TSTP Solution File: COM002_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM002_2 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:44:11 EDT 2023
% Result : Theorem 6.79s 1.72s
% Output : Proof 10.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM002_2 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 13:24:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.52/0.59 ________ _____
% 0.52/0.59 ___ __ \_________(_)________________________________
% 0.52/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.52/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.52/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.59 (2023-06-19)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2023
% 0.52/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.59 Amanda Stjerna.
% 0.52/0.59 Free software under BSD-3-Clause.
% 0.52/0.59
% 0.52/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.59
% 0.52/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.60 Running up to 7 provers in parallel.
% 0.52/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.52/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.70/1.12 Prover 1: Preprocessing ...
% 2.70/1.12 Prover 4: Preprocessing ...
% 2.70/1.15 Prover 3: Preprocessing ...
% 2.70/1.15 Prover 6: Preprocessing ...
% 2.70/1.16 Prover 5: Preprocessing ...
% 2.70/1.16 Prover 2: Preprocessing ...
% 2.70/1.16 Prover 0: Preprocessing ...
% 4.58/1.36 Prover 6: Constructing countermodel ...
% 4.58/1.36 Prover 1: Constructing countermodel ...
% 4.58/1.37 Prover 3: Constructing countermodel ...
% 4.58/1.37 Prover 5: Proving ...
% 4.58/1.37 Prover 2: Proving ...
% 4.58/1.41 Prover 4: Constructing countermodel ...
% 4.58/1.42 Prover 0: Proving ...
% 6.79/1.72 Prover 3: proved (1105ms)
% 6.79/1.72
% 6.79/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.79/1.72
% 6.79/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.79/1.73 Prover 6: stopped
% 6.79/1.73 Prover 2: stopped
% 6.79/1.73 Prover 5: stopped
% 6.79/1.73 Prover 0: stopped
% 6.79/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.79/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.79/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.79/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.48/1.77 Prover 8: Preprocessing ...
% 7.48/1.78 Prover 7: Preprocessing ...
% 7.48/1.78 Prover 13: Preprocessing ...
% 7.48/1.78 Prover 10: Preprocessing ...
% 7.48/1.79 Prover 11: Preprocessing ...
% 7.86/1.84 Prover 10: Warning: ignoring some quantifiers
% 7.86/1.84 Prover 10: Constructing countermodel ...
% 7.86/1.86 Prover 7: Warning: ignoring some quantifiers
% 7.86/1.87 Prover 7: Constructing countermodel ...
% 7.86/1.87 Prover 13: Warning: ignoring some quantifiers
% 7.86/1.87 Prover 13: Constructing countermodel ...
% 8.38/1.89 Prover 8: Warning: ignoring some quantifiers
% 8.38/1.90 Prover 8: Constructing countermodel ...
% 8.38/1.91 Prover 10: gave up
% 8.38/1.92 Prover 11: Constructing countermodel ...
% 8.38/1.93 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.38/1.96 Prover 16: Preprocessing ...
% 9.06/1.98 Prover 13: gave up
% 9.06/1.98 Prover 7: gave up
% 9.06/1.98 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.40/2.02 Prover 19: Preprocessing ...
% 9.40/2.04 Prover 16: Warning: ignoring some quantifiers
% 9.40/2.05 Prover 16: Constructing countermodel ...
% 9.40/2.09 Prover 19: Warning: ignoring some quantifiers
% 9.40/2.09 Prover 19: Constructing countermodel ...
