TSTP Solution File: SEU157+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU157+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.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 17:42:52 EDT 2023
% Result : Theorem 13.41s 2.56s
% Output : Proof 16.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU157+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 14:19:31 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.46/1.15 Prover 1: Preprocessing ...
% 3.46/1.15 Prover 4: Preprocessing ...
% 3.46/1.19 Prover 3: Preprocessing ...
% 3.46/1.19 Prover 0: Preprocessing ...
% 3.46/1.19 Prover 5: Preprocessing ...
% 3.46/1.19 Prover 2: Preprocessing ...
% 3.46/1.21 Prover 6: Preprocessing ...
% 9.21/2.12 Prover 5: Proving ...
% 9.21/2.12 Prover 1: Warning: ignoring some quantifiers
% 10.50/2.19 Prover 3: Warning: ignoring some quantifiers
% 10.50/2.21 Prover 1: Constructing countermodel ...
% 11.00/2.24 Prover 3: Constructing countermodel ...
% 11.00/2.25 Prover 4: Warning: ignoring some quantifiers
% 11.00/2.26 Prover 6: Proving ...
% 11.20/2.29 Prover 2: Proving ...
% 11.92/2.38 Prover 4: Constructing countermodel ...
% 12.48/2.45 Prover 0: Proving ...
% 13.20/2.56 Prover 3: proved (1913ms)
% 13.41/2.56
% 13.41/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.41/2.56
% 13.41/2.57 Prover 2: stopped
% 13.41/2.57 Prover 5: stopped
% 13.41/2.57 Prover 0: stopped
% 13.41/2.57 Prover 6: stopped
% 13.41/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.41/2.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.41/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.41/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.41/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.81/2.72 Prover 11: Preprocessing ...
% 13.81/2.72 Prover 7: Preprocessing ...
% 13.81/2.72 Prover 13: Preprocessing ...
% 13.81/2.74 Prover 8: Preprocessing ...
% 13.81/2.74 Prover 10: Preprocessing ...
% 14.53/2.83 Prover 1: Found proof (size 41)
% 14.53/2.83 Prover 1: proved (2193ms)
% 14.53/2.83 Prover 7: stopped
% 14.53/2.84 Prover 4: stopped
% 14.53/2.85 Prover 10: stopped
% 14.53/2.85 Prover 11: stopped
% 14.53/2.86 Prover 13: stopped
% 15.81/2.95 Prover 8: Warning: ignoring some quantifiers
% 15.81/2.98 Prover 8: Constructing countermodel ...
% 15.81/2.99 Prover 8: stopped
% 15.81/2.99
% 15.81/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.81/2.99
% 15.81/3.00 % SZS output start Proof for theBenchmark
% 15.81/3.01 Assumptions after simplification:
% 15.81/3.01 ---------------------------------
% 15.81/3.01
% 15.81/3.01 (d2_zfmisc_1)
% 16.28/3.04 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 16.28/3.04 (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.28/3.04 [v4: $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ! [v6:
% 16.28/3.04 $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v7) = v4) | ~ $i(v7) | ~
% 16.28/3.04 $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, v2) = v9 & in(v6, v1) =
% 16.28/3.04 v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & (v5 = 0 | ? [v6: $i] : ?
% 16.28/3.04 [v7: $i] : (ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0
% 16.28/3.04 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 16.28/3.04 (cartesian_product2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( !
% 16.28/3.04 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | !
% 16.28/3.04 [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) |
% 16.28/3.04 ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0)
% 16.28/3.04 = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: $i] : ( ~ (in(v3,
% 16.28/3.04 v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v4,
% 16.28/3.04 v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & $i(v4)))))
% 16.28/3.04
% 16.28/3.04 (l55_zfmisc_1)
% 16.28/3.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 16.28/3.04 $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : (cartesian_product2(v2,
% 16.28/3.04 v3) = v5 & ordered_pair(v0, v1) = v4 & in(v4, v5) = v6 & in(v1, v3) = v8 &
% 16.28/3.04 in(v0, v2) = v7 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v8
% 16.28/3.04 = 0 & v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)))))
% 16.28/3.04
% 16.28/3.04 (t33_zfmisc_1)
% 16.28/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 16.28/3.05 (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) |
% 16.28/3.05 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0))
% 16.28/3.05
% 16.28/3.05 (function-axioms)
% 16.28/3.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.28/3.05 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 16.28/3.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.28/3.05 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 16.28/3.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.28/3.05 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 16.28/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.28/3.05 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 16.28/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.28/3.05 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 16.28/3.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.28/3.05 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 16.28/3.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.28/3.05 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 16.28/3.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 16.28/3.05 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 16.28/3.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.28/3.05 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 16.28/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.28/3.05 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 16.28/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 16.28/3.05 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.28/3.05 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i]
% 16.28/3.05 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 16.28/3.05 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.28/3.05 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 16.28/3.05
% 16.28/3.05 Further assumptions not needed in the proof:
% 16.28/3.05 --------------------------------------------
% 16.28/3.05 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 16.28/3.05 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 16.28/3.05 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d3_tarski, d3_xboole_0,
% 16.28/3.05 d4_tarski, d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0, dt_k1_tarski,
% 16.28/3.05 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 16.28/3.05 dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, fc1_xboole_0,
% 16.28/3.05 fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 16.28/3.05 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1,
% 16.28/3.05 l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1,
% 16.28/3.05 l50_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 16.28/3.05 symmetry_r1_xboole_0, t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1,
% 16.28/3.05 t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole,
% 16.28/3.05 t2_tarski, t2_xboole_1, t33_xboole_1, t36_xboole_1, t37_xboole_1, t39_xboole_1,
% 16.28/3.05 t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1,
% 16.28/3.05 t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1, t69_enumset1, t6_boole,
% 16.28/3.05 t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1,
% 16.28/3.05 t8_zfmisc_1, t9_zfmisc_1
% 16.28/3.05
% 16.28/3.05 Those formulas are unsatisfiable:
% 16.28/3.05 ---------------------------------
% 16.28/3.05
% 16.28/3.05 Begin of proof
% 16.28/3.05 |
% 16.28/3.05 | ALPHA: (d2_zfmisc_1) implies:
% 16.28/3.06 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0,
% 16.28/3.06 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 16.28/3.06 | [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5:
% 16.28/3.06 | $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6)
