TSTP Solution File: SET914+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET914+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 : n013.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 15:27:00 EDT 2023
% Result : Theorem 6.41s 1.67s
% Output : Proof 8.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET914+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 12:44:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.25/1.01 Prover 4: Preprocessing ...
% 2.25/1.01 Prover 1: Preprocessing ...
% 2.39/1.05 Prover 6: Preprocessing ...
% 2.39/1.05 Prover 3: Preprocessing ...
% 2.39/1.05 Prover 5: Preprocessing ...
% 2.39/1.05 Prover 2: Preprocessing ...
% 2.39/1.05 Prover 0: Preprocessing ...
% 4.18/1.34 Prover 1: Warning: ignoring some quantifiers
% 4.18/1.38 Prover 3: Warning: ignoring some quantifiers
% 4.18/1.40 Prover 6: Proving ...
% 4.18/1.40 Prover 5: Proving ...
% 4.18/1.40 Prover 1: Constructing countermodel ...
% 4.64/1.40 Prover 3: Constructing countermodel ...
% 4.64/1.41 Prover 4: Warning: ignoring some quantifiers
% 5.13/1.43 Prover 4: Constructing countermodel ...
% 5.13/1.43 Prover 2: Proving ...
% 5.13/1.43 Prover 0: Proving ...
% 6.41/1.66 Prover 3: proved (1044ms)
% 6.41/1.66
% 6.41/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.41/1.67
% 6.92/1.67 Prover 6: stopped
% 6.92/1.67 Prover 5: stopped
% 6.92/1.67 Prover 2: stopped
% 6.96/1.68 Prover 0: stopped
% 6.96/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.96/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.96/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.96/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.96/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.14/1.71 Prover 11: Preprocessing ...
% 7.14/1.71 Prover 10: Preprocessing ...
% 7.14/1.71 Prover 7: Preprocessing ...
% 7.14/1.72 Prover 13: Preprocessing ...
% 7.14/1.72 Prover 8: Preprocessing ...
% 7.28/1.73 Prover 1: Found proof (size 45)
% 7.28/1.73 Prover 1: proved (1117ms)
% 7.28/1.73 Prover 4: stopped
% 7.28/1.74 Prover 7: stopped
% 7.28/1.74 Prover 10: stopped
% 7.28/1.75 Prover 13: stopped
% 7.28/1.75 Prover 11: stopped
% 7.28/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.28/1.78 Prover 8: Constructing countermodel ...
% 7.28/1.78 Prover 8: stopped
% 7.28/1.78
% 7.28/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.28/1.79
% 7.28/1.80 % SZS output start Proof for theBenchmark
% 7.28/1.80 Assumptions after simplification:
% 7.28/1.80 ---------------------------------
% 7.28/1.80
% 7.28/1.80 (commutativity_k2_tarski)
% 7.80/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 7.80/1.83 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 7.80/1.83
% 7.80/1.83 (commutativity_k3_xboole_0)
% 7.80/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 7.80/1.83 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 7.80/1.83
% 7.80/1.83 (d1_xboole_0)
% 7.80/1.83 $i(empty_set) & ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) & ?
% 7.80/1.83 [v0: $i] : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : (in(v1, v0) = 0 &
% 7.80/1.83 $i(v1)))
% 7.80/1.83
% 7.80/1.83 (d2_tarski)
% 7.80/1.84 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 7.80/1.84 (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 7.80/1.84 $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 =
% 7.80/1.84 v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0: $i]
% 7.80/1.84 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) |
% 7.80/1.84 ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3,
% 7.80/1.84 v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3: $i]
% 7.80/1.84 : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0) | ~ $i(v3))))
% 7.80/1.84
% 7.80/1.84 (d3_xboole_0)
% 7.80/1.84 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 7.80/1.84 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.80/1.84 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 &
% 7.80/1.84 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) |
