TSTP Solution File: SET983+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET983+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 : n028.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 15:27:16 EDT 2023
% Result : Theorem 5.76s 1.50s
% Output : Proof 7.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n028.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 : Sat Aug 26 13:03:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.84/0.95 Prover 4: Preprocessing ...
% 1.84/0.95 Prover 1: Preprocessing ...
% 2.34/1.00 Prover 0: Preprocessing ...
% 2.34/1.00 Prover 5: Preprocessing ...
% 2.34/1.00 Prover 3: Preprocessing ...
% 2.34/1.00 Prover 2: Preprocessing ...
% 2.34/1.00 Prover 6: Preprocessing ...
% 3.26/1.20 Prover 1: Warning: ignoring some quantifiers
% 3.90/1.23 Prover 6: Proving ...
% 3.90/1.23 Prover 1: Constructing countermodel ...
% 3.90/1.23 Prover 5: Proving ...
% 3.90/1.23 Prover 3: Warning: ignoring some quantifiers
% 3.90/1.24 Prover 3: Constructing countermodel ...
% 3.90/1.25 Prover 2: Proving ...
% 3.90/1.27 Prover 4: Warning: ignoring some quantifiers
% 4.41/1.28 Prover 4: Constructing countermodel ...
% 4.41/1.30 Prover 0: Proving ...
% 5.76/1.50 Prover 0: proved (879ms)
% 5.76/1.50
% 5.76/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.76/1.50
% 5.76/1.50 Prover 6: stopped
% 5.76/1.50 Prover 5: stopped
% 5.76/1.50 Prover 3: stopped
% 5.76/1.50 Prover 2: stopped
% 5.76/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.76/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.76/1.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.76/1.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.76/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.05/1.52 Prover 10: Preprocessing ...
% 6.13/1.52 Prover 11: Preprocessing ...
% 6.13/1.53 Prover 13: Preprocessing ...
% 6.13/1.53 Prover 7: Preprocessing ...
% 6.13/1.54 Prover 8: Preprocessing ...
% 6.13/1.58 Prover 10: Warning: ignoring some quantifiers
% 6.13/1.59 Prover 10: Constructing countermodel ...
% 6.13/1.59 Prover 13: Warning: ignoring some quantifiers
% 6.13/1.59 Prover 13: Constructing countermodel ...
% 6.13/1.60 Prover 8: Warning: ignoring some quantifiers
% 6.13/1.60 Prover 7: Warning: ignoring some quantifiers
% 6.13/1.60 Prover 7: Constructing countermodel ...
% 6.13/1.61 Prover 4: Found proof (size 31)
% 6.74/1.61 Prover 8: Constructing countermodel ...
% 6.74/1.61 Prover 4: proved (984ms)
% 6.74/1.61 Prover 7: stopped
% 6.74/1.61 Prover 1: stopped
% 6.74/1.61 Prover 13: stopped
% 6.74/1.61 Prover 10: stopped
% 6.74/1.61 Prover 8: stopped
% 6.74/1.62 Prover 11: Warning: ignoring some quantifiers
% 6.74/1.63 Prover 11: Constructing countermodel ...
