TSTP Solution File: SET995+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET995+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 : n001.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 15:27:19 EDT 2023
% Result : Theorem 15.40s 2.81s
% Output : Proof 15.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET995+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 : n001.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 09:06:00 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/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.20/1.04 Prover 4: Preprocessing ...
% 2.20/1.04 Prover 1: Preprocessing ...
% 2.81/1.08 Prover 3: Preprocessing ...
% 2.81/1.08 Prover 5: Preprocessing ...
% 2.81/1.08 Prover 2: Preprocessing ...
% 2.81/1.08 Prover 6: Preprocessing ...
% 2.81/1.08 Prover 0: Preprocessing ...
% 5.26/1.52 Prover 1: Warning: ignoring some quantifiers
% 5.26/1.55 Prover 1: Constructing countermodel ...
% 5.26/1.57 Prover 5: Proving ...
% 5.26/1.58 Prover 3: Warning: ignoring some quantifiers
% 5.26/1.59 Prover 3: Constructing countermodel ...
% 6.09/1.60 Prover 6: Proving ...
% 6.68/1.62 Prover 2: Proving ...
% 7.12/1.71 Prover 4: Warning: ignoring some quantifiers
% 7.94/1.80 Prover 4: Constructing countermodel ...
% 8.34/1.90 Prover 0: Proving ...
% 10.20/2.23 Prover 3: gave up
% 10.20/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.20/2.27 Prover 7: Preprocessing ...
% 12.24/2.39 Prover 7: Warning: ignoring some quantifiers
% 12.24/2.41 Prover 7: Constructing countermodel ...
% 15.40/2.80 Prover 7: Found proof (size 33)
% 15.40/2.80 Prover 7: proved (571ms)
% 15.40/2.80 Prover 1: stopped
% 15.40/2.80 Prover 0: stopped
% 15.40/2.80 Prover 2: stopped
% 15.40/2.80 Prover 4: stopped
% 15.40/2.80 Prover 6: stopped
% 15.40/2.81 Prover 5: stopped
% 15.40/2.81
% 15.40/2.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.40/2.81
% 15.40/2.81 % SZS output start Proof for theBenchmark
% 15.40/2.81 Assumptions after simplification:
% 15.40/2.81 ---------------------------------
% 15.40/2.82
% 15.40/2.82 (d1_tarski)
% 15.40/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 15.40/2.84 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 15.40/2.84 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 15.40/2.84 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 15.40/2.84 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 15.40/2.84 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 15.40/2.84
% 15.40/2.84 (d5_funct_1)
% 15.40/2.85 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 15.40/2.85 relation(v0) | ~ function(v0) | ? [v2: $i] : (relation_dom(v0) = v2 &
% 15.40/2.85 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3) | ~ $i(v4)
% 15.40/2.85 | ~ $i(v3) | ~ $i(v1) | ~ in(v4, v2) | in(v3, v1)) & ! [v3: $i] : (
% 15.40/2.85 ~ $i(v3) | ~ $i(v1) | ~ in(v3, v1) | ? [v4: $i] : (apply(v0, v4) = v3
% 15.40/2.85 & $i(v4) & in(v4, v2))) & ? [v3: $i] : (v3 = v1 | ~ $i(v3) | ? [v4:
% 15.40/2.85 $i] : ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) |
% 15.40/2.85 ! [v7: $i] : ( ~ (apply(v0, v7) = v4) | ~ $i(v7) | ~ in(v7, v2)))
% 15.40/2.85 & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) & !
% 15.40/2.85 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 15.40/2.85 relation(v0) | ~ function(v0) | ? [v2: $i] : (relation_rng(v0) = v2 &
% 15.40/2.85 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3) | ~ $i(v4)
% 15.40/2.85 | ~ $i(v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3: $i] : ( ~ $i(v3) |
% 15.40/2.85 ~ in(v3, v2) | ? [v4: $i] : (apply(v0, v4) = v3 & $i(v4) & in(v4, v1)))
% 15.40/2.85 & ? [v3: $i] : (v3 = v2 | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 15.40/2.85 $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) | ! [v7: $i] : ( ~ (apply(v0,
% 15.40/2.85 v7) = v4) | ~ $i(v7) | ~ in(v7, v1))) & (in(v4, v3) | (v6 =
% 15.40/2.85 v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 15.40/2.85
% 15.40/2.85 (t17_funct_1)
% 15.40/2.86 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 15.40/2.86 = v1) & relation_rng(v4) = v3 & relation_rng(v1) = v3 & relation_dom(v4) =
% 15.40/2.86 v2 & relation_dom(v1) = v2 & singleton(v0) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 15.40/2.86 $i(v1) & $i(v0) & relation(v4) & relation(v1) & function(v4) & function(v1))
% 15.40/2.86
% 15.40/2.86 (t9_funct_1)
% 15.40/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (relation_dom(v2) =
% 15.40/2.86 v1) | ~ (relation_dom(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ relation(v2)
% 15.40/2.86 | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3: $i] : ?
