))))
% 28.38/5.07 |
% 28.38/5.07 | DELTA: instantiating (modus_ponens) with fresh symbols all_30_0, all_30_1,
% 28.38/5.07 | all_30_2, all_30_3, all_30_4, all_30_5 gives:
% 28.38/5.07 | (12) $i(all_30_4) & $i(all_30_5) & ((all_30_1 = 0 & all_30_3 = 0 & ~
% 28.38/5.07 | (all_30_0 = 0) & implies(all_30_5, all_30_4) = all_30_2 &
% 28.38/5.07 | is_a_theorem(all_30_2) = 0 & is_a_theorem(all_30_4) = all_30_0 &
% 28.38/5.07 | is_a_theorem(all_30_5) = 0 & $i(all_30_2) & ~ modus_ponens) |
% 28.38/5.07 | (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 28.38/5.07 | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 28.38/5.07 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & is_a_theorem(v1) = 0) |
% 28.38/5.07 | ( ~ (v4 = 0) & is_a_theorem(v2) = v4) | ( ~ (v3 = 0) &
% 28.38/5.07 | is_a_theorem(v0) = v3)))))
% 28.38/5.07 |
% 28.38/5.07 | ALPHA: (12) implies:
% 28.38/5.07 | (13) (all_30_1 = 0 & all_30_3 = 0 & ~ (all_30_0 = 0) & implies(all_30_5,
% 28.38/5.07 | all_30_4) = all_30_2 & is_a_theorem(all_30_2) = 0 &
% 28.38/5.08 | is_a_theorem(all_30_4) = all_30_0 & is_a_theorem(all_30_5) = 0 &
% 28.38/5.08 | $i(all_30_2) & ~ modus_ponens) | (modus_ponens & ! [v0: $i] : !
% 28.38/5.08 | [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~
% 28.38/5.08 | $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 28.38/5.08 | is_a_theorem(v1) = 0) | ( ~ (v4 = 0) & is_a_theorem(v2) = v4)
% 28.38/5.08 | | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))))
% 28.38/5.08 |
% 28.38/5.08 | DELTA: instantiating (cn1) with fresh symbols all_41_0, all_41_1, all_41_2,
% 28.38/5.08 | all_41_3, all_41_4, all_41_5, all_41_6, all_41_7, all_41_8 gives:
% 28.38/5.08 | (14) $i(all_41_6) & $i(all_41_7) & $i(all_41_8) & (( ~ (all_41_0 = 0) &
% 28.38/5.08 | implies(all_41_4, all_41_3) = all_41_2 & implies(all_41_5,
% 28.38/5.08 | all_41_2) = all_41_1 & implies(all_41_7, all_41_6) = all_41_4 &
% 28.38/5.08 | implies(all_41_8, all_41_6) = all_41_3 & implies(all_41_8,
% 28.38/5.08 | all_41_7) = all_41_5 & is_a_theorem(all_41_1) = all_41_0 &
% 28.38/5.08 | $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & $i(all_41_4) &
% 28.38/5.08 | $i(all_41_5) & ~ cn1) | (cn1 & ! [v0: $i] : ! [v1: $i] : !
% 28.38/5.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 28.38/5.08 | (implies(v3, v4) = v5) | ~ (implies(v1, v2) = v3) | ~
% 28.38/5.08 | (implies(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 28.38/5.08 | [v6: $i] : ? [v7: $i] : (implies(v6, v5) = v7 & implies(v0, v1)
% 28.38/5.08 | = v6 & is_a_theorem(v7) = 0 & $i(v7) & $i(v6)))))
% 28.38/5.08 |
% 28.38/5.08 | ALPHA: (14) implies:
% 28.38/5.08 | (15) ( ~ (all_41_0 = 0) & implies(all_41_4, all_41_3) = all_41_2 &
% 28.38/5.08 | implies(all_41_5, all_41_2) = all_41_1 & implies(all_41_7, all_41_6)
% 28.38/5.08 | = all_41_4 & implies(all_41_8, all_41_6) = all_41_3 &
% 28.38/5.08 | implies(all_41_8, all_41_7) = all_41_5 & is_a_theorem(all_41_1) =
% 28.38/5.08 | all_41_0 & $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & $i(all_41_4)
% 28.38/5.08 | & $i(all_41_5) & ~ cn1) | (cn1 & ! [v0: $i] : ! [v1: $i] : !