% 6.74/1.64 Prover 11: stopped
% 6.74/1.64
% 6.74/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.74/1.64
% 6.74/1.65 % SZS output start Proof for theBenchmark
% 6.74/1.65 Assumptions after simplification:
% 6.74/1.65 ---------------------------------
% 6.74/1.65
% 6.74/1.65 (d3_xboole_0)
% 7.12/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.12/1.70 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 7.12/1.70 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 7.12/1.70 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 7.12/1.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 7.12/1.70 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 7.12/1.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 7.12/1.70 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 7.12/1.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 7.12/1.70 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 7.12/1.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 7.12/1.70 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 7.12/1.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 7.12/1.70 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 7.12/1.70 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 7.12/1.70 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 7.12/1.70 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.12/1.70 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 7.12/1.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 7.12/1.70 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 7.12/1.70 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 7.12/1.70 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.12/1.70 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 7.12/1.70 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 7.12/1.70 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 7.12/1.70 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 7.12/1.70
% 7.12/1.70 (t123_zfmisc_1)
% 7.12/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 7.12/1.70 $i] : ! [v6: $i] : ( ~ (cartesian_product2(v4, v5) = v6) | ~
% 7.12/1.71 (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v0, v1) = v4) | ~
% 7.12/1.71 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] :
% 7.12/1.71 (cartesian_product2(v1, v3) = v8 & cartesian_product2(v0, v2) = v7 &
% 7.12/1.71 set_intersection2(v7, v8) = v6 & $i(v8) & $i(v7) & $i(v6))) & ! [v0: $i]
% 7.12/1.71 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 7.12/1.71 [v6: $i] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0,
% 7.12/1.71 v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2)
% 7.12/1.71 | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] :
% 7.12/1.71 (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 &
% 7.12/1.71 set_intersection2(v0, v1) = v7 & $i(v8) & $i(v7) & $i(v6)))
% 7.12/1.71
% 7.12/1.71 (t137_zfmisc_1)
% 7.12/1.71 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.12/1.71 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int]
% 7.12/1.71 : ( ~ (v10 = 0) & cartesian_product2(v7, v8) = v9 & cartesian_product2(v3, v4)
% 7.12/1.71 = v6 & cartesian_product2(v1, v2) = v5 & set_intersection2(v2, v4) = v8 &
% 7.12/1.71 set_intersection2(v1, v3) = v7 & in(v0, v9) = v10 & in(v0, v6) = 0 & in(v0,
% 7.12/1.71 v5) = 0 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 7.12/1.71 $i(v2) & $i(v1) & $i(v0))
% 7.12/1.71
% 7.12/1.71 (function-axioms)
% 7.12/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.12/1.71 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 7.12/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.12/1.71 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 7.12/1.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.12/1.71 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.12/1.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.12/1.71 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.12/1.71
% 7.12/1.71 Further assumptions not needed in the proof:
% 7.12/1.71 --------------------------------------------
% 7.12/1.71 antisymmetry_r2_hidden, commutativity_k3_xboole_0, idempotence_k3_xboole_0,
