TSTP Solution File: SEU169+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU169+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 : 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 17:43:00 EDT 2023
% Result : Theorem 14.62s 2.91s
% Output : Proof 18.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU169+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 : n005.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 14:24:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.66 ________ _____
% 0.21/0.66 ___ __ \_________(_)________________________________
% 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66
% 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66 (2023-06-19)
% 0.21/0.66
% 0.21/0.66 (c) Philipp Rümmer, 2009-2023
% 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66 Amanda Stjerna.
% 0.21/0.66 Free software under BSD-3-Clause.
% 0.21/0.66
% 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66
% 0.21/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.67 Running up to 7 provers in parallel.
% 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.43/1.35 Prover 4: Preprocessing ...
% 3.43/1.36 Prover 1: Preprocessing ...
% 3.43/1.40 Prover 0: Preprocessing ...
% 3.43/1.40 Prover 5: Preprocessing ...
% 3.43/1.40 Prover 2: Preprocessing ...
% 3.43/1.40 Prover 3: Preprocessing ...
% 3.43/1.40 Prover 6: Preprocessing ...
% 11.83/2.45 Prover 1: Warning: ignoring some quantifiers
% 11.83/2.46 Prover 5: Proving ...
% 12.66/2.56 Prover 1: Constructing countermodel ...
% 12.83/2.57 Prover 3: Warning: ignoring some quantifiers
% 12.83/2.58 Prover 6: Proving ...
% 12.83/2.61 Prover 3: Constructing countermodel ...
% 13.53/2.66 Prover 4: Warning: ignoring some quantifiers
% 13.53/2.73 Prover 4: Constructing countermodel ...
% 13.53/2.78 Prover 2: Proving ...
% 13.53/2.85 Prover 0: Proving ...
% 14.62/2.91 Prover 3: proved (2220ms)
% 14.62/2.91
% 14.62/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.62/2.91
% 14.62/2.91 Prover 5: stopped
% 14.62/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.62/2.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.62/2.92 Prover 2: stopped
% 14.62/2.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.33/2.93 Prover 0: stopped
% 15.33/2.95 Prover 6: stopped
% 15.33/2.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.33/2.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.82/3.01 Prover 1: Found proof (size 39)
% 15.82/3.01 Prover 1: proved (2327ms)
% 15.82/3.01 Prover 4: stopped
% 15.82/3.06 Prover 8: Preprocessing ...
% 16.43/3.06 Prover 10: Preprocessing ...
% 16.43/3.07 Prover 7: Preprocessing ...
% 16.43/3.07 Prover 11: Preprocessing ...
% 16.52/3.08 Prover 13: Preprocessing ...
% 16.77/3.13 Prover 10: stopped
% 16.94/3.15 Prover 7: stopped
% 16.94/3.17 Prover 11: stopped
% 16.94/3.17 Prover 13: stopped
% 17.44/3.26 Prover 8: Warning: ignoring some quantifiers
% 17.44/3.28 Prover 8: Constructing countermodel ...
% 17.76/3.29 Prover 8: stopped
% 17.76/3.29
% 17.76/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.76/3.29
% 17.76/3.30 % SZS output start Proof for theBenchmark
% 17.76/3.31 Assumptions after simplification:
% 17.76/3.31 ---------------------------------
% 17.76/3.31
% 17.76/3.31 (d2_subset_1)
% 17.76/3.33 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~
% 17.76/3.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 &
% 17.76/3.33 empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) |
% 17.76/3.33 v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 17.76/3.33 (element(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 17.76/3.33 : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & (
% 17.76/3.33 ~ (v2 = 0) | v4 = 0)))))
% 17.76/3.33
% 17.76/3.33 (d4_tarski)
% 17.76/3.34 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~
% 17.76/3.34 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3)
% 17.76/3.34 & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v3, v5) = 0) | ~ $i(v5) | ? [v6:
% 17.76/3.34 int] : ( ~ (v6 = 0) & in(v5, v1) = v6))) & (v4 = 0 | ? [v5: $i] :
% 17.76/3.34 (in(v5, v1) = 0 & in(v3, v5) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1:
% 17.76/3.34 $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 17.76/3.34 int] : (v3 = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~
% 17.76/3.34 (in(v2, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & in(v4,
% 17.76/3.34 v0) = v5))) & ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ?