% 15.40/2.86 [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3)
% 15.40/2.86 = v4 & $i(v5) & $i(v4) & $i(v3) & in(v3, v1)))
% 15.40/2.86
% 15.40/2.86 (function-axioms)
% 15.40/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.40/2.86 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 15.40/2.86 : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) &
% 15.40/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1)
% 15.40/2.86 | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.40/2.86 (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 15.40/2.86 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 15.40/2.86 (singleton(v2) = v0))
% 15.40/2.86
% 15.40/2.86 Further assumptions not needed in the proof:
% 15.40/2.86 --------------------------------------------
% 15.40/2.86 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1,
% 15.40/2.86 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc2_subset_1, fc4_relat_1,
% 15.40/2.86 fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1,
% 15.40/2.86 rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0,
% 15.40/2.86 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset,
% 15.40/2.86 t5_subset, t6_boole, t7_boole, t8_boole
% 15.40/2.86
% 15.40/2.86 Those formulas are unsatisfiable:
% 15.40/2.86 ---------------------------------
% 15.40/2.86
% 15.40/2.86 Begin of proof
% 15.40/2.86 |
% 15.40/2.86 | ALPHA: (d1_tarski) implies:
% 15.40/2.86 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 15.40/2.86 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 15.40/2.86 |
% 15.40/2.86 | ALPHA: (d5_funct_1) implies:
% 15.40/2.86 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 15.40/2.86 | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : (relation_rng(v0) =
% 15.40/2.86 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3)
% 15.40/2.86 | | ~ $i(v4) | ~ $i(v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3:
% 15.40/2.87 | $i] : ( ~ $i(v3) | ~ in(v3, v2) | ? [v4: $i] : (apply(v0, v4) =
% 15.40/2.87 | v3 & $i(v4) & in(v4, v1))) & ? [v3: $i] : (v3 = v2 | ~ $i(v3)
% 15.40/2.87 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v4) & (
% 15.40/2.87 | ~ in(v4, v3) | ! [v7: $i] : ( ~ (apply(v0, v7) = v4) | ~
% 15.40/2.87 | $i(v7) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 &
% 15.40/2.87 | apply(v0, v5) = v4 & in(v5, v1)))))))
% 15.40/2.87 |
% 15.40/2.87 | ALPHA: (function-axioms) implies:
% 15.40/2.87 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.40/2.87 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 15.40/2.87 |
% 15.40/2.87 | DELTA: instantiating (t17_funct_1) with fresh symbols all_42_0, all_42_1,
% 15.40/2.87 | all_42_2, all_42_3, all_42_4 gives:
% 15.40/2.87 | (4) ~ (all_42_0 = all_42_3) & relation_rng(all_42_0) = all_42_1 &
% 15.40/2.87 | relation_rng(all_42_3) = all_42_1 & relation_dom(all_42_0) = all_42_2 &
% 15.40/2.87 | relation_dom(all_42_3) = all_42_2 & singleton(all_42_4) = all_42_1 &
% 15.40/2.87 | $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & $i(all_42_3) &
% 15.40/2.87 | $i(all_42_4) & relation(all_42_0) & relation(all_42_3) &
% 15.40/2.87 | function(all_42_0) & function(all_42_3)
% 15.40/2.87 |
% 15.40/2.87 | ALPHA: (4) implies:
% 15.40/2.87 | (5) ~ (all_42_0 = all_42_3)
% 15.40/2.87 | (6) function(all_42_3)
% 15.40/2.87 | (7) function(all_42_0)
% 15.40/2.87 | (8) relation(all_42_3)
% 15.40/2.87 | (9) relation(all_42_0)
% 15.40/2.87 | (10) $i(all_42_4)
% 15.40/2.87 | (11) $i(all_42_3)
% 15.40/2.87 | (12) $i(all_42_0)
% 15.40/2.87 | (13) singleton(all_42_4) = all_42_1
% 15.40/2.87 | (14) relation_dom(all_42_3) = all_42_2
% 15.40/2.87 | (15) relation_dom(all_42_0) = all_42_2
% 15.40/2.87 | (16) relation_rng(all_42_3) = all_42_1
% 15.40/2.87 | (17) relation_rng(all_42_0) = all_42_1
% 15.40/2.87 |
% 15.40/2.87 | GROUND_INST: instantiating (2) with all_42_3, all_42_2, simplifying with (6),
% 15.40/2.87 | (8), (11), (14) gives:
% 15.40/2.87 | (18) ? [v0: $i] : (relation_rng(all_42_3) = v0 & $i(v0) & ! [v1: $i] : !
