TSTP Solution File: LCL456+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL456+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 : n032.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 08:11:21 EDT 2023
% Result : Theorem 12.82s 2.37s
% Output : Proof 26.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri Aug 25 01:27:27 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.50 ________ _____
% 0.14/0.50 ___ __ \_________(_)________________________________
% 0.14/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.50
% 0.14/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.50 (2023-06-19)
% 0.14/0.50
% 0.14/0.50 (c) Philipp Rümmer, 2009-2023
% 0.14/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.50 Amanda Stjerna.
% 0.14/0.50 Free software under BSD-3-Clause.
% 0.14/0.50
% 0.14/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.50
% 0.14/0.50 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.51 Running up to 7 provers in parallel.
% 0.14/0.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.52 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.52 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.52 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.52 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.76/0.95 Prover 4: Preprocessing ...
% 2.76/0.95 Prover 1: Preprocessing ...
% 2.94/0.98 Prover 2: Preprocessing ...
% 2.94/0.98 Prover 6: Preprocessing ...
% 2.94/0.98 Prover 5: Preprocessing ...
% 2.94/0.98 Prover 3: Preprocessing ...
% 2.94/0.98 Prover 0: Preprocessing ...
% 7.57/1.63 Prover 6: Constructing countermodel ...
% 7.57/1.64 Prover 1: Constructing countermodel ...
% 7.57/1.64 Prover 4: Constructing countermodel ...
% 7.76/1.65 Prover 5: Proving ...
% 7.76/1.66 Prover 3: Constructing countermodel ...
% 8.35/1.74 Prover 0: Proving ...
% 8.35/1.77 Prover 2: Proving ...
% 12.82/2.36 Prover 0: proved (1847ms)
% 12.82/2.37
% 12.82/2.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.82/2.37
% 13.13/2.38 Prover 3: stopped
% 13.13/2.39 Prover 6: stopped
% 13.13/2.40 Prover 2: stopped
% 13.13/2.40 Prover 5: stopped
% 13.13/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.13/2.43 Prover 1: gave up
% 13.60/2.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.60/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.60/2.44 Prover 7: Preprocessing ...
% 13.60/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.60/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.60/2.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.60/2.45 Prover 8: Preprocessing ...
% 13.60/2.45 Prover 10: Preprocessing ...
% 13.71/2.51 Prover 11: Preprocessing ...
% 13.71/2.52 Prover 13: Preprocessing ...
% 14.10/2.52 Prover 16: Preprocessing ...
% 14.40/2.60 Prover 7: Constructing countermodel ...
% 15.02/2.63 Prover 13: Warning: ignoring some quantifiers
% 15.02/2.64 Prover 16: Warning: ignoring some quantifiers
% 15.02/2.64 Prover 16: Constructing countermodel ...
% 15.02/2.65 Prover 8: Warning: ignoring some quantifiers
% 15.02/2.66 Prover 11: Constructing countermodel ...
% 15.02/2.66 Prover 13: Constructing countermodel ...
% 15.02/2.66 Prover 10: Constructing countermodel ...
% 15.02/2.67 Prover 8: Constructing countermodel ...
% 17.14/2.96 Prover 13: gave up
% 17.14/2.96 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 17.74/3.02 Prover 19: Preprocessing ...
% 17.74/3.05 Prover 8: gave up
% 17.74/3.06 Prover 10: gave up
% 18.27/3.13 Prover 19: Warning: ignoring some quantifiers
% 18.27/3.13 Prover 19: Constructing countermodel ...
% 19.43/3.27 Prover 19: gave up
% 24.11/3.89 Prover 16: gave up
% 25.54/4.14 Prover 7: Found proof (size 74)
% 25.54/4.14 Prover 7: proved (1767ms)
% 25.54/4.15 Prover 4: stopped
% 25.54/4.15 Prover 11: stopped
% 25.54/4.15
% 25.54/4.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.54/4.15
% 25.54/4.16 % SZS output start Proof for theBenchmark
% 25.54/4.16 Assumptions after simplification:
% 25.54/4.16 ---------------------------------
% 25.54/4.16
% 25.54/4.16 (hilbert_implies_1)
% 25.54/4.17 implies_1
% 25.54/4.17
% 25.54/4.17 (hilbert_modus_ponens)
% 25.54/4.17 modus_ponens
% 25.54/4.17
% 25.54/4.17 (hilbert_op_implies_and)
% 25.54/4.17 op_implies_and
% 25.54/4.17
% 25.54/4.17 (hilbert_or_1)
% 25.54/4.17 or_1
% 25.54/4.17
% 25.54/4.17 (hilbert_or_2)
% 25.54/4.17 or_2
% 25.54/4.17
% 25.54/4.17 (hilbert_or_3)
% 25.54/4.17 or_3
% 25.54/4.17
% 25.54/4.17 (implies_1)
% 25.54/4.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) &
% 25.54/4.19 ((implies(v1, v0) = v2 & implies(v0, v2) = v3 & $i(v3) & $i(v2) & ~
% 25.54/4.19 implies_1 & ~ is_a_theorem(v3)) | (implies_1 & ! [v4: $i] : ! [v5:
% 25.54/4.19 $i] : ! [v6: $i] : ( ~ (implies(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4)
% 25.54/4.19 | ? [v7: $i] : (implies(v4, v6) = v7 & $i(v7) & is_a_theorem(v7))))))
% 25.54/4.19
% 25.54/4.19 (modus_ponens)
% 25.54/4.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ((implies(v0, v1)
% 25.54/4.19 = v2 & $i(v2) & is_a_theorem(v2) & is_a_theorem(v0) & ~
% 25.54/4.19 is_a_theorem(v1) & ~ modus_ponens) | (modus_ponens & ! [v3: $i] : !
