TSTP Solution File: SET968+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET968+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 : n014.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 15:27:13 EDT 2023
% Result : Theorem 6.57s 1.72s
% Output : Proof 10.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET968+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35 % Computer : n014.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 14:59:02 EDT 2023
% 0.17/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.02/1.00 Prover 1: Preprocessing ...
% 2.02/1.00 Prover 4: Preprocessing ...
% 2.50/1.06 Prover 2: Preprocessing ...
% 2.50/1.06 Prover 6: Preprocessing ...
% 2.50/1.06 Prover 5: Preprocessing ...
% 2.50/1.06 Prover 3: Preprocessing ...
% 2.50/1.06 Prover 0: Preprocessing ...
% 3.70/1.26 Prover 1: Warning: ignoring some quantifiers
% 3.94/1.27 Prover 3: Warning: ignoring some quantifiers
% 3.94/1.27 Prover 1: Constructing countermodel ...
% 3.94/1.27 Prover 6: Proving ...
% 3.94/1.27 Prover 5: Proving ...
% 3.94/1.28 Prover 3: Constructing countermodel ...
% 3.94/1.29 Prover 4: Constructing countermodel ...
% 3.94/1.32 Prover 0: Proving ...
% 4.46/1.37 Prover 2: Proving ...
% 6.57/1.71 Prover 0: proved (1066ms)
% 6.57/1.71
% 6.57/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.57/1.72
% 6.57/1.72 Prover 2: stopped
% 6.57/1.72 Prover 6: stopped
% 7.17/1.73 Prover 5: stopped
% 7.17/1.74 Prover 3: stopped
% 7.17/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.17/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.17/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.17/1.74 Prover 8: Preprocessing ...
% 7.17/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.17/1.75 Prover 7: Preprocessing ...
% 7.17/1.75 Prover 10: Preprocessing ...
% 7.17/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.17/1.77 Prover 13: Preprocessing ...
% 7.59/1.78 Prover 11: Preprocessing ...
% 7.59/1.78 Prover 8: Warning: ignoring some quantifiers
% 7.59/1.79 Prover 8: Constructing countermodel ...
% 7.59/1.81 Prover 10: Constructing countermodel ...
% 7.59/1.82 Prover 7: Constructing countermodel ...
% 7.59/1.84 Prover 13: Warning: ignoring some quantifiers
% 7.59/1.84 Prover 13: Constructing countermodel ...
% 8.11/1.86 Prover 11: Constructing countermodel ...
% 8.79/2.07 Prover 10: Found proof (size 38)
% 8.79/2.07 Prover 10: proved (336ms)
% 8.79/2.07 Prover 13: stopped
% 8.79/2.07 Prover 8: stopped
% 8.79/2.07 Prover 1: stopped
% 8.79/2.07 Prover 4: stopped
% 8.79/2.07 Prover 11: stopped
% 8.79/2.07 Prover 7: stopped
% 8.79/2.07
% 8.79/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.79/2.07
% 8.79/2.09 % SZS output start Proof for theBenchmark
% 8.79/2.09 Assumptions after simplification:
% 8.79/2.09 ---------------------------------
% 8.79/2.09
% 8.79/2.09 (commutativity_k2_xboole_0)
% 8.79/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 8.79/2.11 $i(v1) | ~ $i(v0) | (set_union2(v1, v0) = v2 & $i(v2)))
% 8.79/2.11
% 8.79/2.11 (t120_zfmisc_1)
% 8.79/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.79/2.12 $i] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0)
