TSTP Solution File: NUM385+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM385+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 : n001.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 12.33s 4.18s
% Output : Proof 17.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Aug 25 08:23:28 EDT 2023
% 0.11/0.36 % CPUTime :
% 0.17/0.71 ________ _____
% 0.17/0.71 ___ __ \_________(_)________________________________
% 0.17/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.71
% 0.17/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.71 (2023-06-19)
% 0.17/0.71
% 0.17/0.71 (c) Philipp Rümmer, 2009-2023
% 0.17/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.71 Amanda Stjerna.
% 0.17/0.71 Free software under BSD-3-Clause.
% 0.17/0.71
% 0.17/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.71
% 0.17/0.72 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.73 Running up to 7 provers in parallel.
% 0.61/0.80 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.80 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.80 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.80 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.80 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.80 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.81 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.59 Prover 4: Preprocessing ...
% 2.13/1.59 Prover 1: Preprocessing ...
% 3.15/1.79 Prover 5: Preprocessing ...
% 3.15/1.79 Prover 3: Preprocessing ...
% 3.15/1.79 Prover 0: Preprocessing ...
% 3.15/1.79 Prover 2: Preprocessing ...
% 3.15/1.80 Prover 6: Preprocessing ...
% 6.42/2.82 Prover 1: Warning: ignoring some quantifiers
% 6.81/2.83 Prover 5: Proving ...
% 6.81/2.88 Prover 1: Constructing countermodel ...
% 7.12/2.89 Prover 3: Warning: ignoring some quantifiers
% 7.12/2.92 Prover 2: Proving ...
% 7.12/2.96 Prover 3: Constructing countermodel ...
% 7.12/3.00 Prover 6: Proving ...
% 7.12/3.04 Prover 4: Warning: ignoring some quantifiers
% 7.12/3.09 Prover 4: Constructing countermodel ...
% 7.12/3.15 Prover 0: Proving ...
% 9.88/3.56 Prover 3: gave up
% 10.00/3.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.33/3.66 Prover 1: gave up
% 10.33/3.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.33/3.79 Prover 7: Preprocessing ...
% 10.33/3.81 Prover 8: Preprocessing ...
% 12.33/4.13 Prover 7: Warning: ignoring some quantifiers
% 12.33/4.16 Prover 7: Constructing countermodel ...
% 12.33/4.18 Prover 5: proved (3380ms)
% 12.33/4.18
% 12.33/4.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.33/4.18
% 12.33/4.20 Prover 6: stopped
% 12.73/4.22 Prover 2: stopped
% 13.00/4.31 Prover 0: stopped
% 13.00/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.00/4.32 Prover 8: Warning: ignoring some quantifiers
% 13.00/4.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.00/4.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.00/4.32 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.00/4.33 Prover 8: Constructing countermodel ...
% 13.00/4.33 Prover 10: Preprocessing ...
% 13.00/4.37 Prover 13: Preprocessing ...
% 13.48/4.39 Prover 11: Preprocessing ...
% 13.48/4.40 Prover 16: Preprocessing ...
% 13.65/4.52 Prover 10: Warning: ignoring some quantifiers
% 13.65/4.54 Prover 10: Constructing countermodel ...
% 13.65/4.57 Prover 13: Warning: ignoring some quantifiers
% 13.65/4.59 Prover 16: Warning: ignoring some quantifiers
% 13.65/4.60 Prover 13: Constructing countermodel ...
% 13.65/4.62 Prover 16: Constructing countermodel ...
% 14.31/4.79 Prover 11: Warning: ignoring some quantifiers
% 14.31/4.83 Prover 10: gave up
% 14.31/4.84 Prover 11: Constructing countermodel ...
% 14.31/4.84 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 15.93/4.89 Prover 8: gave up
% 16.25/4.95 Prover 19: Preprocessing ...
% 16.42/5.01 Prover 7: Found proof (size 36)
% 16.42/5.01 Prover 7: proved (1426ms)
% 16.42/5.01 Prover 11: stopped
% 16.42/5.01 Prover 16: stopped
% 16.42/5.01 Prover 13: stopped
% 16.42/5.01 Prover 4: stopped
% 17.36/5.26 Prover 19: Warning: ignoring some quantifiers
% 17.51/5.28 Prover 19: Constructing countermodel ...