% 25.54/4.19 [v4: $i] : ! [v5: $i] : ( ~ (implies(v3, v4) = v5) | ~ $i(v4) | ~
% 25.54/4.19 $i(v3) | ~ is_a_theorem(v5) | ~ is_a_theorem(v3) |
% 25.54/4.19 is_a_theorem(v4)))))
% 25.54/4.19
% 25.54/4.19 (op_implies_and)
% 25.54/4.19 ~ op_implies_and | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 25.54/4.19 ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 25.54/4.19 $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : !
% 25.54/4.19 [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 25.54/4.19 | ? [v3: $i] : ? [v4: $i] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) =
% 25.54/4.19 v3 & $i(v4) & $i(v3) & $i(v2))))
% 25.54/4.19
% 25.54/4.19 (or_1)
% 25.54/4.20 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) &
% 25.54/4.20 ((or(v0, v1) = v2 & implies(v0, v2) = v3 & $i(v3) & $i(v2) & ~ or_1 & ~
% 25.54/4.20 is_a_theorem(v3)) | (or_1 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 25.54/4.20 ~ (or(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ? [v7: $i] :
% 25.54/4.20 (implies(v4, v6) = v7 & $i(v7) & is_a_theorem(v7))))))
% 25.54/4.20
% 25.54/4.20 (or_2)
% 25.54/4.20 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) &
% 25.54/4.20 ((or(v0, v1) = v2 & implies(v1, v2) = v3 & $i(v3) & $i(v2) & ~ or_2 & ~
% 25.54/4.20 is_a_theorem(v3)) | (or_2 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 25.54/4.20 ~ (or(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ? [v7: $i] :
% 25.54/4.20 (implies(v5, v6) = v7 & $i(v7) & is_a_theorem(v7))))))
% 25.54/4.20
% 25.54/4.20 (or_3)
% 25.54/4.20 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 25.54/4.20 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 25.54/4.20 ((or(v0, v1) = v5 & implies(v5, v2) = v6 & implies(v4, v6) = v7 &
% 25.54/4.20 implies(v3, v7) = v8 & implies(v1, v2) = v4 & implies(v0, v2) = v3 &
% 25.54/4.20 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ~ or_3 & ~
% 25.54/4.20 is_a_theorem(v8)) | (or_3 & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] :
% 25.54/4.20 ! [v12: $i] : ! [v13: $i] : ( ~ (or(v9, v10) = v12) | ~ (implies(v12,
% 25.54/4.20 v11) = v13) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ? [v14: $i] :
% 25.54/4.20 ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : (implies(v15, v13) = v16
% 25.54/4.20 & implies(v14, v16) = v17 & implies(v10, v11) = v15 & implies(v9,
% 25.54/4.20 v11) = v14 & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 25.54/4.20 is_a_theorem(v17))))))
% 25.54/4.20
% 25.54/4.20 (principia_r3)
% 25.54/4.20 ~ r3
% 25.54/4.20
% 25.54/4.20 (r3)
% 25.54/4.20 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v1)
% 25.54/4.20 & $i(v0) & ((or(v1, v0) = v3 & or(v0, v1) = v2 & implies(v2, v3) = v4 &
% 25.54/4.20 $i(v4) & $i(v3) & $i(v2) & ~ r3 & ~ is_a_theorem(v4)) | (r3 & ! [v5:
% 25.54/4.20 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (or(v6, v5) = v7) | ~ $i(v6) |
% 25.54/4.20 ~ $i(v5) | ? [v8: $i] : ? [v9: $i] : (or(v5, v6) = v8 & implies(v8,
% 25.54/4.20 v7) = v9 & $i(v9) & $i(v8) & is_a_theorem(v9))) & ! [v5: $i] : !
