TSTP Solution File: SEU045+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU045+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 : n031.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 17:42:23 EDT 2023
% Result : Theorem 15.72s 2.86s
% Output : Proof 15.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:57:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 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 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 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 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
% 2.63/1.10 Prover 4: Preprocessing ...
% 2.63/1.10 Prover 1: Preprocessing ...
% 2.99/1.14 Prover 0: Preprocessing ...
% 2.99/1.14 Prover 6: Preprocessing ...
% 2.99/1.14 Prover 5: Preprocessing ...
% 2.99/1.14 Prover 2: Preprocessing ...
% 2.99/1.14 Prover 3: Preprocessing ...
% 6.27/1.58 Prover 1: Warning: ignoring some quantifiers
% 6.27/1.61 Prover 3: Warning: ignoring some quantifiers
% 6.27/1.64 Prover 1: Constructing countermodel ...
% 6.27/1.64 Prover 3: Constructing countermodel ...
% 6.27/1.64 Prover 5: Proving ...
% 6.86/1.66 Prover 6: Proving ...
% 8.08/1.82 Prover 2: Proving ...
% 10.64/2.21 Prover 4: Warning: ignoring some quantifiers
% 11.21/2.25 Prover 0: Proving ...
% 11.52/2.28 Prover 4: Constructing countermodel ...
% 12.18/2.40 Prover 3: gave up
% 12.18/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.73/2.45 Prover 7: Preprocessing ...
% 13.51/2.57 Prover 7: Warning: ignoring some quantifiers
% 13.51/2.59 Prover 7: Constructing countermodel ...
% 14.82/2.72 Prover 1: gave up
% 14.82/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.07/2.76 Prover 8: Preprocessing ...
% 15.72/2.84 Prover 7: Found proof (size 20)
% 15.72/2.84 Prover 7: proved (430ms)
% 15.72/2.84 Prover 2: stopped
% 15.72/2.84 Prover 0: stopped
% 15.72/2.84 Prover 6: stopped
% 15.72/2.84 Prover 4: stopped
% 15.72/2.84 Prover 5: stopped
% 15.72/2.85 Prover 8: Warning: ignoring some quantifiers
% 15.72/2.85 Prover 8: Constructing countermodel ...
% 15.72/2.86 Prover 8: stopped
% 15.72/2.86
% 15.72/2.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.72/2.86
% 15.72/2.86 % SZS output start Proof for theBenchmark
% 15.72/2.86 Assumptions after simplification:
% 15.72/2.86 ---------------------------------
% 15.72/2.87
% 15.72/2.87 (dt_k8_relat_1)
% 15.96/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 15.96/2.89 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | relation(v2))
% 15.96/2.89
% 15.96/2.89 (fc5_funct_1)
% 15.96/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 15.96/2.89 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ function(v1) | ~ relation(v1) |
% 15.96/2.89 function(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.96/2.89 (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 15.96/2.89 function(v1) | ~ relation(v1) | relation(v2))
% 15.96/2.89
% 15.96/2.89 (t85_funct_1)
% 15.96/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.96/2.90 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~
% 15.96/2.90 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ function(v3) | ~ function(v1) | ~
% 15.96/2.90 relation(v3) | ~ relation(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 15.96/2.90 ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) & $i(v6) & ( ~ (v4 = v1) |
% 15.96/2.90 (relation_dom(v3) = v5 & $i(v5) & ! [v11: $i] : ! [v12: $i] : ( ~
% 15.96/2.90 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v12, v0) | ~ in(v11,
% 15.96/2.90 v5) | in(v11, v2)) & ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3,
% 15.96/2.90 v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | in(v12, v0)) & !
% 15.96/2.90 [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) |
% 15.96/2.90 ~ in(v11, v2) | in(v11, v5)) & ! [v11: $i] : ! [v12: $i] : ( ~
% 15.96/2.90 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v1,
% 15.96/2.90 v11) = v12 & $i(v12))) & ! [v11: $i] : ! [v12: $i] : ( ~
% 15.96/2.90 (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v3,
% 15.96/2.90 v11) = v12 & $i(v12))))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3,
% 15.96/2.90 v6) = v8 & apply(v1, v6) = v7 & $i(v8) & $i(v7) & in(v6, v2)) |
% 15.96/2.90 (relation_dom(v3) = v5 & $i(v5) & ( ~ in(v9, v5) | ~ in(v9, v2) |
% 15.96/2.90 (apply(v3, v9) = v10 & $i(v10) & ~ in(v10, v0))) & (in(v9, v2) |
% 15.96/2.90 (apply(v3, v9) = v10 & $i(v10) & in(v10, v0) & in(v9, v5))))))) & ?
