TSTP Solution File: SEU159+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU159+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 : n004.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 17:42:53 EDT 2023
% Result : Theorem 49.86s 7.49s
% Output : Proof 51.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU159+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 21:49:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.66 ________ _____
% 0.19/0.66 ___ __ \_________(_)________________________________
% 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.66
% 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.66 (2023-06-19)
% 0.19/0.66
% 0.19/0.66 (c) Philipp Rümmer, 2009-2023
% 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.66 Amanda Stjerna.
% 0.19/0.66 Free software under BSD-3-Clause.
% 0.19/0.66
% 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.66
% 0.19/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.67 Running up to 7 provers in parallel.
% 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.33/1.23 Prover 4: Preprocessing ...
% 3.33/1.23 Prover 1: Preprocessing ...
% 3.69/1.27 Prover 3: Preprocessing ...
% 3.69/1.27 Prover 0: Preprocessing ...
% 3.69/1.27 Prover 6: Preprocessing ...
% 3.69/1.27 Prover 2: Preprocessing ...
% 3.69/1.27 Prover 5: Preprocessing ...
% 9.00/2.09 Prover 1: Warning: ignoring some quantifiers
% 9.00/2.11 Prover 5: Proving ...
% 10.04/2.18 Prover 1: Constructing countermodel ...
% 10.48/2.22 Prover 3: Warning: ignoring some quantifiers
% 10.48/2.24 Prover 6: Proving ...
% 10.48/2.25 Prover 3: Constructing countermodel ...
% 11.09/2.29 Prover 4: Warning: ignoring some quantifiers
% 11.56/2.39 Prover 2: Proving ...
% 11.56/2.40 Prover 4: Constructing countermodel ...
% 11.56/2.40 Prover 0: Proving ...
% 14.45/2.77 Prover 3: gave up
% 14.45/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.45/2.82 Prover 7: Preprocessing ...
% 16.76/3.07 Prover 7: Warning: ignoring some quantifiers
% 16.76/3.11 Prover 7: Constructing countermodel ...
% 22.04/3.79 Prover 1: gave up
% 22.04/3.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.69/3.89 Prover 8: Preprocessing ...
% 25.08/4.14 Prover 8: Warning: ignoring some quantifiers
% 25.18/4.15 Prover 8: Constructing countermodel ...
% 31.26/4.98 Prover 8: gave up
% 31.26/4.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 31.74/5.05 Prover 9: Preprocessing ...
% 34.09/5.30 Prover 9: Warning: ignoring some quantifiers
% 34.09/5.31 Prover 9: Constructing countermodel ...
% 49.86/7.47 Prover 4: Found proof (size 62)
% 49.86/7.47 Prover 4: proved (6791ms)
% 49.86/7.47 Prover 9: stopped
% 49.86/7.47 Prover 0: stopped
% 49.86/7.48 Prover 2: stopped
% 49.86/7.48 Prover 7: stopped
% 49.86/7.48 Prover 6: stopped
% 49.86/7.49 Prover 5: stopped
% 49.86/7.49
% 49.86/7.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.86/7.49
% 49.86/7.50 % SZS output start Proof for theBenchmark
% 49.86/7.50 Assumptions after simplification:
% 49.86/7.50 ---------------------------------
% 49.86/7.50
% 50.89/7.50 (commutativity_k2_tarski)
% 50.89/7.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 50.89/7.53 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 50.89/7.53 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 50.89/7.53 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 50.89/7.53
% 50.89/7.53 (d2_tarski)
% 50.89/7.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 50.89/7.54 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 50.89/7.54 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 50.89/7.54 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) =
% 50.89/7.54 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 50.89/7.54 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~
% 50.89/7.54 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : !
% 50.89/7.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) =
% 50.89/7.54 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] :
% 50.89/7.54 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) &
% 50.89/7.54 (v5 = 0 | v4 = v2 | v4 = v1)))
% 50.89/7.54
% 50.89/7.54 (d3_tarski)
% 50.89/7.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 50.89/7.54 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 50.89/7.54 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 50.89/7.54 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 50.89/7.54 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 50.89/7.54 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 50.89/7.54 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 50.89/7.54 $i(v0) | in(v2, v1) = 0)
% 50.89/7.54
% 50.89/7.54 (d8_xboole_0)
% 50.89/7.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 50.89/7.55 (proper_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~
% 50.89/7.55 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 50.89/7.55 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 50.89/7.55 int] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1:
% 50.89/7.55 $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 50.89/7.55 proper_subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~
% 50.89/7.55 (subset(v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 50.89/7.55 proper_subset(v0, v0) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 50.89/7.55 (proper_subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0) &
% 50.89/7.55 ! [v0: $i] : ( ~ (proper_subset(v0, v0) = 0) | ~ $i(v0))
% 50.89/7.55
% 50.89/7.55 (t38_zfmisc_1)
% 50.89/7.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 50.89/7.55 any] : ? [v6: any] : (subset(v3, v2) = v4 & unordered_pair(v0, v1) = v3 &
% 50.89/7.55 in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6
% 50.89/7.55 = 0 & v5 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 50.89/7.55
% 50.89/7.55 (function-axioms)
% 50.89/7.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 50.89/7.56 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 50.89/7.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.89/7.56 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 50.89/7.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.89/7.56 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 50.89/7.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.89/7.56 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 50.89/7.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.89/7.56 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 50.89/7.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.89/7.56 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 50.89/7.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.89/7.56 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 50.89/7.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 50.89/7.56 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 50.89/7.56 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.89/7.56 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 50.89/7.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.89/7.56 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 50.89/7.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 50.89/7.56 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 50.89/7.56 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i]
% 50.89/7.56 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 50.89/7.56 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 50.89/7.56 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 50.89/7.56
% 50.89/7.56 Further assumptions not needed in the proof:
% 50.89/7.56 --------------------------------------------
% 50.89/7.56 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_xboole_0,
% 50.89/7.56 commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, d1_xboole_0, d1_zfmisc_1,
% 50.89/7.56 d2_xboole_0, d2_zfmisc_1, d3_xboole_0, d4_tarski, d4_xboole_0, d5_tarski,
% 50.89/7.56 d7_xboole_0, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski,
% 50.89/7.56 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski,
% 50.89/7.56 dt_k4_xboole_0, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0,
% 50.89/7.56 idempotence_k2_xboole_0, idempotence_k3_xboole_0, irreflexivity_r2_xboole_0,
% 50.89/7.56 l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1,
% 50.89/7.56 l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1,
% 50.89/7.56 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0,
% 50.89/7.56 t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1,
% 50.89/7.56 t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1,
% 50.89/7.56 t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1, t37_zfmisc_1,
% 50.89/7.56 t39_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1,
% 50.89/7.56 t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1, t69_enumset1,
