TSTP Solution File: SEU224+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU224+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:43:26 EDT 2023
% Result : Theorem 15.14s 2.83s
% Output : Proof 16.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU224+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:40:20 EDT 2023
% 0.14/0.35 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 2.39/1.06 Prover 4: Preprocessing ...
% 2.39/1.06 Prover 1: Preprocessing ...
% 3.09/1.10 Prover 0: Preprocessing ...
% 3.09/1.10 Prover 6: Preprocessing ...
% 3.09/1.10 Prover 5: Preprocessing ...
% 3.09/1.10 Prover 3: Preprocessing ...
% 3.09/1.10 Prover 2: Preprocessing ...
% 5.90/1.59 Prover 1: Warning: ignoring some quantifiers
% 5.90/1.60 Prover 3: Warning: ignoring some quantifiers
% 5.90/1.62 Prover 5: Proving ...
% 5.90/1.62 Prover 1: Constructing countermodel ...
% 5.90/1.62 Prover 3: Constructing countermodel ...
% 5.90/1.63 Prover 6: Proving ...
% 5.90/1.68 Prover 2: Proving ...
% 8.70/1.91 Prover 4: Warning: ignoring some quantifiers
% 8.93/1.96 Prover 4: Constructing countermodel ...
% 10.17/2.11 Prover 0: Proving ...
% 11.66/2.31 Prover 3: gave up
% 11.66/2.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.90/2.37 Prover 7: Preprocessing ...
% 11.90/2.50 Prover 7: Warning: ignoring some quantifiers
% 11.90/2.51 Prover 7: Constructing countermodel ...
% 15.14/2.82 Prover 7: Found proof (size 34)
% 15.14/2.82 Prover 7: proved (498ms)
% 15.14/2.82 Prover 4: stopped
% 15.14/2.82 Prover 1: stopped
% 15.14/2.82 Prover 0: stopped
% 15.14/2.82 Prover 2: stopped
% 15.14/2.82 Prover 6: stopped
% 15.14/2.83 Prover 5: stopped
% 15.14/2.83
% 15.14/2.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.14/2.83
% 15.14/2.83 % SZS output start Proof for theBenchmark
% 15.14/2.84 Assumptions after simplification:
% 15.14/2.84 ---------------------------------
% 15.14/2.84
% 15.14/2.84 (commutativity_k3_xboole_0)
% 15.14/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 15.14/2.86 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 15.14/2.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 15.14/2.86 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 15.14/2.86
% 15.14/2.86 (d3_xboole_0)
% 15.77/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.77/2.87 (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.77/2.87 $i(v0) | ~ in(v3, v2) | in(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.77/2.87 $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~
% 15.77/2.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) & ! [v0: $i] :
% 15.77/2.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 15.77/2.87 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v1) | ~ in(v3,
% 15.77/2.87 v0) | in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 15.77/2.87 : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.77/2.87 $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4,
% 15.77/2.87 v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 15.77/2.87
% 15.77/2.87 (dt_k7_relat_1)
% 15.77/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 15.77/2.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2))
% 15.77/2.87
% 15.77/2.87 (fc4_funct_1)
% 15.77/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 15.77/2.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) |
% 15.77/2.88 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.77/2.88 (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 15.77/2.88 relation(v0) | ~ function(v0) | function(v2))
% 15.77/2.88
% 15.77/2.88 (l82_funct_1)
% 15.77/2.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 15.77/2.88 $i] : (relation_dom(v3) = v4 & relation_dom_restriction(v2, v0) = v3 &
% 15.77/2.88 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) & function(v2) &
% 15.77/2.88 ((relation_dom(v2) = v5 & $i(v5) & in(v1, v5) & in(v1, v0) & ~ in(v1, v4))
% 15.77/2.88 | (in(v1, v4) & ( ~ in(v1, v0) | (relation_dom(v2) = v5 & $i(v5) & ~
% 15.77/2.88 in(v1, v5))))))
% 15.77/2.88
% 15.77/2.88 (t68_funct_1)
% 15.77/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.77/2.89 (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~
% 15.77/2.89 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ relation(v1) | ~
% 15.77/2.89 function(v3) | ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 15.77/2.89 ? [v8: $i] : ? [v9: $i] : ($i(v7) & ( ~ (v4 = v1) | (v6 = v2 &
% 15.77/2.89 relation_dom(v3) = v5 & set_intersection2(v5, v0) = v2 & $i(v5) &
% 15.77/2.89 $i(v2) & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~
% 15.77/2.89 $i(v10) | ~ in(v10, v2) | (apply(v1, v10) = v11 & $i(v11))) & !
