TSTP Solution File: SEU204+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 17:43:15 EDT 2023
% Result : Theorem 9.48s 2.27s
% Output : Proof 12.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 14:21:52 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.64 ________ _____
% 0.19/0.64 ___ __ \_________(_)________________________________
% 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.64
% 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.64 (2023-06-19)
% 0.19/0.64
% 0.19/0.64 (c) Philipp Rümmer, 2009-2023
% 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.64 Amanda Stjerna.
% 0.19/0.64 Free software under BSD-3-Clause.
% 0.19/0.64
% 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.64
% 0.19/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.66 Running up to 7 provers in parallel.
% 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.21 Prover 1: Preprocessing ...
% 3.32/1.22 Prover 4: Preprocessing ...
% 3.70/1.27 Prover 0: Preprocessing ...
% 3.70/1.27 Prover 2: Preprocessing ...
% 3.70/1.27 Prover 5: Preprocessing ...
% 3.70/1.27 Prover 6: Preprocessing ...
% 3.70/1.27 Prover 3: Preprocessing ...
% 7.22/1.84 Prover 1: Warning: ignoring some quantifiers
% 7.93/1.88 Prover 1: Constructing countermodel ...
% 7.93/1.88 Prover 4: Warning: ignoring some quantifiers
% 8.05/1.89 Prover 5: Proving ...
% 8.05/1.91 Prover 3: Warning: ignoring some quantifiers
% 8.30/1.92 Prover 6: Proving ...
% 8.30/1.93 Prover 2: Proving ...
% 8.30/1.93 Prover 3: Constructing countermodel ...
% 8.30/1.96 Prover 4: Constructing countermodel ...
% 8.90/2.02 Prover 0: Proving ...
% 9.48/2.27 Prover 3: proved (1593ms)
% 9.48/2.27
% 9.48/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.48/2.27
% 9.48/2.29 Prover 2: stopped
% 9.48/2.29 Prover 0: stopped
% 9.48/2.29 Prover 5: stopped
% 9.48/2.30 Prover 6: stopped
% 9.48/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.48/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.48/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.08/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.08/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.46/2.37 Prover 13: Preprocessing ...
% 11.46/2.37 Prover 11: Preprocessing ...
% 11.46/2.38 Prover 7: Preprocessing ...
% 11.46/2.38 Prover 1: Found proof (size 40)
% 11.46/2.38 Prover 1: proved (1714ms)
% 11.46/2.39 Prover 4: stopped
% 11.46/2.39 Prover 10: Preprocessing ...
% 11.46/2.40 Prover 8: Preprocessing ...
% 11.46/2.40 Prover 7: stopped
% 11.46/2.41 Prover 13: stopped
% 11.46/2.41 Prover 11: stopped
% 11.46/2.42 Prover 10: stopped
% 12.01/2.48 Prover 8: Warning: ignoring some quantifiers
% 12.01/2.50 Prover 8: Constructing countermodel ...
% 12.01/2.50 Prover 8: stopped
% 12.01/2.50
% 12.01/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.01/2.50
% 12.01/2.51 % SZS output start Proof for theBenchmark
% 12.01/2.51 Assumptions after simplification:
% 12.01/2.51 ---------------------------------
% 12.01/2.51
% 12.01/2.51 (d13_relat_1)
% 12.37/2.54 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i]
% 12.37/2.54 : ! [v3: $i] : (v3 = v1 | ~ (relation_image(v0, v2) = v3) | ~ $i(v2) |
% 12.37/2.54 ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 & $i(v4) & ( ~
% 12.37/2.54 (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v4) =
% 12.37/2.54 v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 =
% 12.37/2.54 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6: $i] : ? [v7: $i]
% 12.37/2.54 : (ordered_pair(v6, v4) = v7 & in(v7, v0) = 0 & in(v6, v2) = 0 &
% 12.37/2.54 $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 12.37/2.54 (relation_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( ! [v3: $i] :
% 12.37/2.54 ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5: $i]
% 12.37/2.54 : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = v6) | ~ (in(v6, v0) =
% 12.37/2.54 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v1) =
% 12.37/2.54 v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4:
% 12.37/2.54 $i] : ? [v5: $i] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 &
% 12.37/2.54 in(v4, v1) = 0 & $i(v5) & $i(v4)))))))
% 12.37/2.54
% 12.37/2.54 (d3_tarski)
% 12.37/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 12.37/2.55 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 12.37/2.55 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.37/2.55 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 12.37/2.55 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 12.37/2.55
% 12.37/2.55 (d5_relat_1)
% 12.37/2.55 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 12.37/2.55 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 12.37/2.55 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 12.37/2.55 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) =
% 12.37/2.55 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 12.37/2.55 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6)
% 12.37/2.55 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 12.37/2.55 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 12.37/2.55 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 12.37/2.55 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 12.37/2.55 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) &
