TSTP Solution File: NUM386+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM386+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 11:47:32 EDT 2023
% Result : Theorem 10.33s 2.28s
% Output : Proof 13.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:06:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.37/1.11 Prover 4: Preprocessing ...
% 2.37/1.11 Prover 1: Preprocessing ...
% 2.94/1.15 Prover 3: Preprocessing ...
% 2.94/1.15 Prover 5: Preprocessing ...
% 2.94/1.15 Prover 6: Preprocessing ...
% 2.94/1.15 Prover 2: Preprocessing ...
% 2.94/1.16 Prover 0: Preprocessing ...
% 4.40/1.53 Prover 1: Warning: ignoring some quantifiers
% 4.40/1.57 Prover 1: Constructing countermodel ...
% 4.40/1.58 Prover 5: Proving ...
% 5.40/1.60 Prover 4: Warning: ignoring some quantifiers
% 5.40/1.61 Prover 2: Proving ...
% 5.40/1.63 Prover 3: Warning: ignoring some quantifiers
% 6.41/1.64 Prover 4: Constructing countermodel ...
% 6.41/1.65 Prover 3: Constructing countermodel ...
% 6.41/1.66 Prover 6: Proving ...
% 6.88/1.72 Prover 0: Proving ...
% 8.35/1.92 Prover 3: gave up
% 8.63/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.66/1.98 Prover 1: gave up
% 8.66/1.99 Prover 7: Preprocessing ...
% 8.66/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.16/2.04 Prover 8: Preprocessing ...
% 9.61/2.11 Prover 7: Warning: ignoring some quantifiers
% 9.61/2.12 Prover 7: Constructing countermodel ...
% 10.33/2.22 Prover 8: Warning: ignoring some quantifiers
% 10.33/2.23 Prover 8: Constructing countermodel ...
% 10.33/2.28 Prover 0: proved (1655ms)
% 10.33/2.28
% 10.33/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.33/2.28
% 10.33/2.29 Prover 6: stopped
% 10.33/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.33/2.30 Prover 2: stopped
% 10.33/2.30 Prover 5: stopped
% 10.33/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.33/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.33/2.31 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.33/2.34 Prover 11: Preprocessing ...
% 10.91/2.34 Prover 10: Preprocessing ...
% 10.91/2.35 Prover 13: Preprocessing ...
% 10.91/2.36 Prover 16: Preprocessing ...
% 12.02/2.42 Prover 13: Warning: ignoring some quantifiers
% 12.02/2.44 Prover 13: Constructing countermodel ...
% 12.02/2.44 Prover 8: gave up
% 12.02/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.02/2.47 Prover 16: Warning: ignoring some quantifiers
% 12.02/2.47 Prover 19: Preprocessing ...
% 12.02/2.47 Prover 10: Warning: ignoring some quantifiers
% 12.02/2.48 Prover 10: Constructing countermodel ...
% 12.02/2.49 Prover 7: Found proof (size 35)
% 12.02/2.49 Prover 7: proved (555ms)
% 12.02/2.49 Prover 10: stopped
% 12.02/2.49 Prover 13: stopped
% 12.02/2.49 Prover 4: stopped
% 12.02/2.49 Prover 16: Constructing countermodel ...
% 12.02/2.50 Prover 16: stopped
% 12.63/2.51 Prover 11: Warning: ignoring some quantifiers
% 12.63/2.52 Prover 11: Constructing countermodel ...
% 12.63/2.53 Prover 11: stopped
% 12.63/2.56 Prover 19: Warning: ignoring some quantifiers
% 12.63/2.57 Prover 19: Constructing countermodel ...