% 15.77/2.89 [v10: $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ $i(v10) |
% 15.77/2.89 ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & (v4 = v1 | ( ~
% 15.77/2.89 (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) & $i(v8)
% 15.77/2.89 & in(v7, v2)) | ( ~ (v6 = v2) & relation_dom(v3) = v5 &
% 15.77/2.89 set_intersection2(v5, v0) = v6 & $i(v6) & $i(v5))))) & ? [v0: $i] :
% 15.77/2.89 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) =
% 15.77/2.89 v4) | ~ (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 15.77/2.89 relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5:
% 15.77/2.89 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) &
% 15.77/2.89 ((v6 = v2 & set_intersection2(v4, v0) = v2 & $i(v2) & ! [v10: $i] : !
% 15.77/2.89 [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ $i(v10) | ~ in(v10, v2) |
% 15.77/2.89 (apply(v1, v10) = v11 & $i(v11))) & ! [v10: $i] : ! [v11: $i] : (
% 15.77/2.89 ~ (apply(v1, v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | (apply(v3,
% 15.77/2.89 v10) = v11 & $i(v11)))) | ( ~ (v5 = v1) &
% 15.77/2.89 relation_dom_restriction(v3, v0) = v5 & $i(v5))) & ((v5 = v1 &
% 15.77/2.89 relation_dom_restriction(v3, v0) = v1) | ( ~ (v9 = v8) & apply(v3, v7)
% 15.77/2.89 = v9 & apply(v1, v7) = v8 & $i(v9) & $i(v8) & in(v7, v2)) | ( ~ (v6 =
% 15.77/2.89 v2) & set_intersection2(v4, v0) = v6 & $i(v6)))))
% 15.77/2.89
% 15.77/2.89 (function-axioms)
% 15.77/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.77/2.89 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 15.77/2.89 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2)
% 15.77/2.89 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : !
% 15.77/2.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3,
% 15.77/2.89 v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.77/2.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 15.77/2.89 (relation_dom(v2) = v0))
% 15.77/2.89
% 15.77/2.89 Further assumptions not needed in the proof:
% 15.77/2.89 --------------------------------------------
% 15.91/2.89 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k1_funct_1,
% 15.91/2.89 dt_k1_relat_1, dt_k1_xboole_0, dt_k3_xboole_0, dt_m1_subset_1,
% 15.91/2.89 existence_m1_subset_1, fc12_relat_1, fc13_relat_1, fc1_relat_1, fc1_xboole_0,
% 15.91/2.89 fc4_relat_1, fc5_relat_1, fc7_relat_1, idempotence_k3_xboole_0, rc1_funct_1,
% 15.91/2.89 rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1,
% 15.91/2.89 rc3_relat_1, t1_subset, t2_boole, t2_subset, t6_boole, t7_boole, t8_boole
% 15.91/2.89
% 15.91/2.89 Those formulas are unsatisfiable:
% 15.91/2.89 ---------------------------------
% 15.91/2.89
% 15.91/2.89 Begin of proof
% 15.91/2.89 |
% 15.91/2.89 | ALPHA: (commutativity_k3_xboole_0) implies:
% 15.91/2.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 15.91/2.90 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 15.91/2.90 | v2 & $i(v2)))
% 15.91/2.90 |
% 15.91/2.90 | ALPHA: (d3_xboole_0) implies:
% 15.91/2.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.91/2.90 | (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 15.91/2.90 | | ~ $i(v0) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 15.91/2.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.91/2.90 | (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 15.91/2.90 | | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0))
% 15.91/2.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.91/2.90 | (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 15.91/2.90 | | ~ $i(v0) | ~ in(v3, v2) | in(v3, v1))
% 15.91/2.90 |
% 15.91/2.90 | ALPHA: (fc4_funct_1) implies:
% 15.91/2.90 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.91/2.90 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 15.91/2.90 | relation(v0) | ~ function(v0) | function(v2))
% 15.91/2.90 |
% 15.91/2.90 | ALPHA: (t68_funct_1) implies:
% 15.91/2.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 15.91/2.90 | ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) =
% 15.91/2.90 | v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~
% 15.91/2.90 | relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5: $i] : ?
