TSTP Solution File: LCL542+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL542+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 : n024.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 08:11:36 EDT 2023
% Result : Theorem 12.21s 2.57s
% Output : Proof 23.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 17:49:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.17/1.32 Prover 1: Preprocessing ...
% 4.17/1.32 Prover 4: Preprocessing ...
% 4.71/1.38 Prover 2: Preprocessing ...
% 4.71/1.38 Prover 3: Preprocessing ...
% 4.71/1.38 Prover 0: Preprocessing ...
% 4.71/1.38 Prover 6: Preprocessing ...
% 4.71/1.38 Prover 5: Preprocessing ...
% 11.18/2.34 Prover 5: Proving ...
% 11.18/2.37 Prover 6: Constructing countermodel ...
% 11.81/2.38 Prover 1: Constructing countermodel ...
% 11.98/2.42 Prover 4: Constructing countermodel ...
% 11.98/2.44 Prover 3: Constructing countermodel ...
% 11.98/2.48 Prover 0: Proving ...
% 12.21/2.53 Prover 2: Proving ...
% 12.21/2.57 Prover 6: proved (1909ms)
% 12.21/2.57
% 12.21/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.21/2.57
% 12.21/2.57 Prover 0: stopped
% 12.21/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.21/2.57 Prover 3: stopped
% 12.21/2.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.21/2.57 Prover 5: stopped
% 12.21/2.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.21/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.21/2.58 Prover 2: stopped
% 12.21/2.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.98/2.72 Prover 7: Preprocessing ...
% 13.98/2.72 Prover 11: Preprocessing ...
% 13.98/2.73 Prover 13: Preprocessing ...
% 13.98/2.73 Prover 8: Preprocessing ...
% 13.98/2.73 Prover 10: Preprocessing ...
% 16.28/3.06 Prover 13: Warning: ignoring some quantifiers
% 16.28/3.07 Prover 7: Constructing countermodel ...
% 17.02/3.09 Prover 13: Constructing countermodel ...
% 17.02/3.09 Prover 8: Warning: ignoring some quantifiers
% 17.02/3.09 Prover 10: Constructing countermodel ...
% 17.18/3.13 Prover 8: Constructing countermodel ...
% 17.45/3.21 Prover 11: Constructing countermodel ...
% 23.12/3.98 Prover 10: Found proof (size 41)
% 23.12/3.98 Prover 10: proved (1403ms)
% 23.12/3.98 Prover 8: stopped
% 23.12/3.98 Prover 4: stopped
% 23.12/3.98 Prover 1: stopped
% 23.12/3.98 Prover 7: stopped
% 23.88/3.99 Prover 11: stopped
% 23.88/4.00 Prover 13: stopped
% 23.88/4.00
% 23.88/4.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.88/4.00
% 23.88/4.00 % SZS output start Proof for theBenchmark
% 23.88/4.00 Assumptions after simplification:
% 23.88/4.00 ---------------------------------
% 23.88/4.00
% 23.88/4.00 (and_1)
% 23.97/4.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) &
% 23.97/4.03 ((and(v0, v1) = v2 & implies(v2, v0) = v3 & $i(v3) & $i(v2) & ~ and_1 & ~
% 23.97/4.03 is_a_theorem(v3)) | (and_1 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 23.97/4.03 ! [v7: $i] : ( ~ (and(v4, v5) = v6) | ~ (implies(v6, v4) = v7) | ~
% 23.97/4.03 $i(v5) | ~ $i(v4) | is_a_theorem(v7)))))
