TSTP Solution File: SET974+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET974+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 : n003.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 15:27:15 EDT 2023
% Result : Theorem 6.43s 1.62s
% Output : Proof 8.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET974+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 : n003.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 12:47:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.01/1.00 Prover 1: Preprocessing ...
% 2.01/1.00 Prover 4: Preprocessing ...
% 2.48/1.04 Prover 2: Preprocessing ...
% 2.48/1.04 Prover 0: Preprocessing ...
% 2.48/1.04 Prover 3: Preprocessing ...
% 2.48/1.04 Prover 6: Preprocessing ...
% 2.48/1.04 Prover 5: Preprocessing ...
% 4.07/1.33 Prover 1: Warning: ignoring some quantifiers
% 4.07/1.34 Prover 3: Warning: ignoring some quantifiers
% 4.07/1.35 Prover 1: Constructing countermodel ...
% 4.07/1.35 Prover 4: Constructing countermodel ...
% 4.07/1.35 Prover 5: Proving ...
% 4.07/1.35 Prover 2: Proving ...
% 4.07/1.35 Prover 6: Proving ...
% 4.07/1.36 Prover 3: Constructing countermodel ...
% 4.07/1.38 Prover 0: Proving ...
% 6.43/1.62 Prover 0: proved (1009ms)
% 6.43/1.62
% 6.43/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.43/1.62
% 6.43/1.63 Prover 5: stopped
% 6.43/1.63 Prover 6: stopped
% 6.43/1.63 Prover 2: stopped
% 6.43/1.64 Prover 3: stopped
% 6.43/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.43/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.67/1.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.67/1.65 Prover 7: Preprocessing ...
% 6.67/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.67/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.67/1.65 Prover 8: Preprocessing ...
% 6.67/1.68 Prover 13: Preprocessing ...
% 6.67/1.68 Prover 11: Preprocessing ...
% 6.67/1.69 Prover 10: Preprocessing ...
% 6.67/1.72 Prover 8: Warning: ignoring some quantifiers
% 6.67/1.72 Prover 7: Constructing countermodel ...
% 6.67/1.73 Prover 8: Constructing countermodel ...
% 7.32/1.73 Prover 13: Warning: ignoring some quantifiers
% 7.32/1.74 Prover 13: Constructing countermodel ...
% 7.32/1.77 Prover 10: Constructing countermodel ...
% 7.32/1.78 Prover 11: Constructing countermodel ...
% 7.69/1.78 Prover 7: gave up
% 7.69/1.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.69/1.79 Prover 13: gave up
% 7.69/1.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.69/1.79 Prover 10: gave up
% 7.69/1.80 Prover 19: Preprocessing ...
% 7.69/1.81 Prover 16: Preprocessing ...
% 7.69/1.82 Prover 1: Found proof (size 47)
% 7.69/1.82 Prover 1: proved (1208ms)
% 7.69/1.82 Prover 11: stopped
% 7.69/1.82 Prover 8: stopped
% 7.69/1.82 Prover 4: stopped
% 7.69/1.83 Prover 16: stopped
% 8.13/1.86 Prover 19: Warning: ignoring some quantifiers
% 8.21/1.86 Prover 19: Constructing countermodel ...
