TSTP Solution File: SEU167+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU167+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 : n021.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 17:42:59 EDT 2023
% Result : Theorem 13.59s 2.63s
% Output : Proof 16.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU167+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 23:51:39 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.16/1.22 Prover 4: Preprocessing ...
% 3.16/1.22 Prover 1: Preprocessing ...
% 3.65/1.26 Prover 5: Preprocessing ...
% 3.65/1.26 Prover 3: Preprocessing ...
% 3.65/1.26 Prover 0: Preprocessing ...
% 3.65/1.26 Prover 6: Preprocessing ...
% 3.65/1.26 Prover 2: Preprocessing ...
% 8.92/2.16 Prover 1: Warning: ignoring some quantifiers
% 10.42/2.22 Prover 5: Proving ...
% 10.88/2.26 Prover 1: Constructing countermodel ...
% 10.88/2.30 Prover 6: Proving ...
% 11.30/2.32 Prover 3: Warning: ignoring some quantifiers
% 11.30/2.34 Prover 4: Warning: ignoring some quantifiers
% 11.30/2.35 Prover 3: Constructing countermodel ...
% 11.67/2.43 Prover 2: Proving ...
% 12.31/2.47 Prover 4: Constructing countermodel ...
% 12.63/2.53 Prover 0: Proving ...
% 13.59/2.63 Prover 3: proved (2006ms)
% 13.59/2.63
% 13.59/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.59/2.63
% 13.59/2.65 Prover 6: stopped
% 13.59/2.65 Prover 2: stopped
% 13.59/2.66 Prover 0: stopped
% 13.59/2.66 Prover 5: stopped
% 13.59/2.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.59/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.59/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.59/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.59/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.59/2.76 Prover 1: Found proof (size 37)
% 13.59/2.76 Prover 1: proved (2138ms)
% 13.59/2.76 Prover 4: stopped
% 14.77/2.80 Prover 10: Preprocessing ...
% 14.77/2.81 Prover 7: Preprocessing ...
% 14.77/2.82 Prover 11: Preprocessing ...
% 14.77/2.83 Prover 8: Preprocessing ...
% 14.77/2.83 Prover 13: Preprocessing ...
% 15.51/2.88 Prover 7: stopped
% 15.51/2.89 Prover 10: stopped
% 15.79/2.93 Prover 11: stopped
% 15.90/2.95 Prover 13: stopped
% 16.25/3.03 Prover 8: Warning: ignoring some quantifiers
% 16.25/3.05 Prover 8: Constructing countermodel ...
% 16.25/3.07 Prover 8: stopped
% 16.25/3.07
% 16.25/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.25/3.07
% 16.53/3.08 % SZS output start Proof for theBenchmark
% 16.53/3.08 Assumptions after simplification:
% 16.53/3.08 ---------------------------------
% 16.53/3.08
% 16.53/3.08 (d2_zfmisc_1)
% 16.53/3.11 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 16.53/3.11 (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.53/3.11 [v4: $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ! [v6:
% 16.53/3.12 $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v7) = v4) | ~ $i(v7) | ~
% 16.53/3.12 $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, v2) = v9 & in(v6, v1) =
% 16.53/3.12 v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & (v5 = 0 | ? [v6: $i] : ?
% 16.53/3.12 [v7: $i] : (ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0
% 16.53/3.12 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 16.53/3.12 (cartesian_product2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( !
% 16.53/3.12 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | !
% 16.53/3.12 [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) |
% 16.53/3.12 ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0)
% 16.53/3.12 = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: $i] : ( ~ (in(v3,
% 16.53/3.12 v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v4,
% 16.53/3.12 v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & $i(v4)))))
% 16.53/3.12
% 16.53/3.12 (d3_tarski)
% 16.53/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 16.53/3.12 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 16.53/3.12 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.53/3.12 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 16.53/3.12 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 16.53/3.12
% 16.53/3.12 (t119_zfmisc_1)
% 16.53/3.12 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 16.53/3.12 $i] : ? [v6: int] : ( ~ (v6 = 0) & cartesian_product2(v1, v3) = v5 &
% 16.53/3.12 cartesian_product2(v0, v2) = v4 & subset(v4, v5) = v6 & subset(v2, v3) = 0 &
% 16.53/3.12 subset(v0, v1) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.53/3.12
% 16.53/3.12 (function-axioms)
% 16.53/3.12 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.53/3.12 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 16.53/3.12 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.53/3.12 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 16.53/3.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.53/3.12 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 16.53/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.53/3.12 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 16.53/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.53/3.12 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 16.53/3.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.53/3.12 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 16.53/3.12 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.53/3.12 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 16.53/3.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 16.53/3.12 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 16.53/3.12 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.53/3.12 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 16.53/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.53/3.12 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 16.53/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 16.53/3.12 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.53/3.12 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i]
% 16.53/3.12 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 16.53/3.12 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.53/3.12 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 16.53/3.12
% 16.53/3.12 Further assumptions not needed in the proof:
% 16.53/3.12 --------------------------------------------
% 16.53/3.12 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 16.53/3.12 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 16.53/3.12 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d3_xboole_0, d4_tarski,
% 16.53/3.12 d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0, dt_k1_tarski, dt_k1_xboole_0,
% 16.53/3.12 dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_tarski,
% 16.53/3.12 dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, fc1_xboole_0, fc1_zfmisc_1,
% 16.53/3.12 fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 16.53/3.12 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 16.53/3.12 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1,
% 16.53/3.12 l55_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 16.53/3.12 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t12_xboole_1,
% 16.53/3.12 t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1,
% 16.53/3.12 t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1,
% 16.53/3.12 t36_xboole_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1,
% 16.53/3.12 t39_zfmisc_1, t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1,
% 16.53/3.12 t46_zfmisc_1, t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1,
% 16.53/3.12 t65_zfmisc_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1,
% 16.53/3.12 t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1,
% 16.53/3.12 t9_zfmisc_1
% 16.53/3.12
% 16.53/3.12 Those formulas are unsatisfiable:
% 16.53/3.12 ---------------------------------
% 16.53/3.12
% 16.53/3.12 Begin of proof
% 16.53/3.13 |
% 16.53/3.13 | ALPHA: (d2_zfmisc_1) implies:
% 16.53/3.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0,
% 16.53/3.13 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 16.53/3.13 | [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5:
% 16.53/3.13 | $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6)
% 16.53/3.13 | | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 &
% 16.53/3.13 | in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3:
% 16.53/3.13 | $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5:
% 16.53/3.13 | $i] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0)
% 16.53/3.13 | = 0 & $i(v5) & $i(v4)))))
% 16.53/3.13 |
% 16.53/3.13 | ALPHA: (d3_tarski) implies:
% 16.53/3.13 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 16.53/3.13 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1)
% 16.53/3.13 | = 0))
% 16.53/3.13 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 16.53/3.13 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 16.53/3.13 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 16.53/3.13 |
% 16.53/3.13 | ALPHA: (function-axioms) implies:
% 16.53/3.13 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.53/3.13 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 16.53/3.13 |
% 16.53/3.13 | DELTA: instantiating (t119_zfmisc_1) with fresh symbols all_101_0, all_101_1,
% 16.53/3.13 | all_101_2, all_101_3, all_101_4, all_101_5, all_101_6 gives:
% 16.53/3.13 | (5) ~ (all_101_0 = 0) & cartesian_product2(all_101_5, all_101_3) =
% 16.53/3.13 | all_101_1 & cartesian_product2(all_101_6, all_101_4) = all_101_2 &
% 16.53/3.13 | subset(all_101_2, all_101_1) = all_101_0 & subset(all_101_4, all_101_3)
% 16.53/3.13 | = 0 & subset(all_101_6, all_101_5) = 0 & $i(all_101_1) & $i(all_101_2)
% 16.53/3.13 | & $i(all_101_3) & $i(all_101_4) & $i(all_101_5) & $i(all_101_6)
% 16.53/3.13 |
% 16.53/3.13 | ALPHA: (5) implies:
% 16.53/3.13 | (6) ~ (all_101_0 = 0)
% 16.53/3.13 | (7) $i(all_101_6)
% 16.53/3.13 | (8) $i(all_101_5)
% 16.53/3.13 | (9) $i(all_101_4)
% 16.53/3.13 | (10) $i(all_101_3)
% 16.53/3.13 | (11) $i(all_101_2)
% 16.53/3.13 | (12) $i(all_101_1)
% 16.53/3.13 | (13) subset(all_101_6, all_101_5) = 0
% 16.53/3.13 | (14) subset(all_101_4, all_101_3) = 0
% 16.53/3.13 | (15) subset(all_101_2, all_101_1) = all_101_0
% 16.53/3.13 | (16) cartesian_product2(all_101_6, all_101_4) = all_101_2
% 16.53/3.13 | (17) cartesian_product2(all_101_5, all_101_3) = all_101_1
% 16.53/3.13 |
% 16.53/3.13 | GROUND_INST: instantiating (2) with all_101_6, all_101_5, simplifying with
% 16.53/3.13 | (7), (8), (13) gives:
% 16.53/3.14 | (18) ! [v0: $i] : ( ~ (in(v0, all_101_6) = 0) | ~ $i(v0) | in(v0,
% 16.53/3.14 | all_101_5) = 0)
% 16.53/3.14 |
% 16.53/3.14 | GROUND_INST: instantiating (2) with all_101_4, all_101_3, simplifying with
% 16.53/3.14 | (9), (10), (14) gives:
% 16.53/3.14 | (19) ! [v0: $i] : ( ~ (in(v0, all_101_4) = 0) | ~ $i(v0) | in(v0,
% 16.53/3.14 | all_101_3) = 0)
% 16.53/3.14 |
% 16.53/3.14 | GROUND_INST: instantiating (3) with all_101_2, all_101_1, all_101_0,
% 16.53/3.14 | simplifying with (11), (12), (15) gives:
% 16.53/3.14 | (20) all_101_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 16.53/3.14 | all_101_1) = v1 & in(v0, all_101_2) = 0 & $i(v0))
% 16.53/3.14 |
% 16.53/3.14 | GROUND_INST: instantiating (1) with all_101_6, all_101_4, all_101_2,
% 16.53/3.14 | simplifying with (7), (9), (11), (16) gives:
% 16.53/3.14 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_2) = v1) |
% 16.53/3.14 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) =
% 16.53/3.14 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 16.53/3.14 | (in(v3, all_101_4) = v5 & in(v2, all_101_6) = v4 & ( ~ (v5 = 0) |
% 16.53/3.14 | ~ (v4 = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_101_2) = 0) |
% 16.53/3.14 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 &
% 16.53/3.14 | in(v2, all_101_4) = 0 & in(v1, all_101_6) = 0 & $i(v2) & $i(v1)))
% 16.53/3.14 |
% 16.53/3.14 | ALPHA: (21) implies:
% 16.53/3.14 | (22) ! [v0: $i] : ( ~ (in(v0, all_101_2) = 0) | ~ $i(v0) | ? [v1: $i] :
% 16.53/3.14 | ? [v2: $i] : (ordered_pair(v1, v2) = v0 & in(v2, all_101_4) = 0 &
% 16.53/3.14 | in(v1, all_101_6) = 0 & $i(v2) & $i(v1)))
% 16.53/3.14 |
% 16.53/3.14 | GROUND_INST: instantiating (1) with all_101_5, all_101_3, all_101_1,
% 16.53/3.14 | simplifying with (8), (10), (12), (17) gives:
% 16.53/3.14 | (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_1) = v1) |
% 16.53/3.14 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) =
% 16.53/3.14 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 16.53/3.14 | (in(v3, all_101_3) = v5 & in(v2, all_101_5) = v4 & ( ~ (v5 = 0) |
% 16.53/3.14 | ~ (v4 = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_101_1) = 0) |
% 16.53/3.14 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 &
% 16.53/3.14 | in(v2, all_101_3) = 0 & in(v1, all_101_5) = 0 & $i(v2) & $i(v1)))
% 16.53/3.14 |
% 16.53/3.14 | ALPHA: (23) implies:
% 16.53/3.14 | (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_101_1) = v1) |
% 16.53/3.14 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) =
% 16.53/3.14 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 16.53/3.14 | (in(v3, all_101_3) = v5 & in(v2, all_101_5) = v4 & ( ~ (v5 = 0) |
% 16.53/3.14 | ~ (v4 = 0)))))
% 16.53/3.14 |
% 16.53/3.14 | BETA: splitting (20) gives:
% 16.53/3.14 |
% 16.53/3.14 | Case 1:
% 16.53/3.14 | |
% 16.53/3.14 | | (25) all_101_0 = 0
% 16.53/3.14 | |
% 16.53/3.14 | | REDUCE: (6), (25) imply:
% 16.53/3.14 | | (26) $false
% 16.53/3.14 | |
% 16.53/3.14 | | CLOSE: (26) is inconsistent.