% 23.97/4.03
% 23.97/4.03 (axiom_m2)
% 23.97/4.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) &
% 23.97/4.03 ((strict_implies(v2, v0) = v3 & and(v0, v1) = v2 & $i(v3) & $i(v2) & ~
% 23.97/4.03 axiom_m2 & ~ is_a_theorem(v3)) | (axiom_m2 & ! [v4: $i] : ! [v5: $i]
% 23.97/4.03 : ! [v6: $i] : ! [v7: $i] : ( ~ (strict_implies(v6, v4) = v7) | ~
% 23.97/4.03 (and(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | is_a_theorem(v7)))))
% 23.97/4.03
% 23.97/4.03 (hilbert_and_1)
% 23.97/4.03 and_1
% 23.97/4.03
% 23.97/4.03 (hilbert_or_3)
% 23.97/4.03 or_3
% 23.97/4.03
% 23.97/4.03 (km4b_necessitation)
% 23.97/4.03 necessitation
% 23.97/4.03
% 23.97/4.03 (necessitation)
% 23.97/4.03 ? [v0: $i] : ? [v1: $i] : ($i(v0) & ((necessarily(v0) = v1 & $i(v1) &
% 23.97/4.03 is_a_theorem(v0) & ~ necessitation & ~ is_a_theorem(v1)) |
% 23.97/4.03 (necessitation & ! [v2: $i] : ! [v3: $i] : ( ~ (necessarily(v2) = v3) |
% 23.97/4.03 ~ $i(v2) | ~ is_a_theorem(v2) | is_a_theorem(v3)))))
% 23.97/4.03
% 23.97/4.03 (op_strict_implies)
% 23.97/4.04 ~ op_strict_implies | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 23.97/4.04 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 23.97/4.04 (necessarily(v3) = v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2)))
% 23.97/4.04
% 23.97/4.04 (or_3)
% 23.97/4.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 23.97/4.04 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 23.97/4.04 ((or(v0, v1) = v5 & implies(v5, v2) = v6 & implies(v4, v6) = v7 &
% 23.97/4.04 implies(v3, v7) = v8 & implies(v1, v2) = v4 & implies(v0, v2) = v3 &
% 23.97/4.04 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ~ or_3 & ~
% 23.97/4.04 is_a_theorem(v8)) | (or_3 & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] :
% 23.97/4.04 ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 23.97/4.04 : ! [v17: $i] : ( ~ (or(v9, v10) = v14) | ~ (implies(v14, v11) = v15)
% 23.97/4.04 | ~ (implies(v13, v15) = v16) | ~ (implies(v12, v16) = v17) | ~
% 23.97/4.04 (implies(v10, v11) = v13) | ~ (implies(v9, v11) = v12) | ~ $i(v11) |
% 23.97/4.04 ~ $i(v10) | ~ $i(v9) | is_a_theorem(v17)))))
% 23.97/4.04
% 23.97/4.04 (s1_0_axiom_m2)
% 23.97/4.04 ~ axiom_m2
% 23.97/4.04
% 23.97/4.04 (s1_0_op_strict_implies)
% 23.97/4.04 op_strict_implies
% 23.97/4.04
% 23.97/4.04 Further assumptions not needed in the proof:
% 23.97/4.04 --------------------------------------------
% 23.97/4.04 adjunction, and_2, and_3, axiom_4, axiom_5, axiom_B, axiom_K, axiom_M, axiom_m1,
% 23.97/4.04 axiom_m10, axiom_m3, axiom_m4, axiom_m5, axiom_m6, axiom_m7, axiom_m8, axiom_m9,
% 23.97/4.04 axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1,
% 23.97/4.04 equivalence_2, equivalence_3, hilbert_and_2, hilbert_and_3,
% 23.97/4.04 hilbert_equivalence_1, hilbert_equivalence_2, hilbert_equivalence_3,
% 23.97/4.04 hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, hilbert_modus_ponens,
% 23.97/4.04 hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or,
