TSTP Solution File: SET951+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 15:27:10 EDT 2023
% Result : Theorem 8.95s 1.99s
% Output : Proof 11.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:49:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.07/1.03 Prover 1: Preprocessing ...
% 2.07/1.03 Prover 4: Preprocessing ...
% 2.67/1.07 Prover 6: Preprocessing ...
% 2.67/1.07 Prover 5: Preprocessing ...
% 2.67/1.07 Prover 2: Preprocessing ...
% 2.67/1.07 Prover 3: Preprocessing ...
% 2.67/1.07 Prover 0: Preprocessing ...
% 4.58/1.45 Prover 1: Warning: ignoring some quantifiers
% 4.58/1.45 Prover 4: Warning: ignoring some quantifiers
% 4.58/1.47 Prover 5: Proving ...
% 4.58/1.47 Prover 6: Proving ...
% 4.95/1.48 Prover 4: Constructing countermodel ...
% 4.95/1.48 Prover 3: Warning: ignoring some quantifiers
% 4.95/1.48 Prover 1: Constructing countermodel ...
% 4.95/1.49 Prover 3: Constructing countermodel ...
% 4.95/1.52 Prover 0: Proving ...
% 5.79/1.53 Prover 2: Proving ...
% 8.95/1.99 Prover 0: proved (1356ms)
% 8.95/1.99
% 8.95/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.95/1.99
% 8.95/1.99 Prover 3: stopped
% 8.95/2.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.95/2.00 Prover 6: stopped
% 8.95/2.00 Prover 5: stopped
% 8.95/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.95/2.01 Prover 2: stopped
% 8.95/2.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.95/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.95/2.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.95/2.02 Prover 7: Preprocessing ...
% 8.95/2.02 Prover 8: Preprocessing ...
% 8.95/2.04 Prover 13: Preprocessing ...
% 8.95/2.04 Prover 11: Preprocessing ...
% 8.95/2.05 Prover 10: Preprocessing ...
% 8.95/2.11 Prover 7: Warning: ignoring some quantifiers
% 8.95/2.11 Prover 8: Warning: ignoring some quantifiers
% 8.95/2.12 Prover 8: Constructing countermodel ...
% 8.95/2.13 Prover 10: Warning: ignoring some quantifiers
% 8.95/2.13 Prover 7: Constructing countermodel ...
% 8.95/2.13 Prover 10: Constructing countermodel ...
% 8.95/2.15 Prover 13: Warning: ignoring some quantifiers
% 8.95/2.16 Prover 4: Found proof (size 102)
% 8.95/2.16 Prover 4: proved (1518ms)
% 8.95/2.16 Prover 1: stopped
% 8.95/2.16 Prover 10: stopped
% 8.95/2.16 Prover 8: stopped
% 8.95/2.16 Prover 13: Constructing countermodel ...
% 9.88/2.17 Prover 13: stopped
% 9.88/2.17 Prover 7: stopped
% 9.88/2.19 Prover 11: Warning: ignoring some quantifiers
% 9.88/2.20 Prover 11: Constructing countermodel ...
% 9.88/2.20 Prover 11: stopped
% 9.88/2.20
% 9.88/2.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.88/2.20
% 10.56/2.25 % SZS output start Proof for theBenchmark
% 10.56/2.25 Assumptions after simplification:
% 10.56/2.25 ---------------------------------
% 10.56/2.25
% 10.56/2.25 (commutativity_k3_xboole_0)
% 10.87/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 10.87/2.27 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 10.87/2.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 10.87/2.27 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 10.87/2.27
% 10.87/2.27 (d2_zfmisc_1)
% 10.87/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 10.87/2.28 $i] : ! [v6: $i] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~
% 10.87/2.28 (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ~ $i(v6) | ~ $i(v5) |
% 10.87/2.28 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any]
% 10.87/2.28 : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 10.87/2.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.28 (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 10.87/2.28 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] :
% 10.87/2.28 (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) &
% 10.87/2.28 $i(v4))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 =
% 10.87/2.28 v0 | ~ (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.87/2.28 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 10.87/2.28 int] : ? [v9: int] : ? [v10: $i] : (in(v4, v0) = v5 & $i(v7) & $i(v6) &
% 10.87/2.28 $i(v4) & ( ~ (v5 = 0) | ! [v11: $i] : ! [v12: $i] : ( ~
% 10.87/2.28 (ordered_pair(v11, v12) = v4) | ~ $i(v12) | ~ $i(v11) | ? [v13:
% 10.87/2.28 any] : ? [v14: any] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~
% 10.87/2.29 (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 =
% 10.87/2.29 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 10.87/2.29
% 10.87/2.29 (d3_xboole_0)
% 10.87/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.87/2.29 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 10.87/2.29 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 10.87/2.29 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 10.87/2.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 10.87/2.29 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 10.87/2.29 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 10.87/2.29 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 10.87/2.29 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 10.87/2.29 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 10.87/2.29 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 10.87/2.29 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 10.87/2.29 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 10.87/2.30 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.87/2.30 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 10.87/2.30 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 10.87/2.30 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.87/2.30 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 10.87/2.30 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 10.87/2.30 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 10.87/2.30 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 10.87/2.30 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.87/2.30 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 10.87/2.30 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 10.87/2.30 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 10.87/2.30 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 10.87/2.30