% 16.53/3.14 | |
% 16.53/3.14 | Case 2:
% 16.53/3.14 | |
% 16.53/3.14 | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_101_1) = v1 &
% 16.53/3.14 | | in(v0, all_101_2) = 0 & $i(v0))
% 16.53/3.14 | |
% 16.53/3.14 | | DELTA: instantiating (27) with fresh symbols all_131_0, all_131_1 gives:
% 16.53/3.14 | | (28) ~ (all_131_0 = 0) & in(all_131_1, all_101_1) = all_131_0 &
% 16.53/3.14 | | in(all_131_1, all_101_2) = 0 & $i(all_131_1)
% 16.53/3.14 | |
% 16.53/3.14 | | ALPHA: (28) implies:
% 16.53/3.15 | | (29) ~ (all_131_0 = 0)
% 16.53/3.15 | | (30) $i(all_131_1)
% 16.53/3.15 | | (31) in(all_131_1, all_101_2) = 0
% 16.53/3.15 | | (32) in(all_131_1, all_101_1) = all_131_0
% 16.53/3.15 | |
% 16.53/3.15 | | GROUND_INST: instantiating (22) with all_131_1, simplifying with (30), (31)
% 16.53/3.15 | | gives:
% 16.53/3.15 | | (33) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_131_1 &
% 16.53/3.15 | | in(v1, all_101_4) = 0 & in(v0, all_101_6) = 0 & $i(v1) & $i(v0))
% 16.53/3.15 | |
% 16.53/3.15 | | GROUND_INST: instantiating (24) with all_131_1, all_131_0, simplifying with
% 16.53/3.15 | | (30), (32) gives:
% 16.53/3.15 | | (34) all_131_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 16.53/3.15 | | v1) = all_131_1) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 16.53/3.15 | | [v3: any] : (in(v1, all_101_3) = v3 & in(v0, all_101_5) = v2 & ( ~
% 16.53/3.15 | | (v3 = 0) | ~ (v2 = 0))))
% 16.53/3.15 | |
% 16.53/3.15 | | DELTA: instantiating (33) with fresh symbols all_143_0, all_143_1 gives:
% 16.53/3.15 | | (35) ordered_pair(all_143_1, all_143_0) = all_131_1 & in(all_143_0,
% 16.53/3.15 | | all_101_4) = 0 & in(all_143_1, all_101_6) = 0 & $i(all_143_0) &
% 16.53/3.15 | | $i(all_143_1)
% 16.53/3.15 | |
% 16.53/3.15 | | ALPHA: (35) implies:
% 16.53/3.15 | | (36) $i(all_143_1)
% 16.53/3.15 | | (37) $i(all_143_0)
% 16.53/3.15 | | (38) in(all_143_1, all_101_6) = 0
% 16.53/3.15 | | (39) in(all_143_0, all_101_4) = 0
% 16.53/3.15 | | (40) ordered_pair(all_143_1, all_143_0) = all_131_1
% 16.53/3.15 | |
% 16.53/3.15 | | BETA: splitting (34) gives:
% 16.53/3.15 | |
% 16.53/3.15 | | Case 1:
% 16.53/3.15 | | |
% 16.53/3.15 | | | (41) all_131_0 = 0
% 16.53/3.15 | | |
% 16.53/3.15 | | | REDUCE: (29), (41) imply:
% 16.53/3.15 | | | (42) $false
% 16.53/3.15 | | |
% 16.53/3.15 | | | CLOSE: (42) is inconsistent.
