TSTP Solution File: SEU120+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU120+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 : n028.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 17:42:35 EDT 2023
% Result : Theorem 7.32s 1.78s
% Output : Proof 9.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU120+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 : n028.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 17:00:48 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.40/1.00 Prover 1: Preprocessing ...
% 2.40/1.00 Prover 4: Preprocessing ...
% 2.40/1.04 Prover 6: Preprocessing ...
% 2.40/1.04 Prover 0: Preprocessing ...
% 2.40/1.04 Prover 5: Preprocessing ...
% 2.40/1.04 Prover 3: Preprocessing ...
% 2.40/1.05 Prover 2: Preprocessing ...
% 4.38/1.33 Prover 5: Proving ...
% 4.38/1.36 Prover 1: Warning: ignoring some quantifiers
% 4.38/1.36 Prover 6: Proving ...
% 4.38/1.37 Prover 2: Proving ...
% 4.38/1.38 Prover 3: Warning: ignoring some quantifiers
% 4.38/1.38 Prover 1: Constructing countermodel ...
% 4.38/1.39 Prover 3: Constructing countermodel ...
% 4.98/1.39 Prover 4: Warning: ignoring some quantifiers
% 4.98/1.41 Prover 0: Proving ...
% 4.98/1.42 Prover 4: Constructing countermodel ...
% 7.32/1.78 Prover 0: proved (1136ms)
% 7.32/1.78
% 7.32/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.32/1.79
% 7.32/1.79 Prover 3: stopped
% 7.32/1.79 Prover 5: stopped
% 7.94/1.80 Prover 2: stopped
% 7.94/1.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.94/1.80 Prover 6: stopped
% 7.94/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.94/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.94/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.94/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.94/1.81 Prover 7: Preprocessing ...
% 7.94/1.82 Prover 8: Preprocessing ...
% 7.94/1.82 Prover 1: Found proof (size 61)
% 7.94/1.82 Prover 1: proved (1178ms)
% 7.94/1.83 Prover 4: stopped
% 7.94/1.83 Prover 11: Preprocessing ...
% 7.94/1.83 Prover 10: Preprocessing ...
% 7.94/1.84 Prover 13: Preprocessing ...
% 7.94/1.84 Prover 7: stopped
% 7.94/1.85 Prover 10: stopped
% 7.94/1.86 Prover 13: stopped
% 7.94/1.87 Prover 11: stopped
% 8.56/1.90 Prover 8: Warning: ignoring some quantifiers
% 8.66/1.91 Prover 8: Constructing countermodel ...
% 8.66/1.91 Prover 8: stopped
% 8.66/1.91
% 8.66/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.66/1.92
% 8.73/1.92 % SZS output start Proof for theBenchmark
% 8.73/1.93 Assumptions after simplification:
% 8.73/1.93 ---------------------------------
% 8.73/1.93
% 8.73/1.93 (commutativity_k3_xboole_0)
% 8.73/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 8.73/1.95 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 8.73/1.95
% 8.73/1.95 (d1_xboole_0)
% 8.73/1.96 $i(empty_set) & ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) & ?
% 8.73/1.96 [v0: $i] : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : (in(v1, v0) = 0 &
% 8.73/1.96 $i(v1)))
% 8.73/1.96
% 8.73/1.96 (d3_xboole_0)
% 8.73/1.96 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 8.73/1.96 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 8.73/1.96 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 &
% 8.73/1.96 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) |
% 8.73/1.96 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 8.73/1.96 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) |
% 8.73/1.96 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3)
% 8.73/1.96 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~
% 8.73/1.96 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 8.73/1.96 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3,
% 8.73/1.97 v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 8.73/1.97
% 8.73/1.97 (d7_xboole_0)
% 8.73/1.97 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.73/1.97 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 =
% 8.73/1.97 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] :
% 8.73/1.97 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.73/1.97 set_intersection2(v0, v1) = empty_set)
% 8.73/1.97
% 8.73/1.97 (t3_xboole_0)
% 8.73/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 8.73/1.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0 & in(v3, v0) =
% 8.73/1.97 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~
% 8.73/1.97 $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | ?