% 10.87/2.30 (t104_zfmisc_1)
% 10.87/2.30 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.87/2.30 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 10.87/2.30 (cartesian_product2(v3, v4) = v6 & cartesian_product2(v1, v2) = v5 &
% 10.87/2.30 set_intersection2(v5, v6) = v7 & set_intersection2(v2, v4) = v9 &
% 10.87/2.30 set_intersection2(v1, v3) = v8 & in(v0, v7) = 0 & $i(v9) & $i(v8) & $i(v7) &
% 10.87/2.30 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v10: $i]
% 10.87/2.30 : ! [v11: $i] : ( ~ (ordered_pair(v10, v11) = v0) | ~ $i(v11) | ~ $i(v10)
% 10.87/2.30 | ? [v12: any] : ? [v13: any] : (in(v11, v9) = v13 & in(v10, v8) = v12 &
% 10.87/2.30 ( ~ (v13 = 0) | ~ (v12 = 0)))))
% 10.87/2.30
% 10.87/2.30 (t33_zfmisc_1)
% 10.87/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 10.87/2.30 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~
% 10.87/2.30 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 10.87/2.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (ordered_pair(v2, v3) =
% 10.87/2.30 v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 10.87/2.30 ~ $i(v0))
% 10.87/2.30
% 10.87/2.30 (function-axioms)
% 10.87/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 10.87/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 10.87/2.30 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 10.87/2.30 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 10.87/2.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.87/2.30 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 10.87/2.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.87/2.30 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 10.87/2.30 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.87/2.30
% 10.87/2.30 Further assumptions not needed in the proof:
% 10.87/2.30 --------------------------------------------
% 10.87/2.30 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1,
% 10.87/2.30 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 10.87/2.30
% 10.87/2.30 Those formulas are unsatisfiable:
% 10.87/2.30 ---------------------------------
% 10.87/2.30
% 10.87/2.30 Begin of proof
% 10.87/2.30 |
% 10.87/2.30 | ALPHA: (commutativity_k3_xboole_0) implies:
% 10.87/2.31 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 10.87/2.31 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 10.87/2.31 | v2 & $i(v2)))
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (d2_zfmisc_1) implies:
% 10.87/2.31 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.31 | (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) |
% 10.87/2.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] :
% 10.87/2.31 | (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5)
% 10.87/2.31 | & $i(v4)))
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (d3_xboole_0) implies:
% 10.87/2.31 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.31 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) |
% 10.87/2.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.87/2.31 | (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 10.87/2.31 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.31 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ~ $i(v3) |
% 10.87/2.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.87/2.31 | (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 10.87/2.31 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.31 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) |
% 10.87/2.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 10.87/2.31 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 10.87/2.31 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3)
% 10.87/2.31 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 10.87/2.31 | (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 10.87/2.31 | 0))))
% 10.87/2.31 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 10.87/2.31 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3)
% 10.87/2.31 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 10.87/2.31 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 10.87/2.31 | 0))))
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (t33_zfmisc_1) implies:
% 10.87/2.31 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.87/2.31 | (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) =
% 10.87/2.31 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 10.87/2.31 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.87/2.31 | (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) =
% 10.87/2.31 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (function-axioms) implies:
% 10.87/2.31 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 10.87/2.31 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 10.87/2.31 | v0))
% 10.87/2.31 |
% 10.87/2.31 | DELTA: instantiating (t104_zfmisc_1) with fresh symbols all_18_0, all_18_1,
% 10.87/2.31 | all_18_2, all_18_3, all_18_4, all_18_5, all_18_6, all_18_7, all_18_8,
% 10.87/2.31 | all_18_9 gives:
% 10.87/2.32 | (11) cartesian_product2(all_18_6, all_18_5) = all_18_3 &
% 10.87/2.32 | cartesian_product2(all_18_8, all_18_7) = all_18_4 &
% 10.87/2.32 | set_intersection2(all_18_4, all_18_3) = all_18_2 &
% 10.87/2.32 | set_intersection2(all_18_7, all_18_5) = all_18_0 &
% 10.87/2.32 | set_intersection2(all_18_8, all_18_6) = all_18_1 & in(all_18_9,
% 10.87/2.32 | all_18_2) = 0 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) &
% 10.87/2.32 | $i(all_18_3) & $i(all_18_4) & $i(all_18_5) & $i(all_18_6) &
% 10.87/2.32 | $i(all_18_7) & $i(all_18_8) & $i(all_18_9) & ! [v0: $i] : ! [v1: $i]
% 10.87/2.32 | : ( ~ (ordered_pair(v0, v1) = all_18_9) | ~ $i(v1) | ~ $i(v0) | ?
