TSTP Solution File: SET918+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:27:02 EDT 2023
% Result : Theorem 5.64s 2.02s
% Output : Proof 7.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 14:34:25 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.68 ________ _____
% 0.22/0.68 ___ __ \_________(_)________________________________
% 0.22/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.68
% 0.22/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.68 (2023-06-19)
% 0.22/0.68
% 0.22/0.68 (c) Philipp Rümmer, 2009-2023
% 0.22/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.68 Amanda Stjerna.
% 0.22/0.69 Free software under BSD-3-Clause.
% 0.22/0.69
% 0.22/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.69
% 0.22/0.69 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.71 Running up to 7 provers in parallel.
% 0.22/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.60/1.10 Prover 1: Preprocessing ...
% 1.60/1.11 Prover 4: Preprocessing ...
% 2.27/1.20 Prover 5: Preprocessing ...
% 2.27/1.20 Prover 6: Preprocessing ...
% 2.27/1.20 Prover 0: Preprocessing ...
% 2.27/1.20 Prover 2: Preprocessing ...
% 2.27/1.20 Prover 3: Preprocessing ...
% 3.75/1.59 Prover 3: Warning: ignoring some quantifiers
% 3.93/1.59 Prover 1: Warning: ignoring some quantifiers
% 3.93/1.61 Prover 5: Proving ...
% 3.93/1.63 Prover 3: Constructing countermodel ...
% 4.15/1.63 Prover 6: Proving ...
% 4.15/1.64 Prover 1: Constructing countermodel ...
% 4.21/1.65 Prover 4: Warning: ignoring some quantifiers
% 4.21/1.68 Prover 4: Constructing countermodel ...
% 4.21/1.68 Prover 2: Proving ...
% 4.51/1.75 Prover 0: Proving ...
% 5.64/2.02 Prover 3: proved (1279ms)
% 5.64/2.02
% 5.64/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.64/2.02
% 5.64/2.03 Prover 5: stopped
% 5.64/2.04 Prover 2: stopped
% 5.64/2.05 Prover 0: stopped
% 5.64/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.64/2.07 Prover 6: stopped
% 5.64/2.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.64/2.09 Prover 7: Preprocessing ...
% 5.64/2.09 Prover 8: Preprocessing ...
% 5.64/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.64/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.64/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.64/2.12 Prover 10: Preprocessing ...
% 5.64/2.12 Prover 13: Preprocessing ...
% 5.64/2.12 Prover 11: Preprocessing ...
% 6.11/2.15 Prover 7: Warning: ignoring some quantifiers
% 6.11/2.16 Prover 7: Constructing countermodel ...
% 6.11/2.18 Prover 1: Found proof (size 43)
% 6.11/2.18 Prover 1: proved (1463ms)
% 6.11/2.18 Prover 7: stopped
% 6.11/2.18 Prover 13: Warning: ignoring some quantifiers
% 6.11/2.19 Prover 4: Found proof (size 48)
% 6.11/2.19 Prover 4: proved (1450ms)
% 6.11/2.19 Prover 11: stopped
% 6.86/2.20 Prover 13: Constructing countermodel ...
% 6.86/2.21 Prover 8: Warning: ignoring some quantifiers
% 6.86/2.21 Prover 10: Warning: ignoring some quantifiers
% 6.86/2.21 Prover 13: stopped
% 6.86/2.21 Prover 8: Constructing countermodel ...
% 6.86/2.22 Prover 8: stopped
% 6.86/2.22 Prover 10: Constructing countermodel ...