% 8.73/1.97 [v3: int] : ( ~ (v3 = 0) & in(v2, v1) = v3)))
% 8.73/1.97
% 8.73/1.97 (t4_xboole_0)
% 8.73/1.97 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : (disjoint(v0, v1) =
% 8.73/1.97 v2 & set_intersection2(v0, v1) = v3 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 &
% 8.73/1.97 ? [v4: $i] : (in(v4, v3) = 0 & $i(v4))) | ( ~ (v2 = 0) & ! [v4: $i] : (
% 8.73/1.97 ~ (in(v4, v3) = 0) | ~ $i(v4)))))
% 8.73/1.97
% 8.73/1.97 (function-axioms)
% 8.73/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.73/1.98 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 8.73/1.98 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.73/1.98 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 8.73/1.98 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.73/1.98 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 8.73/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.73/1.98 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.73/1.98
% 8.73/1.98 Further assumptions not needed in the proof:
% 8.73/1.98 --------------------------------------------
% 8.73/1.98 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 8.73/1.98 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0
% 8.73/1.98
% 8.73/1.98 Those formulas are unsatisfiable:
% 8.73/1.98 ---------------------------------
% 8.73/1.98
% 8.73/1.98 Begin of proof
% 8.73/1.98 |
% 8.73/1.98 | ALPHA: (d1_xboole_0) implies:
% 8.73/1.98 | (1) ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0))
% 8.73/1.98 |
% 8.73/1.98 | ALPHA: (d3_xboole_0) implies:
% 8.73/1.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0,
% 8.73/1.98 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 8.73/1.98 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 8.73/1.98 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) |
% 8.73/1.98 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) |
% 8.73/1.98 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 &
% 8.73/1.98 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 8.73/1.98 |
% 8.73/1.98 | ALPHA: (d7_xboole_0) implies:
% 8.73/1.98 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 8.73/1.98 | $i(v0) | set_intersection2(v0, v1) = empty_set)
% 8.73/1.98 |
% 8.73/1.98 | ALPHA: (t3_xboole_0) implies:
% 8.73/1.99 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 8.73/1.99 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0
% 8.73/1.99 | & in(v3, v0) = 0 & $i(v3)))
% 8.73/1.99 |
% 8.73/1.99 | ALPHA: (function-axioms) implies:
% 8.73/1.99 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.73/1.99 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.73/1.99 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.73/1.99 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) =
% 8.73/1.99 | v0))
% 8.73/1.99 |
% 8.73/1.99 | DELTA: instantiating (t4_xboole_0) with fresh symbols all_18_0, all_18_1,
% 8.73/1.99 | all_18_2, all_18_3 gives:
% 8.73/1.99 | (7) disjoint(all_18_3, all_18_2) = all_18_1 & set_intersection2(all_18_3,
% 8.73/1.99 | all_18_2) = all_18_0 & $i(all_18_0) & $i(all_18_2) & $i(all_18_3) &
% 8.73/1.99 | ((all_18_1 = 0 & ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0))) | ( ~
% 8.73/1.99 | (all_18_1 = 0) & ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~
% 8.73/1.99 | $i(v0))))
% 8.73/1.99 |
% 8.73/1.99 | ALPHA: (7) implies:
% 8.73/1.99 | (8) $i(all_18_3)
% 8.73/1.99 | (9) $i(all_18_2)
% 8.73/1.99 | (10) $i(all_18_0)
% 8.73/1.99 | (11) set_intersection2(all_18_3, all_18_2) = all_18_0
% 8.73/1.99 | (12) disjoint(all_18_3, all_18_2) = all_18_1
% 8.73/1.99 | (13) (all_18_1 = 0 & ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0))) | ( ~
% 8.73/1.99 | (all_18_1 = 0) & ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~
% 8.73/1.99 | $i(v0)))
% 8.73/1.99 |
% 8.73/1.99 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_0, simplifying
% 8.73/1.99 | with (8), (9), (10), (11) gives:
% 8.73/2.00 | (14) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) |