% 10.87/2.32 | [v2: any] : ? [v3: any] : (in(v1, all_18_0) = v3 & in(v0, all_18_1)
% 10.87/2.32 | = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 10.87/2.32 |
% 10.87/2.32 | ALPHA: (11) implies:
% 10.87/2.32 | (12) $i(all_18_9)
% 10.87/2.32 | (13) $i(all_18_8)
% 10.87/2.32 | (14) $i(all_18_7)
% 10.87/2.32 | (15) $i(all_18_6)
% 10.87/2.32 | (16) $i(all_18_5)
% 10.87/2.32 | (17) $i(all_18_4)
% 10.87/2.32 | (18) $i(all_18_3)
% 10.87/2.32 | (19) $i(all_18_2)
% 10.87/2.32 | (20) in(all_18_9, all_18_2) = 0
% 10.87/2.32 | (21) set_intersection2(all_18_8, all_18_6) = all_18_1
% 10.87/2.32 | (22) set_intersection2(all_18_7, all_18_5) = all_18_0
% 10.87/2.32 | (23) set_intersection2(all_18_4, all_18_3) = all_18_2
% 10.87/2.32 | (24) cartesian_product2(all_18_8, all_18_7) = all_18_4
% 10.87/2.32 | (25) cartesian_product2(all_18_6, all_18_5) = all_18_3
% 10.87/2.32 | (26) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_18_9) | ~
% 10.87/2.32 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_18_0)
% 10.87/2.32 | = v3 & in(v0, all_18_1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 10.87/2.32 |
% 10.87/2.32 | GROUND_INST: instantiating (1) with all_18_6, all_18_8, all_18_1, simplifying
% 10.87/2.32 | with (13), (15), (21) gives:
% 10.87/2.32 | (27) set_intersection2(all_18_6, all_18_8) = all_18_1 & $i(all_18_1)
% 10.87/2.32 |
% 10.87/2.32 | ALPHA: (27) implies:
% 10.87/2.32 | (28) $i(all_18_1)
% 10.87/2.32 |
% 10.87/2.32 | GROUND_INST: instantiating (1) with all_18_5, all_18_7, all_18_0, simplifying
% 10.87/2.32 | with (14), (16), (22) gives:
% 10.87/2.32 | (29) set_intersection2(all_18_5, all_18_7) = all_18_0 & $i(all_18_0)
% 10.87/2.32 |
% 10.87/2.32 | ALPHA: (29) implies:
% 10.87/2.32 | (30) $i(all_18_0)
% 10.87/2.32 |
% 10.87/2.32 | GROUND_INST: instantiating (5) with all_18_4, all_18_3, all_18_2, all_18_9,
% 10.87/2.32 | simplifying with (12), (17), (18), (19), (20), (23) gives:
% 10.87/2.32 | (31) in(all_18_9, all_18_3) = 0 & in(all_18_9, all_18_4) = 0
% 10.87/2.32 |
% 10.87/2.32 | ALPHA: (31) implies:
% 10.87/2.32 | (32) in(all_18_9, all_18_4) = 0
% 10.87/2.32 | (33) in(all_18_9, all_18_3) = 0
% 10.87/2.32 |
% 10.87/2.32 | GROUND_INST: instantiating (2) with all_18_8, all_18_7, all_18_4, all_18_9,
% 10.87/2.32 | simplifying with (12), (13), (14), (17), (24), (32) gives:
% 10.87/2.32 | (34) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_18_9 & in(v1,
% 10.87/2.32 | all_18_7) = 0 & in(v0, all_18_8) = 0 & $i(v1) & $i(v0))
% 10.87/2.32 |
% 10.87/2.33 | GROUND_INST: instantiating (2) with all_18_6, all_18_5, all_18_3, all_18_9,
% 10.87/2.33 | simplifying with (12), (15), (16), (18), (25), (33) gives:
% 10.87/2.33 | (35) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_18_9 & in(v1,
% 10.87/2.33 | all_18_5) = 0 & in(v0, all_18_6) = 0 & $i(v1) & $i(v0))
% 10.87/2.33 |
% 10.87/2.33 | DELTA: instantiating (34) with fresh symbols all_40_0, all_40_1 gives:
% 10.87/2.33 | (36) ordered_pair(all_40_1, all_40_0) = all_18_9 & in(all_40_0, all_18_7) =
% 10.87/2.33 | 0 & in(all_40_1, all_18_8) = 0 & $i(all_40_0) & $i(all_40_1)
% 10.87/2.33 |