% 28.38/5.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 28.38/5.08 | (implies(v3, v4) = v5) | ~ (implies(v1, v2) = v3) | ~
% 28.38/5.08 | (implies(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 28.38/5.08 | [v6: $i] : ? [v7: $i] : (implies(v6, v5) = v7 & implies(v0, v1) =
% 28.38/5.08 | v6 & is_a_theorem(v7) = 0 & $i(v7) & $i(v6))))
% 28.38/5.08 |
% 28.38/5.08 | BETA: splitting (9) gives:
% 28.38/5.08 |
% 28.38/5.08 | Case 1:
% 28.38/5.08 | |
% 28.38/5.08 | | (16) ~ (all_18_0 = 0) & or(all_18_4, all_18_3) = all_18_2 &
% 28.38/5.08 | | implies(all_18_4, all_18_2) = all_18_1 & is_a_theorem(all_18_1) =
% 28.38/5.08 | | all_18_0 & $i(all_18_1) & $i(all_18_2) & ~ or_1
% 28.38/5.08 | |
% 28.38/5.08 | | ALPHA: (16) implies:
% 28.38/5.08 | | (17) ~ (all_18_0 = 0)
% 28.38/5.08 | | (18) $i(all_18_2)
% 28.38/5.08 | | (19) is_a_theorem(all_18_1) = all_18_0
% 28.38/5.08 | | (20) implies(all_18_4, all_18_2) = all_18_1
% 28.38/5.08 | | (21) or(all_18_4, all_18_3) = all_18_2
% 28.38/5.08 | |
% 28.38/5.08 | | BETA: splitting (op_or) gives:
% 28.38/5.08 | |
% 28.38/5.08 | | Case 1:
% 28.38/5.08 | | |
% 28.38/5.08 | | | (22) ~ op_or
% 28.38/5.08 | | |
% 28.38/5.08 | | | PRED_UNIFY: (22), (luka_op_or) imply:
% 28.38/5.08 | | | (23) $false
% 28.38/5.09 | | |
% 28.38/5.09 | | | CLOSE: (23) is inconsistent.
% 28.38/5.09 | | |
% 28.38/5.09 | | Case 2:
% 28.38/5.09 | | |
% 28.38/5.09 | | | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 28.38/5.09 | | | $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) =
% 28.38/5.09 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = v5 &
% 28.38/5.09 | | | not(v4) = v5 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 28.38/5.09 | | | $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 28.38/5.09 | | | $i] : ? [v4: $i] : ? [v5: $i] : (and(v3, v4) = v5 & not(v5)
% 28.38/5.09 | | | = v2 & not(v1) = v4 & not(v0) = v3 & $i(v5) & $i(v4) & $i(v3)
% 28.38/5.09 | | | & $i(v2)))
% 28.38/5.09 | | |
% 28.38/5.09 | | | ALPHA: (24) implies:
% 29.84/5.09 | | | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) |
% 29.84/5.09 | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 29.84/5.09 | | | (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3 &
% 29.84/5.09 | | | $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 29.84/5.09 | | |
% 29.84/5.09 | | | BETA: splitting (op_equiv) gives:
% 29.84/5.09 | | |
% 29.84/5.09 | | | Case 1:
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | (26) ~ op_equiv
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | PRED_UNIFY: (26), (luka_op_equiv) imply:
% 29.84/5.09 | | | | (27) $false
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | CLOSE: (27) is inconsistent.
% 29.84/5.09 | | | |
% 29.84/5.09 | | | Case 2:
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) =
% 29.84/5.09 | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 29.84/5.09 | | | | (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) =
% 29.84/5.09 | | | | v3 & $i(v4) & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i]
% 29.84/5.09 | | | | : ! [v2: $i] : ( ~ (implies(v1, v0) = v2) | ~ $i(v1) | ~
% 29.84/5.09 | | | | $i(v0) | ? [v3: $i] : ? [v4: $i] : (and(v4, v2) = v3 &
% 29.84/5.09 | | | | equiv(v0, v1) = v3 & implies(v0, v1) = v4 & $i(v4) &
% 29.84/5.09 | | | | $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 29.84/5.09 | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 29.84/5.09 | | | | ? [v4: $i] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 &
% 29.84/5.09 | | | | implies(v1, v0) = v4 & $i(v4) & $i(v3)))
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | ALPHA: (28) implies:
% 29.84/5.09 | | | | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) =
% 29.84/5.09 | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 29.84/5.09 | | | | (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4
% 29.84/5.09 | | | | & $i(v4) & $i(v3)))
% 29.84/5.09 | | | | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, v0) =
% 29.84/5.09 | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 29.84/5.09 | | | | (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4
% 29.84/5.09 | | | | & $i(v4) & $i(v3)))
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | BETA: splitting (op_implies_and) gives:
% 29.84/5.09 | | | |
% 29.84/5.09 | | | | Case 1:
% 29.84/5.09 | | | | |
% 29.84/5.09 | | | | | (31) ~ op_implies_and
% 29.84/5.09 | | | | |
% 29.84/5.09 | | | | | PRED_UNIFY: (31), (hilbert_op_implies_and) imply:
% 29.84/5.09 | | | | | (32) $false
% 29.84/5.09 | | | | |
% 29.84/5.09 | | | | | CLOSE: (32) is inconsistent.