% 12.63/2.58 Prover 19: stopped
% 12.63/2.58
% 12.63/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.63/2.58
% 12.63/2.59 % SZS output start Proof for theBenchmark
% 12.63/2.59 Assumptions after simplification:
% 12.63/2.59 ---------------------------------
% 12.63/2.59
% 12.63/2.59 (commutativity_k2_xboole_0)
% 13.07/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 13.07/2.61 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 13.07/2.61 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 13.07/2.61 | (set_union2(v1, v0) = v2 & $i(v2)))
% 13.07/2.61
% 13.07/2.61 (d1_ordinal1)
% 13.07/2.62 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 13.07/2.62 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 13.07/2.62 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 13.07/2.62 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 13.07/2.62
% 13.07/2.62 (d1_tarski)
% 13.07/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 13.07/2.62 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 13.07/2.62 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 13.07/2.62 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 13.07/2.62 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 13.07/2.62 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 13.07/2.62
% 13.07/2.62 (d2_xboole_0)
% 13.07/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0,
% 13.07/2.62 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3,
% 13.07/2.62 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.07/2.62 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 13.07/2.63 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i]
% 13.07/2.63 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~
% 13.07/2.63 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] :
% 13.07/2.63 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) =
% 13.07/2.63 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 13.07/2.63 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 13.07/2.63 | in(v4, v0))))
% 13.07/2.63
% 13.07/2.63 (idempotence_k2_xboole_0)
% 13.07/2.63 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_union2(v0, v0) = v1) | ~
% 13.07/2.63 $i(v0))
% 13.07/2.63
% 13.07/2.63 (t13_ordinal1)
% 13.07/2.63 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & $i(v2) & $i(v1) &
% 13.07/2.63 $i(v0) & (( ~ (v1 = v0) & in(v0, v2) & ~ in(v0, v1)) | ( ~ in(v0, v2) & (v1
% 13.07/2.63 = v0 | in(v0, v1)))))
% 13.07/2.63
% 13.07/2.63 Further assumptions not needed in the proof:
% 13.07/2.63 --------------------------------------------
% 13.07/2.63 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 13.07/2.63 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_relat_1,
% 13.07/2.63 fc2_xboole_0, fc3_xboole_0, fc4_relat_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0,
% 13.07/2.63 rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1,
% 13.07/2.63 rc5_funct_1, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole
% 13.07/2.63
% 13.07/2.63 Those formulas are unsatisfiable:
% 13.07/2.63 ---------------------------------
% 13.07/2.63
% 13.07/2.63 Begin of proof
% 13.07/2.63 |
% 13.07/2.63 | ALPHA: (commutativity_k2_xboole_0) implies:
% 13.07/2.63 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 13.07/2.63 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 13.07/2.63 |
% 13.07/2.63 | ALPHA: (d1_ordinal1) implies:
% 13.07/2.63 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 13.07/2.63 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 13.07/2.63 | $i(v1)))
% 13.07/2.63 |
% 13.07/2.63 | ALPHA: (d1_tarski) implies:
% 13.07/2.63 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 13.07/2.63 | $i(v0) | in(v0, v1))
% 13.07/2.63 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 13.07/2.63 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 13.07/2.63 |
% 13.07/2.63 | ALPHA: (d2_xboole_0) implies:
% 13.07/2.63 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.07/2.63 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.07/2.63 | $i(v0) | ~ in(v3, v0) | in(v3, v2))