% 25.54/4.20 [v6: $i] : ! [v7: $i] : ( ~ (or(v5, v6) = v7) | ~ $i(v6) | ~ $i(v5) |
% 25.54/4.20 ? [v8: $i] : ? [v9: $i] : (or(v6, v5) = v8 & implies(v7, v8) = v9 &
% 25.54/4.20 $i(v9) & $i(v8) & is_a_theorem(v9))))))
% 25.54/4.20
% 25.54/4.20 (function-axioms)
% 25.54/4.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3,
% 25.54/4.21 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.54/4.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) =
% 25.54/4.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 25.54/4.21 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 25.54/4.21 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~
% 25.54/4.21 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 25.54/4.21 | ~ (not(v2) = v1) | ~ (not(v2) = v0))
% 25.54/4.21
% 25.54/4.21 Further assumptions not needed in the proof:
% 25.54/4.21 --------------------------------------------
% 25.54/4.21 and_1, and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3,
% 25.54/4.21 hilbert_and_1, hilbert_and_2, hilbert_and_3, hilbert_equivalence_1,
% 25.54/4.21 hilbert_equivalence_2, hilbert_equivalence_3, hilbert_implies_2,
% 25.54/4.21 hilbert_implies_3, hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_or,
% 25.54/4.21 implies_2, implies_3, kn1, kn2, kn3, modus_tollens, op_and, op_equiv,
% 25.54/4.21 op_implies_or, op_or, principia_op_and, principia_op_equiv,
% 25.54/4.21 principia_op_implies_or, r1, r2, r4, r5, substitution_of_equivalents
% 25.54/4.21
% 25.54/4.21 Those formulas are unsatisfiable:
% 25.54/4.21 ---------------------------------
% 25.54/4.21
% 25.54/4.21 Begin of proof
% 25.54/4.21 |
% 25.54/4.21 | ALPHA: (function-axioms) implies:
% 26.03/4.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 26.03/4.21 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 26.03/4.21 |
% 26.03/4.21 | DELTA: instantiating (modus_ponens) with fresh symbols all_10_0, all_10_1,
% 26.03/4.21 | all_10_2 gives:
% 26.03/4.21 | (2) $i(all_10_1) & $i(all_10_2) & ((implies(all_10_2, all_10_1) = all_10_0
% 26.03/4.21 | & $i(all_10_0) & is_a_theorem(all_10_0) & is_a_theorem(all_10_2) &
% 26.03/4.21 | ~ is_a_theorem(all_10_1) & ~ modus_ponens) | (modus_ponens & !
% 26.03/4.21 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) |
% 26.03/4.21 | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0)
% 26.03/4.21 | | is_a_theorem(v1))))
% 26.03/4.21 |
% 26.03/4.21 | ALPHA: (2) implies:
% 26.03/4.21 | (3) (implies(all_10_2, all_10_1) = all_10_0 & $i(all_10_0) &
% 26.03/4.21 | is_a_theorem(all_10_0) & is_a_theorem(all_10_2) & ~
% 26.03/4.21 | is_a_theorem(all_10_1) & ~ modus_ponens) | (modus_ponens & ! [v0:
% 26.03/4.21 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~
% 26.03/4.21 | $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) |
% 26.03/4.21 | is_a_theorem(v1)))
% 26.03/4.21 |
% 26.03/4.21 | DELTA: instantiating (or_2) with fresh symbols all_16_0, all_16_1, all_16_2,
% 26.03/4.21 | all_16_3 gives:
% 26.03/4.21 | (4) $i(all_16_2) & $i(all_16_3) & ((or(all_16_3, all_16_2) = all_16_1 &
% 26.03/4.21 | implies(all_16_2, all_16_1) = all_16_0 & $i(all_16_0) &
% 26.03/4.21 | $i(all_16_1) & ~ or_2 & ~ is_a_theorem(all_16_0)) | (or_2 & !
% 26.03/4.21 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~
% 26.03/4.21 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v1, v2) = v3 & $i(v3)
% 26.03/4.21 | & is_a_theorem(v3)))))
% 26.03/4.21 |
% 26.03/4.21 | ALPHA: (4) implies:
% 26.03/4.21 | (5) (or(all_16_3, all_16_2) = all_16_1 & implies(all_16_2, all_16_1) =
% 26.03/4.21 | all_16_0 & $i(all_16_0) & $i(all_16_1) & ~ or_2 & ~
% 26.03/4.21 | is_a_theorem(all_16_0)) | (or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 26.03/4.21 | $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 26.03/4.21 | (implies(v1, v2) = v3 & $i(v3) & is_a_theorem(v3))))
% 26.03/4.21 |
% 26.03/4.21 | DELTA: instantiating (or_1) with fresh symbols all_18_0, all_18_1, all_18_2,
% 26.03/4.21 | all_18_3 gives:
% 26.03/4.22 | (6) $i(all_18_2) & $i(all_18_3) & ((or(all_18_3, all_18_2) = all_18_1 &
% 26.03/4.22 | implies(all_18_3, all_18_1) = all_18_0 & $i(all_18_0) &
% 26.03/4.22 | $i(all_18_1) & ~ or_1 & ~ is_a_theorem(all_18_0)) | (or_1 & !