% 29.84/5.09 | | | | |
% 29.84/5.10 | | | | Case 2:
% 29.84/5.10 | | | | |
% 29.84/5.10 | | | | | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 29.84/5.10 | | | | | (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~
% 29.84/5.10 | | | | | $i(v0) | ? [v4: $i] : (not(v3) = v4 & implies(v0, v1) = v4
% 29.84/5.10 | | | | | & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 29.84/5.10 | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 29.84/5.10 | | | | | : ? [v4: $i] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) =
% 29.84/5.10 | | | | | v3 & $i(v4) & $i(v3) & $i(v2)))
% 29.84/5.10 | | | | |
% 29.84/5.10 | | | | | ALPHA: (33) implies:
% 29.84/5.10 | | | | | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1)
% 29.84/5.10 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i]
% 29.84/5.10 | | | | | : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3 & $i(v4) &
% 29.84/5.10 | | | | | $i(v3) & $i(v2)))
% 29.84/5.10 | | | | | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 29.84/5.10 | | | | | (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~
% 29.84/5.10 | | | | | $i(v0) | ? [v4: $i] : (not(v3) = v4 & implies(v0, v1) = v4
% 29.84/5.10 | | | | | & $i(v4)))
% 29.84/5.10 | | | | |
% 29.84/5.10 | | | | | BETA: splitting (11) gives:
% 29.84/5.10 | | | | |
% 29.84/5.10 | | | | | Case 1:
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | (36) ~ (all_24_0 = 0) & not(all_24_5) = all_24_3 &
% 29.84/5.10 | | | | | | implies(all_24_3, all_24_4) = all_24_2 & implies(all_24_5,
% 29.84/5.10 | | | | | | all_24_2) = all_24_1 & is_a_theorem(all_24_1) = all_24_0 &
% 29.84/5.10 | | | | | | $i(all_24_1) & $i(all_24_2) & $i(all_24_3) & ~ cn2
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | ALPHA: (36) implies:
% 29.84/5.10 | | | | | | (37) ~ cn2
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | PRED_UNIFY: (37), (luka_cn2) imply:
% 29.84/5.10 | | | | | | (38) $false
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | CLOSE: (38) is inconsistent.
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | Case 2:
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | (39) cn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 29.84/5.10 | | | | | | : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ $i(v1)
% 29.84/5.10 | | | | | | | ~ $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 &
% 29.84/5.10 | | | | | | is_a_theorem(v4) = 0 & $i(v4)))
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | ALPHA: (39) implies:
% 29.84/5.10 | | | | | | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 29.84/5.10 | | | | | | (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ $i(v1) |
% 29.84/5.10 | | | | | | ~ $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 &
% 29.84/5.10 | | | | | | is_a_theorem(v4) = 0 & $i(v4)))
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | BETA: splitting (13) gives:
% 29.84/5.10 | | | | | |
% 29.84/5.10 | | | | | | Case 1:
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | (41) all_30_1 = 0 & all_30_3 = 0 & ~ (all_30_0 = 0) &
% 29.84/5.10 | | | | | | | implies(all_30_5, all_30_4) = all_30_2 &
% 29.84/5.10 | | | | | | | is_a_theorem(all_30_2) = 0 & is_a_theorem(all_30_4) =
% 29.84/5.10 | | | | | | | all_30_0 & is_a_theorem(all_30_5) = 0 & $i(all_30_2) & ~
% 29.84/5.10 | | | | | | | modus_ponens
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | ALPHA: (41) implies:
% 29.84/5.10 | | | | | | | (42) ~ modus_ponens
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | PRED_UNIFY: (42), (luka_modus_ponens) imply:
% 29.84/5.10 | | | | | | | (43) $false
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | CLOSE: (43) is inconsistent.
