TSTP Solution File: LCL483+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL483+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 : n012.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 08:11:26 EDT 2023
% Result : Theorem 11.26s 2.38s
% Output : Proof 17.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL483+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 18:56:41 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.21/0.65 ________ _____
% 0.21/0.65 ___ __ \_________(_)________________________________
% 0.21/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.65
% 0.21/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.65 (2023-06-19)
% 0.21/0.65
% 0.21/0.65 (c) Philipp Rümmer, 2009-2023
% 0.21/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.65 Amanda Stjerna.
% 0.21/0.65 Free software under BSD-3-Clause.
% 0.21/0.65
% 0.21/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.65
% 0.21/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.66 Running up to 7 provers in parallel.
% 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.21 Prover 1: Preprocessing ...
% 3.32/1.21 Prover 4: Preprocessing ...
% 3.32/1.25 Prover 3: Preprocessing ...
% 3.32/1.25 Prover 2: Preprocessing ...
% 3.32/1.25 Prover 0: Preprocessing ...
% 3.32/1.26 Prover 5: Preprocessing ...
% 3.72/1.26 Prover 6: Preprocessing ...
% 7.87/1.88 Prover 5: Proving ...
% 8.36/1.91 Prover 6: Constructing countermodel ...
% 8.36/1.92 Prover 1: Constructing countermodel ...
% 8.36/1.93 Prover 3: Constructing countermodel ...
% 8.36/1.93 Prover 4: Constructing countermodel ...
% 8.36/1.94 Prover 0: Proving ...
% 9.36/2.05 Prover 2: Proving ...
% 11.26/2.38 Prover 0: proved (1712ms)
% 11.26/2.38
% 11.26/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.26/2.38
% 11.26/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.26/2.39 Prover 3: stopped
% 11.26/2.39 Prover 5: stopped
% 11.26/2.39 Prover 6: stopped
% 11.26/2.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.26/2.40 Prover 2: stopped
% 11.85/2.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.85/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.85/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.85/2.42 Prover 7: Preprocessing ...
% 11.85/2.44 Prover 8: Preprocessing ...
% 11.85/2.46 Prover 11: Preprocessing ...
% 11.85/2.48 Prover 10: Preprocessing ...
% 11.85/2.48 Prover 13: Preprocessing ...
% 13.34/2.61 Prover 8: Warning: ignoring some quantifiers
% 13.34/2.62 Prover 8: Constructing countermodel ...
% 13.47/2.66 Prover 13: Warning: ignoring some quantifiers
% 13.47/2.67 Prover 10: Constructing countermodel ...
% 13.47/2.67 Prover 7: Constructing countermodel ...
% 13.47/2.68 Prover 13: Constructing countermodel ...
% 13.47/2.71 Prover 11: Constructing countermodel ...
% 14.96/2.92 Prover 1: gave up
% 14.96/2.92 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.65/2.97 Prover 16: Preprocessing ...
% 16.29/3.06 Prover 8: gave up
% 16.29/3.07 Prover 16: Warning: ignoring some quantifiers
% 16.29/3.08 Prover 4: Found proof (size 83)
% 16.29/3.08 Prover 4: proved (2401ms)
% 16.29/3.08 Prover 11: stopped
% 16.29/3.08 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 16.29/3.08 Prover 7: stopped
% 16.84/3.08 Prover 13: stopped
% 16.84/3.08 Prover 16: Constructing countermodel ...
% 16.84/3.08 Prover 16: stopped
% 16.84/3.09 Prover 10: stopped
% 16.84/3.10 Prover 19: Preprocessing ...
% 17.29/3.17 Prover 19: Warning: ignoring some quantifiers
% 17.29/3.18 Prover 19: Constructing countermodel ...
% 17.29/3.18 Prover 19: stopped
% 17.29/3.18
% 17.29/3.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.29/3.18
% 17.38/3.19 % SZS output start Proof for theBenchmark
% 17.38/3.20 Assumptions after simplification:
% 17.38/3.20 ---------------------------------
% 17.38/3.20
% 17.38/3.20 (hilbert_modus_tollens)
% 17.38/3.20 ~ modus_tollens
% 17.38/3.20
% 17.38/3.20 (hilbert_op_implies_and)
% 17.38/3.20 op_implies_and
% 17.38/3.20
% 17.38/3.20 (hilbert_op_or)
% 17.38/3.20 op_or
% 17.38/3.20
% 17.38/3.20 (modus_ponens)
% 17.52/3.22 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ?
% 17.52/3.22 [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v2 = 0 & ~ (v5 = 0) & implies(v0,
% 17.52/3.22 v1) = v3 & is_a_theorem(v3) = 0 & is_a_theorem(v1) = v5 &
% 17.52/3.22 is_a_theorem(v0) = 0 & $i(v3) & ~ modus_ponens) | (modus_ponens & !
% 17.52/3.22 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~
% 17.52/3.22 $i(v7) | ~ $i(v6) | ? [v9: any] : ? [v10: any] : ? [v11: any] :
% 17.52/3.22 (is_a_theorem(v8) = v10 & is_a_theorem(v7) = v11 & is_a_theorem(v6) =
% 17.52/3.22 v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))))))
% 17.52/3.22
% 17.52/3.22 (modus_tollens)
% 17.59/3.23 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.59/3.23 $i] : ? [v6: $i] : ? [v7: int] : ($i(v1) & $i(v0) & (( ~ (v7 = 0) &
% 17.59/3.23 not(v1) = v2 & not(v0) = v3 & implies(v4, v5) = v6 & implies(v2, v3) =
% 17.59/3.23 v4 & implies(v0, v1) = v5 & is_a_theorem(v6) = v7 & $i(v6) & $i(v5) &
% 17.59/3.23 $i(v4) & $i(v3) & $i(v2) & ~ modus_tollens) | (modus_tollens & ! [v8:
% 17.59/3.23 $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 17.59/3.23 (not(v9) = v10) | ~ (not(v8) = v11) | ~ (implies(v10, v11) = v12) |
% 17.59/3.23 ~ $i(v9) | ~ $i(v8) | ? [v13: $i] : ? [v14: $i] : (implies(v12,
% 17.59/3.23 v13) = v14 & implies(v8, v9) = v13 & is_a_theorem(v14) = 0 &
% 17.59/3.23 $i(v14) & $i(v13))) & ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 17.59/3.23 (implies(v8, v9) = v10) | ~ $i(v9) | ~ $i(v8) | ? [v11: $i] : ?
