TSTP Solution File: SEU047+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU047+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 : n005.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 17:42:23 EDT 2023
% Result : Theorem 7.45s 1.75s
% Output : Proof 9.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU047+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 : n005.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 : Wed Aug 23 21:40:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.80/1.09 Prover 1: Preprocessing ...
% 2.80/1.09 Prover 4: Preprocessing ...
% 2.80/1.13 Prover 5: Preprocessing ...
% 2.80/1.13 Prover 0: Preprocessing ...
% 2.80/1.14 Prover 3: Preprocessing ...
% 2.80/1.14 Prover 2: Preprocessing ...
% 2.80/1.14 Prover 6: Preprocessing ...
% 4.68/1.42 Prover 1: Warning: ignoring some quantifiers
% 4.68/1.49 Prover 1: Constructing countermodel ...
% 5.30/1.49 Prover 4: Warning: ignoring some quantifiers
% 5.30/1.49 Prover 5: Proving ...
% 5.30/1.49 Prover 2: Proving ...
% 5.30/1.51 Prover 3: Warning: ignoring some quantifiers
% 5.30/1.52 Prover 6: Proving ...
% 5.30/1.52 Prover 3: Constructing countermodel ...
% 5.30/1.53 Prover 4: Constructing countermodel ...
% 6.46/1.61 Prover 0: Proving ...
% 7.45/1.74 Prover 3: proved (1105ms)
% 7.45/1.74
% 7.45/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.45/1.75
% 7.45/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.45/1.76 Prover 6: stopped
% 7.45/1.76 Prover 5: stopped
% 7.45/1.77 Prover 0: stopped
% 7.45/1.77 Prover 2: stopped
% 7.45/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.45/1.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.45/1.79 Prover 7: Preprocessing ...
% 7.45/1.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.86/1.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.86/1.80 Prover 8: Preprocessing ...
% 7.86/1.83 Prover 7: Warning: ignoring some quantifiers
% 7.86/1.83 Prover 11: Preprocessing ...
% 7.86/1.84 Prover 7: Constructing countermodel ...
% 7.86/1.84 Prover 13: Preprocessing ...
% 7.86/1.85 Prover 10: Preprocessing ...
% 8.39/1.89 Prover 8: Warning: ignoring some quantifiers
% 8.39/1.90 Prover 10: Warning: ignoring some quantifiers
% 8.39/1.90 Prover 8: Constructing countermodel ...
% 8.73/1.91 Prover 10: Constructing countermodel ...
% 8.98/1.94 Prover 13: Warning: ignoring some quantifiers
% 8.98/1.95 Prover 13: Constructing countermodel ...
% 8.98/2.00 Prover 11: Warning: ignoring some quantifiers
% 8.98/2.01 Prover 11: Constructing countermodel ...
% 8.98/2.04 Prover 1: Found proof (size 68)
% 8.98/2.04 Prover 1: proved (1406ms)
% 8.98/2.04 Prover 7: stopped
% 8.98/2.04 Prover 8: stopped
% 8.98/2.04 Prover 4: stopped
% 8.98/2.04 Prover 13: stopped
% 8.98/2.04 Prover 10: Found proof (size 15)
% 8.98/2.04 Prover 10: proved (258ms)
% 8.98/2.04 Prover 11: stopped
% 8.98/2.04
% 8.98/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.98/2.04
% 8.98/2.06 % SZS output start Proof for theBenchmark
% 8.98/2.06 Assumptions after simplification:
% 8.98/2.06 ---------------------------------
% 8.98/2.06
% 8.98/2.06 (dt_k8_relat_1)
% 8.98/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 8.98/2.09 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.98/2.09 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 8.98/2.09
% 8.98/2.09 (fc5_funct_1)
% 8.98/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 8.98/2.09 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 8.98/2.09 [v5: any] : ? [v6: any] : (function(v2) = v6 & function(v1) = v4 &