% 17.51/5.31 Prover 19: stopped
% 17.51/5.31
% 17.51/5.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.51/5.31
% 17.51/5.33 % SZS output start Proof for theBenchmark
% 17.51/5.33 Assumptions after simplification:
% 17.51/5.33 ---------------------------------
% 17.51/5.33
% 17.51/5.33 (antisymmetry_r2_hidden)
% 17.78/5.35 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v1, v0) | ~ in(v0,
% 17.78/5.35 v1))
% 17.78/5.35
% 17.78/5.35 (commutativity_k2_xboole_0)
% 17.78/5.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 17.78/5.42 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 17.78/5.42 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 17.78/5.42 | (set_union2(v1, v0) = v2 & $i(v2)))
% 17.78/5.42
% 17.78/5.42 (d1_ordinal1)
% 17.78/5.43 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 17.78/5.44 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 17.78/5.44 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 17.78/5.44 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 17.78/5.44
% 17.78/5.44 (d1_tarski)
% 17.78/5.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 17.78/5.45 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 17.78/5.45 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 17.78/5.45 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 17.78/5.45 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 17.78/5.45 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 17.78/5.45
% 17.78/5.45 (d2_xboole_0)
% 17.78/5.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0,
% 17.78/5.46 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3,
% 17.78/5.46 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.78/5.46 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 17.78/5.46 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i]
% 17.78/5.46 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~
% 17.78/5.46 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] :
% 17.78/5.46 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) =
% 17.78/5.46 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 17.78/5.46 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 17.78/5.46 | in(v4, v0))))
% 17.78/5.46
% 17.78/5.46 (t10_ordinal1)
% 17.78/5.46 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1))
% 17.78/5.46
% 17.78/5.46 (t12_ordinal1)
% 17.78/5.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & succ(v1) = v2 &
% 17.78/5.46 succ(v0) = v2 & $i(v2) & $i(v1) & $i(v0))
% 17.78/5.46
% 17.78/5.46 Further assumptions not needed in the proof:
% 17.78/5.46 --------------------------------------------
% 17.78/5.46 cc1_funct_1, cc1_relat_1, cc2_funct_1, existence_m1_subset_1, fc12_relat_1,
% 17.78/5.46 fc1_ordinal1, fc1_xboole_0, fc2_relat_1, fc2_xboole_0, fc3_xboole_0,
% 17.78/5.46 fc4_relat_1, idempotence_k2_xboole_0, rc1_funct_1, rc1_relat_1, rc1_xboole_0,
% 17.78/5.46 rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1,
% 17.78/5.46 rc5_funct_1, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole
% 17.78/5.46
% 17.78/5.46 Those formulas are unsatisfiable:
% 17.78/5.46 ---------------------------------
% 17.78/5.46
% 17.78/5.46 Begin of proof
% 17.78/5.46 |
% 17.78/5.46 | ALPHA: (commutativity_k2_xboole_0) implies:
% 17.78/5.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 17.78/5.47 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 17.78/5.47 |