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | Case 2:
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | (44) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 29.84/5.10 | | | | | | | ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 29.84/5.10 | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 29.84/5.10 | | | | | | | is_a_theorem(v1) = 0) | ( ~ (v4 = 0) &
% 29.84/5.10 | | | | | | | is_a_theorem(v2) = v4) | ( ~ (v3 = 0) &
% 29.84/5.10 | | | | | | | is_a_theorem(v0) = v3)))
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | ALPHA: (44) implies:
% 29.84/5.10 | | | | | | | (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0,
% 29.84/5.10 | | | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 29.84/5.10 | | | | | | | ? [v4: int] : ? [v5: int] : ((v5 = 0 & is_a_theorem(v1)
% 29.84/5.10 | | | | | | | = 0) | ( ~ (v4 = 0) & is_a_theorem(v2) = v4) | ( ~
% 29.84/5.10 | | | | | | | (v3 = 0) & is_a_theorem(v0) = v3)))
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | BETA: splitting (15) gives:
% 29.84/5.10 | | | | | | |
% 29.84/5.10 | | | | | | | Case 1:
% 29.84/5.10 | | | | | | | |
% 29.84/5.11 | | | | | | | | (46) ~ (all_41_0 = 0) & implies(all_41_4, all_41_3) =
% 29.84/5.11 | | | | | | | | all_41_2 & implies(all_41_5, all_41_2) = all_41_1 &
% 29.84/5.11 | | | | | | | | implies(all_41_7, all_41_6) = all_41_4 &
% 29.84/5.11 | | | | | | | | implies(all_41_8, all_41_6) = all_41_3 &
% 29.84/5.11 | | | | | | | | implies(all_41_8, all_41_7) = all_41_5 &
% 29.84/5.11 | | | | | | | | is_a_theorem(all_41_1) = all_41_0 & $i(all_41_1) &
% 29.84/5.11 | | | | | | | | $i(all_41_2) & $i(all_41_3) & $i(all_41_4) &
% 29.84/5.11 | | | | | | | | $i(all_41_5) & ~ cn1
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | ALPHA: (46) implies:
% 29.84/5.11 | | | | | | | | (47) ~ cn1
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | PRED_UNIFY: (47), (luka_cn1) imply:
% 29.84/5.11 | | | | | | | | (48) $false
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | CLOSE: (48) is inconsistent.
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | Case 2:
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | GROUND_INST: instantiating (30) with all_18_2, all_18_4,
% 29.84/5.11 | | | | | | | | all_18_1, simplifying with (7), (18), (20) gives:
% 29.84/5.11 | | | | | | | | (49) ? [v0: $i] : ? [v1: $i] : (and(v1, all_18_1) = v0 &
% 29.84/5.11 | | | | | | | | equiv(all_18_2, all_18_4) = v0 & implies(all_18_2,
% 29.84/5.11 | | | | | | | | all_18_4) = v1 & $i(v1) & $i(v0))
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | GROUND_INST: instantiating (29) with all_18_4, all_18_2,
% 29.84/5.11 | | | | | | | | all_18_1, simplifying with (7), (18), (20) gives:
% 29.84/5.11 | | | | | | | | (50) ? [v0: $i] : ? [v1: $i] : (and(all_18_1, v1) = v0 &
% 29.84/5.11 | | | | | | | | equiv(all_18_4, all_18_2) = v0 & implies(all_18_2,
% 29.84/5.11 | | | | | | | | all_18_4) = v1 & $i(v1) & $i(v0))
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | GROUND_INST: instantiating (34) with all_18_4, all_18_2,
% 29.84/5.11 | | | | | | | | all_18_1, simplifying with (7), (18), (20) gives:
% 29.84/5.11 | | | | | | | | (51) ? [v0: $i] : ? [v1: $i] : (and(all_18_4, v0) = v1 &
% 29.84/5.11 | | | | | | | | not(v1) = all_18_1 & not(all_18_2) = v0 & $i(v1) &
% 29.84/5.11 | | | | | | | | $i(v0) & $i(all_18_1))
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | GROUND_INST: instantiating (25) with all_18_4, all_18_3,
% 29.84/5.11 | | | | | | | | all_18_2, simplifying with (7), (8), (21) gives:
% 29.84/5.11 | | | | | | | | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (and(v0, v1) =