% 10.87/2.33 | ALPHA: (36) implies:
% 10.87/2.33 | (37) $i(all_40_1)
% 10.87/2.33 | (38) $i(all_40_0)
% 10.87/2.33 | (39) in(all_40_1, all_18_8) = 0
% 10.87/2.33 | (40) in(all_40_0, all_18_7) = 0
% 10.87/2.33 | (41) ordered_pair(all_40_1, all_40_0) = all_18_9
% 10.87/2.33 |
% 10.87/2.33 | DELTA: instantiating (35) with fresh symbols all_42_0, all_42_1 gives:
% 10.87/2.33 | (42) ordered_pair(all_42_1, all_42_0) = all_18_9 & in(all_42_0, all_18_5) =
% 10.87/2.33 | 0 & in(all_42_1, all_18_6) = 0 & $i(all_42_0) & $i(all_42_1)
% 10.87/2.33 |
% 10.87/2.33 | ALPHA: (42) implies:
% 10.87/2.33 | (43) $i(all_42_1)
% 10.87/2.33 | (44) $i(all_42_0)
% 10.87/2.33 | (45) in(all_42_1, all_18_6) = 0
% 10.87/2.33 | (46) in(all_42_0, all_18_5) = 0
% 10.87/2.33 | (47) ordered_pair(all_42_1, all_42_0) = all_18_9
% 10.87/2.33 |
% 10.87/2.33 | GROUND_INST: instantiating (6) with all_18_8, all_18_6, all_18_1, all_40_1, 0,
% 10.87/2.33 | simplifying with (13), (15), (21), (28), (37), (39) gives:
% 10.87/2.33 | (48) ? [v0: any] : ? [v1: any] : (in(all_40_1, all_18_1) = v0 &
% 10.87/2.33 | in(all_40_1, all_18_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.33 |
% 10.87/2.33 | GROUND_INST: instantiating (3) with all_18_8, all_18_6, all_18_1, all_40_1,
% 10.87/2.33 | simplifying with (13), (15), (21), (28), (37), (39) gives:
% 10.87/2.33 | (49) ? [v0: any] : ? [v1: any] : (in(all_40_1, all_18_1) = v1 &
% 10.87/2.33 | in(all_40_1, all_18_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.33 |
% 10.87/2.33 | GROUND_INST: instantiating (6) with all_18_7, all_18_5, all_18_0, all_40_0, 0,
% 10.87/2.33 | simplifying with (14), (16), (22), (30), (38), (40) gives:
% 10.87/2.33 | (50) ? [v0: any] : ? [v1: any] : (in(all_40_0, all_18_0) = v0 &
% 10.87/2.33 | in(all_40_0, all_18_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.33 |
% 10.87/2.33 | GROUND_INST: instantiating (3) with all_18_7, all_18_5, all_18_0, all_40_0,
% 10.87/2.33 | simplifying with (14), (16), (22), (30), (38), (40) gives:
% 10.87/2.33 | (51) ? [v0: any] : ? [v1: any] : (in(all_40_0, all_18_0) = v1 &
% 10.87/2.33 | in(all_40_0, all_18_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.33 |
% 10.87/2.33 | GROUND_INST: instantiating (4) with all_18_8, all_18_6, all_18_1, all_42_1,
% 10.87/2.33 | simplifying with (13), (15), (21), (28), (43), (45) gives:
% 10.87/2.34 | (52) ? [v0: any] : ? [v1: any] : (in(all_42_1, all_18_1) = v1 &
% 10.87/2.34 | in(all_42_1, all_18_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.34 |
% 10.87/2.34 | GROUND_INST: instantiating (7) with all_18_7, all_18_5, all_18_0, all_42_0, 0,
% 10.87/2.34 | simplifying with (14), (16), (22), (30), (44), (46) gives:
% 10.87/2.34 | (53) ? [v0: any] : ? [v1: any] : (in(all_42_0, all_18_0) = v0 &
% 10.87/2.34 | in(all_42_0, all_18_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.34 |
% 10.87/2.34 | GROUND_INST: instantiating (4) with all_18_7, all_18_5, all_18_0, all_42_0,
% 10.87/2.34 | simplifying with (14), (16), (22), (30), (44), (46) gives:
% 10.87/2.34 | (54) ? [v0: any] : ? [v1: any] : (in(all_42_0, all_18_0) = v1 &