% 8.79/2.12 = v3) | ~ (set_union2(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 8.79/2.12 ? [v6: $i] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6 &
% 8.79/2.12 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 8.79/2.12 : ! [v4: $i] : ! [v5: $i] : ( ~ (cartesian_product2(v1, v2) = v4) | ~
% 8.79/2.12 (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ~ $i(v2)
% 8.79/2.12 | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (cartesian_product2(v6, v2) = v5 &
% 8.79/2.12 set_union2(v0, v1) = v6 & $i(v6) & $i(v5)))
% 8.79/2.12
% 8.79/2.12 (t121_zfmisc_1)
% 8.79/2.12 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.79/2.12 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 8.79/2.12 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ( ~ (v13 = v6) &
% 8.79/2.12 cartesian_product2(v4, v5) = v6 & cartesian_product2(v1, v3) = v12 &
% 8.79/2.12 cartesian_product2(v1, v2) = v10 & cartesian_product2(v0, v3) = v8 &
% 8.79/2.12 cartesian_product2(v0, v2) = v7 & set_union2(v11, v12) = v13 &
% 8.79/2.12 set_union2(v9, v10) = v11 & set_union2(v7, v8) = v9 & set_union2(v2, v3) =
% 8.79/2.12 v5 & set_union2(v0, v1) = v4 & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 8.79/2.12 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 8.79/2.12 $i(v1) & $i(v0))
% 8.79/2.12
% 8.79/2.12 (t4_xboole_1)
% 8.79/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 8.79/2.13 (set_union2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ~ $i(v2) | ~
% 8.79/2.13 $i(v1) | ~ $i(v0) | ? [v5: $i] : (set_union2(v1, v2) = v5 & set_union2(v0,
% 8.79/2.13 v5) = v4 & $i(v5) & $i(v4)))
% 8.79/2.13
% 8.79/2.13 (function-axioms)
% 8.79/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.79/2.13 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 8.79/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.79/2.13 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 8.79/2.13
% 8.79/2.13 Further assumptions not needed in the proof:
% 8.79/2.13 --------------------------------------------
% 8.79/2.13 fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0
% 8.79/2.13
% 8.79/2.13 Those formulas are unsatisfiable:
% 8.79/2.13 ---------------------------------
% 8.79/2.13
% 8.79/2.13 Begin of proof
% 8.79/2.13 |
% 8.79/2.13 | ALPHA: (t120_zfmisc_1) implies:
% 8.79/2.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 8.79/2.13 | ! [v5: $i] : ( ~ (cartesian_product2(v1, v2) = v4) | ~
% 8.79/2.13 | (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ~
% 8.79/2.13 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 8.79/2.13 | (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6 & $i(v6) &
% 8.79/2.13 | $i(v5)))
% 8.79/2.13 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 8.79/2.13 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v1) = v4) | ~
% 8.79/2.13 | (cartesian_product2(v2, v0) = v3) | ~ (set_union2(v3, v4) = v5) | ~
% 8.79/2.13 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 8.79/2.13 | (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6 & $i(v6) &
% 8.79/2.13 | $i(v5)))
% 8.79/2.14 |
% 8.79/2.14 | ALPHA: (function-axioms) implies:
% 8.79/2.14 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.79/2.14 | (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 8.79/2.14 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.79/2.14 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) =
% 8.79/2.14 | v0))
% 8.79/2.14 |
% 8.79/2.14 | DELTA: instantiating (t121_zfmisc_1) with fresh symbols all_13_0, all_13_1,
% 8.79/2.14 | all_13_2, all_13_3, all_13_4, all_13_5, all_13_6, all_13_7, all_13_8,
% 8.79/2.14 | all_13_9, all_13_10, all_13_11, all_13_12, all_13_13 gives:
% 8.79/2.14 | (5) ~ (all_13_0 = all_13_7) & cartesian_product2(all_13_9, all_13_8) =
% 8.79/2.14 | all_13_7 & cartesian_product2(all_13_12, all_13_10) = all_13_1 &
% 8.79/2.14 | cartesian_product2(all_13_12, all_13_11) = all_13_3 &
% 8.79/2.14 | cartesian_product2(all_13_13, all_13_10) = all_13_5 &
% 8.79/2.14 | cartesian_product2(all_13_13, all_13_11) = all_13_6 &
% 8.79/2.14 | set_union2(all_13_2, all_13_1) = all_13_0 & set_union2(all_13_4,
% 8.79/2.14 | all_13_3) = all_13_2 & set_union2(all_13_6, all_13_5) = all_13_4 &
% 8.79/2.14 | set_union2(all_13_11, all_13_10) = all_13_8 & set_union2(all_13_13,
% 8.79/2.14 | all_13_12) = all_13_9 & $i(all_13_0) & $i(all_13_1) & $i(all_13_2) &
% 8.79/2.14 | $i(all_13_3) & $i(all_13_4) & $i(all_13_5) & $i(all_13_6) &
% 8.79/2.14 | $i(all_13_7) & $i(all_13_8) & $i(all_13_9) & $i(all_13_10) &
% 8.79/2.14 | $i(all_13_11) & $i(all_13_12) & $i(all_13_13)
% 8.79/2.14 |
% 8.79/2.14 | ALPHA: (5) implies:
% 8.79/2.14 | (6) ~ (all_13_0 = all_13_7)
% 8.79/2.14 | (7) $i(all_13_13)
% 8.79/2.14 | (8) $i(all_13_12)
% 8.79/2.14 | (9) $i(all_13_11)
% 8.79/2.14 | (10) $i(all_13_10)
% 8.79/2.14 | (11) $i(all_13_6)
% 8.79/2.14 | (12) $i(all_13_5)
% 8.79/2.14 | (13) $i(all_13_3)
% 8.79/2.14 | (14) $i(all_13_1)
% 10.03/2.14 | (15) set_union2(all_13_13, all_13_12) = all_13_9
% 10.03/2.14 | (16) set_union2(all_13_11, all_13_10) = all_13_8
% 10.03/2.14 | (17) set_union2(all_13_6, all_13_5) = all_13_4
% 10.03/2.14 | (18) set_union2(all_13_4, all_13_3) = all_13_2
% 10.03/2.14 | (19) set_union2(all_13_2, all_13_1) = all_13_0
% 10.03/2.14 | (20) cartesian_product2(all_13_13, all_13_11) = all_13_6
% 10.03/2.14 | (21) cartesian_product2(all_13_13, all_13_10) = all_13_5
% 10.03/2.14 | (22) cartesian_product2(all_13_12, all_13_11) = all_13_3
% 10.03/2.14 | (23) cartesian_product2(all_13_12, all_13_10) = all_13_1
% 10.03/2.14 | (24) cartesian_product2(all_13_9, all_13_8) = all_13_7
% 10.03/2.14 |
% 10.03/2.15 | GROUND_INST: instantiating (commutativity_k2_xboole_0) with all_13_6,
% 10.03/2.15 | all_13_5, all_13_4, simplifying with (11), (12), (17) gives:
% 10.03/2.15 | (25) set_union2(all_13_5, all_13_6) = all_13_4 & $i(all_13_4)
% 10.03/2.15 |
% 10.03/2.15 | ALPHA: (25) implies:
% 10.03/2.15 | (26) $i(all_13_4)
% 10.03/2.15 | (27) set_union2(all_13_5, all_13_6) = all_13_4
% 10.03/2.15 |
% 10.03/2.15 | GROUND_INST: instantiating (t4_xboole_1) with all_13_4, all_13_3, all_13_1,
% 10.03/2.15 | all_13_2, all_13_0, simplifying with (13), (14), (18), (19), (26)
% 10.03/2.15 | gives:
% 10.03/2.15 | (28) ? [v0: $i] : (set_union2(all_13_3, all_13_1) = v0 &
% 10.03/2.15 | set_union2(all_13_4, v0) = all_13_0 & $i(v0) & $i(all_13_0))
% 10.03/2.15 |