% 8.21/1.87 Prover 19: stopped
% 8.21/1.87
% 8.21/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.21/1.87
% 8.21/1.88 % SZS output start Proof for theBenchmark
% 8.21/1.88 Assumptions after simplification:
% 8.21/1.88 ---------------------------------
% 8.21/1.88
% 8.21/1.88 (t104_zfmisc_1)
% 8.21/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.21/1.91 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cartesian_product2(v3, v4) = v6) | ~
% 8.21/1.91 (cartesian_product2(v1, v2) = v5) | ~ (set_intersection2(v5, v6) = v7) | ~
% 8.21/1.91 (in(v0, v7) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.21/1.91 | ? [v8: $i] : ? [v9: $i] : (set_intersection2(v2, v4) = v9 &
% 8.21/1.91 set_intersection2(v1, v3) = v8 & $i(v9) & $i(v8) & ? [v10: $i] : ? [v11:
% 8.21/1.91 $i] : (ordered_pair(v10, v11) = v0 & in(v11, v9) = 0 & in(v10, v8) = 0 &
% 8.21/1.91 $i(v11) & $i(v10))))
% 8.21/1.91
% 8.21/1.91 (t127_zfmisc_1)
% 8.45/1.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 8.45/1.91 any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 8.45/1.91 cartesian_product2(v1, v3) = v7 & cartesian_product2(v0, v2) = v6 &
% 8.45/1.91 disjoint(v6, v7) = v8 & disjoint(v2, v3) = v5 & disjoint(v0, v1) = v4 &
% 8.45/1.91 $i(v7) & $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v5 = 0 | v4 = 0))
% 8.45/1.91
% 8.45/1.91 (t4_xboole_0)
% 8.45/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 8.45/1.92 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_intersection2(v0, v1) =
% 8.45/1.92 v3 & $i(v3) & ? [v4: $i] : (in(v4, v3) = 0 & $i(v4)))) & ! [v0: $i] : !
% 8.45/1.92 [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 8.45/1.92 (set_intersection2(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ (in(v3, v2) =
% 8.45/1.92 0) | ~ $i(v3))))
% 8.45/1.92
% 8.45/1.92 (function-axioms)
% 8.45/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.93 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 8.45/1.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.45/1.93 $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) &
% 8.45/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.93 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 8.45/1.93 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.93 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 8.45/1.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.93 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.45/1.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.45/1.93 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 8.45/1.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.45/1.93 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 8.45/1.93 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.45/1.93
% 8.45/1.93 Further assumptions not needed in the proof:
% 8.45/1.93 --------------------------------------------
% 8.45/1.93 antisymmetry_r2_hidden, commutativity_k2_tarski, commutativity_k3_xboole_0,
% 8.45/1.93 d5_tarski, fc1_zfmisc_1, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 8.45/1.93 symmetry_r1_xboole_0
% 8.45/1.93
% 8.45/1.93 Those formulas are unsatisfiable:
% 8.45/1.93 ---------------------------------
% 8.45/1.93
% 8.45/1.93 Begin of proof
% 8.45/1.93 |
% 8.45/1.93 | ALPHA: (t4_xboole_0) implies:
% 8.45/1.93 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 8.45/1.93 | $i(v0) | ? [v2: $i] : (set_intersection2(v0, v1) = v2 & $i(v2) & !