% 10.87/2.34 | in(all_42_0, all_18_7) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.87/2.34 |
% 10.87/2.34 | GROUND_INST: instantiating (26) with all_40_1, all_40_0, simplifying with
% 10.87/2.34 | (37), (38), (41) gives:
% 10.87/2.34 | (55) ? [v0: any] : ? [v1: any] : (in(all_40_0, all_18_0) = v1 &
% 10.87/2.34 | in(all_40_1, all_18_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.87/2.34 |
% 10.87/2.34 | GROUND_INST: instantiating (9) with all_40_1, all_40_0, all_42_1, all_42_0,
% 10.87/2.34 | all_18_9, simplifying with (37), (38), (41), (43), (44), (47)
% 10.87/2.34 | gives:
% 10.87/2.34 | (56) all_42_0 = all_40_0
% 10.87/2.34 |
% 10.87/2.34 | GROUND_INST: instantiating (8) with all_40_1, all_40_0, all_42_1, all_42_0,
% 10.87/2.34 | all_18_9, simplifying with (37), (38), (41), (43), (44), (47)
% 10.87/2.34 | gives:
% 10.87/2.34 | (57) all_42_1 = all_40_1
% 10.87/2.34 |
% 10.87/2.34 | GROUND_INST: instantiating (26) with all_42_1, all_42_0, simplifying with
% 10.87/2.34 | (43), (44), (47) gives:
% 10.87/2.34 | (58) ? [v0: any] : ? [v1: any] : (in(all_42_0, all_18_0) = v1 &
% 10.87/2.34 | in(all_42_1, all_18_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.87/2.34 |
% 10.87/2.34 | DELTA: instantiating (54) with fresh symbols all_60_0, all_60_1 gives:
% 10.87/2.34 | (59) in(all_42_0, all_18_0) = all_60_0 & in(all_42_0, all_18_7) = all_60_1
% 10.87/2.34 | & ( ~ (all_60_1 = 0) | all_60_0 = 0)
% 10.87/2.34 |
% 10.87/2.34 | ALPHA: (59) implies:
% 10.87/2.34 | (60) in(all_42_0, all_18_7) = all_60_1
% 10.87/2.34 | (61) in(all_42_0, all_18_0) = all_60_0
% 10.87/2.34 | (62) ~ (all_60_1 = 0) | all_60_0 = 0
% 10.87/2.34 |
% 10.87/2.34 | DELTA: instantiating (53) with fresh symbols all_62_0, all_62_1 gives:
% 10.87/2.34 | (63) in(all_42_0, all_18_0) = all_62_1 & in(all_42_0, all_18_7) = all_62_0
% 10.87/2.34 | & ( ~ (all_62_1 = 0) | all_62_0 = 0)
% 10.87/2.34 |
% 10.87/2.34 | ALPHA: (63) implies:
% 10.87/2.34 | (64) in(all_42_0, all_18_7) = all_62_0
% 10.87/2.34 | (65) in(all_42_0, all_18_0) = all_62_1
% 10.87/2.34 |
% 10.87/2.34 | DELTA: instantiating (52) with fresh symbols all_64_0, all_64_1 gives:
% 10.87/2.34 | (66) in(all_42_1, all_18_1) = all_64_0 & in(all_42_1, all_18_8) = all_64_1
% 10.87/2.34 | & ( ~ (all_64_1 = 0) | all_64_0 = 0)
% 10.87/2.34 |
% 10.87/2.34 | ALPHA: (66) implies:
% 10.87/2.34 | (67) in(all_42_1, all_18_1) = all_64_0
% 10.87/2.34 |
% 10.87/2.34 | DELTA: instantiating (51) with fresh symbols all_68_0, all_68_1 gives:
% 10.87/2.34 | (68) in(all_40_0, all_18_0) = all_68_0 & in(all_40_0, all_18_5) = all_68_1
% 10.87/2.34 | & ( ~ (all_68_1 = 0) | all_68_0 = 0)
% 10.87/2.34 |
% 10.87/2.34 | ALPHA: (68) implies:
% 10.87/2.34 | (69) in(all_40_0, all_18_0) = all_68_0
% 10.87/2.34 |
% 10.87/2.34 | DELTA: instantiating (58) with fresh symbols all_70_0, all_70_1 gives:
% 10.87/2.35 | (70) in(all_42_0, all_18_0) = all_70_0 & in(all_42_1, all_18_1) = all_70_1
% 10.87/2.35 | & ( ~ (all_70_0 = 0) | ~ (all_70_1 = 0))
% 10.87/2.35 |
% 10.87/2.35 | ALPHA: (70) implies:
% 10.87/2.35 | (71) in(all_42_1, all_18_1) = all_70_1
% 10.87/2.35 | (72) in(all_42_0, all_18_0) = all_70_0
