TSTP Solution File: SEU197+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU197+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 : n010.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 17:43:12 EDT 2023
% Result : Theorem 11.96s 2.45s
% Output : Proof 15.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU197+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n010.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 14:23:06 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.43/1.05 Prover 1: Preprocessing ...
% 2.43/1.05 Prover 4: Preprocessing ...
% 2.77/1.08 Prover 2: Preprocessing ...
% 2.77/1.08 Prover 5: Preprocessing ...
% 2.77/1.08 Prover 6: Preprocessing ...
% 2.77/1.08 Prover 3: Preprocessing ...
% 2.77/1.08 Prover 0: Preprocessing ...
% 5.43/1.52 Prover 1: Warning: ignoring some quantifiers
% 5.43/1.52 Prover 3: Warning: ignoring some quantifiers
% 5.43/1.55 Prover 1: Constructing countermodel ...
% 5.43/1.55 Prover 3: Constructing countermodel ...
% 5.43/1.56 Prover 4: Warning: ignoring some quantifiers
% 5.43/1.56 Prover 5: Proving ...
% 6.15/1.58 Prover 4: Constructing countermodel ...
% 6.15/1.59 Prover 6: Proving ...
% 6.43/1.60 Prover 0: Proving ...
% 6.43/1.60 Prover 2: Proving ...
% 11.38/2.37 Prover 3: gave up
% 11.38/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.96/2.40 Prover 7: Preprocessing ...
% 11.96/2.45 Prover 0: proved (1811ms)
% 11.96/2.45
% 11.96/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.96/2.45
% 11.96/2.46 Prover 5: stopped
% 11.96/2.46 Prover 6: stopped
% 11.96/2.47 Prover 2: stopped
% 11.96/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.96/2.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.96/2.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.96/2.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.68/2.48 Prover 7: Warning: ignoring some quantifiers
% 12.68/2.49 Prover 8: Preprocessing ...
% 12.81/2.50 Prover 11: Preprocessing ...
% 12.81/2.50 Prover 10: Preprocessing ...
% 12.81/2.50 Prover 7: Constructing countermodel ...
% 12.96/2.51 Prover 13: Preprocessing ...
% 12.98/2.57 Prover 8: Warning: ignoring some quantifiers
% 12.98/2.58 Prover 8: Constructing countermodel ...
% 13.65/2.61 Prover 10: Warning: ignoring some quantifiers
% 13.65/2.61 Prover 10: Constructing countermodel ...
% 13.65/2.61 Prover 11: Warning: ignoring some quantifiers
% 13.65/2.62 Prover 11: Constructing countermodel ...
% 13.65/2.64 Prover 13: Warning: ignoring some quantifiers
% 13.65/2.67 Prover 13: Constructing countermodel ...
% 14.29/2.74 Prover 10: Found proof (size 26)
% 14.29/2.74 Prover 10: proved (276ms)
% 14.29/2.74 Prover 7: stopped
% 14.29/2.74 Prover 8: stopped
% 14.29/2.74 Prover 4: stopped
% 14.29/2.74 Prover 1: stopped
% 14.29/2.74 Prover 13: stopped
% 14.29/2.74 Prover 11: stopped
% 14.29/2.74
% 14.29/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.29/2.74
% 14.29/2.75 % SZS output start Proof for theBenchmark
% 14.29/2.75 Assumptions after simplification:
% 14.29/2.75 ---------------------------------
% 14.29/2.75
% 14.29/2.75 (d12_relat_1)
% 14.90/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.90/2.78 $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4)
% 14.90/2.78 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 14.90/2.78 relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0: $i] :
% 14.90/2.78 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 14.90/2.78 (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 14.90/2.78 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) |
% 14.90/2.78 ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0: $i] : ! [v1: $i] :
% 14.90/2.78 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 14.90/2.78 (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 14.90/2.78 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) |
% 14.90/2.78 ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0: $i]