% 8.73/2.00 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0,
% 8.73/2.00 | all_18_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 8.73/2.00 | $i] : ( ~ (in(v0, all_18_3) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 8.73/2.00 | [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_2) = v1 & ( ~ (v1
% 8.73/2.00 | = 0) | v2 = 0)))
% 8.73/2.00 |
% 8.73/2.00 | ALPHA: (14) implies:
% 8.73/2.00 | (15) ! [v0: $i] : ( ~ (in(v0, all_18_3) = 0) | ~ $i(v0) | ? [v1: any] :
% 8.73/2.00 | ? [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_2) = v1 & ( ~
% 8.73/2.00 | (v1 = 0) | v2 = 0)))
% 8.73/2.00 | (16) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) |
% 8.73/2.00 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0,
% 8.73/2.00 | all_18_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 8.73/2.00 |
% 8.73/2.00 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_18_3,
% 8.73/2.00 | all_18_2, all_18_0, simplifying with (8), (9), (11) gives:
% 8.73/2.00 | (17) set_intersection2(all_18_2, all_18_3) = all_18_0 & $i(all_18_0)
% 8.73/2.00 |
% 8.73/2.00 | ALPHA: (17) implies:
% 8.73/2.00 | (18) set_intersection2(all_18_2, all_18_3) = all_18_0
% 8.73/2.00 |
% 8.73/2.00 | GROUND_INST: instantiating (4) with all_18_3, all_18_2, all_18_1, simplifying
% 8.73/2.00 | with (8), (9), (12) gives:
% 8.73/2.00 | (19) all_18_1 = 0 | ? [v0: $i] : (in(v0, all_18_2) = 0 & in(v0, all_18_3)
% 8.73/2.00 | = 0 & $i(v0))
% 8.73/2.00 |
% 8.73/2.00 | GROUND_INST: instantiating (2) with all_18_2, all_18_3, all_18_0, simplifying
% 8.73/2.00 | with (8), (9), (10), (18) gives:
% 8.73/2.00 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_2) = v1) | ~ $i(v0) |
% 8.73/2.00 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0,
% 8.73/2.00 | all_18_3) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 8.73/2.00 | $i] : ( ~ (in(v0, all_18_2) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 8.73/2.00 | [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_3) = v1 & ( ~ (v1
% 8.73/2.00 | = 0) | v2 = 0)))
% 8.73/2.00 |
% 8.73/2.00 | ALPHA: (20) implies:
% 8.73/2.00 | (21) ! [v0: $i] : ( ~ (in(v0, all_18_2) = 0) | ~ $i(v0) | ? [v1: any] :
% 8.73/2.00 | ? [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_3) = v1 & ( ~
% 8.73/2.00 | (v1 = 0) | v2 = 0)))
% 8.73/2.01 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_2) = v1) | ~ $i(v0) |
% 8.73/2.01 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0,
% 8.73/2.01 | all_18_3) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 8.73/2.01 |
% 8.73/2.01 | BETA: splitting (13) gives:
% 8.73/2.01 |
% 8.73/2.01 | Case 1:
% 8.73/2.01 | |
% 8.73/2.01 | | (23) all_18_1 = 0 & ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0))
% 8.73/2.01 | |
% 8.73/2.01 | | ALPHA: (23) implies:
% 8.73/2.01 | | (24) all_18_1 = 0
% 8.73/2.01 | | (25) ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0))
% 8.73/2.01 | |
% 8.73/2.01 | | DELTA: instantiating (25) with fresh symbol all_46_0 gives:
% 8.73/2.01 | | (26) in(all_46_0, all_18_0) = 0 & $i(all_46_0)
% 8.73/2.01 | |
% 8.73/2.01 | | ALPHA: (26) implies:
% 8.73/2.01 | | (27) $i(all_46_0)
% 8.73/2.01 | | (28) in(all_46_0, all_18_0) = 0
% 8.73/2.01 | |
% 8.73/2.01 | | REDUCE: (12), (24) imply:
% 8.73/2.01 | | (29) disjoint(all_18_3, all_18_2) = 0
% 8.73/2.01 | |
% 8.73/2.01 | | GROUND_INST: instantiating (3) with all_18_3, all_18_2, simplifying with
% 8.73/2.01 | | (8), (9), (29) gives:
% 8.73/2.01 | | (30) set_intersection2(all_18_3, all_18_2) = empty_set
% 8.73/2.01 | |
% 9.18/2.01 | | GROUND_INST: instantiating (6) with all_18_0, empty_set, all_18_2, all_18_3,
% 9.18/2.01 | | simplifying with (11), (30) gives:
% 9.18/2.01 | | (31) all_18_0 = empty_set
% 9.18/2.01 | |
% 9.18/2.01 | | REDUCE: (28), (31) imply:
% 9.18/2.01 | | (32) in(all_46_0, empty_set) = 0
% 9.18/2.01 | |
% 9.18/2.01 | | GROUND_INST: instantiating (1) with all_46_0, simplifying with (27), (32)
% 9.18/2.01 | | gives:
% 9.18/2.01 | | (33) $false
% 9.18/2.01 | |
% 9.18/2.01 | | CLOSE: (33) is inconsistent.