% 10.06/2.13 Prover 1: Found proof (size 74)
% 10.06/2.13 Prover 1: proved (1520ms)
% 10.06/2.13 Prover 19: stopped
% 10.06/2.13 Prover 16: stopped
% 10.06/2.13 Prover 4: stopped
% 10.06/2.13 Prover 8: stopped
% 10.06/2.13 Prover 11: stopped
% 10.06/2.13
% 10.06/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.06/2.13
% 10.06/2.15 % SZS output start Proof for theBenchmark
% 10.06/2.15 Assumptions after simplification:
% 10.06/2.15 ---------------------------------
% 10.06/2.15
% 10.06/2.15 (conditional_success)
% 10.06/2.18 ! [v0: boolean] : ! [v1: state] : ! [v2: state] : ! [v3: statement] : ( ~
% 10.06/2.18 (ifthen(v0, v2) = v3) | ~ (has(v1, v3) = 0) | ~ boolean(v0) | ~ state(v2)
% 10.06/2.18 | ~ state(v1) | ? [v4: int] : ( ~ (v4 = 0) & fails(v2, v1) = v4))
% 10.06/2.18
% 10.06/2.18 (direct_success)
% 10.06/2.18 ! [v0: state] : ! [v1: state] : ( ~ (follows(v1, v0) = 0) | ~ state(v1) |
% 10.06/2.18 ~ state(v0) | ? [v2: int] : ( ~ (v2 = 0) & fails(v1, v0) = v2))
% 10.06/2.18
% 10.06/2.18 (goto_success)
% 10.48/2.18 ! [v0: label] : ! [v1: state] : ! [v2: state] : ! [v3: statement] : ( ~
% 10.48/2.18 (goto(v0) = v3) | ~ (has(v1, v3) = 0) | ~ (labels(v0, v2) = 0) | ~
% 10.48/2.18 label(v0) | ~ state(v2) | ~ state(v1) | ? [v4: int] : ( ~ (v4 = 0) &
% 10.48/2.18 fails(v2, v1) = v4))
% 10.48/2.18
% 10.48/2.18 (label_state_3)
% 10.48/2.18 labels(loop, p3) = 0 & label(loop) & state(p3)
% 10.48/2.18
% 10.48/2.18 (prove_there_is_a_loop_through_p3)
% 10.48/2.18 fails(p3, p3) = 0 & state(p3)
% 10.48/2.18
% 10.48/2.18 (state_3)
% 10.48/2.18 number(n) & register(register_j) & state(p4) & state(p3) & ? [v0: boolean] :
% 10.48/2.18 ? [v1: statement] : (equal_function(register_j, n) = v0 & ifthen(v0, p4) = v1
% 10.48/2.18 & has(p3, v1) = 0 & boolean(v0) & statement(v1))
% 10.48/2.18
% 10.48/2.18 (state_8)
% 10.48/2.19 label(loop) & state(p8) & ? [v0: statement] : (goto(loop) = v0 & has(p8, v0)
% 10.48/2.19 = 0 & statement(v0))
% 10.48/2.19
% 10.48/2.19 (transition_2_to_3)
% 10.48/2.19 follows(p3, p2) = 0 & state(p3) & state(p2)
% 10.48/2.19
% 10.48/2.19 (transition_3_to_6)
% 10.48/2.19 follows(p6, p3) = 0 & state(p6) & state(p3)
% 10.48/2.19
% 10.48/2.19 (transition_4_to_5)
% 10.48/2.19 follows(p5, p4) = 0 & state(p5) & state(p4)
% 10.48/2.19
% 10.48/2.19 (transition_6_to_7)
% 10.48/2.19 follows(p7, p6) = 0 & state(p7) & state(p6)
% 10.48/2.19
% 10.48/2.19 (transition_7_to_8)
% 10.48/2.19 follows(p8, p7) = 0 & state(p8) & state(p7)
% 10.48/2.19
% 10.48/2.19 (transitivity_of_success)
% 10.48/2.19 ! [v0: state] : ! [v1: state] : ! [v2: state] : ! [v3: int] : ! [v4: int]
% 10.48/2.19 : (v4 = 0 | v3 = 0 | ~ (fails(v2, v0) = v3) | ~ (fails(v0, v1) = v4) | ~
% 10.48/2.19 state(v2) | ~ state(v1) | ~ state(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 10.48/2.19 fails(v2, v1) = v5))
% 10.48/2.19
% 10.48/2.19 (function-axioms)
% 10.48/2.20 ! [v0: number] : ! [v1: number] : ! [v2: number] : ! [v3: register] : (v1
% 10.48/2.20 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: number] :
% 10.48/2.20 ! [v1: number] : ! [v2: register] : ! [v3: number] : (v1 = v0 | ~
% 10.48/2.20 (times(v3, v2) = v1) | ~ (times(v3, v2) = v0)) & ! [v0: boolean] : ! [v1:
% 10.48/2.20 boolean] : ! [v2: number] : ! [v3: register] : (v1 = v0 | ~
% 10.48/2.20 (equal_function(v3, v2) = v1) | ~ (equal_function(v3, v2) = v0)) & ! [v0:
% 10.48/2.20 statement] : ! [v1: statement] : ! [v2: number] : ! [v3: register] : (v1
% 10.48/2.20 = v0 | ~ (assign(v3, v2) = v1) | ~ (assign(v3, v2) = v0)) & ! [v0:
% 10.48/2.20 statement] : ! [v1: statement] : ! [v2: state] : ! [v3: boolean] : (v1 =
% 10.48/2.20 v0 | ~ (ifthen(v3, v2) = v1) | ~ (ifthen(v3, v2) = v0)) & ! [v0:
% 10.48/2.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: statement] : !