% 10.03/2.15 | GROUND_INST: instantiating (2) with all_13_11, all_13_10, all_13_13, all_13_6,
% 10.03/2.15 | all_13_5, all_13_4, simplifying with (7), (9), (10), (17), (20),
% 10.03/2.15 | (21) gives:
% 10.03/2.15 | (29) ? [v0: $i] : (cartesian_product2(all_13_13, v0) = all_13_4 &
% 10.03/2.15 | set_union2(all_13_11, all_13_10) = v0 & $i(v0) & $i(all_13_4))
% 10.03/2.15 |
% 10.03/2.15 | DELTA: instantiating (29) with fresh symbol all_21_0 gives:
% 10.03/2.15 | (30) cartesian_product2(all_13_13, all_21_0) = all_13_4 &
% 10.03/2.15 | set_union2(all_13_11, all_13_10) = all_21_0 & $i(all_21_0) &
% 10.03/2.15 | $i(all_13_4)
% 10.03/2.15 |
% 10.03/2.15 | ALPHA: (30) implies:
% 10.03/2.15 | (31) set_union2(all_13_11, all_13_10) = all_21_0
% 10.03/2.15 | (32) cartesian_product2(all_13_13, all_21_0) = all_13_4
% 10.03/2.15 |
% 10.03/2.15 | DELTA: instantiating (28) with fresh symbol all_25_0 gives:
% 10.03/2.15 | (33) set_union2(all_13_3, all_13_1) = all_25_0 & set_union2(all_13_4,
% 10.03/2.15 | all_25_0) = all_13_0 & $i(all_25_0) & $i(all_13_0)
% 10.03/2.15 |
% 10.03/2.15 | ALPHA: (33) implies:
% 10.03/2.15 | (34) set_union2(all_13_4, all_25_0) = all_13_0
% 10.03/2.15 | (35) set_union2(all_13_3, all_13_1) = all_25_0
% 10.03/2.15 |
% 10.03/2.15 | GROUND_INST: instantiating (3) with all_13_8, all_21_0, all_13_10, all_13_11,
% 10.03/2.15 | simplifying with (16), (31) gives:
% 10.03/2.15 | (36) all_21_0 = all_13_8
% 10.03/2.15 |
% 10.03/2.15 | REDUCE: (32), (36) imply:
% 10.03/2.15 | (37) cartesian_product2(all_13_13, all_13_8) = all_13_4
% 10.03/2.15 |
% 10.03/2.15 | GROUND_INST: instantiating (t4_xboole_1) with all_13_5, all_13_6, all_13_3,
% 10.03/2.15 | all_13_4, all_13_2, simplifying with (11), (12), (13), (18), (27)
% 10.03/2.15 | gives:
% 10.03/2.15 | (38) ? [v0: $i] : (set_union2(all_13_5, v0) = all_13_2 &
% 10.03/2.15 | set_union2(all_13_6, all_13_3) = v0 & $i(v0) & $i(all_13_2))
% 10.03/2.15 |
% 10.03/2.16 | GROUND_INST: instantiating (2) with all_13_11, all_13_10, all_13_12, all_13_3,
% 10.03/2.16 | all_13_1, all_25_0, simplifying with (8), (9), (10), (22), (23),
% 10.03/2.16 | (35) gives:
% 10.03/2.16 | (39) ? [v0: $i] : (cartesian_product2(all_13_12, v0) = all_25_0 &
% 10.03/2.16 | set_union2(all_13_11, all_13_10) = v0 & $i(v0) & $i(all_25_0))
% 10.03/2.16 |
% 10.03/2.16 | DELTA: instantiating (39) with fresh symbol all_39_0 gives:
% 10.03/2.16 | (40) cartesian_product2(all_13_12, all_39_0) = all_25_0 &
% 10.03/2.16 | set_union2(all_13_11, all_13_10) = all_39_0 & $i(all_39_0) &
% 10.03/2.16 | $i(all_25_0)
% 10.03/2.16 |
% 10.03/2.16 | ALPHA: (40) implies:
% 10.03/2.16 | (41) $i(all_39_0)
% 10.03/2.16 | (42) set_union2(all_13_11, all_13_10) = all_39_0
% 10.03/2.16 | (43) cartesian_product2(all_13_12, all_39_0) = all_25_0
% 10.03/2.16 |
% 10.03/2.16 | DELTA: instantiating (38) with fresh symbol all_47_0 gives:
% 10.03/2.16 | (44) set_union2(all_13_5, all_47_0) = all_13_2 & set_union2(all_13_6,
% 10.03/2.16 | all_13_3) = all_47_0 & $i(all_47_0) & $i(all_13_2)
% 10.03/2.16 |
% 10.03/2.16 | ALPHA: (44) implies:
% 10.03/2.16 | (45) set_union2(all_13_6, all_13_3) = all_47_0
% 10.03/2.16 |
% 10.03/2.16 | GROUND_INST: instantiating (3) with all_13_8, all_39_0, all_13_10, all_13_11,