% 14.90/2.78 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 14.90/2.78 (relation_rng_restriction(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0)
% 14.90/2.78 | ~ relation(v3) | ~ relation(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 14.90/2.78 $i] : (ordered_pair(v4, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ in(v6,
% 14.90/2.78 v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) &
% 14.90/2.78 in(v5, v0)))))
% 14.90/2.78
% 14.90/2.78 (d5_relat_1)
% 14.90/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 14.90/2.79 (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) | ~
% 14.90/2.79 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 14.90/2.79 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) =
% 14.90/2.79 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 14.90/2.79 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & $i(v3) &
% 14.90/2.79 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 14.90/2.79 (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 14.90/2.79 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 14.90/2.79 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v3) = v7) | ~ $i(v6) |
% 14.90/2.79 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & $i(v5) &
% 14.90/2.79 in(v5, v1)))))
% 14.90/2.79
% 14.90/2.79 (dt_k8_relat_1)
% 14.90/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 14.90/2.79 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | relation(v2))
% 14.90/2.79
% 14.90/2.79 (t115_relat_1)
% 14.99/2.79 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 14.99/2.79 $i] : (relation_rng(v3) = v4 & relation_rng_restriction(v1, v2) = v3 &
% 14.99/2.79 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) &
% 14.99/2.79 ((relation_rng(v2) = v5 & $i(v5) & in(v0, v5) & in(v0, v1) & ~ in(v0, v4))
% 14.99/2.79 | (in(v0, v4) & ( ~ in(v0, v1) | (relation_rng(v2) = v5 & $i(v5) & ~
% 14.99/2.79 in(v0, v5))))))
% 14.99/2.79
% 14.99/2.79 Further assumptions not needed in the proof:
% 14.99/2.79 --------------------------------------------
% 14.99/2.80 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski,
% 14.99/2.80 dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski, dt_k4_tarski,
% 14.99/2.80 dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1,
% 14.99/2.80 fc3_subset_1, fc4_relat_1, fc6_relat_1, fc8_relat_1, rc1_relat_1, rc1_xboole_0,
% 14.99/2.80 rc2_relat_1, rc2_xboole_0, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole
% 14.99/2.80
% 14.99/2.80 Those formulas are unsatisfiable:
% 14.99/2.80 ---------------------------------
% 14.99/2.80
% 14.99/2.80 Begin of proof
% 14.99/2.80 |
% 14.99/2.80 | ALPHA: (d12_relat_1) implies:
% 14.99/2.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 14.99/2.80 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~
% 14.99/2.80 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 14.99/2.80 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5,
% 14.99/2.80 | v1) | ~ in(v4, v0) | in(v5, v2))
% 14.99/2.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 14.99/2.80 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~
% 14.99/2.80 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 14.99/2.80 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5,
% 14.99/2.80 | v2) | in(v4, v0))
% 14.99/2.80 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 14.99/2.80 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~
% 14.99/2.80 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 14.99/2.80 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5,
% 14.99/2.80 | v2) | in(v5, v1))
% 14.99/2.80 |
% 14.99/2.80 | ALPHA: (d5_relat_1) implies:
% 14.99/2.80 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) |
% 14.99/2.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) |
% 14.99/2.80 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) &
% 14.99/2.80 | $i(v3) & in(v4, v0)))