% 10.48/2.20 [v3: state] : (v1 = v0 | ~ (has(v3, v2) = v1) | ~ (has(v3, v2) = v0)) & !
% 10.48/2.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: state] : !
% 10.48/2.20 [v3: label] : (v1 = v0 | ~ (labels(v3, v2) = v1) | ~ (labels(v3, v2) = v0))
% 10.48/2.20 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: state] :
% 10.48/2.20 ! [v3: state] : (v1 = v0 | ~ (follows(v3, v2) = v1) | ~ (follows(v3, v2) =
% 10.48/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.48/2.20 state] : ! [v3: state] : (v1 = v0 | ~ (fails(v3, v2) = v1) | ~ (fails(v3,
% 10.48/2.20 v2) = v0)) & ! [v0: statement] : ! [v1: statement] : ! [v2: label] :
% 10.48/2.20 (v1 = v0 | ~ (goto(v2) = v1) | ~ (goto(v2) = v0))
% 10.48/2.20
% 10.48/2.20 Further assumptions not needed in the proof:
% 10.48/2.20 --------------------------------------------
% 10.48/2.20 state_1, state_2, state_4, state_6, state_7, transition_1_to_2
% 10.48/2.20
% 10.48/2.20 Those formulas are unsatisfiable:
% 10.48/2.20 ---------------------------------
% 10.48/2.20
% 10.48/2.20 Begin of proof
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (label_state_3) implies:
% 10.48/2.20 | (1) labels(loop, p3) = 0
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (transition_2_to_3) implies:
% 10.48/2.20 | (2) state(p2)
% 10.48/2.20 | (3) follows(p3, p2) = 0
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (state_3) implies:
% 10.48/2.20 | (4) ? [v0: boolean] : ? [v1: statement] : (equal_function(register_j, n)
% 10.48/2.20 | = v0 & ifthen(v0, p4) = v1 & has(p3, v1) = 0 & boolean(v0) &
% 10.48/2.20 | statement(v1))
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (transition_4_to_5) implies:
% 10.48/2.20 | (5) state(p4)
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (transition_3_to_6) implies:
% 10.48/2.20 | (6) follows(p6, p3) = 0
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (transition_6_to_7) implies:
% 10.48/2.20 | (7) state(p6)
% 10.48/2.20 | (8) follows(p7, p6) = 0
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (transition_7_to_8) implies:
% 10.48/2.20 | (9) state(p7)
% 10.48/2.20 | (10) follows(p8, p7) = 0
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (state_8) implies:
% 10.48/2.20 | (11) state(p8)
% 10.48/2.20 | (12) label(loop)
% 10.48/2.20 | (13) ? [v0: statement] : (goto(loop) = v0 & has(p8, v0) = 0 &
% 10.48/2.20 | statement(v0))
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (prove_there_is_a_loop_through_p3) implies:
% 10.48/2.20 | (14) state(p3)
% 10.48/2.20 | (15) fails(p3, p3) = 0
% 10.48/2.20 |
% 10.48/2.20 | ALPHA: (function-axioms) implies:
% 10.48/2.20 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.48/2.20 | state] : ! [v3: state] : (v1 = v0 | ~ (fails(v3, v2) = v1) | ~
% 10.48/2.20 | (fails(v3, v2) = v0))
% 10.48/2.20 |
% 10.48/2.21 | DELTA: instantiating (13) with fresh symbol all_20_0 gives:
% 10.48/2.21 | (17) goto(loop) = all_20_0 & has(p8, all_20_0) = 0 & statement(all_20_0)
% 10.48/2.21 |
% 10.48/2.21 | ALPHA: (17) implies:
% 10.48/2.21 | (18) has(p8, all_20_0) = 0