% 10.03/2.16 | simplifying with (16), (42) gives:
% 10.03/2.16 | (46) all_39_0 = all_13_8
% 10.03/2.16 |
% 10.03/2.16 | REDUCE: (43), (46) imply:
% 10.03/2.16 | (47) cartesian_product2(all_13_12, all_13_8) = all_25_0
% 10.03/2.16 |
% 10.03/2.16 | REDUCE: (41), (46) imply:
% 10.03/2.16 | (48) $i(all_13_8)
% 10.03/2.16 |
% 10.03/2.16 | GROUND_INST: instantiating (1) with all_13_13, all_13_12, all_13_11, all_13_6,
% 10.03/2.16 | all_13_3, all_47_0, simplifying with (7), (8), (9), (20), (22),
% 10.03/2.16 | (45) gives:
% 10.03/2.16 | (49) ? [v0: $i] : (cartesian_product2(v0, all_13_11) = all_47_0 &
% 10.03/2.16 | set_union2(all_13_13, all_13_12) = v0 & $i(v0) & $i(all_47_0))
% 10.03/2.16 |
% 10.03/2.16 | GROUND_INST: instantiating (1) with all_13_13, all_13_12, all_13_8, all_13_4,
% 10.03/2.16 | all_25_0, all_13_0, simplifying with (7), (8), (34), (37), (47),
% 10.03/2.16 | (48) gives:
% 10.03/2.16 | (50) ? [v0: $i] : (cartesian_product2(v0, all_13_8) = all_13_0 &
% 10.03/2.16 | set_union2(all_13_13, all_13_12) = v0 & $i(v0) & $i(all_13_0))
% 10.03/2.16 |
% 10.03/2.16 | DELTA: instantiating (50) with fresh symbol all_59_0 gives:
% 10.03/2.16 | (51) cartesian_product2(all_59_0, all_13_8) = all_13_0 &
% 10.03/2.16 | set_union2(all_13_13, all_13_12) = all_59_0 & $i(all_59_0) &
% 10.03/2.16 | $i(all_13_0)
% 10.03/2.16 |
% 10.03/2.16 | ALPHA: (51) implies:
% 10.03/2.16 | (52) set_union2(all_13_13, all_13_12) = all_59_0
% 10.03/2.16 | (53) cartesian_product2(all_59_0, all_13_8) = all_13_0
% 10.03/2.16 |
% 10.03/2.16 | DELTA: instantiating (49) with fresh symbol all_75_0 gives:
% 10.03/2.16 | (54) cartesian_product2(all_75_0, all_13_11) = all_47_0 &
% 10.03/2.16 | set_union2(all_13_13, all_13_12) = all_75_0 & $i(all_75_0) &
% 10.03/2.16 | $i(all_47_0)
% 10.03/2.16 |
% 10.03/2.16 | ALPHA: (54) implies:
% 10.03/2.16 | (55) set_union2(all_13_13, all_13_12) = all_75_0
% 10.03/2.16 |
% 10.03/2.16 | GROUND_INST: instantiating (3) with all_13_9, all_75_0, all_13_12, all_13_13,
% 10.03/2.16 | simplifying with (15), (55) gives:
% 10.03/2.16 | (56) all_75_0 = all_13_9
% 10.03/2.16 |
% 10.03/2.16 | GROUND_INST: instantiating (3) with all_59_0, all_75_0, all_13_12, all_13_13,
% 10.03/2.16 | simplifying with (52), (55) gives:
% 10.03/2.16 | (57) all_75_0 = all_59_0
% 10.03/2.16 |
% 10.03/2.16 | COMBINE_EQS: (56), (57) imply:
% 10.03/2.16 | (58) all_59_0 = all_13_9
% 10.03/2.16 |
% 10.03/2.16 | SIMP: (58) implies:
% 10.03/2.16 | (59) all_59_0 = all_13_9
% 10.03/2.16 |
% 10.03/2.16 | REDUCE: (53), (59) imply:
% 10.03/2.16 | (60) cartesian_product2(all_13_9, all_13_8) = all_13_0
% 10.03/2.16 |
% 10.03/2.16 | GROUND_INST: instantiating (4) with all_13_7, all_13_0, all_13_8, all_13_9,
% 10.03/2.16 | simplifying with (24), (60) gives:
% 10.03/2.16 | (61) all_13_0 = all_13_7
% 10.03/2.16 |
% 10.03/2.16 | REDUCE: (6), (61) imply:
% 10.03/2.16 | (62) $false
% 10.03/2.17 |
% 10.03/2.17 | CLOSE: (62) is inconsistent.
% 10.03/2.17 |
% 10.03/2.17 End of proof
% 10.03/2.17 % SZS output end Proof for theBenchmark
% 10.03/2.17
% 10.03/2.17 1541ms
%------------------------------------------------------------------------------