% 17.59/3.23 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (not(v9) = v11 & not(v8) =
% 17.59/3.23 v12 & implies(v13, v10) = v14 & implies(v11, v12) = v13 &
% 17.59/3.23 is_a_theorem(v14) = 0 & $i(v14) & $i(v13) & $i(v12) & $i(v11))))))
% 17.59/3.23
% 17.59/3.23 (op_implies_and)
% 17.59/3.23 ~ op_implies_and | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 17.59/3.23 ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 17.59/3.23 $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : !
% 17.59/3.23 [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 17.59/3.23 | ? [v3: $i] : ? [v4: $i] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) =
% 17.59/3.23 v3 & $i(v4) & $i(v3) & $i(v2))))
% 17.59/3.23
% 17.59/3.23 (op_implies_or)
% 17.59/3.23 ~ op_implies_or | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 17.59/3.23 ~ (or(v2, v1) = v3) | ~ (not(v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 17.59/3.23 (implies(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.59/3.23 : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (or(v3,
% 17.59/3.23 v1) = v2 & not(v0) = v3 & $i(v3) & $i(v2))))
% 17.59/3.23
% 17.59/3.23 (op_or)
% 17.59/3.24 ~ op_or | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.59/3.24 $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ~
% 17.59/3.24 $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = v5 & not(v4) = v5 &
% 17.59/3.24 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) =
% 17.59/3.24 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 17.59/3.24 (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3 & $i(v5) &
% 17.59/3.24 $i(v4) & $i(v3) & $i(v2))))
% 17.59/3.24
% 17.59/3.24 (principia_modus_ponens)
% 17.59/3.24 modus_ponens
% 17.59/3.24
% 17.59/3.24 (principia_op_implies_or)
% 17.59/3.24 op_implies_or
% 17.59/3.24
% 17.59/3.24 (principia_r3)
% 17.59/3.24 r3
% 17.59/3.24
% 17.59/3.24 (principia_r4)
% 17.59/3.24 r4
% 17.59/3.24
% 17.59/3.24 (r3)
% 17.59/3.24 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.59/3.24 int] : ($i(v1) & $i(v0) & (( ~ (v5 = 0) & or(v1, v0) = v3 & or(v0, v1) = v2
% 17.59/3.24 & implies(v2, v3) = v4 & is_a_theorem(v4) = v5 & $i(v4) & $i(v3) &
% 17.59/3.24 $i(v2) & ~ r3) | (r3 & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 17.59/3.24 (or(v7, v6) = v8) | ~ $i(v7) | ~ $i(v6) | ? [v9: $i] : ? [v10: $i]
% 17.59/3.24 : (or(v6, v7) = v9 & implies(v9, v8) = v10 & is_a_theorem(v10) = 0 &
% 17.59/3.24 $i(v10) & $i(v9))) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 17.59/3.24 (or(v6, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ? [v9: $i] : ? [v10: $i]
% 17.59/3.24 : (or(v7, v6) = v9 & implies(v8, v9) = v10 & is_a_theorem(v10) = 0 &
% 17.59/3.24 $i(v10) & $i(v9))))))
% 17.59/3.24
% 17.59/3.24 (r4)
% 17.59/3.24 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.59/3.24 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ($i(v2) & $i(v1) & $i(v0) &
% 17.59/3.24 (( ~ (v8 = 0) & or(v1, v5) = v6 & or(v1, v2) = v3 & or(v0, v3) = v4 & or(v0,
% 17.59/3.24 v2) = v5 & implies(v4, v6) = v7 & is_a_theorem(v7) = v8 & $i(v7) &
% 17.59/3.24 $i(v6) & $i(v5) & $i(v4) & $i(v3) & ~ r4) | (r4 & ! [v9: $i] : !
% 17.59/3.24 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ (or(v10,
% 17.59/3.24 v12) = v13) | ~ (or(v9, v11) = v12) | ~ $i(v11) | ~ $i(v10) |
% 17.59/3.24 ~ $i(v9) | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : (or(v10, v11)
% 17.59/3.24 = v14 & or(v9, v14) = v15 & implies(v15, v13) = v16 &
% 17.59/3.24 is_a_theorem(v16) = 0 & $i(v16) & $i(v15) & $i(v14))) & ! [v9: $i]
% 17.59/3.24 : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~
% 17.59/3.24 (or(v10, v11) = v12) | ~ (or(v9, v12) = v13) | ~ $i(v11) | ~
% 17.59/3.24 $i(v10) | ~ $i(v9) | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] :
% 17.59/3.24 (or(v10, v14) = v15 & or(v9, v11) = v14 & implies(v13, v15) = v16 &
% 17.59/3.24 is_a_theorem(v16) = 0 & $i(v16) & $i(v15) & $i(v14))))))
% 17.59/3.24
% 17.59/3.24 (function-axioms)
% 17.59/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3,
% 17.59/3.25 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.59/3.25 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) =
% 17.59/3.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.59/3.25 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.59/3.25 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~
% 17.59/3.25 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 17.59/3.25 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.59/3.25 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1)
% 17.59/3.25 | ~ (is_a_theorem(v2) = v0))
% 17.59/3.25
% 17.59/3.25 Further assumptions not needed in the proof:
% 17.59/3.25 --------------------------------------------
% 17.59/3.25 and_1, and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3,
% 17.59/3.25 hilbert_op_equiv, implies_1, implies_2, implies_3, kn1, kn2, kn3, op_and,
% 17.59/3.25 op_equiv, or_1, or_2, or_3, principia_op_and, principia_op_equiv, principia_r1,
% 17.59/3.25 principia_r2, principia_r5, r1, r2, r5, substitution_of_equivalents
% 17.59/3.25
% 17.59/3.25 Those formulas are unsatisfiable:
% 17.59/3.25 ---------------------------------
% 17.59/3.25
% 17.59/3.25 Begin of proof
% 17.59/3.25 |
% 17.59/3.25 | ALPHA: (function-axioms) implies:
% 17.59/3.25 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.59/3.25 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 17.59/3.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1)