% 8.45/1.93 | [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3))))
% 8.45/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 8.45/1.93 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 8.45/1.93 | (set_intersection2(v0, v1) = v3 & $i(v3) & ? [v4: $i] : (in(v4, v3)
% 8.45/1.93 | = 0 & $i(v4))))
% 8.45/1.93 |
% 8.45/1.93 | ALPHA: (function-axioms) implies:
% 8.45/1.93 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.93 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) =
% 8.45/1.93 | v0))
% 8.45/1.93 |
% 8.45/1.93 | DELTA: instantiating (t127_zfmisc_1) with fresh symbols all_17_0, all_17_1,
% 8.45/1.93 | all_17_2, all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8
% 8.45/1.93 | gives:
% 8.45/1.94 | (4) ~ (all_17_0 = 0) & cartesian_product2(all_17_7, all_17_5) = all_17_1 &
% 8.45/1.94 | cartesian_product2(all_17_8, all_17_6) = all_17_2 & disjoint(all_17_2,
% 8.45/1.94 | all_17_1) = all_17_0 & disjoint(all_17_6, all_17_5) = all_17_3 &
% 8.45/1.94 | disjoint(all_17_8, all_17_7) = all_17_4 & $i(all_17_1) & $i(all_17_2) &
% 8.45/1.94 | $i(all_17_5) & $i(all_17_6) & $i(all_17_7) & $i(all_17_8) & (all_17_3 =
% 8.45/1.94 | 0 | all_17_4 = 0)
% 8.45/1.94 |
% 8.45/1.94 | ALPHA: (4) implies:
% 8.45/1.94 | (5) ~ (all_17_0 = 0)
% 8.45/1.94 | (6) $i(all_17_8)
% 8.45/1.94 | (7) $i(all_17_7)
% 8.45/1.94 | (8) $i(all_17_6)
% 8.45/1.94 | (9) $i(all_17_5)
% 8.45/1.94 | (10) $i(all_17_2)
% 8.45/1.94 | (11) $i(all_17_1)
% 8.45/1.94 | (12) disjoint(all_17_8, all_17_7) = all_17_4
% 8.45/1.94 | (13) disjoint(all_17_6, all_17_5) = all_17_3
% 8.45/1.94 | (14) disjoint(all_17_2, all_17_1) = all_17_0
% 8.45/1.94 | (15) cartesian_product2(all_17_8, all_17_6) = all_17_2
% 8.45/1.94 | (16) cartesian_product2(all_17_7, all_17_5) = all_17_1
% 8.45/1.94 | (17) all_17_3 = 0 | all_17_4 = 0
% 8.45/1.94 |
% 8.45/1.94 | GROUND_INST: instantiating (2) with all_17_2, all_17_1, all_17_0, simplifying
% 8.45/1.94 | with (10), (11), (14) gives:
% 8.45/1.94 | (18) all_17_0 = 0 | ? [v0: $i] : (set_intersection2(all_17_2, all_17_1) =
% 8.45/1.94 | v0 & $i(v0) & ? [v1: $i] : (in(v1, v0) = 0 & $i(v1)))
% 8.45/1.94 |
% 8.45/1.94 | BETA: splitting (17) gives:
% 8.45/1.94 |
% 8.45/1.94 | Case 1:
% 8.45/1.94 | |
% 8.45/1.94 | | (19) all_17_3 = 0
% 8.45/1.94 | |
% 8.45/1.94 | | REDUCE: (13), (19) imply:
% 8.45/1.94 | | (20) disjoint(all_17_6, all_17_5) = 0
% 8.45/1.94 | |
% 8.45/1.94 | | BETA: splitting (18) gives:
% 8.45/1.94 | |
% 8.45/1.94 | | Case 1:
% 8.45/1.94 | | |
% 8.45/1.94 | | | (21) all_17_0 = 0
% 8.45/1.94 | | |
% 8.45/1.94 | | | REDUCE: (5), (21) imply:
% 8.45/1.94 | | | (22) $false
% 8.45/1.94 | | |
% 8.45/1.94 | | | CLOSE: (22) is inconsistent.
% 8.45/1.94 | | |
% 8.45/1.94 | | Case 2:
% 8.45/1.94 | | |
% 8.45/1.94 | | | (23) ? [v0: $i] : (set_intersection2(all_17_2, all_17_1) = v0 & $i(v0)
% 8.45/1.94 | | | & ? [v1: $i] : (in(v1, v0) = 0 & $i(v1)))
% 8.45/1.94 | | |
% 8.45/1.94 | | | DELTA: instantiating (23) with fresh symbol all_30_0 gives:
% 8.45/1.95 | | | (24) set_intersection2(all_17_2, all_17_1) = all_30_0 & $i(all_30_0) &
% 8.45/1.95 | | | ? [v0: $i] : (in(v0, all_30_0) = 0 & $i(v0))
% 8.45/1.95 | | |
% 8.45/1.95 | | | ALPHA: (24) implies:
% 8.45/1.95 | | | (25) set_intersection2(all_17_2, all_17_1) = all_30_0
% 8.45/1.95 | | | (26) ? [v0: $i] : (in(v0, all_30_0) = 0 & $i(v0))
% 8.45/1.95 | | |
% 8.45/1.95 | | | DELTA: instantiating (26) with fresh symbol all_32_0 gives:
% 8.45/1.95 | | | (27) in(all_32_0, all_30_0) = 0 & $i(all_32_0)
% 8.45/1.95 | | |
% 8.45/1.95 | | | ALPHA: (27) implies:
% 8.45/1.95 | | | (28) $i(all_32_0)
% 8.45/1.95 | | | (29) in(all_32_0, all_30_0) = 0
% 8.45/1.95 | | |
% 8.45/1.95 | | | GROUND_INST: instantiating (t104_zfmisc_1) with all_32_0, all_17_8,
% 8.45/1.95 | | | all_17_6, all_17_7, all_17_5, all_17_2, all_17_1, all_30_0,
% 8.45/1.95 | | | simplifying with (6), (7), (8), (9), (15), (16), (25), (28),
% 8.45/1.95 | | | (29) gives:
% 8.45/1.95 | | | (30) ? [v0: $i] : ? [v1: $i] : (set_intersection2(all_17_6, all_17_5)
% 8.45/1.95 | | | = v1 & set_intersection2(all_17_8, all_17_7) = v0 & $i(v1) &
% 8.45/1.95 | | | $i(v0) & ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) =
% 8.45/1.95 | | | all_32_0 & in(v3, v1) = 0 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 8.45/1.95 | | |
% 8.45/1.95 | | | GROUND_INST: instantiating (1) with all_17_6, all_17_5, simplifying with
% 8.45/1.95 | | | (8), (9), (20) gives:
% 8.45/1.95 | | | (31) ? [v0: $i] : (set_intersection2(all_17_6, all_17_5) = v0 & $i(v0)
% 8.45/1.95 | | | & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1)))
% 8.45/1.95 | | |
% 8.45/1.95 | | | DELTA: instantiating (31) with fresh symbol all_42_0 gives:
% 8.45/1.95 | | | (32) set_intersection2(all_17_6, all_17_5) = all_42_0 & $i(all_42_0) &
% 8.45/1.95 | | | ! [v0: $i] : ( ~ (in(v0, all_42_0) = 0) | ~ $i(v0))
% 8.45/1.95 | | |
% 8.45/1.95 | | | ALPHA: (32) implies:
% 8.45/1.96 | | | (33) set_intersection2(all_17_6, all_17_5) = all_42_0
% 8.45/1.96 | | | (34) ! [v0: $i] : ( ~ (in(v0, all_42_0) = 0) | ~ $i(v0))
% 8.45/1.96 | | |
% 8.45/1.96 | | | DELTA: instantiating (30) with fresh symbols all_45_0, all_45_1 gives:
% 8.45/1.96 | | | (35) set_intersection2(all_17_6, all_17_5) = all_45_0 &
% 8.45/1.96 | | | set_intersection2(all_17_8, all_17_7) = all_45_1 & $i(all_45_0) &
% 8.45/1.96 | | | $i(all_45_1) & ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) =
% 8.45/1.96 | | | all_32_0 & in(v1, all_45_0) = 0 & in(v0, all_45_1) = 0 & $i(v1)
% 8.45/1.96 | | | & $i(v0))
% 8.45/1.96 | | |
% 8.45/1.96 | | | ALPHA: (35) implies:
% 8.45/1.96 | | | (36) set_intersection2(all_17_6, all_17_5) = all_45_0
% 8.45/1.96 | | | (37) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_32_0 &
% 8.45/1.96 | | | in(v1, all_45_0) = 0 & in(v0, all_45_1) = 0 & $i(v1) & $i(v0))
% 8.45/1.96 | | |
% 8.45/1.96 | | | DELTA: instantiating (37) with fresh symbols all_47_0, all_47_1 gives:
% 8.45/1.96 | | | (38) ordered_pair(all_47_1, all_47_0) = all_32_0 & in(all_47_0,
% 8.45/1.96 | | | all_45_0) = 0 & in(all_47_1, all_45_1) = 0 & $i(all_47_0) &
% 8.45/1.96 | | | $i(all_47_1)
% 8.45/1.96 | | |
% 8.45/1.96 | | | ALPHA: (38) implies:
% 8.45/1.96 | | | (39) $i(all_47_0)
% 8.45/1.96 | | | (40) in(all_47_0, all_45_0) = 0
% 8.45/1.96 | | |
% 8.45/1.96 | | | GROUND_INST: instantiating (3) with all_42_0, all_45_0, all_17_5,
% 8.45/1.96 | | | all_17_6, simplifying with (33), (36) gives:
% 8.45/1.96 | | | (41) all_45_0 = all_42_0
% 8.45/1.96 | | |
% 8.45/1.96 | | | REDUCE: (40), (41) imply:
% 8.45/1.96 | | | (42) in(all_47_0, all_42_0) = 0
% 8.45/1.96 | | |
% 8.45/1.96 | | | GROUND_INST: instantiating (34) with all_47_0, simplifying with (39), (42)
% 8.45/1.96 | | | gives:
% 8.45/1.96 | | | (43) $false
% 8.45/1.96 | | |
% 8.45/1.96 | | | CLOSE: (43) is inconsistent.