% 6.86/2.22 Prover 10: stopped
% 6.86/2.22
% 6.86/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.86/2.22
% 6.86/2.24 % SZS output start Proof for theBenchmark
% 6.86/2.24 Assumptions after simplification:
% 6.86/2.24 ---------------------------------
% 6.86/2.24
% 6.86/2.24 (commutativity_k2_tarski)
% 7.04/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 7.04/2.30 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 7.04/2.30
% 7.04/2.30 (commutativity_k3_xboole_0)
% 7.04/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 7.04/2.30 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 7.04/2.30
% 7.04/2.30 (d1_tarski)
% 7.04/2.31 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) |
% 7.04/2.31 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 &
% 7.04/2.31 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i]
% 7.04/2.31 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2:
% 7.04/2.31 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 =
% 7.04/2.31 0 | ~ (in(v0, v1) = v2))))
% 7.04/2.31
% 7.04/2.31 (d2_tarski)
% 7.04/2.32 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 7.04/2.32 (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 7.04/2.32 $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 =
% 7.04/2.32 v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0: $i]
% 7.04/2.32 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) |
% 7.04/2.32 ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3,
% 7.04/2.32 v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3: $i]
% 7.04/2.32 : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0) | ~ $i(v3))))
% 7.04/2.32
% 7.04/2.32 (d3_xboole_0)
% 7.04/2.33 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 7.04/2.33 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.04/2.33 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 &
% 7.04/2.33 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) |
% 7.04/2.33 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 7.04/2.33 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) |
% 7.04/2.33 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3)
% 7.04/2.33 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~
% 7.04/2.33 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 7.04/2.33 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3,
% 7.04/2.34 v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 7.04/2.34
% 7.04/2.34 (t59_zfmisc_1)
% 7.04/2.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v1
% 7.04/2.34 = v0) & singleton(v0) = v4 & set_intersection2(v3, v2) = v4 &
% 7.04/2.34 unordered_pair(v0, v1) = v3 & in(v1, v2) = 0 & $i(v4) & $i(v3) & $i(v2) &
% 7.04/2.34 $i(v1) & $i(v0))
% 7.04/2.34
% 7.04/2.34 (function-axioms)
% 7.04/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.04/2.35 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 7.04/2.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.04/2.35 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.04/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.04/2.35 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.04/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.04/2.35 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 7.04/2.35 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.04/2.35
% 7.04/2.35 Further assumptions not needed in the proof:
% 7.04/2.35 --------------------------------------------