% 17.59/3.25 | | ~ (not(v2) = v0))
% 17.59/3.25 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.59/3.25 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 17.59/3.25 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.59/3.25 | (or(v3, v2) = v1) | ~ (or(v3, v2) = v0))
% 17.59/3.25 |
% 17.59/3.25 | DELTA: instantiating (modus_ponens) with fresh symbols all_30_0, all_30_1,
% 17.59/3.25 | all_30_2, all_30_3, all_30_4, all_30_5 gives:
% 17.59/3.25 | (5) $i(all_30_4) & $i(all_30_5) & ((all_30_1 = 0 & all_30_3 = 0 & ~
% 17.59/3.25 | (all_30_0 = 0) & implies(all_30_5, all_30_4) = all_30_2 &
% 17.59/3.25 | is_a_theorem(all_30_2) = 0 & is_a_theorem(all_30_4) = all_30_0 &
% 17.59/3.25 | is_a_theorem(all_30_5) = 0 & $i(all_30_2) & ~ modus_ponens) |
% 17.59/3.25 | (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.59/3.25 | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 17.59/3.25 | ? [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 &
% 17.59/3.25 | is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ (v4 = 0) |
% 17.59/3.25 | ~ (v3 = 0) | v5 = 0)))))
% 17.59/3.25 |
% 17.59/3.25 | ALPHA: (5) implies:
% 17.59/3.25 | (6) (all_30_1 = 0 & all_30_3 = 0 & ~ (all_30_0 = 0) & implies(all_30_5,
% 17.59/3.25 | all_30_4) = all_30_2 & is_a_theorem(all_30_2) = 0 &
% 17.59/3.25 | is_a_theorem(all_30_4) = all_30_0 & is_a_theorem(all_30_5) = 0 &
% 17.59/3.25 | $i(all_30_2) & ~ modus_ponens) | (modus_ponens & ! [v0: $i] : !
% 17.59/3.25 | [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~
% 17.59/3.25 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 17.59/3.25 | (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 & is_a_theorem(v0) =
% 17.59/3.25 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))))
% 17.59/3.25 |
% 17.59/3.25 | DELTA: instantiating (r3) with fresh symbols all_45_0, all_45_1, all_45_2,
% 17.59/3.25 | all_45_3, all_45_4, all_45_5 gives:
% 17.59/3.26 | (7) $i(all_45_4) & $i(all_45_5) & (( ~ (all_45_0 = 0) & or(all_45_4,
% 17.59/3.26 | all_45_5) = all_45_2 & or(all_45_5, all_45_4) = all_45_3 &
% 17.59/3.26 | implies(all_45_3, all_45_2) = all_45_1 & is_a_theorem(all_45_1) =
% 17.59/3.26 | all_45_0 & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & ~ r3) |
% 17.59/3.26 | (r3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v1, v0) = v2)
% 17.59/3.26 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (or(v0, v1)
% 17.59/3.26 | = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0 & $i(v4) &
% 17.59/3.26 | $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.59/3.26 | (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 17.59/3.26 | $i] : (or(v1, v0) = v3 & implies(v2, v3) = v4 &
% 17.59/3.26 | is_a_theorem(v4) = 0 & $i(v4) & $i(v3)))))
% 17.59/3.26 |
% 17.59/3.26 | ALPHA: (7) implies:
% 17.59/3.26 | (8) ( ~ (all_45_0 = 0) & or(all_45_4, all_45_5) = all_45_2 & or(all_45_5,
% 17.59/3.26 | all_45_4) = all_45_3 & implies(all_45_3, all_45_2) = all_45_1 &
% 17.59/3.26 | is_a_theorem(all_45_1) = all_45_0 & $i(all_45_1) & $i(all_45_2) &
% 17.59/3.26 | $i(all_45_3) & ~ r3) | (r3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.59/3.26 | : ( ~ (or(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 17.59/3.26 | [v4: $i] : (or(v0, v1) = v3 & implies(v3, v2) = v4 &
% 17.59/3.26 | is_a_theorem(v4) = 0 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1:
% 17.59/3.26 | $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 17.59/3.26 | ? [v3: $i] : ? [v4: $i] : (or(v1, v0) = v3 & implies(v2, v3) = v4
% 17.59/3.26 | & is_a_theorem(v4) = 0 & $i(v4) & $i(v3))))
% 17.59/3.26 |
% 17.59/3.26 | DELTA: instantiating (modus_tollens) with fresh symbols all_51_0, all_51_1,
% 17.59/3.26 | all_51_2, all_51_3, all_51_4, all_51_5, all_51_6, all_51_7 gives:
% 17.59/3.26 | (9) $i(all_51_6) & $i(all_51_7) & (( ~ (all_51_0 = 0) & not(all_51_6) =
% 17.59/3.26 | all_51_5 & not(all_51_7) = all_51_4 & implies(all_51_3, all_51_2) =
% 17.59/3.26 | all_51_1 & implies(all_51_5, all_51_4) = all_51_3 &
% 17.59/3.26 | implies(all_51_7, all_51_6) = all_51_2 & is_a_theorem(all_51_1) =
% 17.59/3.26 | all_51_0 & $i(all_51_1) & $i(all_51_2) & $i(all_51_3) &
% 17.59/3.26 | $i(all_51_4) & $i(all_51_5) & ~ modus_tollens) | (modus_tollens &
% 17.59/3.26 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.59/3.26 | : ( ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~ (implies(v2, v3) =
% 17.59/3.26 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 17.59/3.26 | (implies(v4, v5) = v6 & implies(v0, v1) = v5 & is_a_theorem(v6) =
% 17.59/3.26 | 0 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.59/3.26 | : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 17.59/3.26 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (not(v1) = v3 &
% 17.59/3.26 | not(v0) = v4 & implies(v5, v2) = v6 & implies(v3, v4) = v5 &
% 17.59/3.26 | is_a_theorem(v6) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)))))
% 17.59/3.26 |
% 17.59/3.26 | ALPHA: (9) implies:
% 17.59/3.26 | (10) $i(all_51_7)
% 17.59/3.26 | (11) $i(all_51_6)
% 17.59/3.26 | (12) ( ~ (all_51_0 = 0) & not(all_51_6) = all_51_5 & not(all_51_7) =
% 17.59/3.26 | all_51_4 & implies(all_51_3, all_51_2) = all_51_1 &
% 17.59/3.26 | implies(all_51_5, all_51_4) = all_51_3 & implies(all_51_7, all_51_6)
% 17.59/3.26 | = all_51_2 & is_a_theorem(all_51_1) = all_51_0 & $i(all_51_1) &
% 17.59/3.26 | $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & $i(all_51_5) & ~
% 17.59/3.26 | modus_tollens) | (modus_tollens & ! [v0: $i] : ! [v1: $i] : !