% 29.84/5.11 | | | | | | | | v2 & not(v2) = all_18_2 & not(all_18_3) = v1 &
% 29.84/5.11 | | | | | | | | not(all_18_4) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 29.84/5.11 | | | | | | | | $i(all_18_2))
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | DELTA: instantiating (50) with fresh symbols all_95_0, all_95_1
% 29.84/5.11 | | | | | | | | gives:
% 29.84/5.11 | | | | | | | | (53) and(all_18_1, all_95_0) = all_95_1 & equiv(all_18_4,
% 29.84/5.11 | | | | | | | | all_18_2) = all_95_1 & implies(all_18_2, all_18_4) =
% 29.84/5.11 | | | | | | | | all_95_0 & $i(all_95_0) & $i(all_95_1)
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | ALPHA: (53) implies:
% 29.84/5.11 | | | | | | | | (54) $i(all_95_1)
% 29.84/5.11 | | | | | | | | (55) implies(all_18_2, all_18_4) = all_95_0
% 29.84/5.11 | | | | | | | | (56) and(all_18_1, all_95_0) = all_95_1
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | DELTA: instantiating (49) with fresh symbols all_97_0, all_97_1
% 29.84/5.11 | | | | | | | | gives:
% 29.84/5.11 | | | | | | | | (57) and(all_97_0, all_18_1) = all_97_1 & equiv(all_18_2,
% 29.84/5.11 | | | | | | | | all_18_4) = all_97_1 & implies(all_18_2, all_18_4) =
% 29.84/5.11 | | | | | | | | all_97_0 & $i(all_97_0) & $i(all_97_1)
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | ALPHA: (57) implies:
% 29.84/5.11 | | | | | | | | (58) implies(all_18_2, all_18_4) = all_97_0
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | DELTA: instantiating (51) with fresh symbols all_100_0,
% 29.84/5.11 | | | | | | | | all_100_1 gives:
% 29.84/5.11 | | | | | | | | (59) and(all_18_4, all_100_1) = all_100_0 & not(all_100_0) =
% 29.84/5.11 | | | | | | | | all_18_1 & not(all_18_2) = all_100_1 & $i(all_100_0) &
% 29.84/5.11 | | | | | | | | $i(all_100_1) & $i(all_18_1)
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | ALPHA: (59) implies:
% 29.84/5.11 | | | | | | | | (60) $i(all_18_1)
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | DELTA: instantiating (52) with fresh symbols all_102_0,
% 29.84/5.11 | | | | | | | | all_102_1, all_102_2 gives:
% 29.84/5.11 | | | | | | | | (61) and(all_102_2, all_102_1) = all_102_0 & not(all_102_0) =
% 29.84/5.11 | | | | | | | | all_18_2 & not(all_18_3) = all_102_1 & not(all_18_4) =
% 29.84/5.11 | | | | | | | | all_102_2 & $i(all_102_0) & $i(all_102_1) &
% 29.84/5.11 | | | | | | | | $i(all_102_2) & $i(all_18_2)
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | ALPHA: (61) implies:
% 29.84/5.11 | | | | | | | | (62) $i(all_102_2)
% 29.84/5.11 | | | | | | | | (63) not(all_18_4) = all_102_2
% 29.84/5.11 | | | | | | | | (64) not(all_18_3) = all_102_1
% 29.84/5.11 | | | | | | | | (65) not(all_102_0) = all_18_2
% 29.84/5.11 | | | | | | | | (66) and(all_102_2, all_102_1) = all_102_0
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | GROUND_INST: instantiating (3) with all_95_0, all_97_0,
% 29.84/5.11 | | | | | | | | all_18_4, all_18_2, simplifying with (55), (58)
% 29.84/5.11 | | | | | | | | gives:
% 29.84/5.11 | | | | | | | | (67) all_97_0 = all_95_0
% 29.84/5.11 | | | | | | | |
% 29.84/5.11 | | | | | | | | GROUND_INST: instantiating (34) with all_18_2, all_18_4,
% 29.84/5.11 | | | | | | | | all_95_0, simplifying with (7), (18), (55) gives:
% 29.84/5.12 | | | | | | | | (68) ? [v0: $i] : ? [v1: $i] : (and(all_18_2, v0) = v1 &
% 29.84/5.12 | | | | | | | | not(v1) = all_95_0 & not(all_18_4) = v0 & $i(v1) &
% 29.84/5.12 | | | | | | | | $i(v0) & $i(all_95_0))
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | GROUND_INST: instantiating (35) with all_102_2, all_18_3,