% 17.76/3.34 [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3)))))
% 17.76/3.34
% 17.76/3.34 (fc1_subset_1)
% 17.76/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int]
% 17.76/3.34 : ( ~ (v2 = 0) & empty(v1) = v2))
% 17.76/3.34
% 17.76/3.34 (l3_subset_1)
% 17.76/3.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (element(v1, v2) = 0 & powerset(v0)
% 17.76/3.34 = v2 & $i(v2) & $i(v1) & $i(v0) & ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 17.76/3.34 & in(v3, v1) = 0 & in(v3, v0) = v4 & $i(v3)))
% 17.76/3.34
% 17.76/3.34 (t99_zfmisc_1)
% 17.76/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | union(v1) =
% 17.76/3.34 v0)
% 17.76/3.34
% 17.76/3.34 (function-axioms)
% 17.76/3.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.76/3.35 [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 17.76/3.35 (are_equipotent(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.76/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 17.76/3.35 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.76/3.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 17.76/3.35 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.76/3.35 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 17.76/3.35 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.76/3.35 : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 17.76/3.35 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.76/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 17.76/3.35 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.76/3.35 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.76/3.35 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.76/3.35 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) =
% 17.76/3.35 v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.76/3.35 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~
% 17.76/3.35 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.76/3.35 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 17.76/3.35 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.76/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.76/3.35 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 17.76/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.76/3.35 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 17.76/3.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 17.76/3.35 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 17.76/3.35 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.76/3.35 $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) =
% 17.76/3.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.76/3.35 (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 17.76/3.35
% 17.76/3.35 Further assumptions not needed in the proof:
% 17.76/3.35 --------------------------------------------
% 17.76/3.35 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 17.76/3.35 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 17.76/3.35 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski,
% 17.76/3.35 d3_xboole_0, d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0, dt_k1_tarski,
% 17.76/3.35 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 17.76/3.35 dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, dt_m1_subset_1,
% 17.76/3.35 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0,
% 17.76/3.35 idempotence_k2_xboole_0, idempotence_k3_xboole_0, irreflexivity_r2_xboole_0,
% 17.76/3.35 l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1,
% 17.76/3.35 l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1,
% 17.76/3.35 rc1_subset_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 17.76/3.35 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1,
% 17.76/3.35 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1,
% 17.76/3.35 t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1,
% 17.76/3.35 t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1, t37_zfmisc_1,
% 17.76/3.35 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_xboole_0, t3_xboole_1,
% 17.76/3.35 t40_xboole_1, t45_xboole_1, t46_zfmisc_1, t48_xboole_1, t4_boole, t4_xboole_0,
% 17.76/3.35 t60_xboole_1, t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_boole, t6_zfmisc_1,
% 17.76/3.35 t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1,
% 17.76/3.35 t92_zfmisc_1, t9_tarski, t9_zfmisc_1
% 17.76/3.35
% 17.76/3.35 Those formulas are unsatisfiable:
% 17.76/3.35 ---------------------------------
% 17.76/3.35
% 17.76/3.35 Begin of proof
% 17.76/3.35 |
% 17.76/3.35 | ALPHA: (d2_subset_1) implies:
% 17.76/3.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 17.76/3.35 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3
% 17.76/3.35 | & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 =
% 17.76/3.35 | 0) | v4 = 0)))))
% 17.76/3.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 17.76/3.35 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4
% 17.76/3.35 | & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2
% 17.76/3.36 | = 0) | v4 = 0)))))
% 17.76/3.36 |
% 17.76/3.36 | ALPHA: (d4_tarski) implies:
% 17.76/3.36 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~
% 17.76/3.36 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) = v3)
% 17.76/3.36 | | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v2, v4) = 0) | ~ $i(v4) | ?