% 15.91/2.90 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ( ~
% 15.91/2.90 | (v4 = v1) | (v6 = v2 & relation_dom(v3) = v5 &
% 15.91/2.90 | set_intersection2(v5, v0) = v2 & $i(v5) & $i(v2) & ! [v10: $i]
% 15.91/2.90 | : ! [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ $i(v10) | ~
% 15.91/2.90 | in(v10, v2) | (apply(v1, v10) = v11 & $i(v11))) & ! [v10:
% 15.91/2.90 | $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ $i(v10)
% 15.91/2.90 | | ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & (v4
% 15.91/2.90 | = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 &
% 15.91/2.90 | $i(v9) & $i(v8) & in(v7, v2)) | ( ~ (v6 = v2) &
% 15.91/2.90 | relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & $i(v6)
% 15.91/2.90 | & $i(v5)))))
% 15.91/2.90 |
% 15.91/2.90 | ALPHA: (function-axioms) implies:
% 15.91/2.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.91/2.90 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 15.91/2.90 |
% 15.91/2.90 | DELTA: instantiating (l82_funct_1) with fresh symbols all_43_0, all_43_1,
% 15.91/2.90 | all_43_2, all_43_3, all_43_4, all_43_5 gives:
% 15.91/2.90 | (8) relation_dom(all_43_2) = all_43_1 & relation_dom_restriction(all_43_3,
% 15.91/2.90 | all_43_5) = all_43_2 & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) &
% 15.91/2.90 | $i(all_43_4) & $i(all_43_5) & relation(all_43_3) & function(all_43_3) &
% 15.91/2.90 | ((relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & in(all_43_4,
% 15.91/2.90 | all_43_0) & in(all_43_4, all_43_5) & ~ in(all_43_4, all_43_1)) |
% 15.91/2.90 | (in(all_43_4, all_43_1) & ( ~ in(all_43_4, all_43_5) |
% 15.91/2.90 | (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~
% 15.91/2.90 | in(all_43_4, all_43_0)))))
% 15.91/2.90 |
% 15.91/2.90 | ALPHA: (8) implies:
% 15.91/2.91 | (9) function(all_43_3)
% 15.91/2.91 | (10) relation(all_43_3)
% 15.91/2.91 | (11) $i(all_43_5)
% 15.91/2.91 | (12) $i(all_43_4)
% 15.91/2.91 | (13) $i(all_43_3)
% 15.91/2.91 | (14) $i(all_43_2)
% 15.91/2.91 | (15) relation_dom_restriction(all_43_3, all_43_5) = all_43_2
% 15.91/2.91 | (16) relation_dom(all_43_2) = all_43_1
% 15.91/2.91 | (17) (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & in(all_43_4,
% 15.91/2.91 | all_43_0) & in(all_43_4, all_43_5) & ~ in(all_43_4, all_43_1)) |
% 15.91/2.91 | (in(all_43_4, all_43_1) & ( ~ in(all_43_4, all_43_5) |
% 15.91/2.91 | (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~
% 15.91/2.91 | in(all_43_4, all_43_0))))
% 15.91/2.91 |
% 15.91/2.91 | GROUND_INST: instantiating (5) with all_43_3, all_43_5, all_43_2, simplifying
% 15.91/2.91 | with (9), (10), (11), (13), (15) gives:
% 15.91/2.91 | (18) function(all_43_2)
% 15.91/2.91 |
% 15.91/2.91 | GROUND_INST: instantiating (dt_k7_relat_1) with all_43_3, all_43_5, all_43_2,
% 15.91/2.91 | simplifying with (10), (11), (13), (15) gives:
% 15.91/2.91 | (19) relation(all_43_2)
% 15.91/2.91 |
% 15.91/2.91 | GROUND_INST: instantiating (6) with all_43_5, all_43_2, all_43_1, all_43_3,
% 15.91/2.91 | all_43_2, simplifying with (9), (10), (11), (13), (14), (15),