% 29.84/5.12 | | | | | | | | all_102_1, all_102_0, simplifying with (8), (62),
% 29.84/5.12 | | | | | | | | (64), (66) gives:
% 29.84/5.12 | | | | | | | | (69) ? [v0: $i] : (not(all_102_0) = v0 & implies(all_102_2,
% 29.84/5.12 | | | | | | | | all_18_3) = v0 & $i(v0))
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | DELTA: instantiating (69) with fresh symbol all_119_0 gives:
% 29.84/5.12 | | | | | | | | (70) not(all_102_0) = all_119_0 & implies(all_102_2,
% 29.84/5.12 | | | | | | | | all_18_3) = all_119_0 & $i(all_119_0)
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | ALPHA: (70) implies:
% 29.84/5.12 | | | | | | | | (71) implies(all_102_2, all_18_3) = all_119_0
% 29.84/5.12 | | | | | | | | (72) not(all_102_0) = all_119_0
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | DELTA: instantiating (68) with fresh symbols all_135_0,
% 29.84/5.12 | | | | | | | | all_135_1 gives:
% 29.84/5.12 | | | | | | | | (73) and(all_18_2, all_135_1) = all_135_0 & not(all_135_0) =
% 29.84/5.12 | | | | | | | | all_95_0 & not(all_18_4) = all_135_1 & $i(all_135_0) &
% 29.84/5.12 | | | | | | | | $i(all_135_1) & $i(all_95_0)
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | ALPHA: (73) implies:
% 29.84/5.12 | | | | | | | | (74) $i(all_95_0)
% 29.84/5.12 | | | | | | | | (75) not(all_18_4) = all_135_1
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | GROUND_INST: instantiating (2) with all_102_2, all_135_1,
% 29.84/5.12 | | | | | | | | all_18_4, simplifying with (63), (75) gives:
% 29.84/5.12 | | | | | | | | (76) all_135_1 = all_102_2
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | GROUND_INST: instantiating (2) with all_18_2, all_119_0,
% 29.84/5.12 | | | | | | | | all_102_0, simplifying with (65), (72) gives:
% 29.84/5.12 | | | | | | | | (77) all_119_0 = all_18_2
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | REDUCE: (71), (77) imply:
% 29.84/5.12 | | | | | | | | (78) implies(all_102_2, all_18_3) = all_18_2
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | BETA: splitting (5) gives:
% 29.84/5.12 | | | | | | | |
% 29.84/5.12 | | | | | | | | Case 1:
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | GROUND_INST: instantiating (40) with all_18_4, all_18_3,
% 29.84/5.12 | | | | | | | | | all_102_2, all_18_2, simplifying with (7), (8),
% 29.84/5.12 | | | | | | | | | (63), (78) gives:
% 29.84/5.12 | | | | | | | | | (79) ? [v0: $i] : (implies(all_18_4, all_18_2) = v0 &
% 29.84/5.12 | | | | | | | | | is_a_theorem(v0) = 0 & $i(v0))
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | DELTA: instantiating (79) with fresh symbol all_213_0 gives:
% 29.84/5.12 | | | | | | | | | (80) implies(all_18_4, all_18_2) = all_213_0 &
% 29.84/5.12 | | | | | | | | | is_a_theorem(all_213_0) = 0 & $i(all_213_0)
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | ALPHA: (80) implies:
% 29.84/5.12 | | | | | | | | | (81) implies(all_18_4, all_18_2) = all_213_0
% 29.84/5.12 | | | | | | | | | (82) is_a_theorem(all_213_0) = 0
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | GROUND_INST: instantiating (3) with all_18_1, all_213_0,
% 29.84/5.12 | | | | | | | | | all_18_2, all_18_4, simplifying with (20), (81)
% 29.84/5.12 | | | | | | | | | gives:
% 29.84/5.12 | | | | | | | | | (83) all_213_0 = all_18_1
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | REDUCE: (82), (83) imply:
% 29.84/5.12 | | | | | | | | | (84) is_a_theorem(all_18_1) = 0
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | REF_CLOSE: (1), (17), (19), (84) are inconsistent by sub-proof
% 29.84/5.12 | | | | | | | | | #1.