% 15.40/2.87 | [v2: $i] : ( ~ (apply(all_42_3, v2) = v1) | ~ $i(v2) | ~ $i(v1) |
% 15.40/2.87 | ~ in(v2, all_42_2) | in(v1, v0)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 15.40/2.87 | in(v1, v0) | ? [v2: $i] : (apply(all_42_3, v2) = v1 & $i(v2) &
% 15.40/2.87 | in(v2, all_42_2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ?
% 15.40/2.87 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v3) & $i(v2) & ( ~
% 15.40/2.87 | in(v2, v1) | ! [v5: $i] : ( ~ (apply(all_42_3, v5) = v2) | ~
% 15.40/2.87 | $i(v5) | ~ in(v5, all_42_2))) & (in(v2, v1) | (v4 = v2 &
% 15.40/2.87 | apply(all_42_3, v3) = v2 & in(v3, all_42_2))))))
% 15.40/2.87 |
% 15.40/2.87 | GROUND_INST: instantiating (t9_funct_1) with all_42_3, all_42_2, all_42_0,
% 15.40/2.87 | simplifying with (6), (7), (8), (9), (11), (12), (14), (15)
% 15.40/2.87 | gives:
% 15.40/2.87 | (19) all_42_0 = all_42_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~
% 15.40/2.87 | (v2 = v1) & apply(all_42_0, v0) = v2 & apply(all_42_3, v0) = v1 &
% 15.40/2.87 | $i(v2) & $i(v1) & $i(v0) & in(v0, all_42_2))
% 15.40/2.87 |
% 15.40/2.87 | GROUND_INST: instantiating (t9_funct_1) with all_42_0, all_42_2, all_42_3,
% 15.40/2.87 | simplifying with (6), (7), (8), (9), (11), (12), (14), (15)
% 15.40/2.87 | gives:
% 15.40/2.88 | (20) all_42_0 = all_42_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~
% 15.40/2.88 | (v2 = v1) & apply(all_42_0, v0) = v1 & apply(all_42_3, v0) = v2 &
% 15.40/2.88 | $i(v2) & $i(v1) & $i(v0) & in(v0, all_42_2))
% 15.40/2.88 |
% 15.40/2.88 | GROUND_INST: instantiating (2) with all_42_0, all_42_2, simplifying with (7),
% 15.40/2.88 | (9), (12), (15) gives:
% 15.40/2.88 | (21) ? [v0: $i] : (relation_rng(all_42_0) = v0 & $i(v0) & ! [v1: $i] : !
% 15.40/2.88 | [v2: $i] : ( ~ (apply(all_42_0, v2) = v1) | ~ $i(v2) | ~ $i(v1) |
% 15.40/2.88 | ~ in(v2, all_42_2) | in(v1, v0)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 15.40/2.88 | in(v1, v0) | ? [v2: $i] : (apply(all_42_0, v2) = v1 & $i(v2) &
% 15.40/2.88 | in(v2, all_42_2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ?
% 15.40/2.88 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v3) & $i(v2) & ( ~
% 15.40/2.88 | in(v2, v1) | ! [v5: $i] : ( ~ (apply(all_42_0, v5) = v2) | ~
% 15.40/2.88 | $i(v5) | ~ in(v5, all_42_2))) & (in(v2, v1) | (v4 = v2 &
% 15.40/2.88 | apply(all_42_0, v3) = v2 & in(v3, all_42_2))))))
% 15.40/2.88 |
% 15.40/2.88 | DELTA: instantiating (21) with fresh symbol all_54_0 gives:
% 15.40/2.88 | (22) relation_rng(all_42_0) = all_54_0 & $i(all_54_0) & ! [v0: $i] : !