% 15.91/2.91 | (16), (18), (19) gives:
% 15.91/2.91 | (20) ? [v0: $i] : ? [v1: $i] : (relation_dom(all_43_3) = v0 &
% 15.91/2.91 | set_intersection2(v0, all_43_5) = all_43_1 & $i(v1) & $i(v0) &
% 15.91/2.91 | $i(all_43_1) & ! [v2: $i] : ! [v3: $i] : ( ~ (apply(all_43_2, v2)
% 15.91/2.91 | = v3) | ~ $i(v2) | ~ in(v2, all_43_1) | (apply(all_43_3, v2) =
% 15.91/2.91 | v3 & $i(v3))) & ! [v2: $i] : ! [v3: $i] : ( ~ (apply(all_43_3,
% 15.91/2.91 | v2) = v3) | ~ $i(v2) | ~ in(v2, all_43_1) | (apply(all_43_2,
% 15.91/2.91 | v2) = v3 & $i(v3))))
% 15.91/2.91 |
% 15.91/2.91 | DELTA: instantiating (20) with fresh symbols all_62_0, all_62_1 gives:
% 15.91/2.91 | (21) relation_dom(all_43_3) = all_62_1 & set_intersection2(all_62_1,
% 15.91/2.91 | all_43_5) = all_43_1 & $i(all_62_0) & $i(all_62_1) & $i(all_43_1) &
% 15.91/2.91 | ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_43_2, v0) = v1) | ~ $i(v0)
% 15.91/2.91 | | ~ in(v0, all_43_1) | (apply(all_43_3, v0) = v1 & $i(v1))) & !
% 15.91/2.91 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_43_3, v0) = v1) | ~ $i(v0) |
% 15.91/2.91 | ~ in(v0, all_43_1) | (apply(all_43_2, v0) = v1 & $i(v1)))
% 15.91/2.91 |
% 15.91/2.91 | ALPHA: (21) implies:
% 15.91/2.91 | (22) $i(all_62_1)
% 15.91/2.91 | (23) set_intersection2(all_62_1, all_43_5) = all_43_1
% 15.91/2.91 | (24) relation_dom(all_43_3) = all_62_1
% 15.91/2.91 |
% 15.91/2.91 | GROUND_INST: instantiating (1) with all_43_5, all_62_1, all_43_1, simplifying
% 15.91/2.91 | with (11), (22), (23) gives:
% 15.91/2.91 | (25) set_intersection2(all_43_5, all_62_1) = all_43_1 & $i(all_43_1)
% 15.91/2.91 |
% 15.91/2.91 | ALPHA: (25) implies:
% 15.91/2.91 | (26) $i(all_43_1)
% 15.91/2.91 | (27) set_intersection2(all_43_5, all_62_1) = all_43_1
% 15.91/2.91 |
% 15.91/2.91 | BETA: splitting (17) gives:
% 15.91/2.91 |
% 15.91/2.91 | Case 1:
% 15.91/2.91 | |
% 15.91/2.92 | | (28) relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & in(all_43_4,
% 15.91/2.92 | | all_43_0) & in(all_43_4, all_43_5) & ~ in(all_43_4, all_43_1)
% 15.91/2.92 | |
% 15.91/2.92 | | ALPHA: (28) implies:
% 15.91/2.92 | | (29) ~ in(all_43_4, all_43_1)
% 15.91/2.92 | | (30) in(all_43_4, all_43_5)
% 15.91/2.92 | | (31) in(all_43_4, all_43_0)
% 15.91/2.92 | | (32) relation_dom(all_43_3) = all_43_0
% 15.91/2.92 | |
% 15.91/2.92 | | GROUND_INST: instantiating (7) with all_62_1, all_43_0, all_43_3,
% 15.91/2.92 | | simplifying with (24), (32) gives:
% 15.91/2.92 | | (33) all_62_1 = all_43_0
% 15.91/2.92 | |
% 15.91/2.92 | | REDUCE: (23), (33) imply:
% 15.91/2.92 | | (34) set_intersection2(all_43_0, all_43_5) = all_43_1
% 15.91/2.92 | |
% 15.91/2.92 | | REDUCE: (22), (33) imply:
% 15.91/2.92 | | (35) $i(all_43_0)
% 15.91/2.92 | |
% 15.91/2.92 | | GROUND_INST: instantiating (2) with all_43_0, all_43_5, all_43_1, all_43_4,
% 15.91/2.92 | | simplifying with (11), (12), (26), (29), (30), (31), (34), (35)
% 15.91/2.92 | | gives:
% 15.91/2.92 | | (36) $false
% 15.91/2.92 | |
% 15.91/2.92 | | CLOSE: (36) is inconsistent.