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | Case 2:
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | (85) kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 29.84/5.12 | | | | | | | | | (and(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 29.84/5.12 | | | | | | | | | $i] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0
% 29.84/5.12 | | | | | | | | | & $i(v3)))
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | ALPHA: (85) implies:
% 29.84/5.12 | | | | | | | | | (86) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0,
% 29.84/5.12 | | | | | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 29.84/5.12 | | | | | | | | | : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0 &
% 29.84/5.12 | | | | | | | | | $i(v3)))
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | GROUND_INST: instantiating (86) with all_18_1, all_95_0,
% 29.84/5.12 | | | | | | | | | all_95_1, simplifying with (56), (60), (74) gives:
% 29.84/5.12 | | | | | | | | | (87) ? [v0: $i] : (implies(all_95_1, all_18_1) = v0 &
% 29.84/5.12 | | | | | | | | | is_a_theorem(v0) = 0 & $i(v0))
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | DELTA: instantiating (87) with fresh symbol all_189_0 gives:
% 29.84/5.12 | | | | | | | | | (88) implies(all_95_1, all_18_1) = all_189_0 &
% 29.84/5.12 | | | | | | | | | is_a_theorem(all_189_0) = 0 & $i(all_189_0)
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | ALPHA: (88) implies:
% 29.84/5.12 | | | | | | | | | (89) is_a_theorem(all_189_0) = 0
% 29.84/5.12 | | | | | | | | | (90) implies(all_95_1, all_18_1) = all_189_0
% 29.84/5.12 | | | | | | | | |
% 29.84/5.12 | | | | | | | | | GROUND_INST: instantiating (45) with all_95_1, all_18_1,
% 29.84/5.12 | | | | | | | | | all_189_0, simplifying with (54), (60), (90)
% 29.84/5.12 | | | | | | | | | gives:
% 29.84/5.12 | | | | | | | | | (91) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0
% 29.84/5.12 | | | | | | | | | & is_a_theorem(all_18_1) = 0) | ( ~ (v1 = 0) &
% 29.84/5.12 | | | | | | | | | is_a_theorem(all_189_0) = v1) | ( ~ (v0 = 0) &
% 29.84/5.12 | | | | | | | | | is_a_theorem(all_95_1) = v0))
% 29.84/5.12 | | | | | | | | |
% 29.84/5.13 | | | | | | | | | GROUND_INST: instantiating (40) with all_18_4, all_18_3,
% 29.84/5.13 | | | | | | | | | all_102_2, all_18_2, simplifying with (7), (8),
% 29.84/5.13 | | | | | | | | | (63), (78) gives:
% 29.84/5.13 | | | | | | | | | (92) ? [v0: $i] : (implies(all_18_4, all_18_2) = v0 &
% 29.84/5.13 | | | | | | | | | is_a_theorem(v0) = 0 & $i(v0))
% 29.84/5.13 | | | | | | | | |
% 29.84/5.13 | | | | | | | | | DELTA: instantiating (92) with fresh symbol all_227_0 gives:
% 29.84/5.13 | | | | | | | | | (93) implies(all_18_4, all_18_2) = all_227_0 &
% 29.84/5.13 | | | | | | | | | is_a_theorem(all_227_0) = 0 & $i(all_227_0)
% 29.84/5.13 | | | | | | | | |
% 29.84/5.13 | | | | | | | | | ALPHA: (93) implies:
% 29.84/5.13 | | | | | | | | | (94) is_a_theorem(all_227_0) = 0
% 29.84/5.13 | | | | | | | | | (95) implies(all_18_4, all_18_2) = all_227_0
% 29.84/5.13 | | | | | | | | |
% 29.84/5.13 | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_420_0,
% 29.84/5.13 | | | | | | | | | all_420_1, all_420_2 gives:
% 29.84/5.13 | | | | | | | | | (96) (all_420_0 = 0 & is_a_theorem(all_18_1) = 0) | ( ~
% 29.84/5.13 | | | | | | | | | (all_420_1 = 0) & is_a_theorem(all_189_0) =
% 29.84/5.13 | | | | | | | | | all_420_1) | ( ~ (all_420_2 = 0) &
% 29.84/5.13 | | | | | | | | | is_a_theorem(all_95_1) = all_420_2)
% 29.84/5.13 | | | | | | | | |
% 29.84/5.13 | | | | | | | | | BETA: splitting (96) gives:
% 29.84/5.13 | | | | | | | | |
% 29.84/5.13 | | | | | | | | | Case 1:
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | (97) all_420_0 = 0 & is_a_theorem(all_18_1) = 0
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | ALPHA: (97) implies:
% 29.84/5.13 | | | | | | | | | | (98) is_a_theorem(all_18_1) = 0
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | REF_CLOSE: (1), (17), (19), (98) are inconsistent by
% 29.84/5.13 | | | | | | | | | | sub-proof #1.