% 7.80/1.84 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 7.80/1.84 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) |
% 7.80/1.84 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3)
% 7.80/1.84 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~
% 7.80/1.84 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 7.80/1.84 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3,
% 7.80/1.84 v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 7.80/1.84
% 7.80/1.84 (d7_xboole_0)
% 7.80/1.85 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 7.80/1.85 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 =
% 7.80/1.85 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] :
% 7.80/1.85 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.80/1.85 set_intersection2(v0, v1) = empty_set)
% 7.80/1.85
% 7.80/1.85 (fc1_xboole_0)
% 7.80/1.85 empty(empty_set) = 0 & $i(empty_set)
% 7.80/1.85
% 7.80/1.85 (symmetry_r1_xboole_0)
% 7.80/1.85 ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 7.80/1.85 | disjoint(v1, v0) = 0)
% 7.80/1.85
% 7.80/1.85 (t55_zfmisc_1)
% 7.80/1.85 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (disjoint(v3, v2) = 0
% 7.80/1.85 & unordered_pair(v0, v1) = v3 & in(v0, v2) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 7.80/1.85 $i(v0))
% 7.80/1.85
% 7.80/1.85 (function-axioms)
% 7.80/1.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.80/1.85 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 7.80/1.85 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.80/1.85 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 7.80/1.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.80/1.85 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.80/1.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.80/1.85 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.80/1.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.80/1.85 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.80/1.85
% 7.80/1.85 Further assumptions not needed in the proof:
% 7.80/1.85 --------------------------------------------
% 7.80/1.85 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 7.80/1.85
% 7.80/1.85 Those formulas are unsatisfiable:
% 7.80/1.85 ---------------------------------
% 7.80/1.85
% 7.80/1.85 Begin of proof
% 7.80/1.85 |
% 7.80/1.85 | ALPHA: (d1_xboole_0) implies:
% 7.80/1.85 | (1) ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0))
% 7.80/1.85 |
% 7.80/1.85 | ALPHA: (d2_tarski) implies:
% 7.80/1.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 7.80/1.86 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4:
% 7.80/1.86 | int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1)
% 7.80/1.86 | & ~ (v3 = v0))) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 7.80/1.86 | (in(v3, v2) = 0) | ~ $i(v3))))
% 7.80/1.86 |
% 7.80/1.86 | ALPHA: (d3_xboole_0) implies:
% 7.80/1.86 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0,
% 7.80/1.86 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 7.80/1.86 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 7.80/1.86 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) |
% 7.80/1.86 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) |
% 7.80/1.86 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 &
% 7.80/1.86 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 7.80/1.86 |
% 7.80/1.86 | ALPHA: (d7_xboole_0) implies:
% 7.80/1.86 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 7.80/1.86 | $i(v0) | set_intersection2(v0, v1) = empty_set)
% 7.80/1.86 |
% 7.80/1.86 | ALPHA: (fc1_xboole_0) implies:
% 7.80/1.86 | (5) $i(empty_set)
% 7.80/1.86 |
% 7.80/1.86 | ALPHA: (function-axioms) implies:
% 7.80/1.86 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.80/1.86 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.80/1.86 |
% 7.80/1.86 | DELTA: instantiating (t55_zfmisc_1) with fresh symbols all_19_0, all_19_1,
% 7.80/1.86 | all_19_2, all_19_3 gives:
% 7.80/1.86 | (7) disjoint(all_19_0, all_19_1) = 0 & unordered_pair(all_19_3, all_19_2) =
% 7.80/1.86 | all_19_0 & in(all_19_3, all_19_1) = 0 & $i(all_19_0) & $i(all_19_1) &