% 26.03/4.22 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~
% 26.03/4.22 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v0, v2) = v3 & $i(v3)
% 26.03/4.22 | & is_a_theorem(v3)))))
% 26.03/4.22 |
% 26.03/4.22 | ALPHA: (6) implies:
% 26.03/4.22 | (7) (or(all_18_3, all_18_2) = all_18_1 & implies(all_18_3, all_18_1) =
% 26.03/4.22 | all_18_0 & $i(all_18_0) & $i(all_18_1) & ~ or_1 & ~
% 26.03/4.22 | is_a_theorem(all_18_0)) | (or_1 & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 26.03/4.22 | $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 26.03/4.22 | (implies(v0, v2) = v3 & $i(v3) & is_a_theorem(v3))))
% 26.03/4.22 |
% 26.03/4.22 | DELTA: instantiating (implies_1) with fresh symbols all_22_0, all_22_1,
% 26.03/4.22 | all_22_2, all_22_3 gives:
% 26.03/4.22 | (8) $i(all_22_2) & $i(all_22_3) & ((implies(all_22_2, all_22_3) = all_22_1
% 26.03/4.22 | & implies(all_22_3, all_22_1) = all_22_0 & $i(all_22_0) &
% 26.03/4.22 | $i(all_22_1) & ~ implies_1 & ~ is_a_theorem(all_22_0)) |
% 26.03/4.22 | (implies_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 26.03/4.22 | (implies(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 26.03/4.22 | (implies(v0, v2) = v3 & $i(v3) & is_a_theorem(v3)))))
% 26.03/4.22 |
% 26.03/4.22 | ALPHA: (8) implies:
% 26.03/4.22 | (9) (implies(all_22_2, all_22_3) = all_22_1 & implies(all_22_3, all_22_1) =
% 26.03/4.22 | all_22_0 & $i(all_22_0) & $i(all_22_1) & ~ implies_1 & ~
% 26.03/4.22 | is_a_theorem(all_22_0)) | (implies_1 & ! [v0: $i] : ! [v1: $i] : !
% 26.03/4.22 | [v2: $i] : ( ~ (implies(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 26.03/4.22 | [v3: $i] : (implies(v0, v2) = v3 & $i(v3) & is_a_theorem(v3))))
% 26.03/4.22 |
% 26.03/4.22 | DELTA: instantiating (r3) with fresh symbols all_35_0, all_35_1, all_35_2,
% 26.03/4.22 | all_35_3, all_35_4 gives:
% 26.03/4.22 | (10) $i(all_35_3) & $i(all_35_4) & ((or(all_35_3, all_35_4) = all_35_1 &
% 26.03/4.22 | or(all_35_4, all_35_3) = all_35_2 & implies(all_35_2, all_35_1) =
% 26.03/4.22 | all_35_0 & $i(all_35_0) & $i(all_35_1) & $i(all_35_2) & ~ r3 & ~
% 26.03/4.22 | is_a_theorem(all_35_0)) | (r3 & ! [v0: $i] : ! [v1: $i] : !
% 26.03/4.22 | [v2: $i] : ( ~ (or(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 26.03/4.22 | $i] : ? [v4: $i] : (or(v0, v1) = v3 & implies(v3, v2) = v4 &
% 26.03/4.22 | $i(v4) & $i(v3) & is_a_theorem(v4))) & ! [v0: $i] : ! [v1:
% 26.03/4.22 | $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~
% 26.03/4.22 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (or(v1, v0) = v3 &
% 26.03/4.22 | implies(v2, v3) = v4 & $i(v4) & $i(v3) & is_a_theorem(v4)))))
% 26.03/4.22 |
% 26.03/4.22 | ALPHA: (10) implies:
% 26.03/4.22 | (11) $i(all_35_4)
% 26.03/4.22 | (12) $i(all_35_3)
% 26.03/4.23 | (13) (or(all_35_3, all_35_4) = all_35_1 & or(all_35_4, all_35_3) = all_35_2
% 26.03/4.23 | & implies(all_35_2, all_35_1) = all_35_0 & $i(all_35_0) &
% 26.03/4.23 | $i(all_35_1) & $i(all_35_2) & ~ r3 & ~ is_a_theorem(all_35_0)) |
% 26.03/4.23 | (r3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v1, v0) = v2)
% 26.03/4.23 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (or(v0, v1)
% 26.03/4.23 | = v3 & implies(v3, v2) = v4 & $i(v4) & $i(v3) &
% 26.03/4.23 | is_a_theorem(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 26.03/4.23 | ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 26.03/4.23 | [v4: $i] : (or(v1, v0) = v3 & implies(v2, v3) = v4 & $i(v4) &
% 26.03/4.23 | $i(v3) & is_a_theorem(v4))))
% 26.03/4.23 |
% 26.03/4.23 | DELTA: instantiating (or_3) with fresh symbols all_47_0, all_47_1, all_47_2,
% 26.03/4.23 | all_47_3, all_47_4, all_47_5, all_47_6, all_47_7, all_47_8 gives:
% 26.03/4.23 | (14) $i(all_47_6) & $i(all_47_7) & $i(all_47_8) & ((or(all_47_8, all_47_7)
% 26.03/4.23 | = all_47_3 & implies(all_47_3, all_47_6) = all_47_2 &
% 26.03/4.23 | implies(all_47_4, all_47_2) = all_47_1 & implies(all_47_5,
% 26.03/4.23 | all_47_1) = all_47_0 & implies(all_47_7, all_47_6) = all_47_4 &
% 26.03/4.23 | implies(all_47_8, all_47_6) = all_47_5 & $i(all_47_0) &
% 26.03/4.23 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) &
% 26.03/4.23 | $i(all_47_5) & ~ or_3 & ~ is_a_theorem(all_47_0)) | (or_3 & !