% 16.28/3.06 | | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 &
% 16.28/3.06 | in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3:
% 16.28/3.06 | $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5:
% 16.28/3.06 | $i] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0)
% 16.28/3.06 | = 0 & $i(v5) & $i(v4)))))
% 16.28/3.06 |
% 16.28/3.06 | ALPHA: (function-axioms) implies:
% 16.28/3.06 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.28/3.06 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 16.28/3.06 |
% 16.28/3.06 | DELTA: instantiating (l55_zfmisc_1) with fresh symbols all_101_0, all_101_1,
% 16.28/3.06 | all_101_2, all_101_3, all_101_4, all_101_5, all_101_6, all_101_7,
% 16.28/3.06 | all_101_8 gives:
% 16.28/3.06 | (3) cartesian_product2(all_101_6, all_101_5) = all_101_3 &
% 16.28/3.06 | ordered_pair(all_101_8, all_101_7) = all_101_4 & in(all_101_4,
% 16.28/3.06 | all_101_3) = all_101_2 & in(all_101_7, all_101_5) = all_101_0 &
% 16.28/3.06 | in(all_101_8, all_101_6) = all_101_1 & $i(all_101_3) & $i(all_101_4) &
% 16.28/3.06 | $i(all_101_5) & $i(all_101_6) & $i(all_101_7) & $i(all_101_8) &
% 16.28/3.06 | ((all_101_0 = 0 & all_101_1 = 0 & ~ (all_101_2 = 0)) | (all_101_2 = 0
% 16.28/3.06 | & ( ~ (all_101_0 = 0) | ~ (all_101_1 = 0))))
% 16.28/3.06 |
% 16.28/3.06 | ALPHA: (3) implies:
% 16.28/3.06 | (4) $i(all_101_8)
% 16.28/3.06 | (5) $i(all_101_7)
% 16.28/3.06 | (6) $i(all_101_6)
% 16.28/3.06 | (7) $i(all_101_5)
% 16.28/3.06 | (8) $i(all_101_4)
% 16.28/3.06 | (9) $i(all_101_3)
% 16.28/3.06 | (10) in(all_101_8, all_101_6) = all_101_1
% 16.28/3.06 | (11) in(all_101_7, all_101_5) = all_101_0
% 16.28/3.06 | (12) in(all_101_4, all_101_3) = all_101_2
% 16.28/3.06 | (13) ordered_pair(all_101_8, all_101_7) = all_101_4
% 16.28/3.06 | (14) cartesian_product2(all_101_6, all_101_5) = all_101_3
% 16.28/3.06 | (15) (all_101_0 = 0 & all_101_1 = 0 & ~ (all_101_2 = 0)) | (all_101_2 = 0
% 16.28/3.06 | & ( ~ (all_101_0 = 0) | ~ (all_101_1 = 0)))
% 16.28/3.06 |
% 16.28/3.06 | GROUND_INST: instantiating (1) with all_101_6, all_101_5, all_101_3,
% 16.28/3.06 | simplifying with (6), (7), (9), (14) gives:
% 16.28/3.06 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_3) = v1) |
% 16.28/3.06 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) =
% 16.28/3.06 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 16.28/3.06 | (in(v3, all_101_5) = v5 & in(v2, all_101_6) = v4 & ( ~ (v5 = 0) |
% 16.28/3.06 | ~ (v4 = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_101_3) = 0) |
% 16.28/3.06 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 &
% 16.28/3.06 | in(v2, all_101_5) = 0 & in(v1, all_101_6) = 0 & $i(v2) & $i(v1)))
% 16.28/3.06 |
% 16.28/3.06 | ALPHA: (16) implies:
% 16.28/3.07 | (17) ! [v0: $i] : ( ~ (in(v0, all_101_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 16.28/3.07 | ? [v2: $i] : (ordered_pair(v1, v2) = v0 & in(v2, all_101_5) = 0 &
% 16.28/3.07 | in(v1, all_101_6) = 0 & $i(v2) & $i(v1)))
% 16.28/3.07 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_3) = v1) |
% 16.28/3.07 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) =
% 16.28/3.07 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 16.28/3.07 | (in(v3, all_101_5) = v5 & in(v2, all_101_6) = v4 & ( ~ (v5 = 0) |
% 16.28/3.07 | ~ (v4 = 0)))))
% 16.28/3.07 |
% 16.28/3.07 | GROUND_INST: instantiating (18) with all_101_4, all_101_2, simplifying with
% 16.28/3.07 | (8), (12) gives:
% 16.28/3.07 | (19) all_101_2 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1)
% 16.28/3.07 | = all_101_4) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any]
% 16.28/3.07 | : (in(v1, all_101_5) = v3 & in(v0, all_101_6) = v2 & ( ~ (v3 = 0) |
% 16.28/3.07 | ~ (v2 = 0))))
% 16.28/3.07 |
% 16.28/3.07 | BETA: splitting (15) gives:
% 16.28/3.07 |
% 16.28/3.07 | Case 1:
% 16.28/3.07 | |
% 16.28/3.07 | | (20) all_101_0 = 0 & all_101_1 = 0 & ~ (all_101_2 = 0)
% 16.28/3.07 | |
% 16.28/3.07 | | ALPHA: (20) implies:
% 16.28/3.07 | | (21) all_101_1 = 0
% 16.28/3.07 | | (22) all_101_0 = 0
% 16.28/3.07 | | (23) ~ (all_101_2 = 0)
% 16.28/3.07 | |
% 16.28/3.07 | | REDUCE: (11), (22) imply:
% 16.28/3.07 | | (24) in(all_101_7, all_101_5) = 0
% 16.28/3.07 | |
% 16.28/3.07 | | REDUCE: (10), (21) imply:
% 16.28/3.07 | | (25) in(all_101_8, all_101_6) = 0
% 16.28/3.07 | |
% 16.28/3.07 | | BETA: splitting (19) gives:
% 16.28/3.07 | |
% 16.28/3.07 | | Case 1:
% 16.28/3.07 | | |
% 16.28/3.07 | | | (26) all_101_2 = 0
% 16.28/3.07 | | |
% 16.28/3.07 | | | REDUCE: (23), (26) imply:
% 16.28/3.07 | | | (27) $false
% 16.28/3.07 | | |
% 16.28/3.07 | | | CLOSE: (27) is inconsistent.