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | Case 2:
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | (99) ( ~ (all_420_1 = 0) & is_a_theorem(all_189_0) =
% 29.84/5.13 | | | | | | | | | | all_420_1) | ( ~ (all_420_2 = 0) &
% 29.84/5.13 | | | | | | | | | | is_a_theorem(all_95_1) = all_420_2)
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | BETA: splitting (99) gives:
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | Case 1:
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | (100) ~ (all_420_1 = 0) & is_a_theorem(all_189_0) =
% 29.84/5.13 | | | | | | | | | | | all_420_1
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | ALPHA: (100) implies:
% 29.84/5.13 | | | | | | | | | | | (101) ~ (all_420_1 = 0)
% 29.84/5.13 | | | | | | | | | | | (102) is_a_theorem(all_189_0) = all_420_1
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | GROUND_INST: instantiating (1) with 0, all_420_1, all_189_0,
% 29.84/5.13 | | | | | | | | | | | simplifying with (89), (102) gives:
% 29.84/5.13 | | | | | | | | | | | (103) all_420_1 = 0
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | REDUCE: (101), (103) imply:
% 29.84/5.13 | | | | | | | | | | | (104) $false
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | CLOSE: (104) is inconsistent.
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | Case 2:
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_18_1, all_227_0,
% 29.84/5.13 | | | | | | | | | | | all_18_2, all_18_4, simplifying with (20), (95)
% 29.84/5.13 | | | | | | | | | | | gives:
% 29.84/5.13 | | | | | | | | | | | (105) all_227_0 = all_18_1
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | REDUCE: (94), (105) imply:
% 29.84/5.13 | | | | | | | | | | | (106) is_a_theorem(all_18_1) = 0
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | | REF_CLOSE: (1), (17), (19), (106) are inconsistent by
% 29.84/5.13 | | | | | | | | | | | sub-proof #1.
% 29.84/5.13 | | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | | End of split
% 29.84/5.13 | | | | | | | | | |
% 29.84/5.13 | | | | | | | | | End of split
% 29.84/5.13 | | | | | | | | |
% 29.84/5.13 | | | | | | | | End of split
% 29.84/5.13 | | | | | | | |
% 29.84/5.13 | | | | | | | End of split
% 29.84/5.13 | | | | | | |
% 29.84/5.13 | | | | | | End of split
% 29.84/5.13 | | | | | |
% 29.84/5.13 | | | | | End of split
% 29.84/5.13 | | | | |
% 29.84/5.13 | | | | End of split
% 29.84/5.13 | | | |
% 29.84/5.13 | | | End of split
% 29.84/5.13 | | |
% 29.84/5.13 | | End of split
% 29.84/5.13 | |
% 29.84/5.13 | Case 2:
% 29.84/5.13 | |
% 29.84/5.13 | | (107) or_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) =
% 29.84/5.13 | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v0, v2) =
% 29.84/5.13 | | v3 & is_a_theorem(v3) = 0 & $i(v3)))
% 29.84/5.13 | |
% 29.84/5.13 | | ALPHA: (107) implies:
% 29.84/5.13 | | (108) or_1
% 29.84/5.13 | |
% 29.84/5.13 | | PRED_UNIFY: (108), (hilbert_or_1) imply:
% 29.84/5.13 | | (109) $false
% 29.84/5.13 | |
% 29.84/5.13 | | CLOSE: (109) is inconsistent.
% 29.84/5.13 | |
% 29.84/5.13 | End of split
% 29.84/5.13 |
% 29.84/5.13 End of proof
% 29.84/5.13
% 29.84/5.13 Sub-proof #1 shows that the following formulas are inconsistent:
% 29.84/5.13 ----------------------------------------------------------------
% 29.84/5.13 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 29.84/5.13 (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 29.84/5.13 (2) is_a_theorem(all_18_1) = all_18_0
% 29.84/5.13 (3) is_a_theorem(all_18_1) = 0
% 29.84/5.13 (4) ~ (all_18_0 = 0)
% 29.84/5.13
% 29.84/5.13 Begin of proof
% 29.84/5.13 |
% 29.84/5.13 | GROUND_INST: instantiating (1) with all_18_0, 0, all_18_1, simplifying with
% 29.84/5.13 | (2), (3) gives:
% 29.84/5.13 | (5) all_18_0 = 0
% 29.84/5.13 |
% 29.84/5.13 | REDUCE: (4), (5) imply:
% 29.84/5.13 | (6) $false
% 29.84/5.13 |
% 29.84/5.13 | CLOSE: (6) is inconsistent.
% 29.84/5.13 |
% 29.84/5.13 End of proof
% 29.84/5.13 % SZS output end Proof for theBenchmark
% 29.84/5.13
% 29.84/5.13 4523ms
%------------------------------------------------------------------------------