% 12.37/2.55 $i(v3)))))))
% 12.37/2.55
% 12.37/2.55 (fc6_relat_1)
% 12.37/2.55 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 12.37/2.55 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 12.37/2.55 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 12.37/2.55
% 12.37/2.55 (t144_relat_1)
% 12.37/2.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 12.37/2.55 = 0) & relation_rng(v1) = v3 & subset(v2, v3) = v4 & relation_image(v1,
% 12.37/2.55 v0) = v2 & relation(v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.37/2.55
% 12.37/2.55 (function-axioms)
% 12.37/2.55 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.37/2.55 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 12.37/2.55 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.37/2.55 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 12.37/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.37/2.55 (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0:
% 12.37/2.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.37/2.55 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 12.37/2.55 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 12.37/2.55 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 12.37/2.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.37/2.55 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 12.37/2.55 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 12.37/2.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.37/2.55 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 12.37/2.55 : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) =
% 12.37/2.55 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.37/2.55 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 12.37/2.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.37/2.55 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 12.37/2.55
% 12.37/2.55 Further assumptions not needed in the proof:
% 12.37/2.55 --------------------------------------------
% 12.37/2.55 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski,
% 12.37/2.55 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski,
% 12.37/2.55 dt_k4_tarski, dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1,
% 12.37/2.55 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1,
% 12.37/2.55 fc4_relat_1, fc8_relat_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1,
% 12.37/2.55 rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski, t1_subset, t2_subset,
% 12.37/2.55 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 12.37/2.55
% 12.37/2.55 Those formulas are unsatisfiable:
% 12.37/2.55 ---------------------------------
% 12.37/2.55
% 12.37/2.55 Begin of proof
% 12.37/2.56 |
% 12.37/2.56 | ALPHA: (d3_tarski) implies:
% 12.37/2.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 12.37/2.56 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 12.37/2.56 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 12.37/2.56 |
% 12.37/2.56 | ALPHA: (function-axioms) implies:
% 12.37/2.56 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.37/2.56 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 12.37/2.56 |
% 12.37/2.56 | DELTA: instantiating (t144_relat_1) with fresh symbols all_38_0, all_38_1,
% 12.37/2.56 | all_38_2, all_38_3, all_38_4 gives:
% 12.37/2.56 | (3) ~ (all_38_0 = 0) & relation_rng(all_38_3) = all_38_1 &
% 12.37/2.56 | subset(all_38_2, all_38_1) = all_38_0 & relation_image(all_38_3,
% 12.37/2.56 | all_38_4) = all_38_2 & relation(all_38_3) = 0 & $i(all_38_1) &
% 12.37/2.56 | $i(all_38_2) & $i(all_38_3) & $i(all_38_4)
% 12.37/2.56 |
% 12.37/2.56 | ALPHA: (3) implies:
% 12.37/2.56 | (4) ~ (all_38_0 = 0)
% 12.37/2.56 | (5) $i(all_38_4)
% 12.37/2.56 | (6) $i(all_38_3)
% 12.37/2.56 | (7) $i(all_38_2)
% 12.37/2.56 | (8) $i(all_38_1)
% 12.37/2.56 | (9) relation(all_38_3) = 0
% 12.37/2.56 | (10) relation_image(all_38_3, all_38_4) = all_38_2
% 12.37/2.56 | (11) subset(all_38_2, all_38_1) = all_38_0
% 12.37/2.56 | (12) relation_rng(all_38_3) = all_38_1
% 12.37/2.56 |
% 12.37/2.56 | GROUND_INST: instantiating (d13_relat_1) with all_38_3, simplifying with (6),
% 12.37/2.56 | (9) gives:
% 12.37/2.56 | (13) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 12.37/2.56 | (relation_image(all_38_3, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.37/2.56 | [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) |
% 12.37/2.56 | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = v6) | ~
% 12.37/2.56 | (in(v6, all_38_3) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 =
% 12.37/2.56 | 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ? [v6:
% 12.37/2.56 | $i] : (ordered_pair(v5, v3) = v6 & in(v6, all_38_3) = 0 &
% 12.37/2.56 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1:
% 12.37/2.56 | $i] : ( ~ (relation_image(all_38_3, v0) = v1) | ~ $i(v1) | ~
% 12.37/2.56 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) =
% 12.37/2.56 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 12.37/2.56 | (ordered_pair(v4, v2) = v5) | ~ (in(v5, all_38_3) = 0) | ~
% 12.37/2.56 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & !
% 12.37/2.56 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 12.37/2.56 | [v4: $i] : (ordered_pair(v3, v2) = v4 & in(v4, all_38_3) = 0 &
% 12.37/2.56 | in(v3, v0) = 0 & $i(v4) & $i(v3)))))
% 12.37/2.56 |
% 12.37/2.57 | ALPHA: (13) implies:
% 12.37/2.57 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_38_3, v0) = v1) |
% 12.37/2.57 | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.37/2.57 | (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 12.37/2.57 | (ordered_pair(v4, v2) = v5) | ~ (in(v5, all_38_3) = 0) | ~
% 12.37/2.57 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & !
% 12.37/2.57 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 12.37/2.57 | [v4: $i] : (ordered_pair(v3, v2) = v4 & in(v4, all_38_3) = 0 &
% 12.37/2.57 | in(v3, v0) = 0 & $i(v4) & $i(v3)))))
% 12.37/2.57 |
% 12.37/2.57 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, all_38_0, simplifying
% 12.37/2.57 | with (7), (8), (11) gives:
% 12.37/2.57 | (15) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 12.37/2.57 | all_38_1) = v1 & in(v0, all_38_2) = 0 & $i(v0))
% 12.37/2.57 |
% 12.37/2.57 | GROUND_INST: instantiating (fc6_relat_1) with all_38_3, all_38_1, simplifying
% 12.37/2.57 | with (6), (12) gives:
% 12.37/2.57 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_38_3) = v1
% 12.37/2.57 | & empty(all_38_1) = v2 & empty(all_38_3) = v0 & ( ~ (v2 = 0) | ~
% 12.37/2.57 | (v1 = 0) | v0 = 0))
% 12.37/2.57 |
% 12.37/2.57 | GROUND_INST: instantiating (d5_relat_1) with all_38_3, all_38_1, simplifying
% 12.37/2.57 | with (6), (12) gives:
% 12.59/2.57 | (17) ? [v0: int] : ( ~ (v0 = 0) & relation(all_38_3) = v0) | ( ? [v0: any]
% 12.59/2.57 | : (v0 = all_38_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 12.59/2.57 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 12.59/2.57 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_38_3) = 0) |
% 12.59/2.57 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 12.59/2.57 | (ordered_pair(v3, v1) = v4 & in(v4, all_38_3) = 0 & $i(v4) &
% 12.59/2.57 | $i(v3))))) & ( ~ $i(all_38_1) | ( ! [v0: $i] : ! [v1: int]
% 12.59/2.57 | : (v1 = 0 | ~ (in(v0, all_38_1) = v1) | ~ $i(v0) | ! [v2: $i]
% 12.59/2.57 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 12.59/2.57 | all_38_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 12.59/2.57 | all_38_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.59/2.57 | (ordered_pair(v1, v0) = v2 & in(v2, all_38_3) = 0 & $i(v2) &
% 12.59/2.57 | $i(v1))))))
% 12.59/2.57 |
% 12.59/2.57 | GROUND_INST: instantiating (14) with all_38_4, all_38_2, simplifying with (5),
% 12.59/2.57 | (7), (10) gives:
% 12.59/2.57 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_2) = v1) | ~
% 12.59/2.57 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3)
% 12.59/2.57 | | ~ (in(v3, all_38_3) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 12.59/2.57 | 0) & in(v2, all_38_4) = v4))) & ! [v0: $i] : ( ~ (in(v0,
% 12.59/2.57 | all_38_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.59/2.57 | (ordered_pair(v1, v0) = v2 & in(v2, all_38_3) = 0 & in(v1, all_38_4)
% 12.59/2.57 | = 0 & $i(v2) & $i(v1)))
% 12.59/2.57 |
% 12.59/2.57 | ALPHA: (18) implies:
% 12.59/2.57 | (19) ! [v0: $i] : ( ~ (in(v0, all_38_2) = 0) | ~ $i(v0) | ? [v1: $i] :
% 12.59/2.57 | ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_38_3) = 0 &
% 12.59/2.57 | in(v1, all_38_4) = 0 & $i(v2) & $i(v1)))
% 12.59/2.57 |
% 12.59/2.57 | DELTA: instantiating (16) with fresh symbols all_51_0, all_51_1, all_51_2
% 12.59/2.57 | gives:
% 12.59/2.58 | (20) relation(all_38_3) = all_51_1 & empty(all_38_1) = all_51_0 &
% 12.59/2.58 | empty(all_38_3) = all_51_2 & ( ~ (all_51_0 = 0) | ~ (all_51_1 = 0) |
% 12.59/2.58 | all_51_2 = 0)
% 12.59/2.58 |
% 12.59/2.58 | ALPHA: (20) implies:
% 12.59/2.58 | (21) relation(all_38_3) = all_51_1
% 12.59/2.58 |
% 12.59/2.58 | BETA: splitting (15) gives:
% 12.59/2.58 |
% 12.59/2.58 | Case 1:
% 12.59/2.58 | |
% 12.59/2.58 | | (22) all_38_0 = 0
% 12.59/2.58 | |
% 12.59/2.58 | | REDUCE: (4), (22) imply:
% 12.59/2.58 | | (23) $false
% 12.59/2.58 | |
% 12.59/2.58 | | CLOSE: (23) is inconsistent.