% 17.59/3.26 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (not(v1) = v2) | ~
% 17.59/3.26 | (not(v0) = v3) | ~ (implies(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0)
% 17.59/3.26 | | ? [v5: $i] : ? [v6: $i] : (implies(v4, v5) = v6 & implies(v0,
% 17.59/3.26 | v1) = v5 & is_a_theorem(v6) = 0 & $i(v6) & $i(v5))) & ! [v0:
% 17.59/3.26 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~
% 17.59/3.26 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 17.59/3.26 | [v6: $i] : (not(v1) = v3 & not(v0) = v4 & implies(v5, v2) = v6 &
% 17.59/3.26 | implies(v3, v4) = v5 & is_a_theorem(v6) = 0 & $i(v6) & $i(v5) &
% 17.59/3.26 | $i(v4) & $i(v3))))
% 17.59/3.26 |
% 17.59/3.26 | DELTA: instantiating (r4) with fresh symbols all_53_0, all_53_1, all_53_2,
% 17.59/3.26 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7, all_53_8 gives:
% 17.59/3.27 | (13) $i(all_53_6) & $i(all_53_7) & $i(all_53_8) & (( ~ (all_53_0 = 0) &
% 17.59/3.27 | or(all_53_7, all_53_3) = all_53_2 & or(all_53_7, all_53_6) =
% 17.59/3.27 | all_53_5 & or(all_53_8, all_53_5) = all_53_4 & or(all_53_8,
% 17.59/3.27 | all_53_6) = all_53_3 & implies(all_53_4, all_53_2) = all_53_1 &
% 17.59/3.27 | is_a_theorem(all_53_1) = all_53_0 & $i(all_53_1) & $i(all_53_2) &
% 17.59/3.27 | $i(all_53_3) & $i(all_53_4) & $i(all_53_5) & ~ r4) | (r4 & !
% 17.59/3.27 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.59/3.27 | ( ~ (or(v1, v3) = v4) | ~ (or(v0, v2) = v3) | ~ $i(v2) | ~
% 17.59/3.27 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 17.59/3.27 | (or(v1, v2) = v5 & or(v0, v5) = v6 & implies(v6, v4) = v7 &
% 17.59/3.27 | is_a_theorem(v7) = 0 & $i(v7) & $i(v6) & $i(v5))) & ! [v0:
% 17.59/3.27 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 17.59/3.27 | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ $i(v2) | ~
% 17.59/3.27 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 17.59/3.27 | (or(v1, v5) = v6 & or(v0, v2) = v5 & implies(v4, v6) = v7 &
% 17.59/3.27 | is_a_theorem(v7) = 0 & $i(v7) & $i(v6) & $i(v5)))))
% 17.59/3.27 |
% 17.59/3.27 | ALPHA: (13) implies:
% 17.59/3.27 | (14) ( ~ (all_53_0 = 0) & or(all_53_7, all_53_3) = all_53_2 & or(all_53_7,
% 17.59/3.27 | all_53_6) = all_53_5 & or(all_53_8, all_53_5) = all_53_4 &
% 17.59/3.27 | or(all_53_8, all_53_6) = all_53_3 & implies(all_53_4, all_53_2) =
% 17.59/3.27 | all_53_1 & is_a_theorem(all_53_1) = all_53_0 & $i(all_53_1) &
% 17.59/3.27 | $i(all_53_2) & $i(all_53_3) & $i(all_53_4) & $i(all_53_5) & ~ r4) |
% 17.59/3.27 | (r4 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.59/3.27 | $i] : ( ~ (or(v1, v3) = v4) | ~ (or(v0, v2) = v3) | ~ $i(v2) |
% 17.59/3.27 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 17.59/3.27 | (or(v1, v2) = v5 & or(v0, v5) = v6 & implies(v6, v4) = v7 &
% 17.59/3.27 | is_a_theorem(v7) = 0 & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i]
% 17.59/3.27 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 17.59/3.27 | (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) |
% 17.59/3.27 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (or(v1, v5)
% 17.59/3.27 | = v6 & or(v0, v2) = v5 & implies(v4, v6) = v7 & is_a_theorem(v7)
% 17.59/3.27 | = 0 & $i(v7) & $i(v6) & $i(v5))))
% 17.59/3.27 |
% 17.59/3.27 | BETA: splitting (12) gives:
% 17.59/3.27 |
% 17.59/3.27 | Case 1:
% 17.59/3.27 | |
% 17.59/3.27 | | (15) ~ (all_51_0 = 0) & not(all_51_6) = all_51_5 & not(all_51_7) =
% 17.59/3.27 | | all_51_4 & implies(all_51_3, all_51_2) = all_51_1 &
% 17.59/3.27 | | implies(all_51_5, all_51_4) = all_51_3 & implies(all_51_7, all_51_6)
% 17.59/3.27 | | = all_51_2 & is_a_theorem(all_51_1) = all_51_0 & $i(all_51_1) &
% 17.59/3.27 | | $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & $i(all_51_5) & ~
% 17.59/3.27 | | modus_tollens
% 17.59/3.27 | |
% 17.59/3.27 | | ALPHA: (15) implies:
% 17.59/3.27 | | (16) ~ (all_51_0 = 0)
% 17.59/3.27 | | (17) $i(all_51_5)
% 17.59/3.27 | | (18) $i(all_51_4)
% 17.59/3.27 | | (19) $i(all_51_3)
% 17.59/3.27 | | (20) $i(all_51_2)
% 17.59/3.27 | | (21) is_a_theorem(all_51_1) = all_51_0
% 17.59/3.27 | | (22) implies(all_51_7, all_51_6) = all_51_2
% 17.59/3.27 | | (23) implies(all_51_5, all_51_4) = all_51_3
% 17.59/3.27 | | (24) implies(all_51_3, all_51_2) = all_51_1
% 17.59/3.27 | | (25) not(all_51_7) = all_51_4
% 17.59/3.27 | | (26) not(all_51_6) = all_51_5
% 17.59/3.27 | |
% 17.59/3.27 | | BETA: splitting (op_or) gives:
% 17.59/3.27 | |
% 17.59/3.27 | | Case 1:
% 17.59/3.27 | | |
% 17.59/3.27 | | | (27) ~ op_or
% 17.59/3.27 | | |
% 17.59/3.27 | | | PRED_UNIFY: (27), (hilbert_op_or) imply:
% 17.59/3.27 | | | (28) $false
% 17.59/3.27 | | |
% 17.59/3.27 | | | CLOSE: (28) is inconsistent.