% 23.97/4.04 hilbert_or_1, hilbert_or_2, implies_1, implies_2, implies_3, km4b_axiom_4,
% 23.97/4.05 km4b_axiom_B, km4b_axiom_K, km4b_axiom_M, km4b_op_possibly, kn1, kn2, kn3,
% 23.97/4.05 modus_ponens, modus_ponens_strict_implies, modus_tollens, op_and, op_equiv,
% 23.97/4.05 op_implies_and, op_implies_or, op_necessarily, op_or, op_possibly,
% 23.97/4.05 op_strict_equiv, or_1, or_2, r1, r2, r3, r4, r5, s1_0_op_equiv, s1_0_op_implies,
% 23.97/4.05 s1_0_op_or, s1_0_op_possibly, s1_0_op_strict_equiv, substitution_of_equivalents,
% 23.97/4.05 substitution_strict_equiv
% 23.97/4.05
% 23.97/4.05 Those formulas are unsatisfiable:
% 23.97/4.05 ---------------------------------
% 23.97/4.05
% 23.97/4.05 Begin of proof
% 23.97/4.05 |
% 23.97/4.05 | DELTA: instantiating (necessitation) with fresh symbols all_4_0, all_4_1
% 23.97/4.05 | gives:
% 23.97/4.05 | (1) $i(all_4_1) & ((necessarily(all_4_1) = all_4_0 & $i(all_4_0) &
% 23.97/4.05 | is_a_theorem(all_4_1) & ~ necessitation & ~
% 23.97/4.05 | is_a_theorem(all_4_0)) | (necessitation & ! [v0: $i] : ! [v1: $i]
% 23.97/4.05 | : ( ~ (necessarily(v0) = v1) | ~ $i(v0) | ~ is_a_theorem(v0) |
% 23.97/4.05 | is_a_theorem(v1))))
% 23.97/4.05 |
% 23.97/4.05 | ALPHA: (1) implies:
% 23.97/4.05 | (2) (necessarily(all_4_1) = all_4_0 & $i(all_4_0) & is_a_theorem(all_4_1) &
% 23.97/4.05 | ~ necessitation & ~ is_a_theorem(all_4_0)) | (necessitation & !
% 23.97/4.05 | [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) = v1) | ~ $i(v0) | ~
% 23.97/4.05 | is_a_theorem(v0) | is_a_theorem(v1)))
% 23.97/4.05 |
% 23.97/4.05 | DELTA: instantiating (axiom_m2) with fresh symbols all_20_0, all_20_1,
% 23.97/4.05 | all_20_2, all_20_3 gives:
% 23.97/4.05 | (3) $i(all_20_2) & $i(all_20_3) & ((strict_implies(all_20_1, all_20_3) =
% 23.97/4.05 | all_20_0 & and(all_20_3, all_20_2) = all_20_1 & $i(all_20_0) &
% 23.97/4.05 | $i(all_20_1) & ~ axiom_m2 & ~ is_a_theorem(all_20_0)) | (axiom_m2
% 23.97/4.05 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.97/4.05 | (strict_implies(v2, v0) = v3) | ~ (and(v0, v1) = v2) | ~ $i(v1)
% 23.97/4.05 | | ~ $i(v0) | is_a_theorem(v3))))
% 23.97/4.05 |
% 23.97/4.05 | ALPHA: (3) implies:
% 23.97/4.05 | (4) $i(all_20_3)
% 23.97/4.05 | (5) $i(all_20_2)
% 23.97/4.06 | (6) (strict_implies(all_20_1, all_20_3) = all_20_0 & and(all_20_3,
% 23.97/4.06 | all_20_2) = all_20_1 & $i(all_20_0) & $i(all_20_1) & ~ axiom_m2 &
% 23.97/4.06 | ~ is_a_theorem(all_20_0)) | (axiom_m2 & ! [v0: $i] : ! [v1: $i] :
% 23.97/4.06 | ! [v2: $i] : ! [v3: $i] : ( ~ (strict_implies(v2, v0) = v3) | ~
% 23.97/4.06 | (and(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | is_a_theorem(v3)))
% 23.97/4.06 |
% 23.97/4.06 | DELTA: instantiating (and_1) with fresh symbols all_22_0, all_22_1, all_22_2,
% 23.97/4.06 | all_22_3 gives:
% 23.97/4.06 | (7) $i(all_22_2) & $i(all_22_3) & ((and(all_22_3, all_22_2) = all_22_1 &
% 23.97/4.06 | implies(all_22_1, all_22_3) = all_22_0 & $i(all_22_0) &
% 23.97/4.06 | $i(all_22_1) & ~ and_1 & ~ is_a_theorem(all_22_0)) | (and_1 & !