% 8.98/2.09 relation(v2) = v5 & relation(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 =
% 8.98/2.09 0 & v5 = 0))))
% 8.98/2.09
% 8.98/2.09 (t129_relat_1)
% 8.98/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 8.98/2.10 | ~ (relation_rng_restriction(v1, v3) = v4) | ~
% 8.98/2.10 (relation_rng_restriction(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.98/2.10 | ? [v5: any] : ? [v6: any] : (subset(v0, v1) = v6 & relation(v2) = v5 & (
% 8.98/2.10 ~ (v6 = 0) | ~ (v5 = 0))))
% 8.98/2.10
% 8.98/2.10 (t130_relat_1)
% 8.98/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 8.98/2.10 (relation_rng_restriction(v1, v2) = v3) | ~ (relation_rng_restriction(v0,
% 8.98/2.10 v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 8.98/2.10 any] : ? [v7: $i] : (relation_rng_restriction(v0, v2) = v7 & subset(v0,
% 8.98/2.10 v1) = v6 & relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v7
% 8.98/2.10 = v4)))
% 8.98/2.10
% 8.98/2.10 (t97_funct_1)
% 8.98/2.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.98/2.10 $i] : ? [v6: $i] : (relation_rng_restriction(v1, v3) = v4 &
% 8.98/2.10 relation_rng_restriction(v1, v2) = v5 & relation_rng_restriction(v0, v5) =
% 8.98/2.10 v6 & relation_rng_restriction(v0, v2) = v3 & subset(v0, v1) = 0 &
% 8.98/2.10 function(v2) = 0 & relation(v2) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 8.98/2.10 $i(v2) & $i(v1) & $i(v0) & ( ~ (v6 = v3) | ~ (v4 = v3)))
% 8.98/2.10
% 8.98/2.10 (function-axioms)
% 8.98/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.98/2.11 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 8.98/2.11 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.98/2.11 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 8.98/2.11 (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.98/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 8.98/2.11 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.98/2.11 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 8.98/2.11 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.98/2.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 8.98/2.11 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.98/2.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 8.98/2.11 (function(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 8.98/2.11 ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: MultipleValueBool]
% 8.98/2.11 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 8.98/2.11 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 8.98/2.11 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 8.98/2.11 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0:
% 8.98/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.98/2.11 ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.98/2.11
% 8.98/2.11 Further assumptions not needed in the proof:
% 8.98/2.11 --------------------------------------------
% 8.98/2.11 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 8.98/2.11 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 8.98/2.11 rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1,
% 8.98/2.11 rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski,
% 8.98/2.11 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 8.98/2.11 t8_boole
% 8.98/2.11
% 8.98/2.11 Those formulas are unsatisfiable:
% 8.98/2.11 ---------------------------------
% 8.98/2.11
% 8.98/2.11 Begin of proof
% 8.98/2.11 |
% 8.98/2.11 | ALPHA: (function-axioms) implies:
% 8.98/2.11 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.98/2.11 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.98/2.11 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.98/2.11 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 8.98/2.12 | = v0))