% 16.28/3.07 | | |
% 16.28/3.07 | | Case 2:
% 16.28/3.07 | | |
% 16.28/3.07 | | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_101_4)
% 16.28/3.07 | | | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 16.28/3.07 | | | all_101_5) = v3 & in(v0, all_101_6) = v2 & ( ~ (v3 = 0) | ~
% 16.28/3.07 | | | (v2 = 0))))
% 16.28/3.07 | | |
% 16.28/3.07 | | | GROUND_INST: instantiating (28) with all_101_8, all_101_7, simplifying
% 16.28/3.07 | | | with (4), (5), (13) gives:
% 16.28/3.07 | | | (29) ? [v0: any] : ? [v1: any] : (in(all_101_7, all_101_5) = v1 &
% 16.28/3.07 | | | in(all_101_8, all_101_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 16.28/3.07 | | |
% 16.28/3.07 | | | DELTA: instantiating (29) with fresh symbols all_142_0, all_142_1 gives:
% 16.28/3.07 | | | (30) in(all_101_7, all_101_5) = all_142_0 & in(all_101_8, all_101_6) =
% 16.28/3.07 | | | all_142_1 & ( ~ (all_142_0 = 0) | ~ (all_142_1 = 0))
% 16.28/3.07 | | |
% 16.28/3.07 | | | ALPHA: (30) implies:
% 16.28/3.07 | | | (31) in(all_101_8, all_101_6) = all_142_1
% 16.28/3.07 | | | (32) in(all_101_7, all_101_5) = all_142_0
% 16.28/3.07 | | | (33) ~ (all_142_0 = 0) | ~ (all_142_1 = 0)
% 16.28/3.07 | | |
% 16.28/3.07 | | | GROUND_INST: instantiating (2) with 0, all_142_1, all_101_6, all_101_8,
% 16.28/3.07 | | | simplifying with (25), (31) gives:
% 16.28/3.07 | | | (34) all_142_1 = 0
% 16.28/3.07 | | |
% 16.28/3.08 | | | GROUND_INST: instantiating (2) with 0, all_142_0, all_101_5, all_101_7,
% 16.28/3.08 | | | simplifying with (24), (32) gives:
% 16.28/3.08 | | | (35) all_142_0 = 0
% 16.28/3.08 | | |
% 16.28/3.08 | | | BETA: splitting (33) gives:
% 16.28/3.08 | | |
% 16.28/3.08 | | | Case 1:
% 16.28/3.08 | | | |
% 16.28/3.08 | | | | (36) ~ (all_142_0 = 0)
% 16.28/3.08 | | | |
% 16.28/3.08 | | | | REDUCE: (35), (36) imply:
% 16.28/3.08 | | | | (37) $false
% 16.28/3.08 | | | |
% 16.28/3.08 | | | | CLOSE: (37) is inconsistent.
% 16.28/3.08 | | | |
% 16.28/3.08 | | | Case 2:
% 16.28/3.08 | | | |
% 16.28/3.08 | | | | (38) ~ (all_142_1 = 0)
% 16.28/3.08 | | | |
% 16.28/3.08 | | | | REDUCE: (34), (38) imply:
% 16.28/3.08 | | | | (39) $false
% 16.28/3.08 | | | |
% 16.28/3.08 | | | | CLOSE: (39) is inconsistent.
