TSTP Solution File: SET916+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET916+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 : n011.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 15:27:01 EDT 2023
% Result : Theorem 7.57s 1.80s
% Output : Proof 10.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:08:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.04 Prover 1: Preprocessing ...
% 2.13/1.04 Prover 4: Preprocessing ...
% 2.62/1.09 Prover 5: Preprocessing ...
% 2.62/1.09 Prover 3: Preprocessing ...
% 2.62/1.09 Prover 2: Preprocessing ...
% 2.62/1.09 Prover 0: Preprocessing ...
% 2.62/1.09 Prover 6: Preprocessing ...
% 4.77/1.39 Prover 6: Proving ...
% 4.77/1.39 Prover 5: Proving ...
% 4.77/1.39 Prover 3: Warning: ignoring some quantifiers
% 4.77/1.39 Prover 1: Warning: ignoring some quantifiers
% 4.77/1.40 Prover 3: Constructing countermodel ...
% 4.77/1.41 Prover 1: Constructing countermodel ...
% 4.77/1.43 Prover 4: Warning: ignoring some quantifiers
% 4.77/1.44 Prover 2: Proving ...
% 4.77/1.45 Prover 4: Constructing countermodel ...
% 5.22/1.46 Prover 0: Proving ...
% 7.00/1.74 Prover 3: gave up
% 7.00/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.57/1.77 Prover 7: Preprocessing ...
% 7.57/1.79 Prover 0: proved (1152ms)
% 7.57/1.79
% 7.57/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.57/1.80
% 7.57/1.80 Prover 5: stopped
% 7.57/1.80 Prover 2: stopped
% 7.89/1.81 Prover 6: stopped
% 7.89/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.89/1.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.89/1.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.89/1.82 Prover 7: Warning: ignoring some quantifiers
% 7.89/1.82 Prover 10: Preprocessing ...
% 7.89/1.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.89/1.83 Prover 7: Constructing countermodel ...
% 7.89/1.83 Prover 8: Preprocessing ...
% 7.89/1.84 Prover 13: Preprocessing ...
% 7.89/1.85 Prover 11: Preprocessing ...
% 7.89/1.86 Prover 10: Warning: ignoring some quantifiers
% 7.89/1.86 Prover 10: Constructing countermodel ...
% 7.89/1.87 Prover 7: gave up
% 7.89/1.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.89/1.89 Prover 16: Preprocessing ...
% 7.89/1.90 Prover 10: gave up
% 8.23/1.91 Prover 13: Warning: ignoring some quantifiers
% 8.23/1.91 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.23/1.92 Prover 8: Warning: ignoring some quantifiers
% 8.23/1.92 Prover 8: Constructing countermodel ...
% 8.23/1.92 Prover 13: Constructing countermodel ...
% 8.23/1.92 Prover 19: Preprocessing ...
% 8.23/1.95 Prover 16: Warning: ignoring some quantifiers
% 8.23/1.95 Prover 16: Constructing countermodel ...
% 8.23/1.98 Prover 11: Warning: ignoring some quantifiers
% 8.23/1.99 Prover 11: Constructing countermodel ...
% 9.22/2.02 Prover 19: Warning: ignoring some quantifiers
% 9.22/2.03 Prover 19: Constructing countermodel ...
% 9.67/2.05 Prover 8: gave up
% 9.70/2.08 Prover 13: gave up
% 9.98/2.10 Prover 4: Found proof (size 36)
% 9.98/2.10 Prover 4: proved (1451ms)
% 9.98/2.10 Prover 19: stopped
% 9.98/2.10 Prover 16: stopped
% 9.98/2.10 Prover 11: stopped
% 9.98/2.10 Prover 1: stopped
% 9.98/2.11
% 9.98/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.98/2.11
% 9.98/2.12 % SZS output start Proof for theBenchmark
% 9.98/2.12 Assumptions after simplification:
% 9.98/2.12 ---------------------------------
% 9.98/2.12
% 9.98/2.12 (commutativity_k2_tarski)
% 10.18/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 10.18/2.16 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 10.18/2.16 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 10.18/2.16 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 10.18/2.16
% 10.18/2.16 (d2_tarski)
% 10.18/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 10.18/2.16 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 10.18/2.16 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 10.18/2.16 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) =
% 10.18/2.16 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 10.18/2.16 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~
% 10.18/2.16 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : !
% 10.18/2.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) =
% 10.18/2.16 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] :
% 10.18/2.16 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) &
% 10.18/2.17 (v5 = 0 | v4 = v2 | v4 = v1)))
% 10.18/2.17
% 10.18/2.17 (d3_xboole_0)
% 10.18/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.18/2.18 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 10.18/2.18 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 10.18/2.18 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 10.18/2.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 10.18/2.18 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 10.18/2.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 10.18/2.18 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 10.18/2.18 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 10.18/2.18 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 10.18/2.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 10.18/2.18 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 10.18/2.18 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 10.18/2.18 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.18/2.18 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 10.18/2.18 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 10.18/2.18 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.18/2.18 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 10.18/2.18 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 10.18/2.18 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 10.18/2.18 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 10.18/2.18 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.18/2.18 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 10.18/2.18 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 10.18/2.18 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 10.18/2.18 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 10.18/2.18
% 10.18/2.18 (t4_xboole_0)
% 10.18/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.18/2.18 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 10.18/2.18 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) &
% 10.18/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 10.18/2.18 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 10.18/2.18 (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) & !
% 10.18/2.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 10.18/2.18 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) &
% 10.18/2.18 ((v5 = 0 & in(v4, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))) & ! [v0:
% 10.18/2.18 $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 10.18/2.18 [v2: $i] : (set_intersection2(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ( ~
% 10.18/2.18 (in(v3, v2) = 0) | ~ $i(v3))))
% 10.18/2.18
% 10.18/2.18 (t57_zfmisc_1)
% 10.18/2.18 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ?
% 10.18/2.18 [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v4 = 0) & ~ (v3 = 0) &
% 10.18/2.18 disjoint(v5, v1) = v6 & unordered_pair(v0, v2) = v5 & in(v2, v1) = v4 &
% 10.18/2.18 in(v0, v1) = v3 & $i(v5) & $i(v2) & $i(v1) & $i(v0))
% 10.18/2.18
% 10.18/2.18 (function-axioms)
% 10.18/2.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.18/2.18 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 10.18/2.18 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.18/2.18 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 10.18/2.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.18/2.18 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 10.18/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.18/2.18 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 10.18/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.18/2.18 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 10.18/2.18
% 10.18/2.18 Further assumptions not needed in the proof:
% 10.18/2.18 --------------------------------------------
% 10.18/2.18 antisymmetry_r2_hidden, commutativity_k3_xboole_0, idempotence_k3_xboole_0,