% 15.91/2.92 | |
% 15.91/2.92 | Case 2:
% 15.91/2.92 | |
% 15.91/2.92 | | (37) in(all_43_4, all_43_1) & ( ~ in(all_43_4, all_43_5) |
% 15.91/2.92 | | (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~
% 15.91/2.92 | | in(all_43_4, all_43_0)))
% 15.91/2.92 | |
% 15.91/2.92 | | ALPHA: (37) implies:
% 15.91/2.92 | | (38) in(all_43_4, all_43_1)
% 15.91/2.92 | | (39) ~ in(all_43_4, all_43_5) | (relation_dom(all_43_3) = all_43_0 &
% 15.91/2.92 | | $i(all_43_0) & ~ in(all_43_4, all_43_0))
% 15.91/2.92 | |
% 15.91/2.92 | | GROUND_INST: instantiating (4) with all_43_5, all_62_1, all_43_1, all_43_4,
% 15.91/2.92 | | simplifying with (11), (12), (22), (26), (27), (38) gives:
% 15.91/2.92 | | (40) in(all_43_4, all_62_1)
% 15.91/2.92 | |
% 15.91/2.92 | | GROUND_INST: instantiating (3) with all_43_5, all_62_1, all_43_1, all_43_4,
% 15.91/2.92 | | simplifying with (11), (12), (22), (26), (27), (38) gives:
% 15.91/2.92 | | (41) in(all_43_4, all_43_5)
% 15.91/2.92 | |
% 15.91/2.92 | | BETA: splitting (39) gives:
% 15.91/2.92 | |
% 15.91/2.92 | | Case 1:
% 15.91/2.92 | | |
% 15.91/2.92 | | | (42) ~ in(all_43_4, all_43_5)
% 15.91/2.92 | | |
% 15.91/2.92 | | | PRED_UNIFY: (41), (42) imply:
% 15.91/2.92 | | | (43) $false
% 15.91/2.92 | | |
% 15.91/2.92 | | | CLOSE: (43) is inconsistent.
% 15.91/2.92 | | |
% 15.91/2.92 | | Case 2:
% 15.91/2.92 | | |
% 15.91/2.92 | | | (44) relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~ in(all_43_4,
% 15.91/2.92 | | | all_43_0)
% 15.91/2.92 | | |
% 15.91/2.92 | | | ALPHA: (44) implies:
% 16.06/2.92 | | | (45) ~ in(all_43_4, all_43_0)
% 16.06/2.92 | | | (46) relation_dom(all_43_3) = all_43_0
% 16.06/2.92 | | |
% 16.06/2.92 | | | GROUND_INST: instantiating (7) with all_62_1, all_43_0, all_43_3,
% 16.06/2.92 | | | simplifying with (24), (46) gives:
% 16.06/2.92 | | | (47) all_62_1 = all_43_0
% 16.06/2.92 | | |
% 16.06/2.92 | | | PRED_UNIFY: (40), (45) imply:
% 16.06/2.92 | | | (48) ~ (all_62_1 = all_43_0)
% 16.06/2.92 | | |
% 16.06/2.92 | | | REDUCE: (47), (48) imply:
% 16.06/2.92 | | | (49) $false
% 16.06/2.92 | | |
% 16.06/2.92 | | | CLOSE: (49) is inconsistent.
% 16.06/2.92 | | |
% 16.06/2.92 | | End of split
% 16.06/2.92 | |
% 16.06/2.92 | End of split
% 16.06/2.92 |
% 16.06/2.92 End of proof
% 16.06/2.93 % SZS output end Proof for theBenchmark
% 16.06/2.93
% 16.06/2.93 2303ms
%------------------------------------------------------------------------------