% 16.28/3.08 | | | |
% 16.28/3.08 | | | End of split
% 16.28/3.08 | | |
% 16.28/3.08 | | End of split
% 16.28/3.08 | |
% 16.28/3.08 | Case 2:
% 16.28/3.08 | |
% 16.28/3.08 | | (40) all_101_2 = 0 & ( ~ (all_101_0 = 0) | ~ (all_101_1 = 0))
% 16.28/3.08 | |
% 16.28/3.08 | | ALPHA: (40) implies:
% 16.28/3.08 | | (41) all_101_2 = 0
% 16.28/3.08 | | (42) ~ (all_101_0 = 0) | ~ (all_101_1 = 0)
% 16.28/3.08 | |
% 16.28/3.08 | | REDUCE: (12), (41) imply:
% 16.28/3.08 | | (43) in(all_101_4, all_101_3) = 0
% 16.28/3.08 | |
% 16.28/3.08 | | GROUND_INST: instantiating (17) with all_101_4, simplifying with (8), (43)
% 16.28/3.08 | | gives:
% 16.28/3.08 | | (44) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_101_4 &
% 16.28/3.08 | | in(v1, all_101_5) = 0 & in(v0, all_101_6) = 0 & $i(v1) & $i(v0))
% 16.28/3.08 | |
% 16.28/3.08 | | DELTA: instantiating (44) with fresh symbols all_146_0, all_146_1 gives:
% 16.28/3.08 | | (45) ordered_pair(all_146_1, all_146_0) = all_101_4 & in(all_146_0,
% 16.28/3.08 | | all_101_5) = 0 & in(all_146_1, all_101_6) = 0 & $i(all_146_0) &
% 16.28/3.08 | | $i(all_146_1)
% 16.28/3.08 | |
% 16.28/3.08 | | ALPHA: (45) implies:
% 16.28/3.08 | | (46) $i(all_146_1)
% 16.28/3.08 | | (47) $i(all_146_0)
% 16.28/3.08 | | (48) in(all_146_1, all_101_6) = 0
% 16.28/3.08 | | (49) in(all_146_0, all_101_5) = 0
% 16.28/3.08 | | (50) ordered_pair(all_146_1, all_146_0) = all_101_4
% 16.28/3.08 | |
% 16.28/3.08 | | GROUND_INST: instantiating (t33_zfmisc_1) with all_101_8, all_101_7,
% 16.28/3.08 | | all_146_1, all_146_0, all_101_4, simplifying with (4), (5),
% 16.28/3.08 | | (13), (46), (47), (50) gives:
% 16.28/3.08 | | (51) all_146_0 = all_101_7 & all_146_1 = all_101_8
% 16.28/3.08 | |
% 16.28/3.08 | | ALPHA: (51) implies:
% 16.28/3.08 | | (52) all_146_1 = all_101_8
% 16.28/3.08 | | (53) all_146_0 = all_101_7
% 16.28/3.08 | |
% 16.28/3.08 | | REDUCE: (49), (53) imply:
% 16.28/3.08 | | (54) in(all_101_7, all_101_5) = 0
% 16.28/3.08 | |
% 16.28/3.08 | | REDUCE: (48), (52) imply:
% 16.28/3.08 | | (55) in(all_101_8, all_101_6) = 0
% 16.28/3.08 | |
% 16.28/3.08 | | GROUND_INST: instantiating (2) with all_101_1, 0, all_101_6, all_101_8,
% 16.28/3.08 | | simplifying with (10), (55) gives:
% 16.28/3.08 | | (56) all_101_1 = 0
% 16.28/3.08 | |
% 16.28/3.08 | | GROUND_INST: instantiating (2) with all_101_0, 0, all_101_5, all_101_7,
% 16.28/3.08 | | simplifying with (11), (54) gives:
% 16.28/3.08 | | (57) all_101_0 = 0
% 16.28/3.08 | |
% 16.28/3.08 | | BETA: splitting (42) gives:
% 16.28/3.08 | |
% 16.28/3.08 | | Case 1:
% 16.28/3.08 | | |
% 16.28/3.08 | | | (58) ~ (all_101_0 = 0)
% 16.28/3.08 | | |
% 16.28/3.08 | | | REDUCE: (57), (58) imply:
% 16.28/3.08 | | | (59) $false
% 16.28/3.08 | | |
% 16.28/3.08 | | | CLOSE: (59) is inconsistent.
% 16.28/3.08 | | |
% 16.28/3.08 | | Case 2:
% 16.28/3.08 | | |
% 16.28/3.08 | | | (60) ~ (all_101_1 = 0)
% 16.28/3.08 | | |
% 16.28/3.08 | | | REDUCE: (56), (60) imply:
% 16.28/3.08 | | | (61) $false
% 16.28/3.08 | | |
% 16.28/3.08 | | | CLOSE: (61) is inconsistent.
% 16.28/3.08 | | |
% 16.28/3.08 | | End of split
% 16.28/3.08 | |
% 16.28/3.08 | End of split
% 16.28/3.08 |
% 16.28/3.08 End of proof
% 16.28/3.08 % SZS output end Proof for theBenchmark
% 16.28/3.08
% 16.28/3.08 2469ms
%------------------------------------------------------------------------------