% 17.76/3.36 | [v5: int] : ( ~ (v5 = 0) & in(v4, v0) = v5))) & ! [v2: $i] : (
% 17.76/3.36 | ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (in(v3, v0) = 0 &
% 17.76/3.36 | in(v2, v3) = 0 & $i(v3)))))
% 17.76/3.36 |
% 17.76/3.36 | ALPHA: (function-axioms) implies:
% 17.76/3.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.76/3.36 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 17.76/3.36 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.76/3.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 17.76/3.36 |
% 17.76/3.36 | DELTA: instantiating (l3_subset_1) with fresh symbols all_101_0, all_101_1,
% 17.76/3.36 | all_101_2 gives:
% 17.76/3.36 | (6) element(all_101_1, all_101_0) = 0 & powerset(all_101_2) = all_101_0 &
% 17.76/3.36 | $i(all_101_0) & $i(all_101_1) & $i(all_101_2) & ? [v0: $i] : ? [v1:
% 17.76/3.36 | int] : ( ~ (v1 = 0) & in(v0, all_101_1) = 0 & in(v0, all_101_2) = v1
% 17.76/3.36 | & $i(v0))
% 17.76/3.36 |
% 17.76/3.36 | ALPHA: (6) implies:
% 17.76/3.36 | (7) $i(all_101_2)
% 17.76/3.36 | (8) $i(all_101_1)
% 17.76/3.36 | (9) $i(all_101_0)
% 17.76/3.36 | (10) powerset(all_101_2) = all_101_0
% 17.76/3.36 | (11) element(all_101_1, all_101_0) = 0
% 17.76/3.36 | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_101_1) = 0 &
% 17.76/3.36 | in(v0, all_101_2) = v1 & $i(v0))
% 17.76/3.36 |
% 17.76/3.36 | DELTA: instantiating (12) with fresh symbols all_122_0, all_122_1 gives:
% 17.76/3.36 | (13) ~ (all_122_0 = 0) & in(all_122_1, all_101_1) = 0 & in(all_122_1,
% 17.76/3.36 | all_101_2) = all_122_0 & $i(all_122_1)
% 17.76/3.36 |
% 17.76/3.36 | ALPHA: (13) implies:
% 17.76/3.36 | (14) ~ (all_122_0 = 0)
% 17.76/3.36 | (15) $i(all_122_1)
% 17.76/3.36 | (16) in(all_122_1, all_101_2) = all_122_0
% 17.76/3.36 | (17) in(all_122_1, all_101_1) = 0
% 17.76/3.36 |
% 17.76/3.36 | GROUND_INST: instantiating (t99_zfmisc_1) with all_101_2, all_101_0,
% 17.76/3.36 | simplifying with (7), (10) gives:
% 18.12/3.36 | (18) union(all_101_0) = all_101_2
% 18.12/3.36 |
% 18.12/3.36 | GROUND_INST: instantiating (fc1_subset_1) with all_101_2, all_101_0,
% 18.12/3.36 | simplifying with (7), (10) gives:
% 18.12/3.36 | (19) ? [v0: int] : ( ~ (v0 = 0) & empty(all_101_0) = v0)
% 18.12/3.36 |
% 18.12/3.37 | GROUND_INST: instantiating (2) with all_101_0, all_101_1, 0, simplifying with
% 18.12/3.37 | (8), (9), (11) gives:
% 18.12/3.37 | (20) ? [v0: any] : ? [v1: any] : (empty(all_101_0) = v0 &
% 18.12/3.37 | empty(all_101_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 18.12/3.37 |
% 18.12/3.37 | GROUND_INST: instantiating (1) with all_101_0, all_101_1, 0, simplifying with
% 18.12/3.37 | (8), (9), (11) gives:
% 18.12/3.37 | (21) ? [v0: any] : ? [v1: any] : (empty(all_101_0) = v0 & in(all_101_1,