% 15.40/2.88 | [v1: $i] : ( ~ (apply(all_42_0, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 15.40/2.88 | in(v1, all_42_2) | in(v0, all_54_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.40/2.88 | in(v0, all_54_0) | ? [v1: $i] : (apply(all_42_0, v1) = v0 & $i(v1)
% 15.40/2.88 | & in(v1, all_42_2))) & ? [v0: any] : (v0 = all_54_0 | ~ $i(v0) |
% 15.40/2.88 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v2) & $i(v1) & ( ~
% 15.40/2.88 | in(v1, v0) | ! [v4: $i] : ( ~ (apply(all_42_0, v4) = v1) | ~
% 15.40/2.88 | $i(v4) | ~ in(v4, all_42_2))) & (in(v1, v0) | (v3 = v1 &
% 15.40/2.88 | apply(all_42_0, v2) = v1 & in(v2, all_42_2)))))
% 15.40/2.88 |
% 15.40/2.88 | ALPHA: (22) implies:
% 15.40/2.88 | (23) $i(all_54_0)
% 15.40/2.88 | (24) relation_rng(all_42_0) = all_54_0
% 15.40/2.88 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_0, v1) = v0) | ~ $i(v1)
% 15.40/2.88 | | ~ $i(v0) | ~ in(v1, all_42_2) | in(v0, all_54_0))
% 15.40/2.88 |
% 15.40/2.88 | DELTA: instantiating (18) with fresh symbol all_58_0 gives:
% 15.40/2.88 | (26) relation_rng(all_42_3) = all_58_0 & $i(all_58_0) & ! [v0: $i] : !
% 15.40/2.88 | [v1: $i] : ( ~ (apply(all_42_3, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 15.40/2.88 | in(v1, all_42_2) | in(v0, all_58_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.40/2.88 | in(v0, all_58_0) | ? [v1: $i] : (apply(all_42_3, v1) = v0 & $i(v1)
% 15.40/2.88 | & in(v1, all_42_2))) & ? [v0: any] : (v0 = all_58_0 | ~ $i(v0) |
% 15.40/2.88 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v2) & $i(v1) & ( ~
% 15.40/2.88 | in(v1, v0) | ! [v4: $i] : ( ~ (apply(all_42_3, v4) = v1) | ~
% 15.40/2.88 | $i(v4) | ~ in(v4, all_42_2))) & (in(v1, v0) | (v3 = v1 &
% 15.40/2.88 | apply(all_42_3, v2) = v1 & in(v2, all_42_2)))))
% 15.40/2.88 |
% 15.40/2.88 | ALPHA: (26) implies:
% 15.40/2.88 | (27) relation_rng(all_42_3) = all_58_0
% 15.40/2.88 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_3, v1) = v0) | ~ $i(v1)
% 15.40/2.88 | | ~ $i(v0) | ~ in(v1, all_42_2) | in(v0, all_58_0))
% 15.40/2.88 |
% 15.40/2.88 | BETA: splitting (20) gives:
% 15.40/2.88 |
% 15.40/2.88 | Case 1:
% 15.40/2.88 | |
% 15.40/2.89 | | (29) all_42_0 = all_42_3
% 15.40/2.89 | |
% 15.40/2.89 | | REDUCE: (5), (29) imply:
% 15.40/2.89 | | (30) $false
% 15.40/2.89 | |
% 15.40/2.89 | | CLOSE: (30) is inconsistent.