% 15.96/2.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.96/2.90 (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 15.96/2.90 | ~ $i(v0) | ~ function(v3) | ~ function(v1) | ~ relation(v3) | ~
% 15.96/2.90 relation(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 15.96/2.90 [v9: $i] : ? [v10: $i] : ($i(v9) & $i(v6) & ((v5 = v1 &
% 15.96/2.90 relation_rng_restriction(v0, v3) = v1) | ( ~ (v8 = v7) & apply(v3, v6)
% 15.96/2.90 = v8 & apply(v1, v6) = v7 & $i(v8) & $i(v7) & in(v6, v2)) | (( ~
% 15.96/2.90 in(v9, v4) | ~ in(v9, v2) | (apply(v3, v9) = v10 & $i(v10) & ~
% 15.96/2.90 in(v10, v0))) & (in(v9, v2) | (apply(v3, v9) = v10 & $i(v10) &
% 15.96/2.90 in(v10, v0) & in(v9, v4))))) & (( ~ (v5 = v1) &
% 15.96/2.90 relation_rng_restriction(v0, v3) = v5 & $i(v5)) | ( ! [v11: $i] : !
% 15.96/2.90 [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v12, v0) |
% 15.96/2.90 ~ in(v11, v4) | in(v11, v2)) & ! [v11: $i] : ! [v12: $i] : ( ~
% 15.96/2.90 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | in(v12, v0))
% 15.96/2.90 & ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~
% 15.96/2.90 $i(v11) | ~ in(v11, v2) | in(v11, v4)) & ! [v11: $i] : ! [v12:
% 15.96/2.90 $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) |
% 15.96/2.90 (apply(v1, v11) = v12 & $i(v12))) & ! [v11: $i] : ! [v12: $i] : (
% 15.96/2.91 ~ (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v3,
% 15.96/2.91 v11) = v12 & $i(v12)))))))
% 15.96/2.91
% 15.96/2.91 (t87_funct_1)
% 15.96/2.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 15.96/2.91 $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v3, v1) = v5 & apply(v2, v1) = v6
% 15.96/2.91 & relation_rng_restriction(v0, v2) = v3 & relation_dom(v3) = v4 & $i(v6) &
% 15.96/2.91 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & in(v1, v4) &
% 15.96/2.91 function(v2) & relation(v2))
% 15.96/2.91
% 15.96/2.91 (function-axioms)
% 15.96/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.96/2.91 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 15.96/2.91 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2)
% 15.96/2.91 = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : !
% 15.96/2.91 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 15.96/2.91 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 15.96/2.91 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 15.96/2.91
% 15.96/2.91 Further assumptions not needed in the proof:
% 15.96/2.91 --------------------------------------------
% 15.96/2.91 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 15.96/2.91 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 15.96/2.91 fc5_relat_1, fc7_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 15.96/2.91 rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1,
% 15.96/2.91 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 15.96/2.91 t6_boole, t7_boole, t8_boole
% 15.96/2.91
% 15.96/2.91 Those formulas are unsatisfiable:
% 15.96/2.91 ---------------------------------
% 15.96/2.91
% 15.96/2.91 Begin of proof
% 15.96/2.91 |
% 15.96/2.91 | ALPHA: (fc5_funct_1) implies:
% 15.96/2.91 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.96/2.91 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 15.96/2.91 | function(v1) | ~ relation(v1) | function(v2))
% 15.96/2.91 |
% 15.96/2.91 | ALPHA: (t85_funct_1) implies:
% 15.96/2.91 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 15.96/2.91 | ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) =
% 15.96/2.91 | v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ function(v3) | ~
% 15.96/2.91 | function(v1) | ~ relation(v3) | ~ relation(v1) | ? [v5: $i] : ?
% 15.96/2.91 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 15.96/2.91 | ($i(v9) & $i(v6) & ( ~ (v4 = v1) | (relation_dom(v3) = v5 & $i(v5) &
% 15.96/2.91 | ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~
% 15.96/2.91 | $i(v11) | ~ in(v12, v0) | ~ in(v11, v5) | in(v11, v2)) & !
% 15.96/2.91 | [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~
% 15.96/2.91 | $i(v11) | ~ in(v11, v2) | in(v12, v0)) & ! [v11: $i] : !