% 9.18/2.01 | |
% 9.18/2.01 | Case 2:
% 9.18/2.01 | |
% 9.18/2.01 | | (34) ~ (all_18_1 = 0) & ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~
% 9.18/2.01 | | $i(v0))
% 9.18/2.01 | |
% 9.18/2.01 | | ALPHA: (34) implies:
% 9.18/2.01 | | (35) ~ (all_18_1 = 0)
% 9.18/2.01 | | (36) ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~ $i(v0))
% 9.18/2.01 | |
% 9.18/2.01 | | BETA: splitting (19) gives:
% 9.18/2.01 | |
% 9.18/2.01 | | Case 1:
% 9.18/2.01 | | |
% 9.18/2.01 | | | (37) all_18_1 = 0
% 9.18/2.01 | | |
% 9.18/2.01 | | | REDUCE: (35), (37) imply:
% 9.18/2.01 | | | (38) $false
% 9.18/2.01 | | |
% 9.18/2.01 | | | CLOSE: (38) is inconsistent.
% 9.18/2.01 | | |
% 9.18/2.01 | | Case 2:
% 9.18/2.01 | | |
% 9.18/2.01 | | | (39) ? [v0: $i] : (in(v0, all_18_2) = 0 & in(v0, all_18_3) = 0 &
% 9.18/2.01 | | | $i(v0))
% 9.18/2.01 | | |
% 9.18/2.01 | | | DELTA: instantiating (39) with fresh symbol all_57_0 gives:
% 9.18/2.01 | | | (40) in(all_57_0, all_18_2) = 0 & in(all_57_0, all_18_3) = 0 &
% 9.18/2.01 | | | $i(all_57_0)
% 9.18/2.01 | | |
% 9.18/2.01 | | | ALPHA: (40) implies:
% 9.18/2.02 | | | (41) $i(all_57_0)
% 9.18/2.02 | | | (42) in(all_57_0, all_18_3) = 0
% 9.18/2.02 | | | (43) in(all_57_0, all_18_2) = 0
% 9.18/2.02 | | |
% 9.18/2.02 | | | GROUND_INST: instantiating (15) with all_57_0, simplifying with (41), (42)
% 9.18/2.02 | | | gives:
% 9.18/2.02 | | | (44) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v1 &
% 9.18/2.02 | | | in(all_57_0, all_18_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 9.18/2.02 | | |
% 9.18/2.02 | | | GROUND_INST: instantiating (16) with all_57_0, 0, simplifying with (41),
% 9.18/2.02 | | | (42) gives:
% 9.18/2.02 | | | (45) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v0 &
% 9.18/2.02 | | | in(all_57_0, all_18_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 9.18/2.02 | | |
% 9.18/2.02 | | | GROUND_INST: instantiating (21) with all_57_0, simplifying with (41), (43)
% 9.18/2.02 | | | gives:
% 9.18/2.02 | | | (46) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v1 &
% 9.18/2.02 | | | in(all_57_0, all_18_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 9.18/2.02 | | |
% 9.18/2.02 | | | GROUND_INST: instantiating (22) with all_57_0, 0, simplifying with (41),
% 9.18/2.02 | | | (43) gives:
% 9.18/2.02 | | | (47) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v0 &
% 9.18/2.02 | | | in(all_57_0, all_18_3) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 9.18/2.02 | | |
% 9.18/2.02 | | | DELTA: instantiating (44) with fresh symbols all_72_0, all_72_1 gives:
% 9.18/2.02 | | | (48) in(all_57_0, all_18_0) = all_72_0 & in(all_57_0, all_18_2) =
% 9.18/2.02 | | | all_72_1 & ( ~ (all_72_1 = 0) | all_72_0 = 0)
% 9.18/2.02 | | |
% 9.18/2.02 | | | ALPHA: (48) implies:
% 9.18/2.02 | | | (49) in(all_57_0, all_18_2) = all_72_1
% 9.18/2.02 | | | (50) in(all_57_0, all_18_0) = all_72_0
% 9.18/2.02 | | | (51) ~ (all_72_1 = 0) | all_72_0 = 0
% 9.18/2.02 | | |
% 9.18/2.02 | | | DELTA: instantiating (46) with fresh symbols all_74_0, all_74_1 gives:
% 9.18/2.02 | | | (52) in(all_57_0, all_18_0) = all_74_0 & in(all_57_0, all_18_3) =
% 9.18/2.02 | | | all_74_1 & ( ~ (all_74_1 = 0) | all_74_0 = 0)
% 9.18/2.02 | | |
% 9.18/2.02 | | | ALPHA: (52) implies:
% 9.18/2.02 | | | (53) in(all_57_0, all_18_0) = all_74_0
% 9.18/2.02 | | |
% 9.18/2.02 | | | DELTA: instantiating (45) with fresh symbols all_76_0, all_76_1 gives:
% 9.18/2.02 | | | (54) in(all_57_0, all_18_0) = all_76_1 & in(all_57_0, all_18_2) =
% 9.18/2.02 | | | all_76_0 & ( ~ (all_76_1 = 0) | all_76_0 = 0)
% 9.18/2.02 | | |
% 9.18/2.02 | | | ALPHA: (54) implies:
% 9.18/2.02 | | | (55) in(all_57_0, all_18_2) = all_76_0
% 9.18/2.02 | | | (56) in(all_57_0, all_18_0) = all_76_1
% 9.18/2.02 | | |
% 9.18/2.02 | | | DELTA: instantiating (47) with fresh symbols all_78_0, all_78_1 gives:
% 9.18/2.02 | | | (57) in(all_57_0, all_18_0) = all_78_1 & in(all_57_0, all_18_3) =
% 9.18/2.02 | | | all_78_0 & ( ~ (all_78_1 = 0) | all_78_0 = 0)
% 9.18/2.02 | | |
% 9.18/2.02 | | | ALPHA: (57) implies:
% 9.18/2.02 | | | (58) in(all_57_0, all_18_0) = all_78_1
% 9.18/2.02 | | |
% 9.18/2.02 | | | GROUND_INST: instantiating (5) with 0, all_76_0, all_18_2, all_57_0,
% 9.18/2.02 | | | simplifying with (43), (55) gives:
% 9.18/2.02 | | | (59) all_76_0 = 0
% 9.18/2.02 | | |
% 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_72_1, all_76_0, all_18_2,
% 9.18/2.03 | | | all_57_0, simplifying with (49), (55) gives:
% 9.18/2.03 | | | (60) all_76_0 = all_72_1
% 9.18/2.03 | | |
% 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_72_0, all_76_1, all_18_0,
% 9.18/2.03 | | | all_57_0, simplifying with (50), (56) gives:
% 9.18/2.03 | | | (61) all_76_1 = all_72_0
% 9.18/2.03 | | |
% 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_76_1, all_78_1, all_18_0,
% 9.18/2.03 | | | all_57_0, simplifying with (56), (58) gives:
% 9.18/2.03 | | | (62) all_78_1 = all_76_1
% 9.18/2.03 | | |
% 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_74_0, all_78_1, all_18_0,
% 9.18/2.03 | | | all_57_0, simplifying with (53), (58) gives:
% 9.18/2.03 | | | (63) all_78_1 = all_74_0
% 9.18/2.03 | | |
% 9.18/2.03 | | | COMBINE_EQS: (62), (63) imply:
% 9.18/2.03 | | | (64) all_76_1 = all_74_0
% 9.18/2.03 | | |
% 9.18/2.03 | | | SIMP: (64) implies:
% 9.18/2.03 | | | (65) all_76_1 = all_74_0
% 9.18/2.03 | | |
% 9.18/2.03 | | | COMBINE_EQS: (59), (60) imply:
% 9.18/2.03 | | | (66) all_72_1 = 0
% 9.18/2.03 | | |
% 9.18/2.03 | | | COMBINE_EQS: (61), (65) imply:
% 9.18/2.03 | | | (67) all_74_0 = all_72_0
% 9.18/2.03 | | |
% 9.18/2.03 | | | SIMP: (67) implies:
% 9.18/2.03 | | | (68) all_74_0 = all_72_0
% 9.18/2.03 | | |
% 9.18/2.03 | | | BETA: splitting (51) gives:
% 9.18/2.03 | | |
% 9.18/2.03 | | | Case 1:
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | (69) ~ (all_72_1 = 0)
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | REDUCE: (66), (69) imply:
% 9.18/2.03 | | | | (70) $false
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | CLOSE: (70) is inconsistent.
% 9.18/2.03 | | | |
% 9.18/2.03 | | | Case 2:
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | (71) all_72_0 = 0
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | REDUCE: (50), (71) imply:
% 9.18/2.03 | | | | (72) in(all_57_0, all_18_0) = 0
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | GROUND_INST: instantiating (36) with all_57_0, simplifying with (41),
% 9.18/2.03 | | | | (72) gives:
% 9.18/2.03 | | | | (73) $false
% 9.18/2.03 | | | |
% 9.18/2.03 | | | | CLOSE: (73) is inconsistent.
% 9.18/2.03 | | | |
% 9.18/2.03 | | | End of split
% 9.18/2.03 | | |
% 9.18/2.03 | | End of split
% 9.18/2.03 | |
% 9.18/2.03 | End of split
% 9.18/2.03 |
% 9.18/2.03 End of proof
% 9.18/2.03 % SZS output end Proof for theBenchmark
% 9.18/2.03
% 9.18/2.03 1401ms
%------------------------------------------------------------------------------