% 13.07/2.63 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.07/2.63 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.07/2.63 | $i(v0) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 13.07/2.63 |
% 13.07/2.64 | DELTA: instantiating (t13_ordinal1) with fresh symbols all_46_0, all_46_1,
% 13.07/2.64 | all_46_2 gives:
% 13.07/2.64 | (7) succ(all_46_1) = all_46_0 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2)
% 13.07/2.64 | & (( ~ (all_46_1 = all_46_2) & in(all_46_2, all_46_0) & ~ in(all_46_2,
% 13.07/2.64 | all_46_1)) | ( ~ in(all_46_2, all_46_0) & (all_46_1 = all_46_2 |
% 13.07/2.64 | in(all_46_2, all_46_1))))
% 13.07/2.64 |
% 13.07/2.64 | ALPHA: (7) implies:
% 13.07/2.64 | (8) $i(all_46_2)
% 13.07/2.64 | (9) $i(all_46_1)
% 13.07/2.64 | (10) succ(all_46_1) = all_46_0
% 13.07/2.64 | (11) ( ~ (all_46_1 = all_46_2) & in(all_46_2, all_46_0) & ~ in(all_46_2,
% 13.07/2.64 | all_46_1)) | ( ~ in(all_46_2, all_46_0) & (all_46_1 = all_46_2 |
% 13.07/2.64 | in(all_46_2, all_46_1)))
% 13.07/2.64 |
% 13.07/2.64 | GROUND_INST: instantiating (2) with all_46_1, all_46_0, simplifying with (9),
% 13.07/2.64 | (10) gives:
% 13.07/2.64 | (12) ? [v0: $i] : (singleton(all_46_1) = v0 & set_union2(all_46_1, v0) =
% 13.07/2.64 | all_46_0 & $i(v0) & $i(all_46_0))
% 13.07/2.64 |
% 13.07/2.64 | DELTA: instantiating (12) with fresh symbol all_60_0 gives:
% 13.07/2.64 | (13) singleton(all_46_1) = all_60_0 & set_union2(all_46_1, all_60_0) =
% 13.07/2.64 | all_46_0 & $i(all_60_0) & $i(all_46_0)
% 13.07/2.64 |
% 13.07/2.64 | ALPHA: (13) implies:
% 13.07/2.64 | (14) $i(all_60_0)
% 13.07/2.64 | (15) set_union2(all_46_1, all_60_0) = all_46_0
% 13.07/2.64 | (16) singleton(all_46_1) = all_60_0
% 13.07/2.64 |
% 13.07/2.64 | GROUND_INST: instantiating (idempotence_k2_xboole_0) with all_46_1, all_46_0,
% 13.07/2.64 | simplifying with (9) gives:
% 13.07/2.64 | (17) all_46_0 = all_46_1 | ~ (set_union2(all_46_1, all_46_1) = all_46_0)
% 13.07/2.64 |
% 13.07/2.64 | GROUND_INST: instantiating (1) with all_60_0, all_46_1, all_46_0, simplifying
% 13.07/2.64 | with (9), (14), (15) gives:
% 13.07/2.64 | (18) set_union2(all_60_0, all_46_1) = all_46_0 & $i(all_46_0)
% 13.07/2.64 |
% 13.07/2.64 | ALPHA: (18) implies:
% 13.07/2.64 | (19) $i(all_46_0)
% 13.07/2.64 | (20) set_union2(all_60_0, all_46_1) = all_46_0
% 13.07/2.64 |
% 13.07/2.64 | GROUND_INST: instantiating (3) with all_46_1, all_60_0, simplifying with (9),
% 13.07/2.64 | (14), (16) gives:
% 13.07/2.64 | (21) in(all_46_1, all_60_0)
% 13.07/2.64 |
% 13.07/2.64 | GROUND_INST: instantiating (5) with all_60_0, all_46_1, all_46_0, all_46_1,
% 13.07/2.64 | simplifying with (9), (14), (19), (20), (21) gives:
% 13.07/2.64 | (22) in(all_46_1, all_46_0)
% 13.07/2.64 |
% 13.07/2.64 | BETA: splitting (11) gives:
% 13.07/2.64 |
% 13.07/2.64 | Case 1:
% 13.07/2.64 | |
% 13.07/2.64 | | (23) ~ (all_46_1 = all_46_2) & in(all_46_2, all_46_0) & ~ in(all_46_2,
% 13.07/2.64 | | all_46_1)
% 13.07/2.64 | |
% 13.07/2.64 | | ALPHA: (23) implies:
% 13.07/2.64 | | (24) ~ (all_46_1 = all_46_2)
% 13.07/2.64 | | (25) ~ in(all_46_2, all_46_1)
% 13.07/2.64 | | (26) in(all_46_2, all_46_0)
% 13.07/2.64 | |
% 13.07/2.64 | | PRED_UNIFY: (25), (26) imply:
% 13.07/2.64 | | (27) ~ (all_46_0 = all_46_1)
% 13.07/2.64 | |
% 13.07/2.64 | | BETA: splitting (17) gives:
% 13.07/2.64 | |
% 13.07/2.64 | | Case 1:
% 13.07/2.64 | | |
% 13.07/2.64 | | |
% 13.07/2.64 | | | GROUND_INST: instantiating (6) with all_46_1, all_60_0, all_46_0,
% 13.07/2.64 | | | all_46_2, simplifying with (8), (9), (14), (15), (19), (25),
% 13.07/2.64 | | | (26) gives:
% 13.07/2.64 | | | (28) in(all_46_2, all_60_0)
% 13.07/2.64 | | |
% 13.07/2.65 | | | GROUND_INST: instantiating (4) with all_46_1, all_60_0, all_46_2,
% 13.07/2.65 | | | simplifying with (8), (9), (14), (16), (28) gives:
% 13.07/2.65 | | | (29) all_46_1 = all_46_2
% 13.07/2.65 | | |
% 13.07/2.65 | | | REDUCE: (24), (29) imply:
% 13.07/2.65 | | | (30) $false
% 13.07/2.65 | | |
% 13.07/2.65 | | | CLOSE: (30) is inconsistent.