% 50.89/7.56 t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole,
% 50.89/7.56 t8_xboole_1, t8_zfmisc_1, t9_zfmisc_1
% 50.89/7.56
% 50.89/7.56 Those formulas are unsatisfiable:
% 50.89/7.56 ---------------------------------
% 50.89/7.56
% 50.89/7.56 Begin of proof
% 50.89/7.56 |
% 50.89/7.57 | ALPHA: (commutativity_k2_tarski) implies:
% 50.89/7.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 50.89/7.57 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 50.89/7.57 | $i(v2)))
% 50.89/7.57 |
% 50.89/7.57 | ALPHA: (d2_tarski) implies:
% 50.89/7.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 50.89/7.57 | (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v2) | ~
% 50.89/7.57 | $i(v1) | ~ $i(v0))
% 50.89/7.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 50.89/7.57 | (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3) | ~ $i(v2) | ~
% 50.89/7.57 | $i(v1) | ~ $i(v0))
% 50.89/7.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 =
% 50.89/7.57 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~
% 50.89/7.57 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 50.89/7.57 |
% 50.89/7.57 | ALPHA: (d3_tarski) implies:
% 50.89/7.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 50.89/7.57 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 50.89/7.57 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 50.89/7.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 50.89/7.57 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 50.89/7.57 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 50.89/7.57 |
% 50.89/7.57 | ALPHA: (d8_xboole_0) implies:
% 50.89/7.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 50.89/7.57 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 50.89/7.57 | proper_subset(v0, v1) = v3))
% 50.89/7.57 |
% 50.89/7.57 | ALPHA: (function-axioms) implies:
% 50.89/7.58 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.89/7.58 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 50.89/7.58 |
% 50.89/7.58 | DELTA: instantiating (t38_zfmisc_1) with fresh symbols all_91_0, all_91_1,
% 50.89/7.58 | all_91_2, all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 50.89/7.58 | (9) subset(all_91_3, all_91_4) = all_91_2 & unordered_pair(all_91_6,
% 50.89/7.58 | all_91_5) = all_91_3 & in(all_91_5, all_91_4) = all_91_0 &
% 50.89/7.58 | in(all_91_6, all_91_4) = all_91_1 & $i(all_91_3) & $i(all_91_4) &
% 50.89/7.58 | $i(all_91_5) & $i(all_91_6) & ((all_91_0 = 0 & all_91_1 = 0 & ~
% 50.89/7.58 | (all_91_2 = 0)) | (all_91_2 = 0 & ( ~ (all_91_0 = 0) | ~ (all_91_1
% 50.89/7.58 | = 0))))
% 50.89/7.58 |
% 50.89/7.58 | ALPHA: (9) implies:
% 50.89/7.58 | (10) $i(all_91_6)
% 50.89/7.58 | (11) $i(all_91_5)
% 50.89/7.58 | (12) $i(all_91_4)
% 50.89/7.58 | (13) in(all_91_6, all_91_4) = all_91_1
% 51.48/7.58 | (14) in(all_91_5, all_91_4) = all_91_0
% 51.48/7.58 | (15) unordered_pair(all_91_6, all_91_5) = all_91_3
% 51.48/7.58 | (16) subset(all_91_3, all_91_4) = all_91_2
% 51.48/7.58 | (17) (all_91_0 = 0 & all_91_1 = 0 & ~ (all_91_2 = 0)) | (all_91_2 = 0 & (
% 51.48/7.58 | ~ (all_91_0 = 0) | ~ (all_91_1 = 0)))
% 51.48/7.58 |
% 51.48/7.58 | GROUND_INST: instantiating (1) with all_91_5, all_91_6, all_91_3, simplifying
% 51.48/7.58 | with (10), (11), (15) gives:
% 51.48/7.58 | (18) unordered_pair(all_91_5, all_91_6) = all_91_3 & $i(all_91_3)
% 51.48/7.58 |
% 51.48/7.58 | ALPHA: (18) implies:
% 51.48/7.58 | (19) $i(all_91_3)
% 51.48/7.58 |
% 51.48/7.58 | GROUND_INST: instantiating (5) with all_91_3, all_91_4, all_91_2, simplifying
% 51.48/7.58 | with (12), (16), (19) gives:
% 51.48/7.58 | (20) all_91_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 51.48/7.58 | all_91_3) = 0 & in(v0, all_91_4) = v1 & $i(v0))
% 51.50/7.58 |
% 51.50/7.58 | GROUND_INST: instantiating (7) with all_91_3, all_91_4, all_91_2, simplifying
% 51.50/7.58 | with (12), (16), (19) gives:
% 51.50/7.58 | (21) all_91_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & proper_subset(all_91_3,
% 51.50/7.58 | all_91_4) = v0)
% 51.50/7.58 |
% 51.50/7.58 | BETA: splitting (17) gives:
% 51.50/7.58 |
% 51.50/7.58 | Case 1:
% 51.50/7.58 | |
% 51.50/7.58 | | (22) all_91_0 = 0 & all_91_1 = 0 & ~ (all_91_2 = 0)
% 51.50/7.58 | |
% 51.50/7.58 | | ALPHA: (22) implies:
% 51.50/7.58 | | (23) all_91_1 = 0
% 51.50/7.58 | | (24) all_91_0 = 0
% 51.50/7.58 | | (25) ~ (all_91_2 = 0)
% 51.50/7.58 | |
% 51.50/7.58 | | REDUCE: (14), (24) imply:
% 51.50/7.58 | | (26) in(all_91_5, all_91_4) = 0
% 51.50/7.58 | |
% 51.50/7.58 | | REDUCE: (13), (23) imply:
% 51.50/7.58 | | (27) in(all_91_6, all_91_4) = 0
% 51.50/7.58 | |
% 51.50/7.58 | | BETA: splitting (20) gives:
% 51.50/7.58 | |
% 51.50/7.58 | | Case 1:
% 51.50/7.58 | | |
% 51.50/7.58 | | | (28) all_91_2 = 0
% 51.50/7.59 | | |
% 51.50/7.59 | | | REDUCE: (25), (28) imply:
% 51.50/7.59 | | | (29) $false
% 51.50/7.59 | | |
% 51.50/7.59 | | | CLOSE: (29) is inconsistent.