% 14.99/2.81 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 14.99/2.81 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~
% 14.99/2.81 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 14.99/2.81 | in(v4, v0) | in(v2, v1))
% 14.99/2.81 |
% 14.99/2.81 | DELTA: instantiating (t115_relat_1) with fresh symbols all_32_0, all_32_1,
% 14.99/2.81 | all_32_2, all_32_3, all_32_4, all_32_5 gives:
% 14.99/2.81 | (6) relation_rng(all_32_2) = all_32_1 & relation_rng_restriction(all_32_4,
% 14.99/2.81 | all_32_3) = all_32_2 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) &
% 14.99/2.81 | $i(all_32_4) & $i(all_32_5) & relation(all_32_3) &
% 14.99/2.81 | ((relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & in(all_32_5,
% 14.99/2.81 | all_32_0) & in(all_32_5, all_32_4) & ~ in(all_32_5, all_32_1)) |
% 14.99/2.81 | (in(all_32_5, all_32_1) & ( ~ in(all_32_5, all_32_4) |
% 14.99/2.81 | (relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & ~
% 14.99/2.81 | in(all_32_5, all_32_0)))))
% 14.99/2.81 |
% 14.99/2.81 | ALPHA: (6) implies:
% 14.99/2.81 | (7) relation(all_32_3)
% 14.99/2.81 | (8) $i(all_32_5)
% 14.99/2.81 | (9) $i(all_32_4)
% 14.99/2.81 | (10) $i(all_32_3)
% 14.99/2.81 | (11) $i(all_32_2)
% 14.99/2.81 | (12) $i(all_32_1)
% 14.99/2.81 | (13) relation_rng_restriction(all_32_4, all_32_3) = all_32_2
% 14.99/2.81 | (14) relation_rng(all_32_2) = all_32_1
% 14.99/2.81 | (15) (relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & in(all_32_5,
% 14.99/2.81 | all_32_0) & in(all_32_5, all_32_4) & ~ in(all_32_5, all_32_1)) |
% 14.99/2.81 | (in(all_32_5, all_32_1) & ( ~ in(all_32_5, all_32_4) |
% 14.99/2.81 | (relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & ~
% 14.99/2.81 | in(all_32_5, all_32_0))))
% 14.99/2.81 |
% 14.99/2.81 | GROUND_INST: instantiating (dt_k8_relat_1) with all_32_4, all_32_3, all_32_2,
% 14.99/2.81 | simplifying with (7), (9), (10), (13) gives:
% 14.99/2.81 | (16) relation(all_32_2)
% 14.99/2.81 |
% 14.99/2.81 | BETA: splitting (15) gives:
% 14.99/2.81 |
% 14.99/2.81 | Case 1:
% 14.99/2.81 | |
% 15.08/2.81 | | (17) relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & in(all_32_5,
% 15.08/2.81 | | all_32_0) & in(all_32_5, all_32_4) & ~ in(all_32_5, all_32_1)
% 15.08/2.81 | |
% 15.08/2.81 | | ALPHA: (17) implies:
% 15.08/2.81 | | (18) ~ in(all_32_5, all_32_1)
% 15.08/2.81 | | (19) in(all_32_5, all_32_4)
% 15.08/2.81 | | (20) in(all_32_5, all_32_0)
% 15.08/2.81 | | (21) $i(all_32_0)
% 15.08/2.81 | | (22) relation_rng(all_32_3) = all_32_0
% 15.08/2.81 | |
% 15.08/2.81 | | GROUND_INST: instantiating (4) with all_32_3, all_32_0, all_32_5,
% 15.08/2.81 | | simplifying with (7), (8), (10), (20), (21), (22) gives:
% 15.08/2.81 | | (23) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_32_5) = v1 &
% 15.08/2.81 | | $i(v1) & $i(v0) & in(v1, all_32_3))
% 15.08/2.81 | |
% 15.08/2.81 | | DELTA: instantiating (23) with fresh symbols all_60_0, all_60_1 gives:
% 15.08/2.81 | | (24) ordered_pair(all_60_1, all_32_5) = all_60_0 & $i(all_60_0) &
% 15.08/2.81 | | $i(all_60_1) & in(all_60_0, all_32_3)
% 15.08/2.81 | |
% 15.08/2.81 | | ALPHA: (24) implies:
% 15.08/2.82 | | (25) in(all_60_0, all_32_3)
% 15.08/2.82 | | (26) $i(all_60_1)
% 15.08/2.82 | | (27) ordered_pair(all_60_1, all_32_5) = all_60_0
% 15.08/2.82 | |
% 15.08/2.82 | | GROUND_INST: instantiating (1) with all_32_4, all_32_3, all_32_2, all_60_1,
% 15.08/2.82 | | all_32_5, all_60_0, simplifying with (7), (8), (9), (10), (11),
% 15.08/2.82 | | (13), (16), (19), (25), (26), (27) gives:
% 15.08/2.82 | | (28) in(all_60_0, all_32_2)
% 15.08/2.82 | |
% 15.08/2.82 | | GROUND_INST: instantiating (5) with all_32_2, all_32_1, all_32_5, all_60_1,
% 15.08/2.82 | | all_60_0, simplifying with (8), (11), (12), (14), (16), (18),
% 15.08/2.82 | | (26), (27), (28) gives:
% 15.08/2.82 | | (29) $false
% 15.08/2.82 | |
% 15.08/2.82 | | CLOSE: (29) is inconsistent.