% 12.59/2.58 | |
% 12.59/2.58 | Case 2:
% 12.59/2.58 | |
% 12.59/2.58 | | (24) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_38_1) = v1 &
% 12.59/2.58 | | in(v0, all_38_2) = 0 & $i(v0))
% 12.59/2.58 | |
% 12.59/2.58 | | DELTA: instantiating (24) with fresh symbols all_67_0, all_67_1 gives:
% 12.59/2.58 | | (25) ~ (all_67_0 = 0) & in(all_67_1, all_38_1) = all_67_0 & in(all_67_1,
% 12.59/2.58 | | all_38_2) = 0 & $i(all_67_1)
% 12.59/2.58 | |
% 12.59/2.58 | | ALPHA: (25) implies:
% 12.59/2.58 | | (26) ~ (all_67_0 = 0)
% 12.59/2.58 | | (27) $i(all_67_1)
% 12.59/2.58 | | (28) in(all_67_1, all_38_2) = 0
% 12.59/2.58 | | (29) in(all_67_1, all_38_1) = all_67_0
% 12.59/2.58 | |
% 12.59/2.58 | | GROUND_INST: instantiating (2) with 0, all_51_1, all_38_3, simplifying with
% 12.59/2.58 | | (9), (21) gives:
% 12.59/2.58 | | (30) all_51_1 = 0
% 12.59/2.58 | |
% 12.59/2.58 | | BETA: splitting (17) gives:
% 12.59/2.58 | |
% 12.59/2.58 | | Case 1:
% 12.59/2.58 | | |
% 12.59/2.58 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & relation(all_38_3) = v0)
% 12.59/2.58 | | |
% 12.59/2.58 | | | DELTA: instantiating (31) with fresh symbol all_76_0 gives:
% 12.59/2.58 | | | (32) ~ (all_76_0 = 0) & relation(all_38_3) = all_76_0
% 12.59/2.58 | | |
% 12.59/2.58 | | | ALPHA: (32) implies:
% 12.59/2.58 | | | (33) ~ (all_76_0 = 0)
% 12.59/2.58 | | | (34) relation(all_38_3) = all_76_0
% 12.59/2.58 | | |
% 12.59/2.58 | | | GROUND_INST: instantiating (2) with 0, all_76_0, all_38_3, simplifying
% 12.59/2.58 | | | with (9), (34) gives:
% 12.59/2.58 | | | (35) all_76_0 = 0
% 12.59/2.58 | | |
% 12.59/2.58 | | | REDUCE: (33), (35) imply:
% 12.59/2.58 | | | (36) $false
% 12.59/2.58 | | |
% 12.59/2.58 | | | CLOSE: (36) is inconsistent.