% 23.97/4.06 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0,
% 23.97/4.06 | v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0)
% 23.97/4.06 | | is_a_theorem(v3))))
% 23.97/4.06 |
% 23.97/4.06 | ALPHA: (7) implies:
% 23.97/4.06 | (8) (and(all_22_3, all_22_2) = all_22_1 & implies(all_22_1, all_22_3) =
% 23.97/4.06 | all_22_0 & $i(all_22_0) & $i(all_22_1) & ~ and_1 & ~
% 23.97/4.06 | is_a_theorem(all_22_0)) | (and_1 & ! [v0: $i] : ! [v1: $i] : !
% 23.97/4.06 | [v2: $i] : ! [v3: $i] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0)
% 23.97/4.06 | = v3) | ~ $i(v1) | ~ $i(v0) | is_a_theorem(v3)))
% 23.97/4.06 |
% 23.97/4.06 | DELTA: instantiating (or_3) with fresh symbols all_95_0, all_95_1, all_95_2,
% 23.97/4.06 | all_95_3, all_95_4, all_95_5, all_95_6, all_95_7, all_95_8 gives:
% 23.97/4.06 | (9) $i(all_95_6) & $i(all_95_7) & $i(all_95_8) & ((or(all_95_8, all_95_7) =
% 23.97/4.06 | all_95_3 & implies(all_95_3, all_95_6) = all_95_2 &
% 23.97/4.06 | implies(all_95_4, all_95_2) = all_95_1 & implies(all_95_5,
% 23.97/4.06 | all_95_1) = all_95_0 & implies(all_95_7, all_95_6) = all_95_4 &
% 23.97/4.06 | implies(all_95_8, all_95_6) = all_95_5 & $i(all_95_0) &
% 23.97/4.06 | $i(all_95_1) & $i(all_95_2) & $i(all_95_3) & $i(all_95_4) &
% 23.97/4.06 | $i(all_95_5) & ~ or_3 & ~ is_a_theorem(all_95_0)) | (or_3 & !
% 23.97/4.06 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 23.97/4.06 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (or(v0,
% 23.97/4.06 | v1) = v5) | ~ (implies(v5, v2) = v6) | ~ (implies(v4, v6) =
% 23.97/4.06 | v7) | ~ (implies(v3, v7) = v8) | ~ (implies(v1, v2) = v4) |
% 23.97/4.06 | ~ (implies(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.97/4.06 | is_a_theorem(v8))))
% 23.97/4.06 |
% 23.97/4.06 | ALPHA: (9) implies:
% 23.97/4.06 | (10) (or(all_95_8, all_95_7) = all_95_3 & implies(all_95_3, all_95_6) =
% 23.97/4.06 | all_95_2 & implies(all_95_4, all_95_2) = all_95_1 &
% 23.97/4.06 | implies(all_95_5, all_95_1) = all_95_0 & implies(all_95_7, all_95_6)
% 23.97/4.06 | = all_95_4 & implies(all_95_8, all_95_6) = all_95_5 & $i(all_95_0) &
% 23.97/4.06 | $i(all_95_1) & $i(all_95_2) & $i(all_95_3) & $i(all_95_4) &
% 23.97/4.06 | $i(all_95_5) & ~ or_3 & ~ is_a_theorem(all_95_0)) | (or_3 & !