% 8.98/2.12 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.98/2.12 | (relation_rng_restriction(v3, v2) = v1) | ~
% 8.98/2.12 | (relation_rng_restriction(v3, v2) = v0))
% 8.98/2.12 |
% 8.98/2.12 | DELTA: instantiating (t97_funct_1) with fresh symbols all_42_0, all_42_1,
% 8.98/2.12 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6 gives:
% 8.98/2.12 | (4) relation_rng_restriction(all_42_5, all_42_3) = all_42_2 &
% 8.98/2.12 | relation_rng_restriction(all_42_5, all_42_4) = all_42_1 &
% 8.98/2.12 | relation_rng_restriction(all_42_6, all_42_1) = all_42_0 &
% 8.98/2.12 | relation_rng_restriction(all_42_6, all_42_4) = all_42_3 &
% 8.98/2.12 | subset(all_42_6, all_42_5) = 0 & function(all_42_4) = 0 &
% 8.98/2.12 | relation(all_42_4) = 0 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) &
% 8.98/2.12 | $i(all_42_3) & $i(all_42_4) & $i(all_42_5) & $i(all_42_6) & ( ~
% 8.98/2.12 | (all_42_0 = all_42_3) | ~ (all_42_2 = all_42_3))
% 8.98/2.12 |
% 8.98/2.12 | ALPHA: (4) implies:
% 8.98/2.12 | (5) $i(all_42_6)
% 8.98/2.12 | (6) $i(all_42_5)
% 8.98/2.12 | (7) $i(all_42_4)
% 8.98/2.12 | (8) relation(all_42_4) = 0
% 8.98/2.12 | (9) subset(all_42_6, all_42_5) = 0
% 8.98/2.12 | (10) relation_rng_restriction(all_42_6, all_42_4) = all_42_3
% 8.98/2.12 | (11) relation_rng_restriction(all_42_6, all_42_1) = all_42_0
% 8.98/2.12 | (12) relation_rng_restriction(all_42_5, all_42_4) = all_42_1
% 8.98/2.12 | (13) relation_rng_restriction(all_42_5, all_42_3) = all_42_2
% 8.98/2.12 | (14) ~ (all_42_0 = all_42_3) | ~ (all_42_2 = all_42_3)
% 8.98/2.12 |
% 8.98/2.12 | GROUND_INST: instantiating (fc5_funct_1) with all_42_6, all_42_4, all_42_3,
% 8.98/2.12 | simplifying with (5), (7), (10) gives:
% 8.98/2.12 | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 8.98/2.12 | (function(all_42_3) = v3 & function(all_42_4) = v1 &
% 8.98/2.12 | relation(all_42_3) = v2 & relation(all_42_4) = v0 & ( ~ (v1 = 0) |
% 8.98/2.12 | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 8.98/2.12 |
% 8.98/2.12 | GROUND_INST: instantiating (dt_k8_relat_1) with all_42_6, all_42_4, all_42_3,
% 8.98/2.12 | simplifying with (5), (7), (10) gives:
% 8.98/2.12 | (16) ? [v0: any] : ? [v1: any] : (relation(all_42_3) = v1 &
% 8.98/2.12 | relation(all_42_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 8.98/2.12 |
% 8.98/2.12 | GROUND_INST: instantiating (t130_relat_1) with all_42_6, all_42_5, all_42_4,
% 8.98/2.12 | all_42_1, all_42_0, simplifying with (5), (6), (7), (11), (12)
% 8.98/2.12 | gives:
% 8.98/2.13 | (17) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 8.98/2.13 | (relation_rng_restriction(all_42_6, all_42_4) = v2 & subset(all_42_6,
% 8.98/2.13 | all_42_5) = v1 & relation(all_42_4) = v0 & $i(v2) & ( ~ (v1 = 0) |
% 8.98/2.13 | ~ (v0 = 0) | v2 = all_42_0))
% 8.98/2.13 |
% 8.98/2.13 | GROUND_INST: instantiating (fc5_funct_1) with all_42_5, all_42_4, all_42_1,
% 8.98/2.13 | simplifying with (6), (7), (12) gives:
% 8.98/2.13 | (18) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 8.98/2.13 | (function(all_42_1) = v3 & function(all_42_4) = v1 &
% 8.98/2.13 | relation(all_42_1) = v2 & relation(all_42_4) = v0 & ( ~ (v1 = 0) |
% 8.98/2.13 | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 8.98/2.13 |
% 8.98/2.13 | GROUND_INST: instantiating (dt_k8_relat_1) with all_42_5, all_42_4, all_42_1,
% 8.98/2.13 | simplifying with (6), (7), (12) gives:
% 8.98/2.13 | (19) ? [v0: any] : ? [v1: any] : (relation(all_42_1) = v1 &
% 8.98/2.13 | relation(all_42_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 8.98/2.13 |