% 17.59/3.27 | | |
% 17.59/3.28 | | Case 2:
% 17.59/3.28 | | |
% 17.59/3.28 | | | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.59/3.28 | | | $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) =
% 17.59/3.28 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = v5 &
% 17.59/3.28 | | | not(v4) = v5 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.59/3.28 | | | $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 17.59/3.28 | | | $i] : ? [v4: $i] : ? [v5: $i] : (and(v3, v4) = v5 & not(v5)
% 17.59/3.28 | | | = v2 & not(v1) = v4 & not(v0) = v3 & $i(v5) & $i(v4) & $i(v3)
% 17.59/3.28 | | | & $i(v2)))
% 17.59/3.28 | | |
% 17.59/3.28 | | | ALPHA: (29) implies:
% 17.59/3.28 | | | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.59/3.28 | | | $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) =
% 17.59/3.28 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = v5 &
% 17.59/3.28 | | | not(v4) = v5 & $i(v5)))
% 17.59/3.28 | | |
% 17.59/3.28 | | | BETA: splitting (op_implies_or) gives:
% 17.59/3.28 | | |
% 17.59/3.28 | | | Case 1:
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | (31) ~ op_implies_or
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | PRED_UNIFY: (31), (principia_op_implies_or) imply:
% 17.59/3.28 | | | | (32) $false
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | CLOSE: (32) is inconsistent.
% 17.59/3.28 | | | |
% 17.59/3.28 | | | Case 2:
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.59/3.28 | | | | (or(v2, v1) = v3) | ~ (not(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 17.59/3.28 | | | | | (implies(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i]
% 17.59/3.28 | | | | : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~
% 17.59/3.28 | | | | $i(v0) | ? [v3: $i] : (or(v3, v1) = v2 & not(v0) = v3 &
% 17.59/3.28 | | | | $i(v3) & $i(v2)))
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | ALPHA: (33) implies:
% 17.59/3.28 | | | | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) =
% 17.59/3.28 | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (or(v3, v1) = v2
% 17.59/3.28 | | | | & not(v0) = v3 & $i(v3) & $i(v2)))
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | BETA: splitting (op_implies_and) gives:
% 17.59/3.28 | | | |
% 17.59/3.28 | | | | Case 1:
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | (35) ~ op_implies_and
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | PRED_UNIFY: (35), (hilbert_op_implies_and) imply:
% 17.59/3.28 | | | | | (36) $false
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | CLOSE: (36) is inconsistent.
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | Case 2:
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.59/3.28 | | | | | (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~
% 17.59/3.28 | | | | | $i(v0) | ? [v4: $i] : (not(v3) = v4 & implies(v0, v1) = v4
% 17.59/3.28 | | | | | & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.59/3.28 | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 17.59/3.28 | | | | | : ? [v4: $i] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) =
% 17.59/3.28 | | | | | v3 & $i(v4) & $i(v3) & $i(v2)))
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | ALPHA: (37) implies:
% 17.59/3.28 | | | | | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1)
% 17.59/3.28 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i]
% 17.59/3.28 | | | | | : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3 & $i(v4) &
% 17.59/3.28 | | | | | $i(v3) & $i(v2)))
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | BETA: splitting (6) gives:
% 17.59/3.28 | | | | |
% 17.59/3.28 | | | | | Case 1:
% 17.59/3.28 | | | | | |
% 17.59/3.28 | | | | | | (39) all_30_1 = 0 & all_30_3 = 0 & ~ (all_30_0 = 0) &
% 17.59/3.28 | | | | | | implies(all_30_5, all_30_4) = all_30_2 &
% 17.59/3.28 | | | | | | is_a_theorem(all_30_2) = 0 & is_a_theorem(all_30_4) =
% 17.59/3.28 | | | | | | all_30_0 & is_a_theorem(all_30_5) = 0 & $i(all_30_2) & ~
% 17.59/3.28 | | | | | | modus_ponens
% 17.59/3.28 | | | | | |
% 17.59/3.28 | | | | | | ALPHA: (39) implies:
% 17.59/3.28 | | | | | | (40) ~ modus_ponens
% 17.59/3.28 | | | | | |
% 17.59/3.28 | | | | | | PRED_UNIFY: (40), (principia_modus_ponens) imply:
% 17.59/3.28 | | | | | | (41) $false
% 17.59/3.28 | | | | | |
% 17.59/3.28 | | | | | | CLOSE: (41) is inconsistent.