% 7.12/1.71 rc1_xboole_0, rc2_xboole_0
% 7.12/1.71
% 7.12/1.71 Those formulas are unsatisfiable:
% 7.12/1.71 ---------------------------------
% 7.12/1.71
% 7.12/1.71 Begin of proof
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (d3_xboole_0) implies:
% 7.12/1.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.12/1.72 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) |
% 7.12/1.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.12/1.72 | (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 7.12/1.72 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.12/1.72 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ~ $i(v3) |
% 7.12/1.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.12/1.72 | (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (t123_zfmisc_1) implies:
% 7.12/1.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 7.12/1.72 | ! [v5: $i] : ! [v6: $i] : ( ~ (cartesian_product2(v4, v5) = v6) | ~
% 7.12/1.72 | (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v0, v1) =
% 7.12/1.72 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] :
% 7.12/1.72 | ? [v8: $i] : (cartesian_product2(v1, v3) = v8 &
% 7.12/1.72 | cartesian_product2(v0, v2) = v7 & set_intersection2(v7, v8) = v6 &
% 7.12/1.72 | $i(v8) & $i(v7) & $i(v6)))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (function-axioms) implies:
% 7.12/1.73 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.12/1.73 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.12/1.73 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.12/1.73 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) =
% 7.12/1.73 | v0))
% 7.12/1.73 |
% 7.12/1.73 | DELTA: instantiating (t137_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 7.12/1.73 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7, all_14_8,
% 7.12/1.73 | all_14_9, all_14_10 gives:
% 7.12/1.73 | (6) ~ (all_14_0 = 0) & cartesian_product2(all_14_3, all_14_2) = all_14_1 &
% 7.12/1.73 | cartesian_product2(all_14_7, all_14_6) = all_14_4 &
% 7.12/1.73 | cartesian_product2(all_14_9, all_14_8) = all_14_5 &
% 7.12/1.73 | set_intersection2(all_14_8, all_14_6) = all_14_2 &
% 7.12/1.73 | set_intersection2(all_14_9, all_14_7) = all_14_3 & in(all_14_10,
% 7.12/1.73 | all_14_1) = all_14_0 & in(all_14_10, all_14_4) = 0 & in(all_14_10,
% 7.12/1.73 | all_14_5) = 0 & $i(all_14_1) & $i(all_14_2) & $i(all_14_3) &
% 7.12/1.73 | $i(all_14_4) & $i(all_14_5) & $i(all_14_6) & $i(all_14_7) &
% 7.12/1.73 | $i(all_14_8) & $i(all_14_9) & $i(all_14_10)
% 7.12/1.73 |
% 7.12/1.73 | ALPHA: (6) implies:
% 7.12/1.73 | (7) ~ (all_14_0 = 0)
% 7.12/1.73 | (8) $i(all_14_10)
% 7.12/1.73 | (9) $i(all_14_9)
% 7.12/1.73 | (10) $i(all_14_8)
% 7.12/1.73 | (11) $i(all_14_7)
% 7.12/1.73 | (12) $i(all_14_6)
% 7.12/1.73 | (13) in(all_14_10, all_14_5) = 0
% 7.12/1.73 | (14) in(all_14_10, all_14_4) = 0
% 7.12/1.73 | (15) in(all_14_10, all_14_1) = all_14_0
% 7.12/1.73 | (16) set_intersection2(all_14_9, all_14_7) = all_14_3
% 7.12/1.73 | (17) set_intersection2(all_14_8, all_14_6) = all_14_2
% 7.12/1.73 | (18) cartesian_product2(all_14_9, all_14_8) = all_14_5
% 7.12/1.73 | (19) cartesian_product2(all_14_7, all_14_6) = all_14_4
% 7.12/1.73 | (20) cartesian_product2(all_14_3, all_14_2) = all_14_1
% 7.12/1.73 |
% 7.12/1.73 | GROUND_INST: instantiating (3) with all_14_9, all_14_7, all_14_8, all_14_6,
% 7.12/1.73 | all_14_3, all_14_2, all_14_1, simplifying with (9), (10), (11),
% 7.12/1.73 | (12), (16), (17), (20) gives:
% 7.12/1.73 | (21) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_14_7, all_14_6) =
% 7.12/1.73 | v1 & cartesian_product2(all_14_9, all_14_8) = v0 &
% 7.12/1.73 | set_intersection2(v0, v1) = all_14_1 & $i(v1) & $i(v0) &
% 7.12/1.73 | $i(all_14_1))
% 7.12/1.73 |
% 7.12/1.73 | DELTA: instantiating (21) with fresh symbols all_26_0, all_26_1 gives:
% 7.12/1.74 | (22) cartesian_product2(all_14_7, all_14_6) = all_26_0 &
% 7.12/1.74 | cartesian_product2(all_14_9, all_14_8) = all_26_1 &
% 7.12/1.74 | set_intersection2(all_26_1, all_26_0) = all_14_1 & $i(all_26_0) &
% 7.12/1.74 | $i(all_26_1) & $i(all_14_1)