% 15.96/2.91 | [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~
% 15.96/2.91 | in(v11, v2) | in(v11, v5)) & ! [v11: $i] : ! [v12: $i] : (
% 15.96/2.91 | ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) |
% 15.96/2.91 | (apply(v1, v11) = v12 & $i(v12))) & ! [v11: $i] : ! [v12:
% 15.96/2.91 | $i] : ( ~ (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11,
% 15.96/2.91 | v2) | (apply(v3, v11) = v12 & $i(v12))))) & (v4 = v1 | ( ~
% 15.96/2.91 | (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & $i(v8) &
% 15.96/2.91 | $i(v7) & in(v6, v2)) | (relation_dom(v3) = v5 & $i(v5) & ( ~
% 15.96/2.91 | in(v9, v5) | ~ in(v9, v2) | (apply(v3, v9) = v10 & $i(v10) &
% 15.96/2.91 | ~ in(v10, v0))) & (in(v9, v2) | (apply(v3, v9) = v10 &
% 15.96/2.91 | $i(v10) & in(v10, v0) & in(v9, v5)))))))
% 15.96/2.91 |
% 15.96/2.91 | ALPHA: (function-axioms) implies:
% 15.96/2.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.96/2.92 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 15.96/2.92 |
% 15.96/2.92 | DELTA: instantiating (t87_funct_1) with fresh symbols all_42_0, all_42_1,
% 15.96/2.92 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6 gives:
% 15.96/2.92 | (4) ~ (all_42_0 = all_42_1) & apply(all_42_3, all_42_5) = all_42_1 &
% 15.96/2.92 | apply(all_42_4, all_42_5) = all_42_0 &
% 15.96/2.92 | relation_rng_restriction(all_42_6, all_42_4) = all_42_3 &
% 15.96/2.92 | relation_dom(all_42_3) = all_42_2 & $i(all_42_0) & $i(all_42_1) &
% 15.96/2.92 | $i(all_42_2) & $i(all_42_3) & $i(all_42_4) & $i(all_42_5) &
% 15.96/2.92 | $i(all_42_6) & in(all_42_5, all_42_2) & function(all_42_4) &
% 15.96/2.92 | relation(all_42_4)
% 15.96/2.92 |
% 15.96/2.92 | ALPHA: (4) implies:
% 15.96/2.92 | (5) ~ (all_42_0 = all_42_1)
% 15.96/2.92 | (6) relation(all_42_4)
% 15.96/2.92 | (7) function(all_42_4)
% 15.96/2.92 | (8) in(all_42_5, all_42_2)
% 15.96/2.92 | (9) $i(all_42_6)
% 15.96/2.92 | (10) $i(all_42_5)
% 15.96/2.92 | (11) $i(all_42_4)
% 15.96/2.92 | (12) $i(all_42_3)
% 15.96/2.92 | (13) relation_dom(all_42_3) = all_42_2
% 15.96/2.92 | (14) relation_rng_restriction(all_42_6, all_42_4) = all_42_3
% 15.96/2.92 | (15) apply(all_42_4, all_42_5) = all_42_0
% 15.96/2.92 | (16) apply(all_42_3, all_42_5) = all_42_1
% 15.96/2.92 |
% 15.96/2.92 | GROUND_INST: instantiating (3) with all_42_0, all_42_1, all_42_5, all_42_4,
% 15.96/2.92 | simplifying with (15) gives:
% 15.96/2.92 | (17) all_42_0 = all_42_1 | ~ (apply(all_42_4, all_42_5) = all_42_1)
% 15.96/2.92 |
% 15.96/2.92 | GROUND_INST: instantiating (1) with all_42_6, all_42_4, all_42_3, simplifying
% 15.96/2.92 | with (6), (7), (9), (11), (14) gives:
% 15.96/2.92 | (18) function(all_42_3)
% 15.96/2.92 |
% 15.96/2.92 | GROUND_INST: instantiating (dt_k8_relat_1) with all_42_6, all_42_4, all_42_3,
% 15.96/2.92 | simplifying with (6), (9), (11), (14) gives:
% 15.96/2.92 | (19) relation(all_42_3)
% 15.96/2.92 |
% 15.96/2.92 | GROUND_INST: instantiating (2) with all_42_6, all_42_3, all_42_2, all_42_4,
% 15.96/2.92 | all_42_3, simplifying with (6), (7), (9), (11), (12), (13), (14),
% 15.96/2.92 | (18), (19) gives:
% 15.96/2.92 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_42_4) = v0