% 15.40/2.89 | |
% 15.40/2.89 | Case 2:
% 15.40/2.89 | |
% 15.40/2.89 | | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 15.40/2.89 | | apply(all_42_0, v0) = v1 & apply(all_42_3, v0) = v2 & $i(v2) &
% 15.40/2.89 | | $i(v1) & $i(v0) & in(v0, all_42_2))
% 15.40/2.89 | |
% 15.40/2.89 | | DELTA: instantiating (31) with fresh symbols all_74_0, all_74_1, all_74_2
% 15.40/2.89 | | gives:
% 15.40/2.89 | | (32) ~ (all_74_0 = all_74_1) & apply(all_42_0, all_74_2) = all_74_1 &
% 15.40/2.89 | | apply(all_42_3, all_74_2) = all_74_0 & $i(all_74_0) & $i(all_74_1) &
% 15.40/2.89 | | $i(all_74_2) & in(all_74_2, all_42_2)
% 15.40/2.89 | |
% 15.40/2.89 | | ALPHA: (32) implies:
% 15.40/2.89 | | (33) ~ (all_74_0 = all_74_1)
% 15.40/2.89 | | (34) in(all_74_2, all_42_2)
% 15.40/2.89 | | (35) $i(all_74_2)
% 15.40/2.89 | | (36) $i(all_74_1)
% 15.40/2.89 | | (37) $i(all_74_0)
% 15.40/2.89 | | (38) apply(all_42_3, all_74_2) = all_74_0
% 15.40/2.89 | | (39) apply(all_42_0, all_74_2) = all_74_1
% 15.40/2.89 | |
% 15.40/2.89 | | BETA: splitting (19) gives:
% 15.40/2.89 | |
% 15.40/2.89 | | Case 1:
% 15.40/2.89 | | |
% 15.40/2.89 | | | (40) all_42_0 = all_42_3
% 15.40/2.89 | | |
% 15.40/2.89 | | | REDUCE: (5), (40) imply:
% 15.40/2.89 | | | (41) $false
% 15.40/2.89 | | |
% 15.40/2.89 | | | CLOSE: (41) is inconsistent.
% 15.40/2.89 | | |
% 15.40/2.89 | | Case 2:
% 15.40/2.89 | | |
% 15.40/2.89 | | |
% 15.40/2.89 | | | GROUND_INST: instantiating (3) with all_42_1, all_58_0, all_42_3,
% 15.40/2.89 | | | simplifying with (16), (27) gives:
% 15.40/2.89 | | | (42) all_58_0 = all_42_1
% 15.40/2.89 | | |
% 15.40/2.89 | | | GROUND_INST: instantiating (3) with all_42_1, all_54_0, all_42_0,
% 15.40/2.89 | | | simplifying with (17), (24) gives:
% 15.40/2.89 | | | (43) all_54_0 = all_42_1
% 15.40/2.89 | | |
% 15.40/2.89 | | | REDUCE: (23), (43) imply:
% 15.40/2.89 | | | (44) $i(all_42_1)
% 15.40/2.89 | | |
% 15.40/2.89 | | | GROUND_INST: instantiating (28) with all_74_0, all_74_2, simplifying with
% 15.40/2.89 | | | (34), (35), (37), (38) gives:
% 15.40/2.89 | | | (45) in(all_74_0, all_58_0)
% 15.40/2.89 | | |
% 15.40/2.89 | | | GROUND_INST: instantiating (25) with all_74_1, all_74_2, simplifying with
% 15.40/2.89 | | | (34), (35), (36), (39) gives:
% 15.40/2.89 | | | (46) in(all_74_1, all_54_0)
% 15.40/2.89 | | |
% 15.40/2.89 | | | REDUCE: (42), (45) imply:
% 15.40/2.89 | | | (47) in(all_74_0, all_42_1)
% 15.40/2.89 | | |
% 15.40/2.89 | | | REDUCE: (43), (46) imply:
% 15.40/2.89 | | | (48) in(all_74_1, all_42_1)
% 15.40/2.89 | | |
% 15.40/2.89 | | | GROUND_INST: instantiating (1) with all_42_4, all_42_1, all_74_1,
% 15.40/2.89 | | | simplifying with (10), (13), (36), (44), (48) gives:
% 15.40/2.89 | | | (49) all_74_1 = all_42_4
% 15.40/2.89 | | |
% 15.40/2.89 | | | GROUND_INST: instantiating (1) with all_42_4, all_42_1, all_74_0,
% 15.40/2.89 | | | simplifying with (10), (13), (37), (44), (47) gives:
% 15.40/2.89 | | | (50) all_74_0 = all_42_4
% 15.40/2.89 | | |
% 15.40/2.89 | | | REDUCE: (33), (49), (50) imply:
% 15.40/2.89 | | | (51) $false
% 15.40/2.89 | | |
% 15.40/2.89 | | | CLOSE: (51) is inconsistent.
% 15.40/2.89 | | |
% 15.40/2.89 | | End of split
% 15.40/2.89 | |
% 15.40/2.89 | End of split
% 15.40/2.89 |
% 15.40/2.89 End of proof
% 15.40/2.89 % SZS output end Proof for theBenchmark
% 15.40/2.89
% 15.40/2.89 2304ms
%------------------------------------------------------------------------------