% 10.18/2.18 rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0
% 10.18/2.18
% 10.18/2.18 Those formulas are unsatisfiable:
% 10.18/2.18 ---------------------------------
% 10.18/2.18
% 10.18/2.18 Begin of proof
% 10.18/2.18 |
% 10.18/2.19 | ALPHA: (commutativity_k2_tarski) implies:
% 10.18/2.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 10.18/2.19 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 10.18/2.19 | $i(v2)))
% 10.18/2.19 |
% 10.18/2.19 | ALPHA: (d2_tarski) implies:
% 10.18/2.19 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 =
% 10.18/2.19 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~
% 10.18/2.19 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 10.18/2.19 |
% 10.18/2.19 | ALPHA: (d3_xboole_0) implies:
% 10.18/2.19 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.18/2.19 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) |
% 10.18/2.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 10.18/2.19 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 10.18/2.19 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3)
% 10.18/2.19 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 10.18/2.19 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 10.18/2.19 | 0))))
% 10.18/2.19 |
% 10.18/2.19 | ALPHA: (t4_xboole_0) implies:
% 10.18/2.19 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 10.18/2.19 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 10.18/2.19 | (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3)))
% 10.18/2.19 |
% 10.18/2.19 | ALPHA: (function-axioms) implies:
% 10.18/2.19 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.18/2.19 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.18/2.19 |
% 10.18/2.19 | DELTA: instantiating (t57_zfmisc_1) with fresh symbols all_15_0, all_15_1,
% 10.18/2.19 | all_15_2, all_15_3, all_15_4, all_15_5, all_15_6 gives:
% 10.18/2.19 | (7) ~ (all_15_0 = 0) & ~ (all_15_2 = 0) & ~ (all_15_3 = 0) &
% 10.18/2.19 | disjoint(all_15_1, all_15_5) = all_15_0 & unordered_pair(all_15_6,
% 10.18/2.19 | all_15_4) = all_15_1 & in(all_15_4, all_15_5) = all_15_2 &
% 10.18/2.19 | in(all_15_6, all_15_5) = all_15_3 & $i(all_15_1) & $i(all_15_4) &
% 10.18/2.19 | $i(all_15_5) & $i(all_15_6)
% 10.18/2.19 |
% 10.18/2.19 | ALPHA: (7) implies:
% 10.18/2.19 | (8) ~ (all_15_3 = 0)
% 10.18/2.19 | (9) ~ (all_15_2 = 0)
% 10.18/2.19 | (10) ~ (all_15_0 = 0)
% 10.18/2.19 | (11) $i(all_15_6)
% 10.18/2.19 | (12) $i(all_15_5)
% 10.18/2.19 | (13) $i(all_15_4)
% 10.18/2.19 | (14) in(all_15_6, all_15_5) = all_15_3
% 10.18/2.19 | (15) in(all_15_4, all_15_5) = all_15_2
% 10.18/2.19 | (16) unordered_pair(all_15_6, all_15_4) = all_15_1
% 10.18/2.19 | (17) disjoint(all_15_1, all_15_5) = all_15_0
% 10.18/2.19 |
% 10.18/2.20 | GROUND_INST: instantiating (1) with all_15_4, all_15_6, all_15_1, simplifying
% 10.18/2.20 | with (11), (13), (16) gives:
% 10.18/2.20 | (18) unordered_pair(all_15_4, all_15_6) = all_15_1 & $i(all_15_1)
% 10.18/2.20 |
% 10.18/2.20 | ALPHA: (18) implies:
% 10.18/2.20 | (19) $i(all_15_1)
% 10.18/2.20 |
% 10.18/2.20 | GROUND_INST: instantiating (5) with all_15_1, all_15_5, all_15_0, simplifying
% 10.18/2.20 | with (12), (17), (19) gives:
% 10.18/2.20 | (20) all_15_0 = 0 | ? [v0: $i] : ? [v1: $i] :
% 10.18/2.20 | (set_intersection2(all_15_1, all_15_5) = v0 & in(v1, v0) = 0 & $i(v1)
% 10.18/2.20 | & $i(v0))
% 10.18/2.20 |
% 10.18/2.20 | BETA: splitting (20) gives:
% 10.18/2.20 |
% 10.18/2.20 | Case 1:
% 10.18/2.20 | |
% 10.18/2.20 | | (21) all_15_0 = 0
% 10.18/2.20 | |
% 10.18/2.20 | | REDUCE: (10), (21) imply:
% 10.18/2.20 | | (22) $false
% 10.18/2.20 | |
% 10.18/2.20 | | CLOSE: (22) is inconsistent.
% 10.18/2.20 | |
% 10.18/2.20 | Case 2:
% 10.18/2.20 | |
% 10.18/2.20 | | (23) ? [v0: $i] : ? [v1: $i] : (set_intersection2(all_15_1, all_15_5) =
% 10.18/2.20 | | v0 & in(v1, v0) = 0 & $i(v1) & $i(v0))
% 10.18/2.20 | |
% 10.18/2.20 | | DELTA: instantiating (23) with fresh symbols all_31_0, all_31_1 gives:
% 10.18/2.20 | | (24) set_intersection2(all_15_1, all_15_5) = all_31_1 & in(all_31_0,