% 26.03/4.23 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 26.03/4.23 | ( ~ (or(v0, v1) = v3) | ~ (implies(v3, v2) = v4) | ~ $i(v2) | ~
% 26.03/4.23 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 26.03/4.23 | ? [v8: $i] : (implies(v6, v4) = v7 & implies(v5, v7) = v8 &
% 26.03/4.23 | implies(v1, v2) = v6 & implies(v0, v2) = v5 & $i(v8) & $i(v7)
% 26.03/4.23 | & $i(v6) & $i(v5) & is_a_theorem(v8)))))
% 26.03/4.23 |
% 26.03/4.23 | ALPHA: (14) implies:
% 26.03/4.23 | (15) (or(all_47_8, all_47_7) = all_47_3 & implies(all_47_3, all_47_6) =
% 26.03/4.23 | all_47_2 & implies(all_47_4, all_47_2) = all_47_1 &
% 26.03/4.23 | implies(all_47_5, all_47_1) = all_47_0 & implies(all_47_7, all_47_6)
% 26.03/4.23 | = all_47_4 & implies(all_47_8, all_47_6) = all_47_5 & $i(all_47_0) &
% 26.03/4.23 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) &
% 26.03/4.23 | $i(all_47_5) & ~ or_3 & ~ is_a_theorem(all_47_0)) | (or_3 & !
% 26.03/4.23 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 26.03/4.23 | ~ (or(v0, v1) = v3) | ~ (implies(v3, v2) = v4) | ~ $i(v2) | ~
% 26.03/4.23 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 26.03/4.23 | [v8: $i] : (implies(v6, v4) = v7 & implies(v5, v7) = v8 &
% 26.03/4.23 | implies(v1, v2) = v6 & implies(v0, v2) = v5 & $i(v8) & $i(v7) &
% 26.03/4.23 | $i(v6) & $i(v5) & is_a_theorem(v8))))
% 26.03/4.23 |
% 26.03/4.23 | BETA: splitting (13) gives:
% 26.03/4.23 |
% 26.03/4.23 | Case 1:
% 26.03/4.23 | |
% 26.03/4.23 | | (16) or(all_35_3, all_35_4) = all_35_1 & or(all_35_4, all_35_3) =
% 26.03/4.23 | | all_35_2 & implies(all_35_2, all_35_1) = all_35_0 & $i(all_35_0) &
% 26.03/4.23 | | $i(all_35_1) & $i(all_35_2) & ~ r3 & ~ is_a_theorem(all_35_0)
% 26.03/4.23 | |
% 26.03/4.23 | | ALPHA: (16) implies:
% 26.03/4.23 | | (17) ~ is_a_theorem(all_35_0)
% 26.03/4.23 | | (18) $i(all_35_2)
% 26.03/4.23 | | (19) $i(all_35_1)
% 26.03/4.23 | | (20) implies(all_35_2, all_35_1) = all_35_0
% 26.03/4.23 | | (21) or(all_35_4, all_35_3) = all_35_2
% 26.03/4.23 | | (22) or(all_35_3, all_35_4) = all_35_1
% 26.03/4.23 | |
% 26.03/4.23 | | BETA: splitting (op_implies_and) gives:
% 26.03/4.23 | |
% 26.03/4.23 | | Case 1:
% 26.03/4.23 | | |
% 26.03/4.23 | | | (23) ~ op_implies_and
% 26.03/4.23 | | |
% 26.03/4.23 | | | PRED_UNIFY: (23), (hilbert_op_implies_and) imply:
% 26.03/4.23 | | | (24) $false
% 26.03/4.23 | | |
% 26.03/4.23 | | | CLOSE: (24) is inconsistent.
% 26.03/4.23 | | |
% 26.03/4.23 | | Case 2:
% 26.03/4.23 | | |
% 26.03/4.24 | | | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 26.03/4.24 | | | (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 26.03/4.24 | | | ? [v4: $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) &
% 26.03/4.24 | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) =
% 26.03/4.24 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 26.03/4.24 | | | (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3 & $i(v4) &
% 26.03/4.24 | | | $i(v3) & $i(v2)))
% 26.03/4.24 | | |
% 26.03/4.24 | | | ALPHA: (25) implies:
% 26.03/4.24 | | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) =
% 26.03/4.24 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 26.03/4.24 | | | (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3 & $i(v4) &
% 26.03/4.24 | | | $i(v3) & $i(v2)))
% 26.03/4.24 | | |
% 26.03/4.24 | | | BETA: splitting (5) gives:
% 26.03/4.24 | | |
% 26.03/4.24 | | | Case 1:
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | (27) or(all_16_3, all_16_2) = all_16_1 & implies(all_16_2, all_16_1)
% 26.03/4.24 | | | | = all_16_0 & $i(all_16_0) & $i(all_16_1) & ~ or_2 & ~
% 26.03/4.24 | | | | is_a_theorem(all_16_0)
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | ALPHA: (27) implies:
% 26.03/4.24 | | | | (28) ~ or_2
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | PRED_UNIFY: (28), (hilbert_or_2) imply:
% 26.03/4.24 | | | | (29) $false
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | CLOSE: (29) is inconsistent.