% 8.45/1.96 | | |
% 8.45/1.96 | | End of split
% 8.45/1.96 | |
% 8.45/1.96 | Case 2:
% 8.45/1.96 | |
% 8.45/1.96 | | (44) all_17_4 = 0
% 8.45/1.96 | |
% 8.45/1.96 | | REDUCE: (12), (44) imply:
% 8.45/1.96 | | (45) disjoint(all_17_8, all_17_7) = 0
% 8.45/1.96 | |
% 8.45/1.96 | | BETA: splitting (18) gives:
% 8.45/1.96 | |
% 8.45/1.96 | | Case 1:
% 8.45/1.96 | | |
% 8.45/1.96 | | | (46) all_17_0 = 0
% 8.45/1.96 | | |
% 8.45/1.96 | | | REDUCE: (5), (46) imply:
% 8.45/1.96 | | | (47) $false
% 8.45/1.96 | | |
% 8.45/1.96 | | | CLOSE: (47) is inconsistent.
% 8.45/1.96 | | |
% 8.45/1.96 | | Case 2:
% 8.45/1.96 | | |
% 8.45/1.96 | | | (48) ? [v0: $i] : (set_intersection2(all_17_2, all_17_1) = v0 & $i(v0)
% 8.45/1.96 | | | & ? [v1: $i] : (in(v1, v0) = 0 & $i(v1)))
% 8.45/1.96 | | |
% 8.45/1.96 | | | DELTA: instantiating (48) with fresh symbol all_30_0 gives:
% 8.45/1.96 | | | (49) set_intersection2(all_17_2, all_17_1) = all_30_0 & $i(all_30_0) &
% 8.45/1.96 | | | ? [v0: $i] : (in(v0, all_30_0) = 0 & $i(v0))
% 8.45/1.96 | | |
% 8.45/1.96 | | | ALPHA: (49) implies:
% 8.45/1.97 | | | (50) set_intersection2(all_17_2, all_17_1) = all_30_0
% 8.45/1.97 | | | (51) ? [v0: $i] : (in(v0, all_30_0) = 0 & $i(v0))
% 8.45/1.97 | | |
% 8.45/1.97 | | | DELTA: instantiating (51) with fresh symbol all_32_0 gives:
% 8.45/1.97 | | | (52) in(all_32_0, all_30_0) = 0 & $i(all_32_0)
% 8.45/1.97 | | |
% 8.45/1.97 | | | ALPHA: (52) implies:
% 8.45/1.97 | | | (53) $i(all_32_0)
% 8.45/1.97 | | | (54) in(all_32_0, all_30_0) = 0
% 8.45/1.97 | | |
% 8.45/1.97 | | | GROUND_INST: instantiating (t104_zfmisc_1) with all_32_0, all_17_8,
% 8.45/1.97 | | | all_17_6, all_17_7, all_17_5, all_17_2, all_17_1, all_30_0,
% 8.45/1.97 | | | simplifying with (6), (7), (8), (9), (15), (16), (50), (53),
% 8.45/1.97 | | | (54) gives:
% 8.45/1.97 | | | (55) ? [v0: $i] : ? [v1: $i] : (set_intersection2(all_17_6, all_17_5)
% 8.45/1.97 | | | = v1 & set_intersection2(all_17_8, all_17_7) = v0 & $i(v1) &
% 8.45/1.97 | | | $i(v0) & ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) =
% 8.45/1.97 | | | all_32_0 & in(v3, v1) = 0 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 8.45/1.97 | | |
% 8.45/1.97 | | | GROUND_INST: instantiating (1) with all_17_8, all_17_7, simplifying with
% 8.45/1.97 | | | (6), (7), (45) gives:
% 8.45/1.97 | | | (56) ? [v0: $i] : (set_intersection2(all_17_8, all_17_7) = v0 & $i(v0)
% 8.45/1.97 | | | & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1)))
% 8.45/1.97 | | |