% 17.78/5.47 | ALPHA: (d1_ordinal1) implies:
% 17.78/5.47 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 17.78/5.47 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 17.78/5.47 | $i(v1)))
% 17.78/5.47 |
% 17.78/5.47 | ALPHA: (d1_tarski) implies:
% 17.78/5.48 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 17.78/5.48 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 17.78/5.48 |
% 17.78/5.48 | ALPHA: (d2_xboole_0) implies:
% 17.78/5.48 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.78/5.48 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.78/5.48 | $i(v0) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 17.78/5.48 |
% 17.78/5.48 | DELTA: instantiating (t12_ordinal1) with fresh symbols all_45_0, all_45_1,
% 17.78/5.48 | all_45_2 gives:
% 17.78/5.48 | (5) ~ (all_45_1 = all_45_2) & succ(all_45_1) = all_45_0 & succ(all_45_2) =
% 17.78/5.49 | all_45_0 & $i(all_45_0) & $i(all_45_1) & $i(all_45_2)
% 17.78/5.49 |
% 17.78/5.49 | ALPHA: (5) implies:
% 17.78/5.49 | (6) ~ (all_45_1 = all_45_2)
% 17.78/5.49 | (7) $i(all_45_2)
% 17.78/5.49 | (8) $i(all_45_1)
% 17.78/5.49 | (9) succ(all_45_2) = all_45_0
% 17.78/5.49 | (10) succ(all_45_1) = all_45_0
% 17.78/5.49 |
% 17.78/5.49 | GROUND_INST: instantiating (t10_ordinal1) with all_45_2, all_45_0, simplifying
% 17.78/5.49 | with (7), (9) gives:
% 17.78/5.49 | (11) in(all_45_2, all_45_0)
% 17.78/5.49 |
% 17.78/5.49 | GROUND_INST: instantiating (2) with all_45_2, all_45_0, simplifying with (7),
% 17.78/5.49 | (9) gives:
% 17.78/5.49 | (12) ? [v0: $i] : (singleton(all_45_2) = v0 & set_union2(all_45_2, v0) =
% 17.78/5.49 | all_45_0 & $i(v0) & $i(all_45_0))
% 17.78/5.49 |
% 17.78/5.49 | GROUND_INST: instantiating (t10_ordinal1) with all_45_1, all_45_0, simplifying
% 17.78/5.49 | with (8), (10) gives:
% 17.78/5.49 | (13) in(all_45_1, all_45_0)
% 17.78/5.49 |
% 17.78/5.49 | GROUND_INST: instantiating (2) with all_45_1, all_45_0, simplifying with (8),
% 17.78/5.49 | (10) gives:
% 17.78/5.49 | (14) ? [v0: $i] : (singleton(all_45_1) = v0 & set_union2(all_45_1, v0) =
% 17.78/5.49 | all_45_0 & $i(v0) & $i(all_45_0))
% 17.78/5.49 |
% 17.78/5.49 | DELTA: instantiating (14) with fresh symbol all_61_0 gives:
% 17.78/5.49 | (15) singleton(all_45_1) = all_61_0 & set_union2(all_45_1, all_61_0) =
% 17.78/5.50 | all_45_0 & $i(all_61_0) & $i(all_45_0)
% 17.78/5.50 |
% 17.78/5.50 | ALPHA: (15) implies:
% 17.78/5.50 | (16) $i(all_61_0)
% 17.78/5.50 | (17) set_union2(all_45_1, all_61_0) = all_45_0
% 17.78/5.50 | (18) singleton(all_45_1) = all_61_0
% 17.78/5.50 |
% 17.78/5.50 | DELTA: instantiating (12) with fresh symbol all_63_0 gives:
% 17.78/5.50 | (19) singleton(all_45_2) = all_63_0 & set_union2(all_45_2, all_63_0) =
% 17.78/5.50 | all_45_0 & $i(all_63_0) & $i(all_45_0)
% 17.78/5.50 |
% 17.78/5.50 | ALPHA: (19) implies:
% 17.78/5.50 | (20) $i(all_63_0)
% 17.78/5.50 | (21) set_union2(all_45_2, all_63_0) = all_45_0
% 17.78/5.50 | (22) singleton(all_45_2) = all_63_0
% 17.78/5.50 |
% 17.78/5.50 | GROUND_INST: instantiating (1) with all_63_0, all_45_2, all_45_0, simplifying
% 17.78/5.50 | with (7), (20), (21) gives:
% 17.78/5.50 | (23) set_union2(all_63_0, all_45_2) = all_45_0 & $i(all_45_0)
% 17.78/5.50 |
% 17.78/5.50 | ALPHA: (23) implies:
% 17.78/5.50 | (24) set_union2(all_63_0, all_45_2) = all_45_0
% 17.78/5.50 |