% 8.98/2.13 | GROUND_INST: instantiating (t129_relat_1) with all_42_6, all_42_5, all_42_4,
% 8.98/2.13 | all_42_3, all_42_2, simplifying with (5), (6), (7), (10), (13)
% 8.98/2.13 | gives:
% 8.98/2.13 | (20) all_42_2 = all_42_3 | ? [v0: any] : ? [v1: any] : (subset(all_42_6,
% 8.98/2.13 | all_42_5) = v1 & relation(all_42_4) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 8.98/2.13 | 0)))
% 8.98/2.13 |
% 8.98/2.13 | GROUND_INST: instantiating (t130_relat_1) with all_42_5, all_42_6, all_42_4,
% 8.98/2.13 | all_42_3, all_42_2, simplifying with (5), (6), (7), (10), (13)
% 8.98/2.13 | gives:
% 8.98/2.13 | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 8.98/2.13 | (relation_rng_restriction(all_42_5, all_42_4) = v2 & subset(all_42_5,
% 8.98/2.13 | all_42_6) = v1 & relation(all_42_4) = v0 & $i(v2) & ( ~ (v1 = 0) |
% 8.98/2.13 | ~ (v0 = 0) | v2 = all_42_2))
% 8.98/2.13 |
% 8.98/2.13 | DELTA: instantiating (19) with fresh symbols all_54_0, all_54_1 gives:
% 8.98/2.13 | (22) relation(all_42_1) = all_54_0 & relation(all_42_4) = all_54_1 & ( ~
% 8.98/2.13 | (all_54_1 = 0) | all_54_0 = 0)
% 8.98/2.13 |
% 8.98/2.13 | ALPHA: (22) implies:
% 8.98/2.13 | (23) relation(all_42_4) = all_54_1
% 8.98/2.13 |
% 8.98/2.13 | DELTA: instantiating (16) with fresh symbols all_58_0, all_58_1 gives:
% 8.98/2.13 | (24) relation(all_42_3) = all_58_0 & relation(all_42_4) = all_58_1 & ( ~
% 8.98/2.13 | (all_58_1 = 0) | all_58_0 = 0)
% 8.98/2.13 |
% 8.98/2.13 | ALPHA: (24) implies:
% 8.98/2.13 | (25) relation(all_42_4) = all_58_1
% 8.98/2.13 |
% 8.98/2.13 | DELTA: instantiating (17) with fresh symbols all_60_0, all_60_1, all_60_2
% 8.98/2.13 | gives:
% 8.98/2.13 | (26) relation_rng_restriction(all_42_6, all_42_4) = all_60_0 &
% 8.98/2.13 | subset(all_42_6, all_42_5) = all_60_1 & relation(all_42_4) = all_60_2
% 8.98/2.13 | & $i(all_60_0) & ( ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | all_60_0 =
% 8.98/2.13 | all_42_0)
% 8.98/2.13 |
% 8.98/2.13 | ALPHA: (26) implies:
% 8.98/2.13 | (27) relation(all_42_4) = all_60_2
% 8.98/2.13 | (28) subset(all_42_6, all_42_5) = all_60_1
% 8.98/2.13 | (29) relation_rng_restriction(all_42_6, all_42_4) = all_60_0
% 8.98/2.13 | (30) ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | all_60_0 = all_42_0
% 8.98/2.13 |
% 8.98/2.13 | DELTA: instantiating (21) with fresh symbols all_62_0, all_62_1, all_62_2
% 8.98/2.13 | gives:
% 8.98/2.13 | (31) relation_rng_restriction(all_42_5, all_42_4) = all_62_0 &
% 8.98/2.13 | subset(all_42_5, all_42_6) = all_62_1 & relation(all_42_4) = all_62_2
% 8.98/2.13 | & $i(all_62_0) & ( ~ (all_62_1 = 0) | ~ (all_62_2 = 0) | all_62_0 =
% 8.98/2.13 | all_42_2)
% 8.98/2.13 |
% 8.98/2.13 | ALPHA: (31) implies:
% 8.98/2.13 | (32) relation(all_42_4) = all_62_2
% 8.98/2.13 |
% 8.98/2.13 | DELTA: instantiating (15) with fresh symbols all_66_0, all_66_1, all_66_2,
% 8.98/2.13 | all_66_3 gives:
% 9.87/2.13 | (33) function(all_42_3) = all_66_0 & function(all_42_4) = all_66_2 &
% 9.87/2.13 | relation(all_42_3) = all_66_1 & relation(all_42_4) = all_66_3 & ( ~
% 9.87/2.13 | (all_66_2 = 0) | ~ (all_66_3 = 0) | (all_66_0 = 0 & all_66_1 = 0))
% 9.87/2.13 |
% 9.87/2.13 | ALPHA: (33) implies:
% 9.87/2.13 | (34) relation(all_42_4) = all_66_3
% 9.87/2.13 |
% 9.87/2.13 | DELTA: instantiating (18) with fresh symbols all_68_0, all_68_1, all_68_2,
% 9.87/2.13 | all_68_3 gives:
% 9.87/2.14 | (35) function(all_42_1) = all_68_0 & function(all_42_4) = all_68_2 &
% 9.87/2.14 | relation(all_42_1) = all_68_1 & relation(all_42_4) = all_68_3 & ( ~