% 23.97/4.06 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 23.97/4.06 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (or(v0,
% 23.97/4.06 | v1) = v5) | ~ (implies(v5, v2) = v6) | ~ (implies(v4, v6) =
% 23.97/4.06 | v7) | ~ (implies(v3, v7) = v8) | ~ (implies(v1, v2) = v4) | ~
% 23.97/4.06 | (implies(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.97/4.06 | is_a_theorem(v8)))
% 23.97/4.06 |
% 23.97/4.06 | BETA: splitting (6) gives:
% 23.97/4.06 |
% 23.97/4.06 | Case 1:
% 23.97/4.06 | |
% 23.97/4.06 | | (11) strict_implies(all_20_1, all_20_3) = all_20_0 & and(all_20_3,
% 23.97/4.06 | | all_20_2) = all_20_1 & $i(all_20_0) & $i(all_20_1) & ~ axiom_m2 &
% 23.97/4.06 | | ~ is_a_theorem(all_20_0)
% 23.97/4.06 | |
% 23.97/4.06 | | ALPHA: (11) implies:
% 23.97/4.06 | | (12) ~ is_a_theorem(all_20_0)
% 23.97/4.06 | | (13) $i(all_20_1)
% 23.97/4.06 | | (14) and(all_20_3, all_20_2) = all_20_1
% 23.97/4.06 | | (15) strict_implies(all_20_1, all_20_3) = all_20_0
% 23.97/4.06 | |
% 23.97/4.06 | | BETA: splitting (op_strict_implies) gives:
% 23.97/4.06 | |
% 23.97/4.06 | | Case 1:
% 23.97/4.06 | | |
% 23.97/4.06 | | | (16) ~ op_strict_implies
% 23.97/4.06 | | |
% 23.97/4.06 | | | PRED_UNIFY: (16), (s1_0_op_strict_implies) imply:
% 23.97/4.06 | | | (17) $false
% 23.97/4.06 | | |
% 23.97/4.06 | | | CLOSE: (17) is inconsistent.
% 23.97/4.06 | | |
% 23.97/4.06 | | Case 2:
% 23.97/4.06 | | |
% 23.97/4.07 | | | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (strict_implies(v0,
% 23.97/4.07 | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 23.97/4.07 | | | (necessarily(v3) = v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2)))
% 23.97/4.07 | | |
% 23.97/4.07 | | | BETA: splitting (2) gives:
% 23.97/4.07 | | |
% 23.97/4.07 | | | Case 1:
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | (19) necessarily(all_4_1) = all_4_0 & $i(all_4_0) &
% 23.97/4.07 | | | | is_a_theorem(all_4_1) & ~ necessitation & ~
% 23.97/4.07 | | | | is_a_theorem(all_4_0)
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | ALPHA: (19) implies:
% 23.97/4.07 | | | | (20) ~ necessitation
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | PRED_UNIFY: (20), (km4b_necessitation) imply:
% 23.97/4.07 | | | | (21) $false
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | CLOSE: (21) is inconsistent.
% 23.97/4.07 | | | |
% 23.97/4.07 | | | Case 2:
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | (22) necessitation & ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0)
% 23.97/4.07 | | | | = v1) | ~ $i(v0) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | ALPHA: (22) implies:
% 23.97/4.07 | | | | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) = v1) | ~
% 23.97/4.07 | | | | $i(v0) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | BETA: splitting (8) gives:
% 23.97/4.07 | | | |
% 23.97/4.07 | | | | Case 1:
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | (24) and(all_22_3, all_22_2) = all_22_1 & implies(all_22_1,
% 23.97/4.07 | | | | | all_22_3) = all_22_0 & $i(all_22_0) & $i(all_22_1) & ~
% 23.97/4.07 | | | | | and_1 & ~ is_a_theorem(all_22_0)
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | ALPHA: (24) implies:
% 23.97/4.07 | | | | | (25) ~ and_1
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | PRED_UNIFY: (25), (hilbert_and_1) imply:
% 23.97/4.07 | | | | | (26) $false
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | CLOSE: (26) is inconsistent.