% 17.78/5.50 | GROUND_INST: instantiating (1) with all_61_0, all_45_1, all_45_0, simplifying
% 17.78/5.50 | with (8), (16), (17) gives:
% 17.78/5.50 | (25) set_union2(all_61_0, all_45_1) = all_45_0 & $i(all_45_0)
% 17.78/5.50 |
% 17.78/5.50 | ALPHA: (25) implies:
% 17.78/5.50 | (26) $i(all_45_0)
% 17.78/5.50 | (27) set_union2(all_61_0, all_45_1) = all_45_0
% 17.78/5.50 |
% 17.78/5.50 | GROUND_INST: instantiating (3) with all_45_1, all_61_0, all_45_2, simplifying
% 17.78/5.50 | with (7), (8), (16), (18) gives:
% 17.78/5.50 | (28) all_45_1 = all_45_2 | ~ in(all_45_2, all_61_0)
% 17.78/5.50 |
% 17.78/5.50 | GROUND_INST: instantiating (4) with all_61_0, all_45_1, all_45_0, all_45_2,
% 17.78/5.50 | simplifying with (7), (8), (11), (16), (26), (27) gives:
% 17.78/5.50 | (29) in(all_45_2, all_61_0) | in(all_45_2, all_45_1)
% 17.78/5.50 |
% 17.78/5.51 | GROUND_INST: instantiating (4) with all_63_0, all_45_2, all_45_0, all_45_1,
% 17.78/5.51 | simplifying with (7), (8), (13), (20), (24), (26) gives:
% 17.78/5.51 | (30) in(all_45_1, all_63_0) | in(all_45_1, all_45_2)
% 17.78/5.51 |
% 17.78/5.51 | BETA: splitting (28) gives:
% 17.78/5.51 |
% 17.78/5.51 | Case 1:
% 17.78/5.51 | |
% 17.78/5.51 | | (31) ~ in(all_45_2, all_61_0)
% 17.78/5.51 | |
% 17.78/5.51 | | BETA: splitting (29) gives:
% 17.78/5.51 | |
% 17.78/5.51 | | Case 1:
% 17.78/5.51 | | |
% 17.78/5.51 | | | (32) in(all_45_2, all_61_0)
% 17.78/5.51 | | |
% 17.78/5.51 | | | PRED_UNIFY: (31), (32) imply:
% 17.78/5.51 | | | (33) $false
% 17.78/5.51 | | |
% 17.78/5.51 | | | CLOSE: (33) is inconsistent.
% 17.78/5.51 | | |
% 17.78/5.51 | | Case 2:
% 17.78/5.51 | | |
% 17.78/5.51 | | | (34) in(all_45_2, all_45_1)
% 17.78/5.51 | | |
% 17.78/5.51 | | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with all_45_1,
% 17.78/5.51 | | | all_45_2, simplifying with (7), (8), (34) gives:
% 17.78/5.51 | | | (35) ~ in(all_45_1, all_45_2)
% 17.78/5.51 | | |
% 17.78/5.51 | | | BETA: splitting (30) gives:
% 17.78/5.51 | | |
% 17.78/5.51 | | | Case 1:
% 17.78/5.51 | | | |
% 17.78/5.51 | | | | (36) in(all_45_1, all_63_0)
% 17.78/5.51 | | | |
% 17.78/5.51 | | | | GROUND_INST: instantiating (3) with all_45_2, all_63_0, all_45_1,
% 17.78/5.51 | | | | simplifying with (7), (8), (20), (22), (36) gives:
% 17.78/5.51 | | | | (37) all_45_1 = all_45_2
% 17.78/5.51 | | | |
% 17.78/5.51 | | | | REDUCE: (6), (37) imply:
% 17.78/5.51 | | | | (38) $false
% 17.78/5.51 | | | |
% 17.78/5.51 | | | | CLOSE: (38) is inconsistent.
% 17.78/5.51 | | | |
% 17.78/5.51 | | | Case 2:
% 17.78/5.51 | | | |
% 17.78/5.51 | | | | (39) in(all_45_1, all_45_2)
% 17.78/5.51 | | | |
% 17.78/5.51 | | | | PRED_UNIFY: (35), (39) imply:
% 17.78/5.52 | | | | (40) $false
% 17.78/5.52 | | | |
% 17.78/5.52 | | | | CLOSE: (40) is inconsistent.
% 17.78/5.52 | | | |
% 17.78/5.52 | | | End of split
% 17.78/5.52 | | |
% 17.78/5.52 | | End of split
% 17.78/5.52 | |
% 17.78/5.52 | Case 2:
% 17.78/5.52 | |
% 17.78/5.52 | | (41) all_45_1 = all_45_2
% 17.78/5.52 | |
% 17.78/5.52 | | REDUCE: (6), (41) imply:
% 17.78/5.52 | | (42) $false
% 17.78/5.52 | |
% 17.78/5.52 | | CLOSE: (42) is inconsistent.
% 17.78/5.52 | |
% 17.78/5.52 | End of split
% 17.78/5.52 |
% 17.78/5.52 End of proof
% 17.78/5.52 % SZS output end Proof for theBenchmark
% 17.78/5.52
% 17.78/5.52 4802ms
%------------------------------------------------------------------------------