% 15.08/2.82 | |
% 15.08/2.82 | Case 2:
% 15.08/2.82 | |
% 15.08/2.82 | | (30) in(all_32_5, all_32_1) & ( ~ in(all_32_5, all_32_4) |
% 15.08/2.82 | | (relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & ~
% 15.08/2.82 | | in(all_32_5, all_32_0)))
% 15.08/2.82 | |
% 15.08/2.82 | | ALPHA: (30) implies:
% 15.08/2.82 | | (31) in(all_32_5, all_32_1)
% 15.08/2.82 | | (32) ~ in(all_32_5, all_32_4) | (relation_rng(all_32_3) = all_32_0 &
% 15.08/2.82 | | $i(all_32_0) & ~ in(all_32_5, all_32_0))
% 15.08/2.82 | |
% 15.08/2.82 | | GROUND_INST: instantiating (4) with all_32_2, all_32_1, all_32_5,
% 15.08/2.82 | | simplifying with (8), (11), (12), (14), (16), (31) gives:
% 15.08/2.82 | | (33) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_32_5) = v1 &
% 15.08/2.82 | | $i(v1) & $i(v0) & in(v1, all_32_2))
% 15.08/2.82 | |
% 15.08/2.82 | | DELTA: instantiating (33) with fresh symbols all_60_0, all_60_1 gives:
% 15.08/2.82 | | (34) ordered_pair(all_60_1, all_32_5) = all_60_0 & $i(all_60_0) &
% 15.08/2.82 | | $i(all_60_1) & in(all_60_0, all_32_2)
% 15.08/2.82 | |
% 15.08/2.82 | | ALPHA: (34) implies:
% 15.08/2.82 | | (35) in(all_60_0, all_32_2)
% 15.08/2.82 | | (36) $i(all_60_1)
% 15.08/2.82 | | (37) ordered_pair(all_60_1, all_32_5) = all_60_0
% 15.08/2.82 | |
% 15.08/2.82 | | GROUND_INST: instantiating (3) with all_32_4, all_32_3, all_32_2, all_60_1,
% 15.08/2.82 | | all_32_5, all_60_0, simplifying with (7), (8), (9), (10), (11),
% 15.08/2.82 | | (13), (16), (35), (36), (37) gives:
% 15.08/2.82 | | (38) in(all_60_0, all_32_3)
% 15.08/2.82 | |
% 15.08/2.83 | | GROUND_INST: instantiating (2) with all_32_4, all_32_3, all_32_2, all_60_1,
% 15.08/2.83 | | all_32_5, all_60_0, simplifying with (7), (8), (9), (10), (11),
% 15.08/2.83 | | (13), (16), (35), (36), (37) gives:
% 15.08/2.83 | | (39) in(all_32_5, all_32_4)
% 15.08/2.83 | |
% 15.08/2.83 | | BETA: splitting (32) gives:
% 15.08/2.83 | |
% 15.08/2.83 | | Case 1:
% 15.08/2.83 | | |
% 15.08/2.83 | | | (40) ~ in(all_32_5, all_32_4)
% 15.08/2.83 | | |
% 15.08/2.83 | | | PRED_UNIFY: (39), (40) imply:
% 15.08/2.83 | | | (41) $false
% 15.08/2.83 | | |
% 15.08/2.83 | | | CLOSE: (41) is inconsistent.
% 15.08/2.83 | | |
% 15.08/2.83 | | Case 2:
% 15.08/2.83 | | |
% 15.08/2.83 | | | (42) relation_rng(all_32_3) = all_32_0 & $i(all_32_0) & ~ in(all_32_5,
% 15.08/2.83 | | | all_32_0)
% 15.08/2.83 | | |
% 15.08/2.83 | | | ALPHA: (42) implies:
% 15.08/2.83 | | | (43) ~ in(all_32_5, all_32_0)
% 15.08/2.83 | | | (44) $i(all_32_0)
% 15.08/2.83 | | | (45) relation_rng(all_32_3) = all_32_0
% 15.08/2.83 | | |
% 15.08/2.83 | | | GROUND_INST: instantiating (5) with all_32_3, all_32_0, all_32_5,
% 15.08/2.83 | | | all_60_1, all_60_0, simplifying with (7), (8), (10), (36),
% 15.08/2.83 | | | (37), (38), (43), (44), (45) gives:
% 15.08/2.83 | | | (46) $false
% 15.08/2.83 | | |
% 15.08/2.83 | | | CLOSE: (46) is inconsistent.
% 15.08/2.83 | | |
% 15.08/2.83 | | End of split
% 15.08/2.83 | |
% 15.08/2.83 | End of split
% 15.08/2.83 |
% 15.08/2.83 End of proof
% 15.08/2.83 % SZS output end Proof for theBenchmark
% 15.08/2.83
% 15.08/2.83 2211ms
%------------------------------------------------------------------------------