% 9.87/2.14 | (all_68_2 = 0) | ~ (all_68_3 = 0) | (all_68_0 = 0 & all_68_1 = 0))
% 9.87/2.14 |
% 9.87/2.14 | ALPHA: (35) implies:
% 9.87/2.14 | (36) relation(all_42_4) = all_68_3
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (1) with 0, all_58_1, all_42_4, simplifying with
% 9.87/2.14 | (8), (25) gives:
% 9.87/2.14 | (37) all_58_1 = 0
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (1) with all_58_1, all_60_2, all_42_4, simplifying
% 9.87/2.14 | with (25), (27) gives:
% 9.87/2.14 | (38) all_60_2 = all_58_1
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (1) with all_60_2, all_62_2, all_42_4, simplifying
% 9.87/2.14 | with (27), (32) gives:
% 9.87/2.14 | (39) all_62_2 = all_60_2
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (1) with all_62_2, all_66_3, all_42_4, simplifying
% 9.87/2.14 | with (32), (34) gives:
% 9.87/2.14 | (40) all_66_3 = all_62_2
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (1) with all_66_3, all_68_3, all_42_4, simplifying
% 9.87/2.14 | with (34), (36) gives:
% 9.87/2.14 | (41) all_68_3 = all_66_3
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (1) with all_54_1, all_68_3, all_42_4, simplifying
% 9.87/2.14 | with (23), (36) gives:
% 9.87/2.14 | (42) all_68_3 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (2) with 0, all_60_1, all_42_5, all_42_6,
% 9.87/2.14 | simplifying with (9), (28) gives:
% 9.87/2.14 | (43) all_60_1 = 0
% 9.87/2.14 |
% 9.87/2.14 | GROUND_INST: instantiating (3) with all_42_3, all_60_0, all_42_4, all_42_6,
% 9.87/2.14 | simplifying with (10), (29) gives:
% 9.87/2.14 | (44) all_60_0 = all_42_3
% 9.87/2.14 |
% 9.87/2.14 | COMBINE_EQS: (41), (42) imply:
% 9.87/2.14 | (45) all_66_3 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | SIMP: (45) implies:
% 9.87/2.14 | (46) all_66_3 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | COMBINE_EQS: (40), (46) imply:
% 9.87/2.14 | (47) all_62_2 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | SIMP: (47) implies:
% 9.87/2.14 | (48) all_62_2 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | COMBINE_EQS: (39), (48) imply:
% 9.87/2.14 | (49) all_60_2 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | SIMP: (49) implies:
% 9.87/2.14 | (50) all_60_2 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | COMBINE_EQS: (38), (50) imply:
% 9.87/2.14 | (51) all_58_1 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | SIMP: (51) implies:
% 9.87/2.14 | (52) all_58_1 = all_54_1
% 9.87/2.14 |
% 9.87/2.14 | COMBINE_EQS: (37), (52) imply:
% 9.87/2.14 | (53) all_54_1 = 0
% 9.87/2.14 |
% 9.87/2.14 | COMBINE_EQS: (50), (53) imply:
% 9.87/2.14 | (54) all_60_2 = 0
% 9.87/2.14 |
% 9.87/2.14 | BETA: splitting (20) gives:
% 9.87/2.14 |
% 9.87/2.14 | Case 1:
% 9.87/2.14 | |
% 9.87/2.14 | | (55) all_42_2 = all_42_3
% 9.87/2.14 | |
% 9.87/2.14 | | BETA: splitting (30) gives:
% 9.87/2.14 | |
% 9.87/2.14 | | Case 1:
% 9.87/2.14 | | |
% 9.87/2.14 | | | (56) ~ (all_60_1 = 0)
% 9.87/2.14 | | |
% 9.87/2.14 | | | REDUCE: (43), (56) imply:
% 9.87/2.14 | | | (57) $false
% 9.87/2.14 | | |
% 9.87/2.14 | | | CLOSE: (57) is inconsistent.
% 9.87/2.14 | | |
% 9.87/2.14 | | Case 2:
% 9.87/2.14 | | |
% 9.87/2.14 | | | (58) ~ (all_60_2 = 0) | all_60_0 = all_42_0
% 9.87/2.14 | | |
% 9.87/2.14 | | | BETA: splitting (58) gives:
% 9.87/2.14 | | |
% 9.87/2.14 | | | Case 1:
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | (59) ~ (all_60_2 = 0)
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | REDUCE: (54), (59) imply:
% 9.87/2.14 | | | | (60) $false
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | CLOSE: (60) is inconsistent.