% 10.18/2.20 | | all_31_1) = 0 & $i(all_31_0) & $i(all_31_1)
% 10.18/2.20 | |
% 10.18/2.20 | | ALPHA: (24) implies:
% 10.18/2.20 | | (25) $i(all_31_1)
% 10.18/2.20 | | (26) $i(all_31_0)
% 10.18/2.20 | | (27) in(all_31_0, all_31_1) = 0
% 10.18/2.20 | | (28) set_intersection2(all_15_1, all_15_5) = all_31_1
% 10.18/2.20 | |
% 10.18/2.20 | | GROUND_INST: instantiating (4) with all_15_1, all_15_5, all_31_1, all_15_6,
% 10.18/2.20 | | all_15_3, simplifying with (11), (12), (14), (19), (25), (28)
% 10.18/2.20 | | gives:
% 10.18/2.20 | | (29) ? [v0: any] : ? [v1: any] : (in(all_15_6, all_31_1) = v0 &
% 10.18/2.20 | | in(all_15_6, all_15_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_3 =
% 10.18/2.20 | | 0)))
% 10.18/2.20 | |
% 10.18/2.20 | | GROUND_INST: instantiating (3) with all_15_1, all_15_5, all_31_1, all_31_0,
% 10.18/2.20 | | simplifying with (12), (19), (25), (26), (27), (28) gives:
% 10.18/2.20 | | (30) in(all_31_0, all_15_1) = 0 & in(all_31_0, all_15_5) = 0
% 10.18/2.20 | |
% 10.18/2.20 | | ALPHA: (30) implies:
% 10.18/2.20 | | (31) in(all_31_0, all_15_5) = 0
% 10.18/2.20 | | (32) in(all_31_0, all_15_1) = 0
% 10.18/2.20 | |
% 10.18/2.20 | | DELTA: instantiating (29) with fresh symbols all_46_0, all_46_1 gives:
% 10.18/2.20 | | (33) in(all_15_6, all_31_1) = all_46_1 & in(all_15_6, all_15_1) =
% 10.18/2.20 | | all_46_0 & ( ~ (all_46_1 = 0) | (all_46_0 = 0 & all_15_3 = 0))
% 10.18/2.20 | |
% 10.18/2.20 | | ALPHA: (33) implies:
% 10.18/2.20 | | (34) ~ (all_46_1 = 0) | (all_46_0 = 0 & all_15_3 = 0)
% 10.18/2.20 | |
% 10.18/2.20 | | BETA: splitting (34) gives:
% 10.18/2.20 | |
% 10.18/2.20 | | Case 1:
% 10.18/2.20 | | |
% 10.18/2.20 | | |
% 10.18/2.20 | | | GROUND_INST: instantiating (2) with all_15_6, all_15_4, all_15_1,
% 10.18/2.21 | | | all_31_0, simplifying with (11), (13), (16), (19), (26), (32)
% 10.18/2.21 | | | gives:
% 10.18/2.21 | | | (35) all_31_0 = all_15_4 | all_31_0 = all_15_6
% 10.18/2.21 | | |
% 10.18/2.21 | | | BETA: splitting (35) gives:
% 10.18/2.21 | | |
% 10.18/2.21 | | | Case 1:
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | (36) all_31_0 = all_15_4
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | REDUCE: (31), (36) imply:
% 10.18/2.21 | | | | (37) in(all_15_4, all_15_5) = 0
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | GROUND_INST: instantiating (6) with all_15_2, 0, all_15_5, all_15_4,
% 10.18/2.21 | | | | simplifying with (15), (37) gives:
% 10.18/2.21 | | | | (38) all_15_2 = 0
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | REDUCE: (9), (38) imply:
% 10.18/2.21 | | | | (39) $false
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | CLOSE: (39) is inconsistent.
% 10.18/2.21 | | | |
% 10.18/2.21 | | | Case 2:
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | (40) all_31_0 = all_15_6
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | REDUCE: (31), (40) imply:
% 10.18/2.21 | | | | (41) in(all_15_6, all_15_5) = 0
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | GROUND_INST: instantiating (6) with all_15_3, 0, all_15_5, all_15_6,
% 10.18/2.21 | | | | simplifying with (14), (41) gives:
% 10.18/2.21 | | | | (42) all_15_3 = 0
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | REDUCE: (8), (42) imply:
% 10.18/2.21 | | | | (43) $false
% 10.18/2.21 | | | |
% 10.18/2.21 | | | | CLOSE: (43) is inconsistent.
% 10.18/2.21 | | | |
% 10.18/2.21 | | | End of split
% 10.18/2.21 | | |
% 10.18/2.21 | | Case 2:
% 10.18/2.21 | | |
% 10.18/2.21 | | | (44) all_46_0 = 0 & all_15_3 = 0
% 10.18/2.21 | | |
% 10.18/2.21 | | | ALPHA: (44) implies:
% 10.18/2.21 | | | (45) all_15_3 = 0
% 10.18/2.21 | | |
% 10.18/2.21 | | | REDUCE: (8), (45) imply:
% 10.18/2.21 | | | (46) $false
% 10.18/2.21 | | |
% 10.18/2.21 | | | CLOSE: (46) is inconsistent.
% 10.18/2.21 | | |
% 10.18/2.21 | | End of split
% 10.18/2.21 | |
% 10.18/2.21 | End of split
% 10.18/2.21 |
% 10.18/2.21 End of proof
% 10.18/2.21 % SZS output end Proof for theBenchmark
% 10.18/2.21
% 10.18/2.21 1587ms
%------------------------------------------------------------------------------