% 18.12/3.37 | all_101_0) = v1 & (v1 = 0 | v0 = 0))
% 18.12/3.37 |
% 18.12/3.37 | DELTA: instantiating (19) with fresh symbol all_137_0 gives:
% 18.12/3.37 | (22) ~ (all_137_0 = 0) & empty(all_101_0) = all_137_0
% 18.12/3.37 |
% 18.12/3.37 | ALPHA: (22) implies:
% 18.12/3.37 | (23) ~ (all_137_0 = 0)
% 18.12/3.37 | (24) empty(all_101_0) = all_137_0
% 18.12/3.37 |
% 18.12/3.37 | DELTA: instantiating (21) with fresh symbols all_141_0, all_141_1 gives:
% 18.12/3.37 | (25) empty(all_101_0) = all_141_1 & in(all_101_1, all_101_0) = all_141_0 &
% 18.12/3.37 | (all_141_0 = 0 | all_141_1 = 0)
% 18.12/3.37 |
% 18.12/3.37 | ALPHA: (25) implies:
% 18.12/3.37 | (26) in(all_101_1, all_101_0) = all_141_0
% 18.12/3.37 | (27) empty(all_101_0) = all_141_1
% 18.12/3.37 | (28) all_141_0 = 0 | all_141_1 = 0
% 18.12/3.37 |
% 18.12/3.37 | DELTA: instantiating (20) with fresh symbols all_143_0, all_143_1 gives:
% 18.12/3.37 | (29) empty(all_101_0) = all_143_1 & empty(all_101_1) = all_143_0 & ( ~
% 18.12/3.37 | (all_143_1 = 0) | all_143_0 = 0)
% 18.12/3.37 |
% 18.12/3.37 | ALPHA: (29) implies:
% 18.12/3.37 | (30) empty(all_101_0) = all_143_1
% 18.12/3.37 |
% 18.12/3.37 | GROUND_INST: instantiating (4) with all_141_1, all_143_1, all_101_0,
% 18.12/3.37 | simplifying with (27), (30) gives:
% 18.12/3.37 | (31) all_143_1 = all_141_1
% 18.12/3.37 |
% 18.12/3.37 | GROUND_INST: instantiating (4) with all_137_0, all_143_1, all_101_0,
% 18.12/3.37 | simplifying with (24), (30) gives:
% 18.12/3.37 | (32) all_143_1 = all_137_0
% 18.12/3.37 |
% 18.12/3.37 | COMBINE_EQS: (31), (32) imply:
% 18.12/3.37 | (33) all_141_1 = all_137_0
% 18.12/3.37 |
% 18.12/3.37 | SIMP: (33) implies:
% 18.12/3.37 | (34) all_141_1 = all_137_0
% 18.12/3.37 |
% 18.12/3.37 | BETA: splitting (28) gives:
% 18.12/3.37 |
% 18.12/3.37 | Case 1:
% 18.12/3.37 | |
% 18.12/3.37 | | (35) all_141_0 = 0
% 18.12/3.37 | |
% 18.12/3.37 | | REDUCE: (26), (35) imply:
% 18.12/3.37 | | (36) in(all_101_1, all_101_0) = 0
% 18.12/3.37 | |
% 18.12/3.37 | | GROUND_INST: instantiating (3) with all_101_0, all_101_2, simplifying with
% 18.12/3.37 | | (7), (9), (18) gives:
% 18.12/3.37 | | (37) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_2) = v1) |
% 18.12/3.37 | | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v0, v2) = 0) | ~ $i(v2) | ?
% 18.12/3.37 | | [v3: int] : ( ~ (v3 = 0) & in(v2, all_101_0) = v3))) & ! [v0:
% 18.12/3.37 | | $i] : ( ~ (in(v0, all_101_2) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.12/3.37 | | (in(v1, all_101_0) = 0 & in(v0, v1) = 0 & $i(v1)))
% 18.12/3.37 | |
% 18.12/3.37 | | ALPHA: (37) implies:
% 18.12/3.37 | | (38) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_2) = v1) |
% 18.12/3.37 | | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v0, v2) = 0) | ~ $i(v2) | ?