% 8.45/1.97 | | | DELTA: instantiating (56) with fresh symbol all_51_0 gives:
% 8.45/1.97 | | | (57) set_intersection2(all_17_8, all_17_7) = all_51_0 & $i(all_51_0) &
% 8.45/1.97 | | | ! [v0: $i] : ( ~ (in(v0, all_51_0) = 0) | ~ $i(v0))
% 8.45/1.97 | | |
% 8.45/1.97 | | | ALPHA: (57) implies:
% 8.45/1.97 | | | (58) set_intersection2(all_17_8, all_17_7) = all_51_0
% 8.45/1.97 | | | (59) ! [v0: $i] : ( ~ (in(v0, all_51_0) = 0) | ~ $i(v0))
% 8.45/1.97 | | |
% 8.45/1.97 | | | DELTA: instantiating (55) with fresh symbols all_54_0, all_54_1 gives:
% 8.45/1.97 | | | (60) set_intersection2(all_17_6, all_17_5) = all_54_0 &
% 8.45/1.97 | | | set_intersection2(all_17_8, all_17_7) = all_54_1 & $i(all_54_0) &
% 8.45/1.97 | | | $i(all_54_1) & ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) =
% 8.45/1.97 | | | all_32_0 & in(v1, all_54_0) = 0 & in(v0, all_54_1) = 0 & $i(v1)
% 8.45/1.97 | | | & $i(v0))
% 8.45/1.97 | | |
% 8.45/1.97 | | | ALPHA: (60) implies:
% 8.45/1.97 | | | (61) set_intersection2(all_17_8, all_17_7) = all_54_1
% 8.45/1.98 | | | (62) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_32_0 &
% 8.45/1.98 | | | in(v1, all_54_0) = 0 & in(v0, all_54_1) = 0 & $i(v1) & $i(v0))
% 8.45/1.98 | | |
% 8.45/1.98 | | | DELTA: instantiating (62) with fresh symbols all_56_0, all_56_1 gives:
% 8.45/1.98 | | | (63) ordered_pair(all_56_1, all_56_0) = all_32_0 & in(all_56_0,
% 8.45/1.98 | | | all_54_0) = 0 & in(all_56_1, all_54_1) = 0 & $i(all_56_0) &
% 8.45/1.98 | | | $i(all_56_1)
% 8.45/1.98 | | |
% 8.45/1.98 | | | ALPHA: (63) implies:
% 8.45/1.98 | | | (64) $i(all_56_1)
% 8.45/1.98 | | | (65) in(all_56_1, all_54_1) = 0
% 8.45/1.98 | | |
% 8.45/1.98 | | | GROUND_INST: instantiating (3) with all_51_0, all_54_1, all_17_7,
% 8.45/1.98 | | | all_17_8, simplifying with (58), (61) gives:
% 8.45/1.98 | | | (66) all_54_1 = all_51_0
% 8.45/1.98 | | |
% 8.45/1.98 | | | REDUCE: (65), (66) imply:
% 8.45/1.98 | | | (67) in(all_56_1, all_51_0) = 0
% 8.45/1.98 | | |
% 8.45/1.98 | | | GROUND_INST: instantiating (59) with all_56_1, simplifying with (64), (67)
% 8.45/1.98 | | | gives:
% 8.45/1.98 | | | (68) $false
% 8.45/1.98 | | |
% 8.45/1.98 | | | CLOSE: (68) is inconsistent.
% 8.45/1.98 | | |
% 8.45/1.98 | | End of split
% 8.45/1.98 | |
% 8.45/1.98 | End of split
% 8.45/1.98 |
% 8.45/1.98 End of proof
% 8.45/1.98 % SZS output end Proof for theBenchmark
% 8.45/1.98
% 8.45/1.98 1389ms
%------------------------------------------------------------------------------