% 15.96/2.92 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 15.96/2.92 | (apply(all_42_3, v3) = v4) | ~ $i(v3) | ~ in(v3, all_42_2) |
% 15.96/2.92 | (apply(all_42_4, v3) = v4 & $i(v4))) & ! [v3: $i] : ! [v4: $i] :
% 15.96/2.92 | ( ~ (apply(all_42_4, v3) = v4) | ~ $i(v3) | ~ in(v4, all_42_6) |
% 15.96/2.92 | ~ in(v3, v0) | in(v3, all_42_2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 15.96/2.92 | (apply(all_42_4, v3) = v4) | ~ $i(v3) | ~ in(v3, all_42_2) |
% 15.96/2.92 | in(v4, all_42_6)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 15.96/2.92 | (apply(all_42_4, v3) = v4) | ~ $i(v3) | ~ in(v3, all_42_2) |
% 15.96/2.92 | in(v3, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(all_42_4, v3)
% 15.96/2.92 | = v4) | ~ $i(v3) | ~ in(v3, all_42_2) | (apply(all_42_3, v3) =
% 15.96/2.92 | v4 & $i(v4))))
% 15.96/2.92 |
% 15.96/2.92 | DELTA: instantiating (20) with fresh symbols all_65_0, all_65_1, all_65_2
% 15.96/2.92 | gives:
% 15.96/2.93 | (21) relation_dom(all_42_4) = all_65_2 & $i(all_65_0) & $i(all_65_1) &
% 15.96/2.93 | $i(all_65_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_3, v0) =
% 15.96/2.93 | v1) | ~ $i(v0) | ~ in(v0, all_42_2) | (apply(all_42_4, v0) = v1
% 15.96/2.93 | & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_4, v0)
% 15.96/2.93 | = v1) | ~ $i(v0) | ~ in(v1, all_42_6) | ~ in(v0, all_65_2) |
% 15.96/2.93 | in(v0, all_42_2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_4,
% 15.96/2.93 | v0) = v1) | ~ $i(v0) | ~ in(v0, all_42_2) | in(v1, all_42_6))
% 15.96/2.93 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_4, v0) = v1) | ~
% 15.96/2.93 | $i(v0) | ~ in(v0, all_42_2) | in(v0, all_65_2)) & ! [v0: $i] : !
% 15.96/2.93 | [v1: $i] : ( ~ (apply(all_42_4, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 15.96/2.93 | all_42_2) | (apply(all_42_3, v0) = v1 & $i(v1)))
% 15.96/2.93 |
% 15.96/2.93 | ALPHA: (21) implies:
% 15.96/2.93 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_3, v0) = v1) | ~ $i(v0)
% 15.96/2.93 | | ~ in(v0, all_42_2) | (apply(all_42_4, v0) = v1 & $i(v1)))
% 15.96/2.93 |
% 15.96/2.93 | GROUND_INST: instantiating (22) with all_42_5, all_42_1, simplifying with (8),
% 15.96/2.93 | (10), (16) gives:
% 15.96/2.93 | (23) apply(all_42_4, all_42_5) = all_42_1 & $i(all_42_1)
% 15.96/2.93 |
% 15.96/2.93 | ALPHA: (23) implies:
% 15.96/2.93 | (24) apply(all_42_4, all_42_5) = all_42_1
% 15.96/2.93 |
% 15.96/2.93 | BETA: splitting (17) gives:
% 15.96/2.93 |
% 15.96/2.93 | Case 1:
% 15.96/2.93 | |
% 15.96/2.93 | | (25) ~ (apply(all_42_4, all_42_5) = all_42_1)
% 15.96/2.93 | |
% 15.96/2.93 | | PRED_UNIFY: (24), (25) imply:
% 15.96/2.93 | | (26) $false
% 15.96/2.93 | |
% 15.96/2.93 | | CLOSE: (26) is inconsistent.
% 15.96/2.93 | |
% 15.96/2.93 | Case 2:
% 15.96/2.93 | |
% 15.96/2.93 | | (27) all_42_0 = all_42_1
% 15.96/2.93 | |
% 15.96/2.93 | | REDUCE: (5), (27) imply:
% 15.96/2.93 | | (28) $false
% 15.96/2.93 | |
% 15.96/2.93 | | CLOSE: (28) is inconsistent.
% 15.96/2.93 | |
% 15.96/2.93 | End of split
% 15.96/2.93 |
% 15.96/2.93 End of proof
% 15.96/2.93 % SZS output end Proof for theBenchmark
% 15.96/2.93
% 15.96/2.93 2317ms
%------------------------------------------------------------------------------