% 18.12/3.37 | | [v3: int] : ( ~ (v3 = 0) & in(v2, all_101_0) = v3)))
% 18.12/3.37 | |
% 18.12/3.37 | | GROUND_INST: instantiating (38) with all_122_1, all_122_0, simplifying with
% 18.12/3.37 | | (15), (16) gives:
% 18.12/3.38 | | (39) all_122_0 = 0 | ! [v0: $i] : ( ~ (in(all_122_1, v0) = 0) | ~
% 18.12/3.38 | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_101_0) = v1))
% 18.12/3.38 | |
% 18.12/3.38 | | BETA: splitting (39) gives:
% 18.12/3.38 | |
% 18.12/3.38 | | Case 1:
% 18.12/3.38 | | |
% 18.12/3.38 | | | (40) all_122_0 = 0
% 18.12/3.38 | | |
% 18.12/3.38 | | | REDUCE: (14), (40) imply:
% 18.12/3.38 | | | (41) $false
% 18.18/3.38 | | |
% 18.18/3.38 | | | CLOSE: (41) is inconsistent.
% 18.18/3.38 | | |
% 18.18/3.38 | | Case 2:
% 18.18/3.38 | | |
% 18.18/3.38 | | | (42) ! [v0: $i] : ( ~ (in(all_122_1, v0) = 0) | ~ $i(v0) | ? [v1:
% 18.18/3.38 | | | int] : ( ~ (v1 = 0) & in(v0, all_101_0) = v1))
% 18.18/3.38 | | |
% 18.18/3.38 | | | GROUND_INST: instantiating (42) with all_101_1, simplifying with (8), (17)
% 18.18/3.38 | | | gives:
% 18.18/3.38 | | | (43) ? [v0: int] : ( ~ (v0 = 0) & in(all_101_1, all_101_0) = v0)
% 18.18/3.38 | | |
% 18.18/3.38 | | | DELTA: instantiating (43) with fresh symbol all_167_0 gives:
% 18.18/3.38 | | | (44) ~ (all_167_0 = 0) & in(all_101_1, all_101_0) = all_167_0
% 18.18/3.38 | | |
% 18.18/3.38 | | | ALPHA: (44) implies:
% 18.18/3.38 | | | (45) ~ (all_167_0 = 0)
% 18.18/3.38 | | | (46) in(all_101_1, all_101_0) = all_167_0
% 18.18/3.38 | | |
% 18.18/3.38 | | | GROUND_INST: instantiating (5) with 0, all_167_0, all_101_0, all_101_1,
% 18.18/3.38 | | | simplifying with (36), (46) gives:
% 18.18/3.38 | | | (47) all_167_0 = 0
% 18.18/3.38 | | |
% 18.18/3.38 | | | REDUCE: (45), (47) imply:
% 18.18/3.38 | | | (48) $false
% 18.18/3.38 | | |
% 18.18/3.38 | | | CLOSE: (48) is inconsistent.
% 18.18/3.38 | | |
% 18.18/3.38 | | End of split
% 18.18/3.38 | |
% 18.18/3.38 | Case 2:
% 18.18/3.38 | |
% 18.18/3.38 | | (49) all_141_1 = 0
% 18.18/3.38 | |
% 18.18/3.38 | | COMBINE_EQS: (34), (49) imply:
% 18.18/3.38 | | (50) all_137_0 = 0
% 18.18/3.38 | |
% 18.18/3.38 | | SIMP: (50) implies:
% 18.18/3.38 | | (51) all_137_0 = 0
% 18.18/3.38 | |
% 18.18/3.38 | | REDUCE: (23), (51) imply:
% 18.18/3.38 | | (52) $false
% 18.18/3.38 | |
% 18.18/3.38 | | CLOSE: (52) is inconsistent.
% 18.18/3.38 | |
% 18.18/3.38 | End of split
% 18.18/3.38 |
% 18.18/3.38 End of proof
% 18.18/3.38 % SZS output end Proof for theBenchmark
% 18.18/3.38
% 18.18/3.38 2724ms
%------------------------------------------------------------------------------