% 10.48/2.21 | (19) goto(loop) = all_20_0
% 10.48/2.21 |
% 10.48/2.21 | DELTA: instantiating (4) with fresh symbols all_28_0, all_28_1 gives:
% 10.48/2.21 | (20) equal_function(register_j, n) = all_28_1 & ifthen(all_28_1, p4) =
% 10.48/2.21 | all_28_0 & has(p3, all_28_0) = 0 & boolean(all_28_1) &
% 10.48/2.21 | statement(all_28_0)
% 10.48/2.21 |
% 10.48/2.21 | ALPHA: (20) implies:
% 10.48/2.21 | (21) boolean(all_28_1)
% 10.48/2.21 | (22) has(p3, all_28_0) = 0
% 10.48/2.21 | (23) ifthen(all_28_1, p4) = all_28_0
% 10.48/2.21 |
% 10.48/2.21 | GROUND_INST: instantiating (direct_success) with p2, p3, simplifying with (2),
% 10.48/2.21 | (3), (14) gives:
% 10.48/2.21 | (24) ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p2) = v0)
% 10.48/2.21 |
% 10.48/2.21 | GROUND_INST: instantiating (direct_success) with p3, p6, simplifying with (6),
% 10.48/2.21 | (7), (14) gives:
% 10.48/2.21 | (25) ? [v0: int] : ( ~ (v0 = 0) & fails(p6, p3) = v0)
% 10.48/2.21 |
% 10.48/2.21 | GROUND_INST: instantiating (direct_success) with p6, p7, simplifying with (7),
% 10.48/2.21 | (8), (9) gives:
% 10.48/2.21 | (26) ? [v0: int] : ( ~ (v0 = 0) & fails(p7, p6) = v0)
% 10.48/2.21 |
% 10.48/2.21 | GROUND_INST: instantiating (direct_success) with p7, p8, simplifying with (9),
% 10.48/2.21 | (10), (11) gives:
% 10.48/2.21 | (27) ? [v0: int] : ( ~ (v0 = 0) & fails(p8, p7) = v0)
% 10.48/2.21 |
% 10.48/2.21 | GROUND_INST: instantiating (goto_success) with loop, p8, p3, all_20_0,
% 10.48/2.21 | simplifying with (1), (11), (12), (14), (18), (19) gives:
% 10.48/2.21 | (28) ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p8) = v0)
% 10.48/2.21 |
% 10.48/2.21 | GROUND_INST: instantiating (conditional_success) with all_28_1, p3, p4,
% 10.48/2.21 | all_28_0, simplifying with (5), (14), (21), (22), (23) gives:
% 10.48/2.21 | (29) ? [v0: int] : ( ~ (v0 = 0) & fails(p4, p3) = v0)
% 10.48/2.21 |
% 10.48/2.21 | DELTA: instantiating (29) with fresh symbol all_39_0 gives:
% 10.48/2.21 | (30) ~ (all_39_0 = 0) & fails(p4, p3) = all_39_0
% 10.48/2.21 |
% 10.48/2.21 | ALPHA: (30) implies:
% 10.48/2.21 | (31) ~ (all_39_0 = 0)
% 10.48/2.21 | (32) fails(p4, p3) = all_39_0
% 10.48/2.21 |
% 10.48/2.21 | DELTA: instantiating (28) with fresh symbol all_41_0 gives:
% 10.48/2.21 | (33) ~ (all_41_0 = 0) & fails(p3, p8) = all_41_0
% 10.48/2.21 |
% 10.48/2.21 | ALPHA: (33) implies:
% 10.48/2.21 | (34) ~ (all_41_0 = 0)
% 10.48/2.21 | (35) fails(p3, p8) = all_41_0
% 10.48/2.21 |
% 10.48/2.21 | DELTA: instantiating (27) with fresh symbol all_43_0 gives:
% 10.48/2.21 | (36) ~ (all_43_0 = 0) & fails(p8, p7) = all_43_0
% 10.48/2.21 |
% 10.48/2.21 | ALPHA: (36) implies:
% 10.48/2.22 | (37) ~ (all_43_0 = 0)
% 10.48/2.22 | (38) fails(p8, p7) = all_43_0
% 10.48/2.22 |
% 10.48/2.22 | DELTA: instantiating (26) with fresh symbol all_45_0 gives:
% 10.48/2.22 | (39) ~ (all_45_0 = 0) & fails(p7, p6) = all_45_0
% 10.48/2.22 |
% 10.48/2.22 | ALPHA: (39) implies:
% 10.48/2.22 | (40) ~ (all_45_0 = 0)
% 10.48/2.22 | (41) fails(p7, p6) = all_45_0
% 10.48/2.22 |
% 10.48/2.22 | DELTA: instantiating (25) with fresh symbol all_47_0 gives:
% 10.48/2.22 | (42) ~ (all_47_0 = 0) & fails(p6, p3) = all_47_0
% 10.48/2.22 |
% 10.48/2.22 | ALPHA: (42) implies:
% 10.48/2.22 | (43) ~ (all_47_0 = 0)
% 10.48/2.22 | (44) fails(p6, p3) = all_47_0
% 10.48/2.22 |
% 10.48/2.22 | DELTA: instantiating (24) with fresh symbol all_51_0 gives:
% 10.48/2.22 | (45) ~ (all_51_0 = 0) & fails(p3, p2) = all_51_0
% 10.48/2.22 |
% 10.48/2.22 | ALPHA: (45) implies:
% 10.48/2.22 | (46) ~ (all_51_0 = 0)
% 10.48/2.22 | (47) fails(p3, p2) = all_51_0
% 10.48/2.22 |
% 10.48/2.22 | GROUND_INST: instantiating (transitivity_of_success) with p3, p2, p4,
% 10.48/2.22 | all_39_0, all_51_0, simplifying with (2), (5), (14), (32), (47)
% 10.48/2.22 | gives:
% 10.48/2.22 | (48) all_51_0 = 0 | all_39_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p4,
% 10.48/2.22 | p2) = v0)
% 10.48/2.22 |
% 10.48/2.22 | GROUND_INST: instantiating (transitivity_of_success) with p6, p3, p7,
% 10.48/2.22 | all_45_0, all_47_0, simplifying with (7), (9), (14), (41), (44)
% 10.48/2.22 | gives:
% 10.48/2.22 | (49) all_47_0 = 0 | all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p7,
% 10.48/2.22 | p3) = v0)
% 10.48/2.22 |
% 10.48/2.22 | GROUND_INST: instantiating (transitivity_of_success) with p8, p7, p3,
% 10.48/2.22 | all_41_0, all_43_0, simplifying with (9), (11), (14), (35), (38)
% 10.48/2.22 | gives:
% 10.48/2.22 | (50) all_43_0 = 0 | all_41_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p3,
% 10.48/2.22 | p7) = v0)
% 10.48/2.22 |
% 10.48/2.22 | BETA: splitting (50) gives:
% 10.48/2.22 |
% 10.48/2.22 | Case 1:
% 10.48/2.22 | |
% 10.48/2.22 | | (51) all_43_0 = 0
% 10.48/2.22 | |
% 10.48/2.22 | | REDUCE: (37), (51) imply:
% 10.48/2.22 | | (52) $false
% 10.48/2.22 | |
% 10.48/2.22 | | CLOSE: (52) is inconsistent.
% 10.48/2.22 | |
% 10.48/2.22 | Case 2:
% 10.48/2.22 | |
% 10.48/2.22 | | (53) all_41_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p7) = v0)
% 10.48/2.22 | |
% 10.48/2.22 | | BETA: splitting (53) gives:
% 10.48/2.22 | |
% 10.48/2.22 | | Case 1:
% 10.48/2.22 | | |
% 10.48/2.22 | | | (54) all_41_0 = 0
% 10.48/2.22 | | |
% 10.48/2.22 | | | REDUCE: (34), (54) imply:
% 10.48/2.22 | | | (55) $false
% 10.48/2.22 | | |
% 10.48/2.22 | | | CLOSE: (55) is inconsistent.
% 10.48/2.22 | | |
% 10.48/2.22 | | Case 2:
% 10.48/2.22 | | |
% 10.48/2.22 | | | (56) ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p7) = v0)
% 10.48/2.22 | | |
% 10.48/2.22 | | | DELTA: instantiating (56) with fresh symbol all_66_0 gives:
% 10.48/2.22 | | | (57) ~ (all_66_0 = 0) & fails(p3, p7) = all_66_0
% 10.48/2.22 | | |
% 10.48/2.22 | | | ALPHA: (57) implies:
% 10.48/2.22 | | | (58) ~ (all_66_0 = 0)
% 10.48/2.22 | | | (59) fails(p3, p7) = all_66_0
% 10.48/2.22 | | |
% 10.48/2.22 | | | BETA: splitting (49) gives:
% 10.48/2.22 | | |
% 10.48/2.22 | | | Case 1:
% 10.48/2.22 | | | |
% 10.48/2.22 | | | | (60) all_47_0 = 0
% 10.48/2.22 | | | |
% 10.48/2.22 | | | | REDUCE: (43), (60) imply:
% 10.48/2.22 | | | | (61) $false
% 10.48/2.22 | | | |
% 10.48/2.22 | | | | CLOSE: (61) is inconsistent.