% 10.87/2.35 | (73) ~ (all_70_0 = 0) | ~ (all_70_1 = 0)
% 10.87/2.35 |
% 10.87/2.35 | DELTA: instantiating (55) with fresh symbols all_72_0, all_72_1 gives:
% 10.87/2.35 | (74) in(all_40_0, all_18_0) = all_72_0 & in(all_40_1, all_18_1) = all_72_1
% 10.87/2.35 | & ( ~ (all_72_0 = 0) | ~ (all_72_1 = 0))
% 10.87/2.35 |
% 10.87/2.35 | ALPHA: (74) implies:
% 10.87/2.35 | (75) in(all_40_1, all_18_1) = all_72_1
% 10.87/2.35 | (76) in(all_40_0, all_18_0) = all_72_0
% 10.87/2.35 |
% 10.87/2.35 | DELTA: instantiating (50) with fresh symbols all_74_0, all_74_1 gives:
% 10.87/2.35 | (77) in(all_40_0, all_18_0) = all_74_1 & in(all_40_0, all_18_5) = all_74_0
% 10.87/2.35 | & ( ~ (all_74_1 = 0) | all_74_0 = 0)
% 10.87/2.35 |
% 10.87/2.35 | ALPHA: (77) implies:
% 10.87/2.35 | (78) in(all_40_0, all_18_0) = all_74_1
% 10.87/2.35 |
% 10.87/2.35 | DELTA: instantiating (49) with fresh symbols all_76_0, all_76_1 gives:
% 10.87/2.35 | (79) in(all_40_1, all_18_1) = all_76_0 & in(all_40_1, all_18_6) = all_76_1
% 10.87/2.35 | & ( ~ (all_76_1 = 0) | all_76_0 = 0)
% 10.87/2.35 |
% 10.87/2.35 | ALPHA: (79) implies:
% 10.87/2.35 | (80) in(all_40_1, all_18_6) = all_76_1
% 10.87/2.35 | (81) in(all_40_1, all_18_1) = all_76_0
% 10.87/2.35 | (82) ~ (all_76_1 = 0) | all_76_0 = 0
% 10.87/2.35 |
% 10.87/2.35 | DELTA: instantiating (48) with fresh symbols all_78_0, all_78_1 gives:
% 10.87/2.35 | (83) in(all_40_1, all_18_1) = all_78_1 & in(all_40_1, all_18_6) = all_78_0
% 10.87/2.35 | & ( ~ (all_78_1 = 0) | all_78_0 = 0)
% 10.87/2.35 |
% 10.87/2.35 | ALPHA: (83) implies:
% 10.87/2.35 | (84) in(all_40_1, all_18_6) = all_78_0
% 10.87/2.35 | (85) in(all_40_1, all_18_1) = all_78_1
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (56), (72) imply:
% 10.87/2.35 | (86) in(all_40_0, all_18_0) = all_70_0
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (56), (65) imply:
% 10.87/2.35 | (87) in(all_40_0, all_18_0) = all_62_1
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (56), (61) imply:
% 10.87/2.35 | (88) in(all_40_0, all_18_0) = all_60_0
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (56), (64) imply:
% 10.87/2.35 | (89) in(all_40_0, all_18_7) = all_62_0
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (56), (60) imply:
% 10.87/2.35 | (90) in(all_40_0, all_18_7) = all_60_1
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (57), (71) imply:
% 10.87/2.35 | (91) in(all_40_1, all_18_1) = all_70_1
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (57), (67) imply:
% 10.87/2.35 | (92) in(all_40_1, all_18_1) = all_64_0
% 10.87/2.35 |
% 10.87/2.35 | REDUCE: (45), (57) imply:
% 10.87/2.35 | (93) in(all_40_1, all_18_6) = 0
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_76_1, all_78_0, all_18_6, all_40_1,
% 10.87/2.35 | simplifying with (80), (84) gives:
% 10.87/2.35 | (94) all_78_0 = all_76_1
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with 0, all_78_0, all_18_6, all_40_1,
% 10.87/2.35 | simplifying with (84), (93) gives:
% 10.87/2.35 | (95) all_78_0 = 0
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_72_1, all_76_0, all_18_1, all_40_1,
% 10.87/2.35 | simplifying with (75), (81) gives:
% 10.87/2.35 | (96) all_76_0 = all_72_1
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_70_1, all_76_0, all_18_1, all_40_1,
% 10.87/2.35 | simplifying with (81), (91) gives:
% 10.87/2.35 | (97) all_76_0 = all_70_1
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_72_1, all_78_1, all_18_1, all_40_1,
% 10.87/2.35 | simplifying with (75), (85) gives:
% 10.87/2.35 | (98) all_78_1 = all_72_1
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_64_0, all_78_1, all_18_1, all_40_1,
% 10.87/2.35 | simplifying with (85), (92) gives:
% 10.87/2.35 | (99) all_78_1 = all_64_0
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with 0, all_62_0, all_18_7, all_40_0,
% 10.87/2.35 | simplifying with (40), (89) gives:
% 10.87/2.35 | (100) all_62_0 = 0
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_60_1, all_62_0, all_18_7, all_40_0,
% 10.87/2.35 | simplifying with (89), (90) gives:
% 10.87/2.35 | (101) all_62_0 = all_60_1
% 10.87/2.35 |
% 10.87/2.35 | GROUND_INST: instantiating (10) with all_68_0, all_70_0, all_18_0, all_40_0,
% 10.87/2.35 | simplifying with (69), (86) gives:
% 10.87/2.35 | (102) all_70_0 = all_68_0
% 10.87/2.35 |
% 10.87/2.36 | GROUND_INST: instantiating (10) with all_70_0, all_72_0, all_18_0, all_40_0,
% 10.87/2.36 | simplifying with (76), (86) gives:
% 10.87/2.36 | (103) all_72_0 = all_70_0
% 10.87/2.36 |
% 10.87/2.36 | GROUND_INST: instantiating (10) with all_62_1, all_72_0, all_18_0, all_40_0,
% 10.87/2.36 | simplifying with (76), (87) gives:
% 10.87/2.36 | (104) all_72_0 = all_62_1
% 10.87/2.36 |
% 10.87/2.36 | GROUND_INST: instantiating (10) with all_68_0, all_74_1, all_18_0, all_40_0,
% 10.87/2.36 | simplifying with (69), (78) gives:
% 10.87/2.36 | (105) all_74_1 = all_68_0
% 10.87/2.36 |
% 10.87/2.36 | GROUND_INST: instantiating (10) with all_60_0, all_74_1, all_18_0, all_40_0,
% 10.87/2.36 | simplifying with (78), (88) gives:
% 10.87/2.36 | (106) all_74_1 = all_60_0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (94), (95) imply:
% 10.87/2.36 | (107) all_76_1 = 0
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (107) implies:
% 10.87/2.36 | (108) all_76_1 = 0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (98), (99) imply:
% 10.87/2.36 | (109) all_72_1 = all_64_0
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (109) implies:
% 10.87/2.36 | (110) all_72_1 = all_64_0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (96), (97) imply:
% 10.87/2.36 | (111) all_72_1 = all_70_1
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (111) implies:
% 10.87/2.36 | (112) all_72_1 = all_70_1
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (105), (106) imply:
% 10.87/2.36 | (113) all_68_0 = all_60_0
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (113) implies:
% 10.87/2.36 | (114) all_68_0 = all_60_0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (103), (104) imply:
% 10.87/2.36 | (115) all_70_0 = all_62_1
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (115) implies:
% 10.87/2.36 | (116) all_70_0 = all_62_1
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (110), (112) imply:
% 10.87/2.36 | (117) all_70_1 = all_64_0
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (117) implies:
% 10.87/2.36 | (118) all_70_1 = all_64_0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (102), (116) imply:
% 10.87/2.36 | (119) all_68_0 = all_62_1
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (119) implies:
% 10.87/2.36 | (120) all_68_0 = all_62_1
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (114), (120) imply:
% 10.87/2.36 | (121) all_62_1 = all_60_0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (100), (101) imply:
% 10.87/2.36 | (122) all_60_1 = 0
% 10.87/2.36 |
% 10.87/2.36 | SIMP: (122) implies:
% 10.87/2.36 | (123) all_60_1 = 0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (116), (121) imply:
% 10.87/2.36 | (124) all_70_0 = all_60_0
% 10.87/2.36 |
% 10.87/2.36 | COMBINE_EQS: (97), (118) imply:
% 11.33/2.36 | (125) all_76_0 = all_64_0
% 11.33/2.36 |
% 11.33/2.36 | BETA: splitting (62) gives:
% 11.33/2.36 |
% 11.33/2.36 | Case 1:
% 11.33/2.36 | |
% 11.33/2.36 | | (126) ~ (all_60_1 = 0)
% 11.33/2.36 | |
% 11.33/2.36 | | REDUCE: (123), (126) imply:
% 11.33/2.36 | | (127) $false
% 11.33/2.36 | |
% 11.33/2.36 | | CLOSE: (127) is inconsistent.
% 11.33/2.36 | |
% 11.33/2.36 | Case 2:
% 11.33/2.36 | |
% 11.33/2.36 | | (128) all_60_0 = 0
% 11.33/2.36 | |
% 11.33/2.36 | | COMBINE_EQS: (124), (128) imply:
% 11.33/2.36 | | (129) all_70_0 = 0
% 11.33/2.36 | |
% 11.33/2.36 | | BETA: splitting (73) gives:
% 11.33/2.36 | |
% 11.33/2.36 | | Case 1:
% 11.33/2.36 | | |
% 11.33/2.36 | | | (130) ~ (all_70_0 = 0)
% 11.33/2.36 | | |
% 11.33/2.36 | | | REDUCE: (129), (130) imply:
% 11.33/2.36 | | | (131) $false
% 11.33/2.36 | | |
% 11.33/2.36 | | | CLOSE: (131) is inconsistent.
% 11.33/2.36 | | |
% 11.33/2.36 | | Case 2:
% 11.33/2.36 | | |
% 11.33/2.36 | | | (132) ~ (all_70_1 = 0)
% 11.33/2.36 | | |
% 11.33/2.36 | | | REDUCE: (118), (132) imply:
% 11.33/2.36 | | | (133) ~ (all_64_0 = 0)
% 11.33/2.36 | | |
% 11.33/2.36 | | | BETA: splitting (82) gives:
% 11.33/2.36 | | |
% 11.33/2.36 | | | Case 1:
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | (134) ~ (all_76_1 = 0)
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | REDUCE: (108), (134) imply:
% 11.33/2.36 | | | | (135) $false
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | CLOSE: (135) is inconsistent.
% 11.33/2.36 | | | |
% 11.33/2.36 | | | Case 2:
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | (136) all_76_0 = 0
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | COMBINE_EQS: (125), (136) imply:
% 11.33/2.36 | | | | (137) all_64_0 = 0
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | REDUCE: (133), (137) imply:
% 11.33/2.36 | | | | (138) $false
% 11.33/2.36 | | | |
% 11.33/2.36 | | | | CLOSE: (138) is inconsistent.
% 11.33/2.36 | | | |
% 11.33/2.36 | | | End of split
% 11.33/2.36 | | |
% 11.33/2.36 | | End of split
% 11.33/2.36 | |
% 11.33/2.36 | End of split
% 11.33/2.36 |
% 11.33/2.36 End of proof
% 11.33/2.36 % SZS output end Proof for theBenchmark
% 11.33/2.36
% 11.33/2.36 1746ms
%------------------------------------------------------------------------------