% 7.12/1.74 |
% 7.12/1.74 | ALPHA: (22) implies:
% 7.12/1.74 | (23) $i(all_14_1)
% 7.12/1.74 | (24) $i(all_26_1)
% 7.12/1.74 | (25) $i(all_26_0)
% 7.12/1.74 | (26) set_intersection2(all_26_1, all_26_0) = all_14_1
% 7.12/1.74 | (27) cartesian_product2(all_14_9, all_14_8) = all_26_1
% 7.12/1.74 | (28) cartesian_product2(all_14_7, all_14_6) = all_26_0
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (5) with all_14_5, all_26_1, all_14_8, all_14_9,
% 7.12/1.74 | simplifying with (18), (27) gives:
% 7.12/1.74 | (29) all_26_1 = all_14_5
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (5) with all_14_4, all_26_0, all_14_6, all_14_7,
% 7.12/1.74 | simplifying with (19), (28) gives:
% 7.12/1.74 | (30) all_26_0 = all_14_4
% 7.12/1.74 |
% 7.12/1.74 | REDUCE: (26), (29), (30) imply:
% 7.12/1.74 | (31) set_intersection2(all_14_5, all_14_4) = all_14_1
% 7.12/1.74 |
% 7.12/1.74 | REDUCE: (25), (30) imply:
% 7.12/1.74 | (32) $i(all_14_4)
% 7.12/1.74 |
% 7.12/1.74 | REDUCE: (24), (29) imply:
% 7.12/1.74 | (33) $i(all_14_5)
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (2) with all_14_5, all_14_4, all_14_1, all_14_10,
% 7.12/1.74 | simplifying with (8), (14), (23), (31), (32), (33) gives:
% 7.12/1.74 | (34) ? [v0: any] : ? [v1: any] : (in(all_14_10, all_14_1) = v1 &
% 7.12/1.74 | in(all_14_10, all_14_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (1) with all_14_5, all_14_4, all_14_1, all_14_10,
% 7.12/1.74 | simplifying with (8), (13), (23), (31), (32), (33) gives:
% 7.12/1.74 | (35) ? [v0: any] : ? [v1: any] : (in(all_14_10, all_14_1) = v1 &
% 7.12/1.74 | in(all_14_10, all_14_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.12/1.74 |
% 7.12/1.74 | DELTA: instantiating (35) with fresh symbols all_38_0, all_38_1 gives:
% 7.12/1.75 | (36) in(all_14_10, all_14_1) = all_38_0 & in(all_14_10, all_14_4) =
% 7.12/1.75 | all_38_1 & ( ~ (all_38_1 = 0) | all_38_0 = 0)
% 7.12/1.75 |
% 7.12/1.75 | ALPHA: (36) implies:
% 7.12/1.75 | (37) in(all_14_10, all_14_1) = all_38_0
% 7.12/1.75 |
% 7.12/1.75 | DELTA: instantiating (34) with fresh symbols all_40_0, all_40_1 gives:
% 7.12/1.75 | (38) in(all_14_10, all_14_1) = all_40_0 & in(all_14_10, all_14_5) =
% 7.12/1.75 | all_40_1 & ( ~ (all_40_1 = 0) | all_40_0 = 0)
% 7.12/1.75 |
% 7.12/1.75 | ALPHA: (38) implies:
% 7.12/1.75 | (39) in(all_14_10, all_14_5) = all_40_1
% 7.12/1.75 | (40) in(all_14_10, all_14_1) = all_40_0
% 7.12/1.75 | (41) ~ (all_40_1 = 0) | all_40_0 = 0
% 7.12/1.75 |
% 7.12/1.75 | GROUND_INST: instantiating (4) with 0, all_40_1, all_14_5, all_14_10,
% 7.12/1.75 | simplifying with (13), (39) gives:
% 7.12/1.75 | (42) all_40_1 = 0
% 7.12/1.75 |
% 7.12/1.75 | GROUND_INST: instantiating (4) with all_14_0, all_40_0, all_14_1, all_14_10,
% 7.12/1.75 | simplifying with (15), (40) gives:
% 7.12/1.75 | (43) all_40_0 = all_14_0
% 7.12/1.75 |
% 7.12/1.75 | GROUND_INST: instantiating (4) with all_38_0, all_40_0, all_14_1, all_14_10,
% 7.12/1.75 | simplifying with (37), (40) gives:
% 7.12/1.75 | (44) all_40_0 = all_38_0
% 7.12/1.75 |
% 7.12/1.75 | COMBINE_EQS: (43), (44) imply:
% 7.12/1.75 | (45) all_38_0 = all_14_0
% 7.12/1.75 |
% 7.12/1.75 | BETA: splitting (41) gives:
% 7.12/1.75 |
% 7.12/1.75 | Case 1:
% 7.12/1.75 | |
% 7.12/1.75 | | (46) ~ (all_40_1 = 0)
% 7.12/1.75 | |
% 7.12/1.75 | | REDUCE: (42), (46) imply:
% 7.12/1.75 | | (47) $false
% 7.12/1.75 | |
% 7.12/1.75 | | CLOSE: (47) is inconsistent.
% 7.12/1.75 | |
% 7.12/1.75 | Case 2:
% 7.12/1.75 | |
% 7.12/1.76 | | (48) all_40_0 = 0
% 7.12/1.76 | |
% 7.12/1.76 | | COMBINE_EQS: (43), (48) imply:
% 7.12/1.76 | | (49) all_14_0 = 0
% 7.12/1.76 | |
% 7.12/1.76 | | SIMP: (49) implies:
% 7.12/1.76 | | (50) all_14_0 = 0
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (7), (50) imply:
% 7.12/1.76 | | (51) $false
% 7.12/1.76 | |
% 7.12/1.76 | | CLOSE: (51) is inconsistent.
% 7.12/1.76 | |
% 7.12/1.76 | End of split
% 7.12/1.76 |
% 7.12/1.76 End of proof
% 7.12/1.76 % SZS output end Proof for theBenchmark
% 7.12/1.76
% 7.12/1.76 1156ms
%------------------------------------------------------------------------------