% 16.53/3.15 | | |
% 16.53/3.15 | | Case 2:
% 16.53/3.15 | | |
% 16.53/3.15 | | | (43) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_131_1)
% 16.53/3.15 | | | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 16.53/3.15 | | | all_101_3) = v3 & in(v0, all_101_5) = v2 & ( ~ (v3 = 0) | ~
% 16.53/3.15 | | | (v2 = 0))))
% 16.53/3.15 | | |
% 16.53/3.15 | | | GROUND_INST: instantiating (18) with all_143_1, simplifying with (36),
% 16.53/3.15 | | | (38) gives:
% 16.53/3.15 | | | (44) in(all_143_1, all_101_5) = 0
% 16.53/3.15 | | |
% 16.53/3.15 | | | GROUND_INST: instantiating (19) with all_143_0, simplifying with (37),
% 16.53/3.15 | | | (39) gives:
% 16.53/3.15 | | | (45) in(all_143_0, all_101_3) = 0
% 16.53/3.15 | | |
% 16.53/3.15 | | | GROUND_INST: instantiating (43) with all_143_1, all_143_0, simplifying
% 16.53/3.15 | | | with (36), (37), (40) gives:
% 16.53/3.15 | | | (46) ? [v0: any] : ? [v1: any] : (in(all_143_0, all_101_3) = v1 &
% 16.53/3.15 | | | in(all_143_1, all_101_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 16.53/3.15 | | |
% 16.53/3.15 | | | DELTA: instantiating (46) with fresh symbols all_166_0, all_166_1 gives:
% 16.53/3.15 | | | (47) in(all_143_0, all_101_3) = all_166_0 & in(all_143_1, all_101_5) =
% 16.53/3.15 | | | all_166_1 & ( ~ (all_166_0 = 0) | ~ (all_166_1 = 0))
% 16.53/3.15 | | |
% 16.53/3.15 | | | ALPHA: (47) implies:
% 16.53/3.15 | | | (48) in(all_143_1, all_101_5) = all_166_1
% 16.53/3.15 | | | (49) in(all_143_0, all_101_3) = all_166_0
% 16.53/3.15 | | | (50) ~ (all_166_0 = 0) | ~ (all_166_1 = 0)
% 16.53/3.15 | | |
% 16.53/3.15 | | | GROUND_INST: instantiating (4) with 0, all_166_1, all_101_5, all_143_1,
% 16.53/3.15 | | | simplifying with (44), (48) gives:
% 16.53/3.15 | | | (51) all_166_1 = 0
% 16.53/3.15 | | |
% 16.53/3.15 | | | GROUND_INST: instantiating (4) with 0, all_166_0, all_101_3, all_143_0,
% 16.53/3.15 | | | simplifying with (45), (49) gives:
% 16.53/3.15 | | | (52) all_166_0 = 0
% 16.53/3.15 | | |
% 16.53/3.15 | | | BETA: splitting (50) gives:
% 16.53/3.15 | | |
% 16.53/3.15 | | | Case 1:
% 16.53/3.15 | | | |
% 16.93/3.15 | | | | (53) ~ (all_166_0 = 0)
% 16.93/3.15 | | | |
% 16.93/3.15 | | | | REDUCE: (52), (53) imply:
% 16.93/3.15 | | | | (54) $false
% 16.93/3.15 | | | |
% 16.93/3.15 | | | | CLOSE: (54) is inconsistent.
% 16.93/3.15 | | | |
% 16.93/3.15 | | | Case 2:
% 16.93/3.15 | | | |
% 16.93/3.15 | | | | (55) ~ (all_166_1 = 0)
% 16.93/3.15 | | | |
% 16.93/3.15 | | | | REDUCE: (51), (55) imply:
% 16.93/3.15 | | | | (56) $false
% 16.93/3.15 | | | |
% 16.93/3.15 | | | | CLOSE: (56) is inconsistent.
% 16.93/3.15 | | | |
% 16.93/3.15 | | | End of split
% 16.93/3.15 | | |
% 16.93/3.15 | | End of split
% 16.93/3.15 | |
% 16.93/3.15 | End of split
% 16.93/3.15 |
% 16.93/3.15 End of proof
% 16.93/3.15 % SZS output end Proof for theBenchmark
% 16.93/3.15
% 16.93/3.15 2551ms
%------------------------------------------------------------------------------