% 26.03/4.24 | | | |
% 26.03/4.24 | | | Case 2:
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | (30) or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1)
% 26.03/4.24 | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v1,
% 26.03/4.24 | | | | v2) = v3 & $i(v3) & is_a_theorem(v3)))
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | ALPHA: (30) implies:
% 26.03/4.24 | | | | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2)
% 26.03/4.24 | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v1, v2) = v3
% 26.03/4.24 | | | | & $i(v3) & is_a_theorem(v3)))
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | BETA: splitting (15) gives:
% 26.03/4.24 | | | |
% 26.03/4.24 | | | | Case 1:
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | (32) or(all_47_8, all_47_7) = all_47_3 & implies(all_47_3,
% 26.03/4.24 | | | | | all_47_6) = all_47_2 & implies(all_47_4, all_47_2) =
% 26.03/4.24 | | | | | all_47_1 & implies(all_47_5, all_47_1) = all_47_0 &
% 26.03/4.24 | | | | | implies(all_47_7, all_47_6) = all_47_4 & implies(all_47_8,
% 26.03/4.24 | | | | | all_47_6) = all_47_5 & $i(all_47_0) & $i(all_47_1) &
% 26.03/4.24 | | | | | $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & $i(all_47_5) & ~
% 26.03/4.24 | | | | | or_3 & ~ is_a_theorem(all_47_0)
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | ALPHA: (32) implies:
% 26.03/4.24 | | | | | (33) ~ or_3
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | PRED_UNIFY: (33), (hilbert_or_3) imply:
% 26.03/4.24 | | | | | (34) $false
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | CLOSE: (34) is inconsistent.
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | Case 2:
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | (35) or_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 26.03/4.24 | | | | | ! [v4: $i] : ( ~ (or(v0, v1) = v3) | ~ (implies(v3, v2) =
% 26.03/4.24 | | | | | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ?
% 26.03/4.24 | | | | | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (implies(v6, v4) = v7
% 26.03/4.24 | | | | | & implies(v5, v7) = v8 & implies(v1, v2) = v6 &
% 26.03/4.24 | | | | | implies(v0, v2) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 26.03/4.24 | | | | | is_a_theorem(v8)))
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | ALPHA: (35) implies:
% 26.03/4.24 | | | | | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 26.03/4.24 | | | | | [v4: $i] : ( ~ (or(v0, v1) = v3) | ~ (implies(v3, v2) = v4) |
% 26.03/4.24 | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6:
% 26.03/4.24 | | | | | $i] : ? [v7: $i] : ? [v8: $i] : (implies(v6, v4) = v7 &
% 26.03/4.24 | | | | | implies(v5, v7) = v8 & implies(v1, v2) = v6 & implies(v0,
% 26.03/4.24 | | | | | v2) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 26.03/4.24 | | | | | is_a_theorem(v8)))
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | BETA: splitting (3) gives:
% 26.03/4.24 | | | | |
% 26.03/4.24 | | | | | Case 1:
% 26.03/4.24 | | | | | |
% 26.03/4.24 | | | | | | (37) implies(all_10_2, all_10_1) = all_10_0 & $i(all_10_0) &
% 26.03/4.24 | | | | | | is_a_theorem(all_10_0) & is_a_theorem(all_10_2) & ~
% 26.03/4.24 | | | | | | is_a_theorem(all_10_1) & ~ modus_ponens
% 26.03/4.24 | | | | | |
% 26.03/4.24 | | | | | | ALPHA: (37) implies:
% 26.03/4.24 | | | | | | (38) ~ modus_ponens
% 26.03/4.24 | | | | | |
% 26.03/4.24 | | | | | | PRED_UNIFY: (38), (hilbert_modus_ponens) imply:
% 26.03/4.24 | | | | | | (39) $false
% 26.03/4.24 | | | | | |
% 26.03/4.24 | | | | | | CLOSE: (39) is inconsistent.
% 26.03/4.24 | | | | | |
% 26.03/4.24 | | | | | Case 2:
% 26.03/4.24 | | | | | |
% 26.03/4.25 | | | | | | (40) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 26.03/4.25 | | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.03/4.25 | | | | | | is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 26.03/4.25 | | | | | |
% 26.03/4.25 | | | | | | ALPHA: (40) implies:
% 26.03/4.25 | | | | | | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0,
% 26.03/4.25 | | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.03/4.25 | | | | | | is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 26.03/4.25 | | | | | |
% 26.03/4.25 | | | | | | BETA: splitting (7) gives:
% 26.03/4.25 | | | | | |
% 26.03/4.25 | | | | | | Case 1:
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | (42) or(all_18_3, all_18_2) = all_18_1 & implies(all_18_3,
% 26.03/4.25 | | | | | | | all_18_1) = all_18_0 & $i(all_18_0) & $i(all_18_1) & ~
% 26.03/4.25 | | | | | | | or_1 & ~ is_a_theorem(all_18_0)
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | ALPHA: (42) implies:
% 26.03/4.25 | | | | | | | (43) ~ or_1
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | PRED_UNIFY: (43), (hilbert_or_1) imply:
% 26.03/4.25 | | | | | | | (44) $false
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | CLOSE: (44) is inconsistent.