% 51.50/7.59 | | |
% 51.50/7.59 | | Case 2:
% 51.50/7.59 | | |
% 51.50/7.59 | | | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_91_3) = 0 &
% 51.50/7.59 | | | in(v0, all_91_4) = v1 & $i(v0))
% 51.50/7.59 | | |
% 51.50/7.59 | | | DELTA: instantiating (30) with fresh symbols all_274_0, all_274_1 gives:
% 51.50/7.59 | | | (31) ~ (all_274_0 = 0) & in(all_274_1, all_91_3) = 0 & in(all_274_1,
% 51.50/7.59 | | | all_91_4) = all_274_0 & $i(all_274_1)
% 51.50/7.59 | | |
% 51.50/7.59 | | | ALPHA: (31) implies:
% 51.50/7.59 | | | (32) ~ (all_274_0 = 0)
% 51.50/7.59 | | | (33) $i(all_274_1)
% 51.50/7.59 | | | (34) in(all_274_1, all_91_4) = all_274_0
% 51.50/7.59 | | | (35) in(all_274_1, all_91_3) = 0
% 51.50/7.59 | | |
% 51.50/7.59 | | | BETA: splitting (21) gives:
% 51.50/7.59 | | |
% 51.50/7.59 | | | Case 1:
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | (36) all_91_2 = 0
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | REDUCE: (25), (36) imply:
% 51.50/7.59 | | | | (37) $false
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | CLOSE: (37) is inconsistent.
% 51.50/7.59 | | | |
% 51.50/7.59 | | | Case 2:
% 51.50/7.59 | | | |
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | GROUND_INST: instantiating (4) with all_91_6, all_91_5, all_91_3,
% 51.50/7.59 | | | | all_274_1, simplifying with (10), (11), (15), (19), (33),
% 51.50/7.59 | | | | (35) gives:
% 51.50/7.59 | | | | (38) all_274_1 = all_91_5 | all_274_1 = all_91_6
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | BETA: splitting (38) gives:
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | Case 1:
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | (39) all_274_1 = all_91_5
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | REDUCE: (34), (39) imply:
% 51.50/7.59 | | | | | (40) in(all_91_5, all_91_4) = all_274_0
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | GROUND_INST: instantiating (8) with 0, all_274_0, all_91_4, all_91_5,
% 51.50/7.59 | | | | | simplifying with (26), (40) gives:
% 51.50/7.59 | | | | | (41) all_274_0 = 0
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | REDUCE: (32), (41) imply:
% 51.50/7.59 | | | | | (42) $false
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | CLOSE: (42) is inconsistent.
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | Case 2:
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | (43) all_274_1 = all_91_6
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | REDUCE: (34), (43) imply:
% 51.50/7.59 | | | | | (44) in(all_91_6, all_91_4) = all_274_0
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | GROUND_INST: instantiating (8) with 0, all_274_0, all_91_4, all_91_6,
% 51.50/7.59 | | | | | simplifying with (27), (44) gives:
% 51.50/7.59 | | | | | (45) all_274_0 = 0
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | REDUCE: (32), (45) imply:
% 51.50/7.59 | | | | | (46) $false
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | | CLOSE: (46) is inconsistent.
% 51.50/7.59 | | | | |
% 51.50/7.59 | | | | End of split
% 51.50/7.59 | | | |
% 51.50/7.59 | | | End of split
% 51.50/7.59 | | |
% 51.50/7.59 | | End of split
% 51.50/7.59 | |
% 51.50/7.59 | Case 2:
% 51.50/7.59 | |
% 51.50/7.59 | | (47) all_91_2 = 0 & ( ~ (all_91_0 = 0) | ~ (all_91_1 = 0))
% 51.50/7.59 | |
% 51.50/7.59 | | ALPHA: (47) implies:
% 51.50/7.59 | | (48) all_91_2 = 0
% 51.50/7.59 | | (49) ~ (all_91_0 = 0) | ~ (all_91_1 = 0)
% 51.50/7.59 | |
% 51.50/7.59 | | REDUCE: (16), (48) imply:
% 51.50/7.59 | | (50) subset(all_91_3, all_91_4) = 0
% 51.50/7.59 | |
% 51.50/7.59 | | GROUND_INST: instantiating (6) with all_91_3, all_91_4, all_91_5, all_91_0,
% 51.50/7.59 | | simplifying with (11), (12), (14), (19), (50) gives:
% 51.50/7.59 | | (51) all_91_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_91_5, all_91_3)
% 51.50/7.59 | | = v0)
% 51.50/7.59 | |
% 51.50/7.59 | | GROUND_INST: instantiating (6) with all_91_3, all_91_4, all_91_6, all_91_1,
% 51.50/7.59 | | simplifying with (10), (12), (13), (19), (50) gives:
% 51.50/7.59 | | (52) all_91_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_91_6, all_91_3)
% 51.50/7.59 | | = v0)
% 51.50/7.59 | |
% 51.50/7.59 | | BETA: splitting (49) gives:
% 51.50/7.59 | |
% 51.50/7.59 | | Case 1:
% 51.50/7.59 | | |
% 51.50/7.59 | | | (53) ~ (all_91_0 = 0)
% 51.50/7.59 | | |
% 51.50/7.59 | | | BETA: splitting (51) gives:
% 51.50/7.59 | | |
% 51.50/7.59 | | | Case 1:
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | (54) all_91_0 = 0
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | REDUCE: (53), (54) imply:
% 51.50/7.59 | | | | (55) $false
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | CLOSE: (55) is inconsistent.