% 7.04/2.35 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 7.04/2.35
% 7.04/2.35 Those formulas are unsatisfiable:
% 7.04/2.35 ---------------------------------
% 7.04/2.35
% 7.04/2.35 Begin of proof
% 7.04/2.35 |
% 7.04/2.35 | ALPHA: (d1_tarski) implies:
% 7.04/2.35 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 7.04/2.35 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) &
% 7.04/2.35 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2))))
% 7.04/2.35 |
% 7.04/2.35 | ALPHA: (d2_tarski) implies:
% 7.41/2.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 7.41/2.35 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4:
% 7.41/2.35 | int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1)
% 7.41/2.35 | & ~ (v3 = v0))) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 7.41/2.35 | (in(v3, v2) = 0) | ~ $i(v3))))
% 7.41/2.36 |
% 7.41/2.36 | ALPHA: (d3_xboole_0) implies:
% 7.41/2.36 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0,
% 7.41/2.36 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 7.41/2.36 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 7.41/2.36 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) |
% 7.41/2.36 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) |
% 7.41/2.36 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 &
% 7.41/2.36 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 7.41/2.36 |
% 7.41/2.36 | ALPHA: (function-axioms) implies:
% 7.41/2.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.41/2.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.41/2.36 |
% 7.41/2.36 | DELTA: instantiating (t59_zfmisc_1) with fresh symbols all_17_0, all_17_1,
% 7.41/2.36 | all_17_2, all_17_3, all_17_4 gives:
% 7.41/2.36 | (5) ~ (all_17_3 = all_17_4) & singleton(all_17_4) = all_17_0 &
% 7.41/2.36 | set_intersection2(all_17_1, all_17_2) = all_17_0 &
% 7.41/2.36 | unordered_pair(all_17_4, all_17_3) = all_17_1 & in(all_17_3, all_17_2)
% 7.41/2.36 | = 0 & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) & $i(all_17_3) &
% 7.41/2.36 | $i(all_17_4)
% 7.41/2.36 |
% 7.41/2.36 | ALPHA: (5) implies:
% 7.41/2.37 | (6) ~ (all_17_3 = all_17_4)
% 7.41/2.37 | (7) $i(all_17_4)
% 7.41/2.37 | (8) $i(all_17_3)
% 7.41/2.37 | (9) $i(all_17_2)
% 7.41/2.37 | (10) $i(all_17_0)
% 7.41/2.37 | (11) in(all_17_3, all_17_2) = 0
% 7.41/2.37 | (12) unordered_pair(all_17_4, all_17_3) = all_17_1
% 7.41/2.37 | (13) set_intersection2(all_17_1, all_17_2) = all_17_0
% 7.41/2.37 | (14) singleton(all_17_4) = all_17_0
% 7.41/2.37 |
% 7.41/2.37 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_17_4, all_17_3,
% 7.41/2.37 | all_17_1, simplifying with (7), (8), (12) gives:
% 7.41/2.37 | (15) unordered_pair(all_17_3, all_17_4) = all_17_1 & $i(all_17_1)
% 7.41/2.37 |
% 7.41/2.37 | ALPHA: (15) implies:
% 7.41/2.37 | (16) $i(all_17_1)
% 7.41/2.37 | (17) unordered_pair(all_17_3, all_17_4) = all_17_1
% 7.41/2.37 |
% 7.41/2.37 | GROUND_INST: instantiating (3) with all_17_1, all_17_2, all_17_0, simplifying
% 7.41/2.37 | with (9), (10), (13), (16) gives:
% 7.41/2.37 | (18) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_1) = v1) | ~ $i(v0) |
% 7.41/2.37 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0,
% 7.41/2.37 | all_17_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 7.41/2.37 | $i] : ( ~ (in(v0, all_17_1) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 7.41/2.37 | [v2: any] : (in(v0, all_17_0) = v2 & in(v0, all_17_2) = v1 & ( ~ (v1