% 10.48/2.22 | | | |
% 10.48/2.22 | | | Case 2:
% 10.48/2.22 | | | |
% 10.48/2.23 | | | | (62) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p7, p3) = v0)
% 10.48/2.23 | | | |
% 10.48/2.23 | | | | BETA: splitting (48) gives:
% 10.48/2.23 | | | |
% 10.48/2.23 | | | | Case 1:
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | | (63) all_51_0 = 0
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | | REDUCE: (46), (63) imply:
% 10.48/2.23 | | | | | (64) $false
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | | CLOSE: (64) is inconsistent.
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | Case 2:
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | | (65) all_39_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p4, p2) =
% 10.48/2.23 | | | | | v0)
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | | BETA: splitting (62) gives:
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | | Case 1:
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | (66) all_45_0 = 0
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | REDUCE: (40), (66) imply:
% 10.48/2.23 | | | | | | (67) $false
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | CLOSE: (67) is inconsistent.
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | Case 2:
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & fails(p7, p3) = v0)
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | DELTA: instantiating (68) with fresh symbol all_96_0 gives:
% 10.48/2.23 | | | | | | (69) ~ (all_96_0 = 0) & fails(p7, p3) = all_96_0
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | ALPHA: (69) implies:
% 10.48/2.23 | | | | | | (70) ~ (all_96_0 = 0)
% 10.48/2.23 | | | | | | (71) fails(p7, p3) = all_96_0
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | BETA: splitting (65) gives:
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | | Case 1:
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | | (72) all_39_0 = 0
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | | REDUCE: (31), (72) imply:
% 10.48/2.23 | | | | | | | (73) $false
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | | CLOSE: (73) is inconsistent.
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | Case 2:
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | | GROUND_INST: instantiating (transitivity_of_success) with p7, p3,
% 10.48/2.23 | | | | | | | p3, all_66_0, all_96_0, simplifying with (9), (14),
% 10.48/2.23 | | | | | | | (59), (71) gives:
% 10.48/2.23 | | | | | | | (74) all_96_0 = 0 | all_66_0 = 0 | ? [v0: int] : ( ~ (v0 = 0)
% 10.48/2.23 | | | | | | | & fails(p3, p3) = v0)
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | | BETA: splitting (74) gives:
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | | Case 1:
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | | (75) all_96_0 = 0
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | | REDUCE: (70), (75) imply:
% 10.48/2.23 | | | | | | | | (76) $false
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | | CLOSE: (76) is inconsistent.
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | Case 2:
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | | (77) all_66_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & fails(p3,
% 10.48/2.23 | | | | | | | | p3) = v0)
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | | BETA: splitting (77) gives:
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | | Case 1:
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | (78) all_66_0 = 0
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | REDUCE: (58), (78) imply:
% 10.48/2.23 | | | | | | | | | (79) $false
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | CLOSE: (79) is inconsistent.
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | Case 2:
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p3) = v0)
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | DELTA: instantiating (80) with fresh symbol all_204_0 gives:
% 10.48/2.23 | | | | | | | | | (81) ~ (all_204_0 = 0) & fails(p3, p3) = all_204_0
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | ALPHA: (81) implies:
% 10.48/2.23 | | | | | | | | | (82) ~ (all_204_0 = 0)
% 10.48/2.23 | | | | | | | | | (83) fails(p3, p3) = all_204_0
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_204_0, p3, p3,
% 10.48/2.23 | | | | | | | | | simplifying with (15), (83) gives:
% 10.48/2.23 | | | | | | | | | (84) all_204_0 = 0
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | REDUCE: (82), (84) imply:
% 10.48/2.23 | | | | | | | | | (85) $false
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | | CLOSE: (85) is inconsistent.
% 10.48/2.23 | | | | | | | | |
% 10.48/2.23 | | | | | | | | End of split
% 10.48/2.23 | | | | | | | |
% 10.48/2.23 | | | | | | | End of split
% 10.48/2.23 | | | | | | |
% 10.48/2.23 | | | | | | End of split
% 10.48/2.23 | | | | | |
% 10.48/2.23 | | | | | End of split
% 10.48/2.23 | | | | |
% 10.48/2.23 | | | | End of split
% 10.48/2.23 | | | |
% 10.48/2.23 | | | End of split
% 10.48/2.23 | | |
% 10.48/2.23 | | End of split
% 10.48/2.23 | |
% 10.48/2.23 | End of split
% 10.48/2.23 |
% 10.48/2.23 End of proof
% 10.48/2.23 % SZS output end Proof for theBenchmark
% 10.48/2.23
% 10.48/2.23 1640ms
%------------------------------------------------------------------------------