% 17.59/3.28 | | | | | |
% 17.59/3.28 | | | | | Case 2:
% 17.59/3.28 | | | | | |
% 17.59/3.29 | | | | | | (42) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.59/3.29 | | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 17.59/3.29 | | | | | | any] : ? [v4: any] : ? [v5: any] : (is_a_theorem(v2) =
% 17.59/3.29 | | | | | | v4 & is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~
% 17.59/3.29 | | | | | | (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 17.59/3.29 | | | | | |
% 17.59/3.29 | | | | | | ALPHA: (42) implies:
% 17.59/3.29 | | | | | | (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0,
% 17.59/3.29 | | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 17.59/3.29 | | | | | | [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 &
% 17.59/3.29 | | | | | | is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ (v4
% 17.59/3.29 | | | | | | = 0) | ~ (v3 = 0) | v5 = 0)))
% 17.59/3.29 | | | | | |
% 17.59/3.29 | | | | | | BETA: splitting (8) gives:
% 17.59/3.29 | | | | | |
% 17.59/3.29 | | | | | | Case 1:
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | (44) ~ (all_45_0 = 0) & or(all_45_4, all_45_5) = all_45_2 &
% 17.59/3.29 | | | | | | | or(all_45_5, all_45_4) = all_45_3 & implies(all_45_3,
% 17.59/3.29 | | | | | | | all_45_2) = all_45_1 & is_a_theorem(all_45_1) = all_45_0
% 17.59/3.29 | | | | | | | & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & ~ r3
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | ALPHA: (44) implies:
% 17.59/3.29 | | | | | | | (45) ~ r3
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | PRED_UNIFY: (45), (principia_r3) imply:
% 17.59/3.29 | | | | | | | (46) $false
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | CLOSE: (46) is inconsistent.
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | Case 2:
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | (47) r3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v1,
% 17.59/3.29 | | | | | | | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 17.59/3.29 | | | | | | | [v4: $i] : (or(v0, v1) = v3 & implies(v3, v2) = v4 &
% 17.59/3.29 | | | | | | | is_a_theorem(v4) = 0 & $i(v4) & $i(v3))) & ! [v0: $i]
% 17.59/3.29 | | | | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~
% 17.59/3.29 | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (or(v1,
% 17.59/3.29 | | | | | | | v0) = v3 & implies(v2, v3) = v4 & is_a_theorem(v4) =
% 17.59/3.29 | | | | | | | 0 & $i(v4) & $i(v3)))
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | ALPHA: (47) implies:
% 17.59/3.29 | | | | | | | (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1)
% 17.59/3.29 | | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 17.59/3.29 | | | | | | | $i] : (or(v1, v0) = v3 & implies(v2, v3) = v4 &
% 17.59/3.29 | | | | | | | is_a_theorem(v4) = 0 & $i(v4) & $i(v3)))
% 17.59/3.29 | | | | | | | (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v1, v0)
% 17.59/3.29 | | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 17.59/3.29 | | | | | | | $i] : (or(v0, v1) = v3 & implies(v3, v2) = v4 &
% 17.59/3.29 | | | | | | | is_a_theorem(v4) = 0 & $i(v4) & $i(v3)))
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | BETA: splitting (14) gives:
% 17.59/3.29 | | | | | | |
% 17.59/3.29 | | | | | | | Case 1:
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | (50) ~ (all_53_0 = 0) & or(all_53_7, all_53_3) = all_53_2 &
% 17.59/3.29 | | | | | | | | or(all_53_7, all_53_6) = all_53_5 & or(all_53_8,
% 17.59/3.29 | | | | | | | | all_53_5) = all_53_4 & or(all_53_8, all_53_6) =
% 17.59/3.29 | | | | | | | | all_53_3 & implies(all_53_4, all_53_2) = all_53_1 &
% 17.59/3.29 | | | | | | | | is_a_theorem(all_53_1) = all_53_0 & $i(all_53_1) &
% 17.59/3.29 | | | | | | | | $i(all_53_2) & $i(all_53_3) & $i(all_53_4) &
% 17.59/3.29 | | | | | | | | $i(all_53_5) & ~ r4
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | ALPHA: (50) implies:
% 17.59/3.29 | | | | | | | | (51) ~ r4
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | PRED_UNIFY: (51), (principia_r4) imply:
% 17.59/3.29 | | | | | | | | (52) $false
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | CLOSE: (52) is inconsistent.