% 7.41/2.37 | = 0) | v2 = 0)))
% 7.41/2.38 |
% 7.41/2.38 | ALPHA: (18) implies:
% 7.41/2.38 | (19) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_1) = v1) | ~ $i(v0) |
% 7.41/2.38 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0,
% 7.41/2.38 | all_17_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 7.41/2.38 |
% 7.41/2.38 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_17_1,
% 7.41/2.38 | all_17_2, all_17_0, simplifying with (9), (13), (16) gives:
% 7.41/2.38 | (20) set_intersection2(all_17_2, all_17_1) = all_17_0 & $i(all_17_0)
% 7.41/2.38 |
% 7.41/2.38 | ALPHA: (20) implies:
% 7.41/2.39 | (21) set_intersection2(all_17_2, all_17_1) = all_17_0
% 7.41/2.39 |
% 7.41/2.39 | GROUND_INST: instantiating (1) with all_17_4, all_17_0, simplifying with (7),
% 7.41/2.39 | (10), (14) gives:
% 7.41/2.39 | (22) ! [v0: any] : (v0 = all_17_4 | ~ (in(v0, all_17_0) = 0) | ~ $i(v0))
% 7.41/2.39 | & ! [v0: int] : (v0 = 0 | ~ (in(all_17_4, all_17_0) = v0))
% 7.41/2.39 |
% 7.41/2.39 | ALPHA: (22) implies:
% 7.41/2.39 | (23) ! [v0: any] : (v0 = all_17_4 | ~ (in(v0, all_17_0) = 0) | ~ $i(v0))
% 7.41/2.39 |
% 7.41/2.39 | GROUND_INST: instantiating (2) with all_17_3, all_17_4, all_17_1, simplifying
% 7.41/2.39 | with (7), (8), (16), (17) gives:
% 7.41/2.39 | (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_17_1) = v1) | ~
% 7.41/2.39 | $i(v0) | ( ~ (v0 = all_17_3) & ~ (v0 = all_17_4))) & ! [v0: any] :
% 7.41/2.39 | (v0 = all_17_3 | v0 = all_17_4 | ~ (in(v0, all_17_1) = 0) | ~
% 7.41/2.39 | $i(v0))
% 7.41/2.39 |
% 7.41/2.39 | ALPHA: (24) implies:
% 7.41/2.39 | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_17_1) = v1) | ~
% 7.41/2.39 | $i(v0) | ( ~ (v0 = all_17_3) & ~ (v0 = all_17_4)))
% 7.41/2.39 |
% 7.41/2.39 | GROUND_INST: instantiating (3) with all_17_2, all_17_1, all_17_0, simplifying
% 7.41/2.39 | with (9), (10), (16), (21) gives:
% 7.41/2.39 | (26) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_2) = v1) | ~ $i(v0) |
% 7.41/2.39 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0,
% 7.41/2.39 | all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 7.41/2.39 | $i] : ( ~ (in(v0, all_17_2) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 7.41/2.39 | [v2: any] : (in(v0, all_17_0) = v2 & in(v0, all_17_1) = v1 & ( ~ (v1
% 7.41/2.39 | = 0) | v2 = 0)))
% 7.41/2.39 |
% 7.41/2.39 | ALPHA: (26) implies:
% 7.41/2.40 | (27) ! [v0: $i] : ( ~ (in(v0, all_17_2) = 0) | ~ $i(v0) | ? [v1: any] :
% 7.41/2.40 | ? [v2: any] : (in(v0, all_17_0) = v2 & in(v0, all_17_1) = v1 & ( ~
% 7.41/2.40 | (v1 = 0) | v2 = 0)))
% 7.57/2.40 | (28) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_2) = v1) | ~ $i(v0) |
% 7.57/2.40 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0,
% 7.57/2.40 | all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 7.57/2.40 |
% 7.57/2.40 | GROUND_INST: instantiating (27) with all_17_3, simplifying with (8), (11)
% 7.57/2.40 | gives:
% 7.57/2.40 | (29) ? [v0: any] : ? [v1: any] : (in(all_17_3, all_17_0) = v1 &
% 7.57/2.40 | in(all_17_3, all_17_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.57/2.40 |
% 7.57/2.40 | GROUND_INST: instantiating (28) with all_17_3, 0, simplifying with (8), (11)
% 7.57/2.40 | gives:
% 7.57/2.40 | (30) ? [v0: any] : ? [v1: any] : (in(all_17_3, all_17_0) = v0 &
% 7.57/2.40 | in(all_17_3, all_17_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 7.57/2.40 |
% 7.57/2.40 | DELTA: instantiating (30) with fresh symbols all_41_0, all_41_1 gives:
% 7.57/2.40 | (31) in(all_17_3, all_17_0) = all_41_1 & in(all_17_3, all_17_1) = all_41_0
% 7.57/2.40 | & ( ~ (all_41_1 = 0) | all_41_0 = 0)
% 7.57/2.40 |
% 7.57/2.40 | ALPHA: (31) implies:
% 7.57/2.40 | (32) in(all_17_3, all_17_1) = all_41_0
% 7.57/2.40 | (33) in(all_17_3, all_17_0) = all_41_1
% 7.57/2.40 |
% 7.57/2.40 | DELTA: instantiating (29) with fresh symbols all_43_0, all_43_1 gives:
% 7.57/2.40 | (34) in(all_17_3, all_17_0) = all_43_0 & in(all_17_3, all_17_1) = all_43_1
% 7.57/2.40 | & ( ~ (all_43_1 = 0) | all_43_0 = 0)
% 7.57/2.40 |
% 7.57/2.40 | ALPHA: (34) implies:
% 7.57/2.40 | (35) in(all_17_3, all_17_1) = all_43_1
% 7.57/2.40 | (36) in(all_17_3, all_17_0) = all_43_0
% 7.57/2.40 | (37) ~ (all_43_1 = 0) | all_43_0 = 0
% 7.57/2.40 |
% 7.57/2.40 | GROUND_INST: instantiating (4) with all_41_0, all_43_1, all_17_1, all_17_3,
% 7.57/2.40 | simplifying with (32), (35) gives:
% 7.57/2.40 | (38) all_43_1 = all_41_0
% 7.57/2.40 |
% 7.57/2.40 | GROUND_INST: instantiating (4) with all_41_1, all_43_0, all_17_0, all_17_3,
% 7.57/2.40 | simplifying with (33), (36) gives:
% 7.57/2.40 | (39) all_43_0 = all_41_1
% 7.57/2.40 |
% 7.57/2.40 | GROUND_INST: instantiating (25) with all_17_3, all_41_0, simplifying with (8),
% 7.57/2.40 | (32) gives:
% 7.57/2.40 | (40) all_41_0 = 0
% 7.57/2.40 |
% 7.57/2.40 | GROUND_INST: instantiating (19) with all_17_3, all_41_0, simplifying with (8),
% 7.57/2.40 | (32) gives:
% 7.57/2.41 | (41) ? [v0: any] : ? [v1: any] : (in(all_17_3, all_17_0) = v0 &
% 7.57/2.41 | in(all_17_3, all_17_2) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_41_0 =
% 7.57/2.41 | 0)))
% 7.57/2.41 |
% 7.57/2.41 | COMBINE_EQS: (38), (40) imply:
% 7.57/2.41 | (42) all_43_1 = 0
% 7.57/2.41 |
% 7.57/2.41 | DELTA: instantiating (41) with fresh symbols all_55_0, all_55_1 gives:
% 7.57/2.41 | (43) in(all_17_3, all_17_0) = all_55_1 & in(all_17_3, all_17_2) = all_55_0
% 7.57/2.41 | & ( ~ (all_55_1 = 0) | (all_55_0 = 0 & all_41_0 = 0))
% 7.57/2.41 |
% 7.57/2.41 | ALPHA: (43) implies:
% 7.57/2.41 | (44) in(all_17_3, all_17_0) = all_55_1
% 7.57/2.41 |
% 7.57/2.41 | BETA: splitting (37) gives:
% 7.57/2.41 |
% 7.57/2.41 | Case 1:
% 7.57/2.41 | |
% 7.57/2.41 | | (45) ~ (all_43_1 = 0)
% 7.57/2.41 | |
% 7.57/2.41 | | REDUCE: (42), (45) imply:
% 7.57/2.41 | | (46) $false
% 7.57/2.42 | |
% 7.57/2.42 | | CLOSE: (46) is inconsistent.
% 7.57/2.42 | |
% 7.57/2.42 | Case 2:
% 7.57/2.42 | |
% 7.57/2.43 | | (47) all_43_0 = 0
% 7.57/2.43 | |
% 7.57/2.43 | | COMBINE_EQS: (39), (47) imply:
% 7.57/2.43 | | (48) all_41_1 = 0
% 7.57/2.43 | |
% 7.57/2.43 | | REDUCE: (33), (48) imply:
% 7.57/2.43 | | (49) in(all_17_3, all_17_0) = 0
% 7.57/2.43 | |
% 7.57/2.43 | | GROUND_INST: instantiating (4) with 0, all_55_1, all_17_0, all_17_3,
% 7.57/2.43 | | simplifying with (44), (49) gives:
% 7.57/2.43 | | (50) all_55_1 = 0
% 7.57/2.43 | |
% 7.57/2.43 | | GROUND_INST: instantiating (23) with all_17_3, simplifying with (8), (49)
% 7.57/2.43 | | gives:
% 7.57/2.43 | | (51) all_17_3 = all_17_4
% 7.57/2.43 | |
% 7.57/2.43 | | REDUCE: (6), (51) imply:
% 7.57/2.43 | | (52) $false
% 7.57/2.43 | |
% 7.57/2.43 | | CLOSE: (52) is inconsistent.
% 7.57/2.43 | |
% 7.57/2.43 | End of split
% 7.57/2.43 |
% 7.57/2.43 End of proof
% 7.57/2.43 % SZS output end Proof for theBenchmark
% 7.57/2.43
% 7.57/2.43 1741ms
%------------------------------------------------------------------------------