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | Case 2:
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | (45) or_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 26.03/4.25 | | | | | | | (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 26.03/4.25 | | | | | | | : (implies(v0, v2) = v3 & $i(v3) & is_a_theorem(v3)))
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | ALPHA: (45) implies:
% 26.03/4.25 | | | | | | | (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1)
% 26.03/4.25 | | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 26.03/4.25 | | | | | | | (implies(v0, v2) = v3 & $i(v3) & is_a_theorem(v3)))
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | BETA: splitting (9) gives:
% 26.03/4.25 | | | | | | |
% 26.03/4.25 | | | | | | | Case 1:
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | (47) implies(all_22_2, all_22_3) = all_22_1 &
% 26.03/4.25 | | | | | | | | implies(all_22_3, all_22_1) = all_22_0 & $i(all_22_0) &
% 26.03/4.25 | | | | | | | | $i(all_22_1) & ~ implies_1 & ~ is_a_theorem(all_22_0)
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | ALPHA: (47) implies:
% 26.03/4.25 | | | | | | | | (48) ~ implies_1
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | PRED_UNIFY: (48), (hilbert_implies_1) imply:
% 26.03/4.25 | | | | | | | | (49) $false
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | CLOSE: (49) is inconsistent.
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | Case 2:
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | GROUND_INST: instantiating (26) with all_35_2, all_35_1,
% 26.03/4.25 | | | | | | | | all_35_0, simplifying with (18), (19), (20) gives:
% 26.03/4.25 | | | | | | | | (50) ? [v0: $i] : ? [v1: $i] : (and(all_35_2, v0) = v1 &
% 26.03/4.25 | | | | | | | | not(v1) = all_35_0 & not(all_35_1) = v0 & $i(v1) &
% 26.03/4.25 | | | | | | | | $i(v0) & $i(all_35_0))
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | GROUND_INST: instantiating (36) with all_35_4, all_35_3,
% 26.03/4.25 | | | | | | | | all_35_1, all_35_2, all_35_0, simplifying with
% 26.03/4.25 | | | | | | | | (11), (12), (19), (20), (21) gives:
% 26.03/4.25 | | | | | | | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 26.03/4.25 | | | | | | | | (implies(v1, all_35_0) = v2 & implies(v0, v2) = v3 &
% 26.03/4.25 | | | | | | | | implies(all_35_3, all_35_1) = v1 & implies(all_35_4,
% 26.03/4.25 | | | | | | | | all_35_1) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 26.03/4.25 | | | | | | | | is_a_theorem(v3))
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | GROUND_INST: instantiating (31) with all_35_3, all_35_4,
% 26.03/4.25 | | | | | | | | all_35_1, simplifying with (11), (12), (22) gives:
% 26.03/4.25 | | | | | | | | (52) ? [v0: $i] : (implies(all_35_4, all_35_1) = v0 & $i(v0)
% 26.03/4.25 | | | | | | | | & is_a_theorem(v0))
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | GROUND_INST: instantiating (46) with all_35_3, all_35_4,
% 26.03/4.25 | | | | | | | | all_35_1, simplifying with (11), (12), (22) gives:
% 26.03/4.25 | | | | | | | | (53) ? [v0: $i] : (implies(all_35_3, all_35_1) = v0 & $i(v0)
% 26.03/4.25 | | | | | | | | & is_a_theorem(v0))
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | DELTA: instantiating (53) with fresh symbol all_143_0 gives:
% 26.03/4.25 | | | | | | | | (54) implies(all_35_3, all_35_1) = all_143_0 & $i(all_143_0)
% 26.03/4.25 | | | | | | | | & is_a_theorem(all_143_0)
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | ALPHA: (54) implies:
% 26.03/4.25 | | | | | | | | (55) is_a_theorem(all_143_0)
% 26.03/4.25 | | | | | | | | (56) implies(all_35_3, all_35_1) = all_143_0
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | DELTA: instantiating (52) with fresh symbol all_151_0 gives:
% 26.03/4.25 | | | | | | | | (57) implies(all_35_4, all_35_1) = all_151_0 & $i(all_151_0)
% 26.03/4.25 | | | | | | | | & is_a_theorem(all_151_0)
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | ALPHA: (57) implies:
% 26.03/4.25 | | | | | | | | (58) is_a_theorem(all_151_0)
% 26.03/4.25 | | | | | | | | (59) implies(all_35_4, all_35_1) = all_151_0
% 26.03/4.25 | | | | | | | |
% 26.03/4.25 | | | | | | | | DELTA: instantiating (50) with fresh symbols all_165_0,
% 26.03/4.25 | | | | | | | | all_165_1 gives:
% 26.03/4.25 | | | | | | | | (60) and(all_35_2, all_165_1) = all_165_0 & not(all_165_0) =
% 26.03/4.26 | | | | | | | | all_35_0 & not(all_35_1) = all_165_1 & $i(all_165_0) &
% 26.03/4.26 | | | | | | | | $i(all_165_1) & $i(all_35_0)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | ALPHA: (60) implies:
% 26.03/4.26 | | | | | | | | (61) $i(all_35_0)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | DELTA: instantiating (51) with fresh symbols all_171_0,
% 26.03/4.26 | | | | | | | | all_171_1, all_171_2, all_171_3 gives:
% 26.03/4.26 | | | | | | | | (62) implies(all_171_2, all_35_0) = all_171_1 &
% 26.03/4.26 | | | | | | | | implies(all_171_3, all_171_1) = all_171_0 &
% 26.03/4.26 | | | | | | | | implies(all_35_3, all_35_1) = all_171_2 &
% 26.03/4.26 | | | | | | | | implies(all_35_4, all_35_1) = all_171_3 & $i(all_171_0)
% 26.03/4.26 | | | | | | | | & $i(all_171_1) & $i(all_171_2) & $i(all_171_3) &
% 26.03/4.26 | | | | | | | | is_a_theorem(all_171_0)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | ALPHA: (62) implies:
% 26.03/4.26 | | | | | | | | (63) is_a_theorem(all_171_0)
% 26.03/4.26 | | | | | | | | (64) $i(all_171_3)
% 26.03/4.26 | | | | | | | | (65) $i(all_171_2)
% 26.03/4.26 | | | | | | | | (66) $i(all_171_1)
% 26.03/4.26 | | | | | | | | (67) implies(all_35_4, all_35_1) = all_171_3
% 26.03/4.26 | | | | | | | | (68) implies(all_35_3, all_35_1) = all_171_2
% 26.03/4.26 | | | | | | | | (69) implies(all_171_3, all_171_1) = all_171_0
% 26.03/4.26 | | | | | | | | (70) implies(all_171_2, all_35_0) = all_171_1
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | GROUND_INST: instantiating (1) with all_151_0, all_171_3,
% 26.03/4.26 | | | | | | | | all_35_1, all_35_4, simplifying with (59), (67)
% 26.03/4.26 | | | | | | | | gives:
% 26.03/4.26 | | | | | | | | (71) all_171_3 = all_151_0
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | GROUND_INST: instantiating (1) with all_143_0, all_171_2,
% 26.03/4.26 | | | | | | | | all_35_1, all_35_3, simplifying with (56), (68)
% 26.03/4.26 | | | | | | | | gives:
% 26.03/4.26 | | | | | | | | (72) all_171_2 = all_143_0
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | REDUCE: (70), (72) imply:
% 26.03/4.26 | | | | | | | | (73) implies(all_143_0, all_35_0) = all_171_1
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | REDUCE: (69), (71) imply:
% 26.03/4.26 | | | | | | | | (74) implies(all_151_0, all_171_1) = all_171_0
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | REDUCE: (65), (72) imply:
% 26.03/4.26 | | | | | | | | (75) $i(all_143_0)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | REDUCE: (64), (71) imply:
% 26.03/4.26 | | | | | | | | (76) $i(all_151_0)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | GROUND_INST: instantiating (41) with all_143_0, all_35_0,
% 26.03/4.26 | | | | | | | | all_171_1, simplifying with (17), (55), (61), (73),
% 26.03/4.26 | | | | | | | | (75) gives:
% 26.03/4.26 | | | | | | | | (77) ~ is_a_theorem(all_171_1)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | GROUND_INST: instantiating (41) with all_151_0, all_171_1,
% 26.03/4.26 | | | | | | | | all_171_0, simplifying with (58), (63), (66), (74),
% 26.03/4.26 | | | | | | | | (76) gives:
% 26.03/4.26 | | | | | | | | (78) is_a_theorem(all_171_1)
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | PRED_UNIFY: (77), (78) imply:
% 26.03/4.26 | | | | | | | | (79) $false
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | | CLOSE: (79) is inconsistent.
% 26.03/4.26 | | | | | | | |
% 26.03/4.26 | | | | | | | End of split
% 26.03/4.26 | | | | | | |
% 26.03/4.26 | | | | | | End of split
% 26.03/4.26 | | | | | |
% 26.03/4.26 | | | | | End of split
% 26.03/4.26 | | | | |
% 26.03/4.26 | | | | End of split
% 26.03/4.26 | | | |
% 26.03/4.26 | | | End of split
% 26.03/4.26 | | |
% 26.03/4.26 | | End of split
% 26.03/4.26 | |
% 26.03/4.26 | Case 2:
% 26.03/4.26 | |
% 26.03/4.26 | | (80) r3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v1, v0) = v2)
% 26.03/4.26 | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (or(v0, v1)
% 26.03/4.26 | | = v3 & implies(v3, v2) = v4 & $i(v4) & $i(v3) &
% 26.03/4.26 | | is_a_theorem(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 26.03/4.26 | | ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 26.03/4.26 | | [v4: $i] : (or(v1, v0) = v3 & implies(v2, v3) = v4 & $i(v4) &
% 26.03/4.26 | | $i(v3) & is_a_theorem(v4)))
% 26.03/4.26 | |
% 26.03/4.26 | | ALPHA: (80) implies:
% 26.03/4.26 | | (81) r3
% 26.03/4.26 | |
% 26.03/4.26 | | PRED_UNIFY: (81), (principia_r3) imply:
% 26.03/4.26 | | (82) $false
% 26.03/4.26 | |
% 26.03/4.26 | | CLOSE: (82) is inconsistent.
% 26.03/4.26 | |
% 26.03/4.26 | End of split
% 26.03/4.26 |
% 26.03/4.26 End of proof
% 26.03/4.26 % SZS output end Proof for theBenchmark
% 26.03/4.26
% 26.03/4.26 3764ms
%------------------------------------------------------------------------------