% 7.80/1.86 | $i(all_19_2) & $i(all_19_3)
% 7.80/1.86 |
% 7.80/1.86 | ALPHA: (7) implies:
% 7.80/1.86 | (8) $i(all_19_3)
% 7.80/1.86 | (9) $i(all_19_2)
% 7.80/1.86 | (10) $i(all_19_1)
% 7.80/1.86 | (11) in(all_19_3, all_19_1) = 0
% 7.80/1.86 | (12) unordered_pair(all_19_3, all_19_2) = all_19_0
% 7.80/1.86 | (13) disjoint(all_19_0, all_19_1) = 0
% 7.80/1.86 |
% 7.80/1.86 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_19_3, all_19_2,
% 7.80/1.86 | all_19_0, simplifying with (8), (9), (12) gives:
% 7.80/1.87 | (14) unordered_pair(all_19_2, all_19_3) = all_19_0 & $i(all_19_0)
% 7.80/1.87 |
% 7.80/1.87 | ALPHA: (14) implies:
% 7.80/1.87 | (15) $i(all_19_0)
% 7.80/1.87 | (16) unordered_pair(all_19_2, all_19_3) = all_19_0
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (symmetry_r1_xboole_0) with all_19_0, all_19_1,
% 7.80/1.87 | simplifying with (10), (13), (15) gives:
% 7.80/1.87 | (17) disjoint(all_19_1, all_19_0) = 0
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (4) with all_19_0, all_19_1, simplifying with (10),
% 7.80/1.87 | (13), (15) gives:
% 7.80/1.87 | (18) set_intersection2(all_19_0, all_19_1) = empty_set
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (2) with all_19_2, all_19_3, all_19_0, simplifying
% 7.80/1.87 | with (8), (9), (15), (16) gives:
% 7.80/1.87 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_19_0) = v1) | ~
% 7.80/1.87 | $i(v0) | ( ~ (v0 = all_19_2) & ~ (v0 = all_19_3))) & ! [v0: any] :
% 7.80/1.87 | (v0 = all_19_2 | v0 = all_19_3 | ~ (in(v0, all_19_0) = 0) | ~
% 7.80/1.87 | $i(v0))
% 7.80/1.87 |
% 7.80/1.87 | ALPHA: (19) implies:
% 7.80/1.87 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_19_0) = v1) | ~
% 7.80/1.87 | $i(v0) | ( ~ (v0 = all_19_2) & ~ (v0 = all_19_3)))
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (3) with all_19_0, all_19_1, empty_set, simplifying
% 7.80/1.87 | with (5), (10), (15), (18) gives:
% 7.80/1.87 | (21) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_19_0) = v1) | ~ $i(v0) |
% 7.80/1.87 | ? [v2: any] : ? [v3: any] : (in(v0, all_19_1) = v3 & in(v0,
% 7.80/1.87 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 7.80/1.87 | $i] : ( ~ (in(v0, all_19_0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 7.80/1.87 | [v2: any] : (in(v0, all_19_1) = v1 & in(v0, empty_set) = v2 & ( ~
% 7.80/1.87 | (v1 = 0) | v2 = 0)))
% 7.80/1.87 |
% 7.80/1.87 | ALPHA: (21) implies:
% 7.80/1.87 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_19_0) = v1) | ~ $i(v0) |
% 7.80/1.87 | ? [v2: any] : ? [v3: any] : (in(v0, all_19_1) = v3 & in(v0,
% 7.80/1.87 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_19_0,
% 7.80/1.87 | all_19_1, empty_set, simplifying with (10), (15), (18) gives:
% 7.80/1.87 | (23) set_intersection2(all_19_1, all_19_0) = empty_set & $i(empty_set)
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (4) with all_19_1, all_19_0, simplifying with (10),
% 7.80/1.87 | (15), (17) gives:
% 7.80/1.87 | (24) set_intersection2(all_19_1, all_19_0) = empty_set
% 7.80/1.87 |
% 7.80/1.87 | GROUND_INST: instantiating (3) with all_19_1, all_19_0, empty_set, simplifying
% 7.80/1.87 | with (5), (10), (15), (24) gives:
% 7.80/1.88 | (25) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_19_1) = v1) | ~ $i(v0) |
% 7.80/1.88 | ? [v2: any] : ? [v3: any] : (in(v0, all_19_0) = v3 & in(v0,
% 7.80/1.88 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 7.80/1.88 | $i] : ( ~ (in(v0, all_19_1) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 7.80/1.88 | [v2: any] : (in(v0, all_19_0) = v1 & in(v0, empty_set) = v2 & ( ~
% 7.80/1.88 | (v1 = 0) | v2 = 0)))
% 7.80/1.88 |
% 7.80/1.88 | ALPHA: (25) implies:
% 7.80/1.88 | (26) ! [v0: $i] : ( ~ (in(v0, all_19_1) = 0) | ~ $i(v0) | ? [v1: any] :
% 7.80/1.88 | ? [v2: any] : (in(v0, all_19_0) = v1 & in(v0, empty_set) = v2 & ( ~
% 7.80/1.88 | (v1 = 0) | v2 = 0)))
% 7.80/1.88 | (27) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_19_1) = v1) | ~ $i(v0) |
% 7.80/1.88 | ? [v2: any] : ? [v3: any] : (in(v0, all_19_0) = v3 & in(v0,