% 12.59/2.58 | | |
% 12.59/2.58 | | Case 2:
% 12.59/2.58 | | |
% 12.59/2.58 | | | (37) ? [v0: any] : (v0 = all_38_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 12.59/2.58 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 12.59/2.58 | | | : ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4,
% 12.59/2.58 | | | all_38_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 12.59/2.58 | | | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_38_3)
% 12.59/2.58 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_38_1) | ( ! [v0:
% 12.59/2.58 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_1) = v1) |
% 12.59/2.58 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2,
% 12.59/2.58 | | | v0) = v3) | ~ (in(v3, all_38_3) = 0) | ~ $i(v2))) &
% 12.59/2.58 | | | ! [v0: $i] : ( ~ (in(v0, all_38_1) = 0) | ~ $i(v0) | ? [v1:
% 12.59/2.58 | | | $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2,
% 12.59/2.58 | | | all_38_3) = 0 & $i(v2) & $i(v1)))))
% 12.59/2.58 | | |
% 12.59/2.58 | | | ALPHA: (37) implies:
% 12.59/2.58 | | | (38) ~ $i(all_38_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 12.59/2.58 | | | (in(v0, all_38_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 12.59/2.58 | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_38_3)
% 12.59/2.59 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_38_1) =
% 12.59/2.59 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.59/2.59 | | | (ordered_pair(v1, v0) = v2 & in(v2, all_38_3) = 0 & $i(v2) &
% 12.59/2.59 | | | $i(v1))))
% 12.59/2.59 | | |
% 12.59/2.59 | | | BETA: splitting (38) gives:
% 12.59/2.59 | | |
% 12.59/2.59 | | | Case 1:
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | (39) ~ $i(all_38_1)
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | PRED_UNIFY: (8), (39) imply:
% 12.59/2.59 | | | | (40) $false
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | CLOSE: (40) is inconsistent.
% 12.59/2.59 | | | |
% 12.59/2.59 | | | Case 2:
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | (41) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_1) =
% 12.59/2.59 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 12.59/2.59 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_38_3) = 0) | ~
% 12.59/2.59 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_38_1) = 0) | ~
% 12.59/2.59 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) =
% 12.59/2.59 | | | | v2 & in(v2, all_38_3) = 0 & $i(v2) & $i(v1)))
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | ALPHA: (41) implies:
% 12.59/2.59 | | | | (42) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_1) =
% 12.59/2.59 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 12.59/2.59 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_38_3) = 0) | ~
% 12.59/2.59 | | | | $i(v2)))
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | GROUND_INST: instantiating (19) with all_67_1, simplifying with (27),
% 12.59/2.59 | | | | (28) gives:
% 12.59/2.59 | | | | (43) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_67_1) = v1 &
% 12.59/2.59 | | | | in(v1, all_38_3) = 0 & in(v0, all_38_4) = 0 & $i(v1) & $i(v0))
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | GROUND_INST: instantiating (42) with all_67_1, all_67_0, simplifying
% 12.59/2.59 | | | | with (27), (29) gives:
% 12.59/2.59 | | | | (44) all_67_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 12.59/2.59 | | | | all_67_1) = v1) | ~ (in(v1, all_38_3) = 0) | ~ $i(v0))
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | DELTA: instantiating (43) with fresh symbols all_90_0, all_90_1 gives:
% 12.59/2.59 | | | | (45) ordered_pair(all_90_1, all_67_1) = all_90_0 & in(all_90_0,
% 12.59/2.59 | | | | all_38_3) = 0 & in(all_90_1, all_38_4) = 0 & $i(all_90_0) &
% 12.59/2.59 | | | | $i(all_90_1)
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | ALPHA: (45) implies:
% 12.59/2.59 | | | | (46) $i(all_90_1)
% 12.59/2.59 | | | | (47) in(all_90_0, all_38_3) = 0
% 12.59/2.59 | | | | (48) ordered_pair(all_90_1, all_67_1) = all_90_0
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | BETA: splitting (44) gives:
% 12.59/2.59 | | | |
% 12.59/2.59 | | | | Case 1:
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | | (49) all_67_0 = 0
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | | REDUCE: (26), (49) imply:
% 12.59/2.59 | | | | | (50) $false
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | | CLOSE: (50) is inconsistent.
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | Case 2:
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, all_67_1) =
% 12.59/2.59 | | | | | v1) | ~ (in(v1, all_38_3) = 0) | ~ $i(v0))
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | | GROUND_INST: instantiating (51) with all_90_1, all_90_0, simplifying
% 12.59/2.59 | | | | | with (46), (47), (48) gives:
% 12.59/2.59 | | | | | (52) $false
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | | CLOSE: (52) is inconsistent.
% 12.59/2.59 | | | | |
% 12.59/2.59 | | | | End of split
% 12.59/2.59 | | | |
% 12.59/2.59 | | | End of split
% 12.59/2.59 | | |
% 12.59/2.59 | | End of split
% 12.59/2.59 | |
% 12.59/2.59 | End of split
% 12.59/2.59 |
% 12.59/2.59 End of proof
% 12.59/2.59 % SZS output end Proof for theBenchmark
% 12.59/2.59
% 12.59/2.59 1948ms
%------------------------------------------------------------------------------