% 13.07/2.65 | | |
% 13.07/2.65 | | Case 2:
% 13.07/2.65 | | |
% 13.07/2.65 | | | (31) all_46_0 = all_46_1
% 13.07/2.65 | | |
% 13.07/2.65 | | | REDUCE: (27), (31) imply:
% 13.07/2.65 | | | (32) $false
% 13.07/2.65 | | |
% 13.07/2.65 | | | CLOSE: (32) is inconsistent.
% 13.07/2.65 | | |
% 13.07/2.65 | | End of split
% 13.07/2.65 | |
% 13.07/2.65 | Case 2:
% 13.07/2.65 | |
% 13.07/2.65 | | (33) ~ in(all_46_2, all_46_0) & (all_46_1 = all_46_2 | in(all_46_2,
% 13.07/2.65 | | all_46_1))
% 13.07/2.65 | |
% 13.07/2.65 | | ALPHA: (33) implies:
% 13.07/2.65 | | (34) ~ in(all_46_2, all_46_0)
% 13.07/2.65 | | (35) all_46_1 = all_46_2 | in(all_46_2, all_46_1)
% 13.07/2.65 | |
% 13.07/2.65 | | PRED_UNIFY: (22), (34) imply:
% 13.07/2.65 | | (36) ~ (all_46_1 = all_46_2)
% 13.07/2.65 | |
% 13.07/2.65 | | BETA: splitting (35) gives:
% 13.07/2.65 | |
% 13.07/2.65 | | Case 1:
% 13.07/2.65 | | |
% 13.07/2.65 | | | (37) in(all_46_2, all_46_1)
% 13.07/2.65 | | |
% 13.07/2.65 | | | GROUND_INST: instantiating (5) with all_46_1, all_60_0, all_46_0,
% 13.07/2.65 | | | all_46_2, simplifying with (8), (9), (14), (15), (19), (34),
% 13.07/2.65 | | | (37) gives:
% 13.07/2.65 | | | (38) $false
% 13.07/2.65 | | |
% 13.07/2.65 | | | CLOSE: (38) is inconsistent.
% 13.07/2.65 | | |
% 13.07/2.65 | | Case 2:
% 13.07/2.65 | | |
% 13.07/2.65 | | | (39) all_46_1 = all_46_2
% 13.07/2.65 | | |
% 13.07/2.65 | | | REDUCE: (36), (39) imply:
% 13.07/2.65 | | | (40) $false
% 13.07/2.65 | | |
% 13.07/2.65 | | | CLOSE: (40) is inconsistent.
% 13.07/2.65 | | |
% 13.07/2.65 | | End of split
% 13.07/2.65 | |
% 13.07/2.65 | End of split
% 13.07/2.65 |
% 13.07/2.65 End of proof
% 13.07/2.65 % SZS output end Proof for theBenchmark
% 13.07/2.65
% 13.07/2.65 2045ms
%------------------------------------------------------------------------------