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | Case 2:
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | (27) and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 23.97/4.07 | | | | | : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~
% 23.97/4.07 | | | | | $i(v1) | ~ $i(v0) | is_a_theorem(v3))
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | ALPHA: (27) implies:
% 23.97/4.07 | | | | | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.97/4.07 | | | | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) |
% 23.97/4.07 | | | | | ~ $i(v0) | is_a_theorem(v3))
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | BETA: splitting (10) gives:
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | | Case 1:
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | (29) or(all_95_8, all_95_7) = all_95_3 & implies(all_95_3,
% 23.97/4.07 | | | | | | all_95_6) = all_95_2 & implies(all_95_4, all_95_2) =
% 23.97/4.07 | | | | | | all_95_1 & implies(all_95_5, all_95_1) = all_95_0 &
% 23.97/4.07 | | | | | | implies(all_95_7, all_95_6) = all_95_4 & implies(all_95_8,
% 23.97/4.07 | | | | | | all_95_6) = all_95_5 & $i(all_95_0) & $i(all_95_1) &
% 23.97/4.07 | | | | | | $i(all_95_2) & $i(all_95_3) & $i(all_95_4) & $i(all_95_5) &
% 23.97/4.07 | | | | | | ~ or_3 & ~ is_a_theorem(all_95_0)
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | ALPHA: (29) implies:
% 23.97/4.07 | | | | | | (30) ~ or_3
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | PRED_UNIFY: (30), (hilbert_or_3) imply:
% 23.97/4.07 | | | | | | (31) $false
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | CLOSE: (31) is inconsistent.
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | Case 2:
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | GROUND_INST: instantiating (18) with all_20_1, all_20_3, all_20_0,
% 23.97/4.07 | | | | | | simplifying with (4), (13), (15) gives:
% 23.97/4.07 | | | | | | (32) ? [v0: $i] : (necessarily(v0) = all_20_0 &
% 23.97/4.07 | | | | | | implies(all_20_1, all_20_3) = v0 & $i(v0) & $i(all_20_0))
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | DELTA: instantiating (32) with fresh symbol all_213_0 gives:
% 23.97/4.07 | | | | | | (33) necessarily(all_213_0) = all_20_0 & implies(all_20_1,
% 23.97/4.07 | | | | | | all_20_3) = all_213_0 & $i(all_213_0) & $i(all_20_0)
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | ALPHA: (33) implies:
% 23.97/4.07 | | | | | | (34) $i(all_213_0)
% 23.97/4.07 | | | | | | (35) implies(all_20_1, all_20_3) = all_213_0
% 23.97/4.07 | | | | | | (36) necessarily(all_213_0) = all_20_0
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | GROUND_INST: instantiating (28) with all_20_3, all_20_2, all_20_1,
% 23.97/4.07 | | | | | | all_213_0, simplifying with (4), (5), (14), (35) gives:
% 23.97/4.07 | | | | | | (37) is_a_theorem(all_213_0)
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | GROUND_INST: instantiating (23) with all_213_0, all_20_0,
% 23.97/4.07 | | | | | | simplifying with (12), (34), (36), (37) gives:
% 23.97/4.07 | | | | | | (38) $false
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | | CLOSE: (38) is inconsistent.
% 23.97/4.07 | | | | | |
% 23.97/4.07 | | | | | End of split
% 23.97/4.07 | | | | |
% 23.97/4.07 | | | | End of split
% 23.97/4.07 | | | |
% 23.97/4.07 | | | End of split
% 23.97/4.07 | | |
% 23.97/4.07 | | End of split
% 23.97/4.07 | |
% 23.97/4.07 | Case 2:
% 23.97/4.07 | |
% 23.97/4.07 | | (39) axiom_m2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 23.97/4.07 | | ~ (strict_implies(v2, v0) = v3) | ~ (and(v0, v1) = v2) | ~
% 23.97/4.07 | | $i(v1) | ~ $i(v0) | is_a_theorem(v3))
% 23.97/4.07 | |
% 23.97/4.08 | | ALPHA: (39) implies:
% 23.97/4.08 | | (40) axiom_m2
% 23.97/4.08 | |
% 23.97/4.08 | | PRED_UNIFY: (40), (s1_0_axiom_m2) imply:
% 23.97/4.08 | | (41) $false
% 23.97/4.08 | |
% 23.97/4.08 | | CLOSE: (41) is inconsistent.
% 23.97/4.08 | |
% 23.97/4.08 | End of split
% 23.97/4.08 |
% 23.97/4.08 End of proof
% 23.97/4.08 % SZS output end Proof for theBenchmark
% 23.97/4.08
% 23.97/4.08 3458ms
%------------------------------------------------------------------------------