% 51.50/7.59 | | | |
% 51.50/7.59 | | | Case 2:
% 51.50/7.59 | | | |
% 51.50/7.59 | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & in(all_91_5, all_91_3) = v0)
% 51.50/7.59 | | | |
% 51.50/7.60 | | | | DELTA: instantiating (56) with fresh symbol all_368_0 gives:
% 51.50/7.60 | | | | (57) ~ (all_368_0 = 0) & in(all_91_5, all_91_3) = all_368_0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | ALPHA: (57) implies:
% 51.50/7.60 | | | | (58) ~ (all_368_0 = 0)
% 51.50/7.60 | | | | (59) in(all_91_5, all_91_3) = all_368_0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | GROUND_INST: instantiating (3) with all_91_6, all_91_5, all_91_3,
% 51.50/7.60 | | | | all_368_0, simplifying with (10), (11), (15), (19), (59)
% 51.50/7.60 | | | | gives:
% 51.50/7.60 | | | | (60) all_368_0 = 0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | REDUCE: (58), (60) imply:
% 51.50/7.60 | | | | (61) $false
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | CLOSE: (61) is inconsistent.
% 51.50/7.60 | | | |
% 51.50/7.60 | | | End of split
% 51.50/7.60 | | |
% 51.50/7.60 | | Case 2:
% 51.50/7.60 | | |
% 51.50/7.60 | | | (62) ~ (all_91_1 = 0)
% 51.50/7.60 | | |
% 51.50/7.60 | | | BETA: splitting (52) gives:
% 51.50/7.60 | | |
% 51.50/7.60 | | | Case 1:
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | (63) all_91_1 = 0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | REDUCE: (62), (63) imply:
% 51.50/7.60 | | | | (64) $false
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | CLOSE: (64) is inconsistent.
% 51.50/7.60 | | | |
% 51.50/7.60 | | | Case 2:
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | (65) ? [v0: int] : ( ~ (v0 = 0) & in(all_91_6, all_91_3) = v0)
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | DELTA: instantiating (65) with fresh symbol all_370_0 gives:
% 51.50/7.60 | | | | (66) ~ (all_370_0 = 0) & in(all_91_6, all_91_3) = all_370_0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | ALPHA: (66) implies:
% 51.50/7.60 | | | | (67) ~ (all_370_0 = 0)
% 51.50/7.60 | | | | (68) in(all_91_6, all_91_3) = all_370_0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | GROUND_INST: instantiating (2) with all_91_6, all_91_5, all_91_3,
% 51.50/7.60 | | | | all_370_0, simplifying with (10), (11), (15), (19), (68)
% 51.50/7.60 | | | | gives:
% 51.50/7.60 | | | | (69) all_370_0 = 0
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | REDUCE: (67), (69) imply:
% 51.50/7.60 | | | | (70) $false
% 51.50/7.60 | | | |
% 51.50/7.60 | | | | CLOSE: (70) is inconsistent.
% 51.50/7.60 | | | |
% 51.50/7.60 | | | End of split
% 51.50/7.60 | | |
% 51.50/7.60 | | End of split
% 51.50/7.60 | |
% 51.50/7.60 | End of split
% 51.50/7.60 |
% 51.50/7.60 End of proof
% 51.50/7.60 % SZS output end Proof for theBenchmark
% 51.50/7.60
% 51.50/7.60 6939ms
%------------------------------------------------------------------------------