% 9.87/2.14 | | | |
% 9.87/2.14 | | | Case 2:
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | (61) all_60_0 = all_42_0
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | COMBINE_EQS: (44), (61) imply:
% 9.87/2.14 | | | | (62) all_42_0 = all_42_3
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | BETA: splitting (14) gives:
% 9.87/2.14 | | | |
% 9.87/2.14 | | | | Case 1:
% 9.87/2.14 | | | | |
% 9.87/2.14 | | | | | (63) ~ (all_42_0 = all_42_3)
% 9.87/2.14 | | | | |
% 9.87/2.14 | | | | | REDUCE: (62), (63) imply:
% 9.87/2.14 | | | | | (64) $false
% 9.87/2.14 | | | | |
% 9.87/2.14 | | | | | CLOSE: (64) is inconsistent.
% 9.87/2.14 | | | | |
% 9.87/2.14 | | | | Case 2:
% 9.87/2.14 | | | | |
% 9.87/2.14 | | | | | (65) ~ (all_42_2 = all_42_3)
% 9.87/2.15 | | | | |
% 9.87/2.15 | | | | | REDUCE: (55), (65) imply:
% 9.87/2.15 | | | | | (66) $false
% 9.87/2.15 | | | | |
% 9.87/2.15 | | | | | CLOSE: (66) is inconsistent.
% 9.87/2.15 | | | | |
% 9.87/2.15 | | | | End of split
% 9.87/2.15 | | | |
% 9.87/2.15 | | | End of split
% 9.87/2.15 | | |
% 9.87/2.15 | | End of split
% 9.87/2.15 | |
% 9.87/2.15 | Case 2:
% 9.87/2.15 | |
% 9.87/2.15 | | (67) ? [v0: any] : ? [v1: any] : (subset(all_42_6, all_42_5) = v1 &
% 9.87/2.15 | | relation(all_42_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.87/2.15 | |
% 9.87/2.15 | | DELTA: instantiating (67) with fresh symbols all_84_0, all_84_1 gives:
% 9.87/2.15 | | (68) subset(all_42_6, all_42_5) = all_84_0 & relation(all_42_4) =
% 9.87/2.15 | | all_84_1 & ( ~ (all_84_0 = 0) | ~ (all_84_1 = 0))
% 9.87/2.15 | |
% 9.87/2.15 | | ALPHA: (68) implies:
% 9.87/2.15 | | (69) relation(all_42_4) = all_84_1
% 9.87/2.15 | | (70) subset(all_42_6, all_42_5) = all_84_0
% 9.87/2.15 | | (71) ~ (all_84_0 = 0) | ~ (all_84_1 = 0)
% 9.87/2.15 | |
% 9.87/2.15 | | GROUND_INST: instantiating (1) with 0, all_84_1, all_42_4, simplifying with
% 9.87/2.15 | | (8), (69) gives:
% 9.87/2.15 | | (72) all_84_1 = 0
% 9.87/2.15 | |
% 9.87/2.15 | | GROUND_INST: instantiating (2) with 0, all_84_0, all_42_5, all_42_6,
% 9.87/2.15 | | simplifying with (9), (70) gives:
% 9.87/2.15 | | (73) all_84_0 = 0
% 9.87/2.15 | |
% 9.87/2.15 | | BETA: splitting (71) gives:
% 9.87/2.15 | |
% 9.87/2.15 | | Case 1:
% 9.87/2.15 | | |
% 9.87/2.15 | | | (74) ~ (all_84_0 = 0)
% 9.87/2.15 | | |
% 9.87/2.15 | | | REDUCE: (73), (74) imply:
% 9.87/2.15 | | | (75) $false
% 9.87/2.15 | | |
% 9.87/2.15 | | | CLOSE: (75) is inconsistent.
% 9.87/2.15 | | |
% 9.87/2.15 | | Case 2:
% 9.87/2.15 | | |
% 9.87/2.15 | | | (76) ~ (all_84_1 = 0)
% 9.87/2.15 | | |
% 9.87/2.15 | | | REDUCE: (72), (76) imply:
% 9.87/2.15 | | | (77) $false
% 9.87/2.15 | | |
% 9.87/2.15 | | | CLOSE: (77) is inconsistent.
% 9.87/2.15 | | |
% 9.87/2.15 | | End of split
% 9.87/2.15 | |
% 9.87/2.15 | End of split
% 9.87/2.15 |
% 9.87/2.15 End of proof
% 9.87/2.15 % SZS output end Proof for theBenchmark
% 9.87/2.15
% 9.87/2.15 1535ms
%------------------------------------------------------------------------------