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | Case 2:
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | GROUND_INST: instantiating (38) with all_51_7, all_51_6,
% 17.59/3.29 | | | | | | | | all_51_2, simplifying with (10), (11), (22) gives:
% 17.59/3.29 | | | | | | | | (53) ? [v0: $i] : ? [v1: $i] : (and(all_51_7, v0) = v1 &
% 17.59/3.29 | | | | | | | | not(v1) = all_51_2 & not(all_51_6) = v0 & $i(v1) &
% 17.59/3.29 | | | | | | | | $i(v0) & $i(all_51_2))
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | GROUND_INST: instantiating (34) with all_51_7, all_51_6,
% 17.59/3.29 | | | | | | | | all_51_2, simplifying with (10), (11), (22) gives:
% 17.59/3.29 | | | | | | | | (54) ? [v0: $i] : (or(v0, all_51_6) = all_51_2 &
% 17.59/3.29 | | | | | | | | not(all_51_7) = v0 & $i(v0) & $i(all_51_2))
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | GROUND_INST: instantiating (38) with all_51_5, all_51_4,
% 17.59/3.29 | | | | | | | | all_51_3, simplifying with (17), (18), (23) gives:
% 17.59/3.29 | | | | | | | | (55) ? [v0: $i] : ? [v1: $i] : (and(all_51_5, v0) = v1 &
% 17.59/3.29 | | | | | | | | not(v1) = all_51_3 & not(all_51_4) = v0 & $i(v1) &
% 17.59/3.29 | | | | | | | | $i(v0) & $i(all_51_3))
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | GROUND_INST: instantiating (43) with all_51_3, all_51_2,
% 17.59/3.29 | | | | | | | | all_51_1, simplifying with (19), (20), (24) gives:
% 17.59/3.29 | | | | | | | | (56) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.59/3.29 | | | | | | | | (is_a_theorem(all_51_1) = v1 & is_a_theorem(all_51_2) =
% 17.59/3.29 | | | | | | | | v2 & is_a_theorem(all_51_3) = v0 & ( ~ (v1 = 0) | ~
% 17.59/3.29 | | | | | | | | (v0 = 0) | v2 = 0))
% 17.59/3.29 | | | | | | | |
% 17.59/3.29 | | | | | | | | DELTA: instantiating (54) with fresh symbol all_115_0 gives:
% 17.59/3.30 | | | | | | | | (57) or(all_115_0, all_51_6) = all_51_2 & not(all_51_7) =
% 17.59/3.30 | | | | | | | | all_115_0 & $i(all_115_0) & $i(all_51_2)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (57) implies:
% 17.59/3.30 | | | | | | | | (58) $i(all_115_0)
% 17.59/3.30 | | | | | | | | (59) not(all_51_7) = all_115_0
% 17.59/3.30 | | | | | | | | (60) or(all_115_0, all_51_6) = all_51_2
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | DELTA: instantiating (53) with fresh symbols all_129_0,
% 17.59/3.30 | | | | | | | | all_129_1 gives:
% 17.59/3.30 | | | | | | | | (61) and(all_51_7, all_129_1) = all_129_0 & not(all_129_0) =
% 17.59/3.30 | | | | | | | | all_51_2 & not(all_51_6) = all_129_1 & $i(all_129_0) &
% 17.59/3.30 | | | | | | | | $i(all_129_1) & $i(all_51_2)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (61) implies:
% 17.59/3.30 | | | | | | | | (62) not(all_51_6) = all_129_1
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | DELTA: instantiating (56) with fresh symbols all_133_0,
% 17.59/3.30 | | | | | | | | all_133_1, all_133_2 gives:
% 17.59/3.30 | | | | | | | | (63) is_a_theorem(all_51_1) = all_133_1 &
% 17.59/3.30 | | | | | | | | is_a_theorem(all_51_2) = all_133_0 &
% 17.59/3.30 | | | | | | | | is_a_theorem(all_51_3) = all_133_2 & ( ~ (all_133_1 = 0)
% 17.59/3.30 | | | | | | | | | ~ (all_133_2 = 0) | all_133_0 = 0)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (63) implies:
% 17.59/3.30 | | | | | | | | (64) is_a_theorem(all_51_1) = all_133_1
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | DELTA: instantiating (55) with fresh symbols all_139_0,
% 17.59/3.30 | | | | | | | | all_139_1 gives:
% 17.59/3.30 | | | | | | | | (65) and(all_51_5, all_139_1) = all_139_0 & not(all_139_0) =
% 17.59/3.30 | | | | | | | | all_51_3 & not(all_51_4) = all_139_1 & $i(all_139_0) &
% 17.59/3.30 | | | | | | | | $i(all_139_1) & $i(all_51_3)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (65) implies:
% 17.59/3.30 | | | | | | | | (66) not(all_51_4) = all_139_1
% 17.59/3.30 | | | | | | | | (67) not(all_139_0) = all_51_3
% 17.59/3.30 | | | | | | | | (68) and(all_51_5, all_139_1) = all_139_0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (1) with all_51_0, all_133_1,
% 17.59/3.30 | | | | | | | | all_51_1, simplifying with (21), (64) gives:
% 17.59/3.30 | | | | | | | | (69) all_133_1 = all_51_0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (2) with all_51_4, all_115_0,
% 17.59/3.30 | | | | | | | | all_51_7, simplifying with (25), (59) gives:
% 17.59/3.30 | | | | | | | | (70) all_115_0 = all_51_4
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (2) with all_51_5, all_129_1,
% 17.59/3.30 | | | | | | | | all_51_6, simplifying with (26), (62) gives:
% 17.59/3.30 | | | | | | | | (71) all_129_1 = all_51_5
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | REDUCE: (60), (70) imply:
% 17.59/3.30 | | | | | | | | (72) or(all_51_4, all_51_6) = all_51_2
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (30) with all_51_6, all_51_4,
% 17.59/3.30 | | | | | | | | all_51_5, all_139_1, all_139_0, simplifying with
% 17.59/3.30 | | | | | | | | (11), (18), (26), (66), (68) gives:
% 17.59/3.30 | | | | | | | | (73) ? [v0: $i] : (or(all_51_6, all_51_4) = v0 &
% 17.59/3.30 | | | | | | | | not(all_139_0) = v0 & $i(v0))
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (49) with all_51_6, all_51_4,
% 17.59/3.30 | | | | | | | | all_51_2, simplifying with (11), (18), (72) gives:
% 17.59/3.30 | | | | | | | | (74) ? [v0: $i] : ? [v1: $i] : (or(all_51_6, all_51_4) = v0
% 17.59/3.30 | | | | | | | | & implies(v0, all_51_2) = v1 & is_a_theorem(v1) = 0 &
% 17.59/3.30 | | | | | | | | $i(v1) & $i(v0))
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (48) with all_51_4, all_51_6,