% 7.80/1.88 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 7.80/1.88 |
% 7.80/1.88 | GROUND_INST: instantiating (26) with all_19_3, simplifying with (8), (11)
% 7.80/1.88 | gives:
% 7.80/1.88 | (28) ? [v0: any] : ? [v1: any] : (in(all_19_3, all_19_0) = v0 &
% 7.80/1.88 | in(all_19_3, empty_set) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 7.80/1.88 |
% 7.80/1.88 | GROUND_INST: instantiating (27) with all_19_3, 0, simplifying with (8), (11)
% 7.80/1.88 | gives:
% 7.80/1.88 | (29) ? [v0: any] : ? [v1: any] : (in(all_19_3, all_19_0) = v1 &
% 7.80/1.88 | in(all_19_3, empty_set) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.80/1.88 |
% 7.80/1.88 | DELTA: instantiating (29) with fresh symbols all_48_0, all_48_1 gives:
% 7.80/1.88 | (30) in(all_19_3, all_19_0) = all_48_0 & in(all_19_3, empty_set) = all_48_1
% 7.80/1.88 | & ( ~ (all_48_1 = 0) | all_48_0 = 0)
% 7.80/1.88 |
% 7.80/1.88 | ALPHA: (30) implies:
% 7.80/1.88 | (31) in(all_19_3, empty_set) = all_48_1
% 7.80/1.88 | (32) in(all_19_3, all_19_0) = all_48_0
% 7.80/1.88 |
% 7.80/1.88 | DELTA: instantiating (28) with fresh symbols all_50_0, all_50_1 gives:
% 7.80/1.88 | (33) in(all_19_3, all_19_0) = all_50_1 & in(all_19_3, empty_set) = all_50_0
% 7.80/1.88 | & ( ~ (all_50_1 = 0) | all_50_0 = 0)
% 7.80/1.88 |
% 7.80/1.88 | ALPHA: (33) implies:
% 7.80/1.88 | (34) in(all_19_3, empty_set) = all_50_0
% 7.80/1.88 | (35) in(all_19_3, all_19_0) = all_50_1
% 7.80/1.88 | (36) ~ (all_50_1 = 0) | all_50_0 = 0
% 7.80/1.88 |
% 7.80/1.88 | GROUND_INST: instantiating (6) with all_48_1, all_50_0, empty_set, all_19_3,
% 7.80/1.88 | simplifying with (31), (34) gives:
% 7.80/1.88 | (37) all_50_0 = all_48_1
% 7.80/1.88 |
% 7.80/1.88 | GROUND_INST: instantiating (6) with all_48_0, all_50_1, all_19_0, all_19_3,
% 7.80/1.88 | simplifying with (32), (35) gives:
% 7.80/1.88 | (38) all_50_1 = all_48_0
% 7.80/1.88 |
% 7.80/1.88 | GROUND_INST: instantiating (20) with all_19_3, all_48_0, simplifying with (8),
% 7.80/1.88 | (32) gives:
% 7.80/1.88 | (39) all_48_0 = 0
% 7.80/1.88 |
% 7.80/1.88 | GROUND_INST: instantiating (22) with all_19_3, all_48_0, simplifying with (8),
% 7.80/1.88 | (32) gives:
% 7.80/1.89 | (40) ? [v0: any] : ? [v1: any] : (in(all_19_3, all_19_1) = v1 &
% 7.80/1.89 | in(all_19_3, empty_set) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_48_0 =
% 7.80/1.89 | 0)))
% 7.80/1.89 |
% 7.80/1.89 | COMBINE_EQS: (38), (39) imply:
% 7.80/1.89 | (41) all_50_1 = 0
% 7.80/1.89 |
% 7.80/1.89 | DELTA: instantiating (40) with fresh symbols all_62_0, all_62_1 gives:
% 7.80/1.89 | (42) in(all_19_3, all_19_1) = all_62_0 & in(all_19_3, empty_set) = all_62_1
% 7.80/1.89 | & ( ~ (all_62_1 = 0) | (all_62_0 = 0 & all_48_0 = 0))
% 7.80/1.89 |
% 7.80/1.89 | ALPHA: (42) implies:
% 7.80/1.89 | (43) in(all_19_3, empty_set) = all_62_1
% 7.80/1.89 |
% 7.80/1.89 | BETA: splitting (36) gives:
% 7.80/1.89 |
% 7.80/1.89 | Case 1:
% 7.80/1.89 | |
% 7.80/1.89 | | (44) ~ (all_50_1 = 0)
% 7.80/1.89 | |
% 7.80/1.89 | | REDUCE: (41), (44) imply:
% 7.80/1.89 | | (45) $false
% 7.80/1.89 | |
% 7.80/1.89 | | CLOSE: (45) is inconsistent.
% 7.80/1.89 | |
% 7.80/1.89 | Case 2:
% 7.80/1.89 | |
% 7.80/1.89 | | (46) all_50_0 = 0
% 7.80/1.89 | |
% 7.80/1.89 | | COMBINE_EQS: (37), (46) imply:
% 7.80/1.89 | | (47) all_48_1 = 0
% 7.80/1.89 | |
% 7.80/1.89 | | REDUCE: (31), (47) imply:
% 8.18/1.89 | | (48) in(all_19_3, empty_set) = 0
% 8.18/1.89 | |
% 8.18/1.89 | | GROUND_INST: instantiating (6) with 0, all_62_1, empty_set, all_19_3,
% 8.18/1.89 | | simplifying with (43), (48) gives:
% 8.18/1.89 | | (49) all_62_1 = 0
% 8.18/1.89 | |
% 8.18/1.89 | | GROUND_INST: instantiating (1) with all_19_3, simplifying with (8), (48)
% 8.18/1.89 | | gives:
% 8.18/1.89 | | (50) $false
% 8.18/1.89 | |
% 8.18/1.89 | | CLOSE: (50) is inconsistent.
% 8.18/1.89 | |
% 8.18/1.89 | End of split
% 8.18/1.89 |
% 8.18/1.89 End of proof
% 8.18/1.89 % SZS output end Proof for theBenchmark
% 8.18/1.89
% 8.18/1.89 1297ms
%------------------------------------------------------------------------------