% 17.59/3.30 | | | | | | | | all_51_2, simplifying with (11), (18), (72) gives:
% 17.59/3.30 | | | | | | | | (75) ? [v0: $i] : ? [v1: $i] : (or(all_51_6, all_51_4) = v0
% 17.59/3.30 | | | | | | | | & implies(all_51_2, v0) = v1 & is_a_theorem(v1) = 0 &
% 17.59/3.30 | | | | | | | | $i(v1) & $i(v0))
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | DELTA: instantiating (73) with fresh symbol all_205_0 gives:
% 17.59/3.30 | | | | | | | | (76) or(all_51_6, all_51_4) = all_205_0 & not(all_139_0) =
% 17.59/3.30 | | | | | | | | all_205_0 & $i(all_205_0)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (76) implies:
% 17.59/3.30 | | | | | | | | (77) not(all_139_0) = all_205_0
% 17.59/3.30 | | | | | | | | (78) or(all_51_6, all_51_4) = all_205_0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | DELTA: instantiating (74) with fresh symbols all_235_0,
% 17.59/3.30 | | | | | | | | all_235_1 gives:
% 17.59/3.30 | | | | | | | | (79) or(all_51_6, all_51_4) = all_235_1 & implies(all_235_1,
% 17.59/3.30 | | | | | | | | all_51_2) = all_235_0 & is_a_theorem(all_235_0) = 0 &
% 17.59/3.30 | | | | | | | | $i(all_235_0) & $i(all_235_1)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (79) implies:
% 17.59/3.30 | | | | | | | | (80) is_a_theorem(all_235_0) = 0
% 17.59/3.30 | | | | | | | | (81) implies(all_235_1, all_51_2) = all_235_0
% 17.59/3.30 | | | | | | | | (82) or(all_51_6, all_51_4) = all_235_1
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | DELTA: instantiating (75) with fresh symbols all_243_0,
% 17.59/3.30 | | | | | | | | all_243_1 gives:
% 17.59/3.30 | | | | | | | | (83) or(all_51_6, all_51_4) = all_243_1 & implies(all_51_2,
% 17.59/3.30 | | | | | | | | all_243_1) = all_243_0 & is_a_theorem(all_243_0) = 0 &
% 17.59/3.30 | | | | | | | | $i(all_243_0) & $i(all_243_1)
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | ALPHA: (83) implies:
% 17.59/3.30 | | | | | | | | (84) or(all_51_6, all_51_4) = all_243_1
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (2) with all_51_3, all_205_0,
% 17.59/3.30 | | | | | | | | all_139_0, simplifying with (67), (77) gives:
% 17.59/3.30 | | | | | | | | (85) all_205_0 = all_51_3
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (4) with all_235_1, all_243_1,
% 17.59/3.30 | | | | | | | | all_51_4, all_51_6, simplifying with (82), (84)
% 17.59/3.30 | | | | | | | | gives:
% 17.59/3.30 | | | | | | | | (86) all_243_1 = all_235_1
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (4) with all_205_0, all_243_1,
% 17.59/3.30 | | | | | | | | all_51_4, all_51_6, simplifying with (78), (84)
% 17.59/3.30 | | | | | | | | gives:
% 17.59/3.30 | | | | | | | | (87) all_243_1 = all_205_0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | COMBINE_EQS: (86), (87) imply:
% 17.59/3.30 | | | | | | | | (88) all_235_1 = all_205_0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | COMBINE_EQS: (85), (88) imply:
% 17.59/3.30 | | | | | | | | (89) all_235_1 = all_51_3
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | REDUCE: (81), (89) imply:
% 17.59/3.30 | | | | | | | | (90) implies(all_51_3, all_51_2) = all_235_0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (3) with all_51_1, all_235_0,
% 17.59/3.30 | | | | | | | | all_51_2, all_51_3, simplifying with (24), (90)
% 17.59/3.30 | | | | | | | | gives:
% 17.59/3.30 | | | | | | | | (91) all_235_0 = all_51_1
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | REDUCE: (80), (91) imply:
% 17.59/3.30 | | | | | | | | (92) is_a_theorem(all_51_1) = 0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | GROUND_INST: instantiating (1) with all_51_0, 0, all_51_1,
% 17.59/3.30 | | | | | | | | simplifying with (21), (92) gives:
% 17.59/3.30 | | | | | | | | (93) all_51_0 = 0
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | REDUCE: (16), (93) imply:
% 17.59/3.30 | | | | | | | | (94) $false
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | | CLOSE: (94) is inconsistent.
% 17.59/3.30 | | | | | | | |
% 17.59/3.30 | | | | | | | End of split
% 17.59/3.31 | | | | | | |
% 17.59/3.31 | | | | | | End of split
% 17.59/3.31 | | | | | |
% 17.59/3.31 | | | | | End of split
% 17.59/3.31 | | | | |
% 17.59/3.31 | | | | End of split
% 17.59/3.31 | | | |
% 17.59/3.31 | | | End of split
% 17.59/3.31 | | |
% 17.59/3.31 | | End of split
% 17.59/3.31 | |
% 17.59/3.31 | Case 2:
% 17.59/3.31 | |
% 17.59/3.31 | | (95) modus_tollens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.59/3.31 | | $i] : ! [v4: $i] : ( ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~
% 17.59/3.31 | | (implies(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ?
% 17.59/3.31 | | [v6: $i] : (implies(v4, v5) = v6 & implies(v0, v1) = v5 &
% 17.59/3.31 | | is_a_theorem(v6) = 0 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1:
% 17.59/3.31 | | $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~
% 17.59/3.31 | | $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 17.59/3.31 | | (not(v1) = v3 & not(v0) = v4 & implies(v5, v2) = v6 & implies(v3,
% 17.59/3.31 | | v4) = v5 & is_a_theorem(v6) = 0 & $i(v6) & $i(v5) & $i(v4) &
% 17.59/3.31 | | $i(v3)))
% 17.59/3.31 | |
% 17.59/3.31 | | ALPHA: (95) implies:
% 17.59/3.31 | | (96) modus_tollens
% 17.59/3.31 | |
% 17.59/3.31 | | PRED_UNIFY: (96), (hilbert_modus_tollens) imply:
% 17.59/3.31 | | (97) $false
% 17.59/3.31 | |
% 17.59/3.31 | | CLOSE: (97) is inconsistent.
% 17.59/3.31 | |
% 17.59/3.31 | End of split
% 17.59/3.31 |
% 17.59/3.31 End of proof
% 17.59/3.31 % SZS output end Proof for theBenchmark
% 17.59/3.31
% 17.59/3.31 2659ms
%------------------------------------------------------------------------------