TSTP Solution File: REL003+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : REL003+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.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 13:42:42 EDT 2023
% Result : Theorem 5.40s 1.49s
% Output : Proof 7.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL003+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.33 % Computer : n013.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Fri Aug 25 21:25:02 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.45/1.04 Prover 1: Preprocessing ...
% 2.45/1.04 Prover 4: Preprocessing ...
% 2.80/1.08 Prover 2: Preprocessing ...
% 2.80/1.08 Prover 5: Preprocessing ...
% 2.80/1.08 Prover 0: Preprocessing ...
% 2.80/1.08 Prover 6: Preprocessing ...
% 2.80/1.08 Prover 3: Preprocessing ...
% 4.02/1.32 Prover 1: Constructing countermodel ...
% 4.02/1.33 Prover 3: Constructing countermodel ...
% 4.02/1.33 Prover 6: Constructing countermodel ...
% 4.02/1.37 Prover 4: Constructing countermodel ...
% 4.02/1.38 Prover 0: Proving ...
% 4.02/1.39 Prover 5: Proving ...
% 5.40/1.49 Prover 3: proved (862ms)
% 5.40/1.49
% 5.40/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.40/1.49
% 5.40/1.49 Prover 6: stopped
% 5.40/1.49 Prover 0: stopped
% 5.40/1.49 Prover 2: Proving ...
% 5.40/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.40/1.49 Prover 2: stopped
% 5.78/1.50 Prover 5: stopped
% 5.78/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.78/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.78/1.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.78/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.78/1.52 Prover 7: Preprocessing ...
% 5.78/1.53 Prover 8: Preprocessing ...
% 5.78/1.53 Prover 10: Preprocessing ...
% 5.78/1.54 Prover 11: Preprocessing ...
% 5.78/1.55 Prover 13: Preprocessing ...
% 6.32/1.59 Prover 1: Found proof (size 30)
% 6.32/1.59 Prover 1: proved (970ms)
% 6.32/1.59 Prover 4: stopped
% 6.32/1.60 Prover 8: Warning: ignoring some quantifiers
% 6.32/1.62 Prover 8: Constructing countermodel ...
% 6.32/1.62 Prover 8: stopped
% 6.32/1.62 Prover 10: Constructing countermodel ...
% 6.32/1.63 Prover 10: stopped
% 6.32/1.63 Prover 13: Warning: ignoring some quantifiers
% 6.32/1.63 Prover 7: Constructing countermodel ...
% 6.32/1.64 Prover 11: Constructing countermodel ...
% 6.32/1.64 Prover 13: Constructing countermodel ...
% 6.32/1.64 Prover 7: stopped
% 6.32/1.64 Prover 11: stopped
% 6.32/1.65 Prover 13: stopped
% 6.32/1.65
% 6.32/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.32/1.65
% 6.32/1.66 % SZS output start Proof for theBenchmark
% 6.32/1.66 Assumptions after simplification:
% 6.32/1.66 ---------------------------------
% 6.32/1.66
% 6.32/1.66 (converse_additivity)
% 7.01/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.01/1.69 (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ~
% 7.01/1.69 $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & join(v0, v1) = v5 &
% 7.01/1.69 $i(v5) & $i(v4)))
% 7.01/1.69
% 7.01/1.69 (converse_idempotence)
% 7.01/1.69 ! [v0: $i] : ! [v1: $i] : ( ~ (converse(v0) = v1) | ~ $i(v0) | converse(v1)
% 7.01/1.69 = v0)
% 7.01/1.69
% 7.01/1.69 (goals)
% 7.01/1.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.01/1.69 $i] : (converse(v1) = v4 & converse(v0) = v3 & join(v3, v4) = v5 & join(v0,
% 7.01/1.69 v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v5 = v4
% 7.01/1.69 & ~ (v2 = v1)) | (v2 = v1 & ~ (v5 = v4))))
% 7.01/1.69
% 7.01/1.69 (maddux1_join_commutativity)
% 7.01/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ $i(v1)
% 7.01/1.69 | ~ $i(v0) | (join(v1, v0) = v2 & $i(v2)))
% 7.01/1.69
% 7.01/1.69 (function-axioms)
% 7.01/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.01/1.70 (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) & ! [v0: $i] :
% 7.01/1.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (meet(v3, v2) = v1) |
% 7.01/1.70 ~ (meet(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.01/1.70 $i] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) & ! [v0:
% 7.01/1.70 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = v1) | ~
% 7.01/1.70 (converse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 7.01/1.70 ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 7.01/1.70
% 7.01/1.70 Further assumptions not needed in the proof:
% 7.01/1.70 --------------------------------------------
% 7.01/1.70 composition_associativity, composition_distributivity, composition_identity,
% 7.01/1.70 converse_cancellativity, converse_multiplicativity, def_top, def_zero,
% 7.01/1.70 maddux2_join_associativity, maddux3_a_kind_of_de_Morgan,
% 7.01/1.70 maddux4_definiton_of_meet
% 7.01/1.70
% 7.01/1.70 Those formulas are unsatisfiable:
% 7.01/1.70 ---------------------------------
% 7.01/1.70
% 7.01/1.70 Begin of proof
% 7.13/1.70 |
% 7.13/1.70 | ALPHA: (function-axioms) implies:
% 7.13/1.70 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) =
% 7.13/1.70 | v1) | ~ (converse(v2) = v0))
% 7.13/1.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.13/1.70 | (join(v3, v2) = v1) | ~ (join(v3, v2) = v0))
% 7.13/1.70 |
% 7.13/1.70 | DELTA: instantiating (goals) with fresh symbols all_17_0, all_17_1, all_17_2,
% 7.13/1.70 | all_17_3, all_17_4, all_17_5 gives:
% 7.13/1.70 | (3) converse(all_17_4) = all_17_1 & converse(all_17_5) = all_17_2 &
% 7.13/1.70 | join(all_17_2, all_17_1) = all_17_0 & join(all_17_5, all_17_4) =
% 7.13/1.70 | all_17_3 & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) & $i(all_17_3) &
% 7.13/1.70 | $i(all_17_4) & $i(all_17_5) & ((all_17_0 = all_17_1 & ~ (all_17_3 =
% 7.13/1.70 | all_17_4)) | (all_17_3 = all_17_4 & ~ (all_17_0 = all_17_1)))
% 7.13/1.70 |
% 7.13/1.70 | ALPHA: (3) implies:
% 7.13/1.70 | (4) $i(all_17_5)
% 7.13/1.70 | (5) $i(all_17_4)
% 7.13/1.70 | (6) $i(all_17_2)
% 7.13/1.70 | (7) $i(all_17_1)
% 7.13/1.70 | (8) join(all_17_5, all_17_4) = all_17_3
% 7.13/1.71 | (9) join(all_17_2, all_17_1) = all_17_0
% 7.13/1.71 | (10) converse(all_17_5) = all_17_2
% 7.13/1.71 | (11) converse(all_17_4) = all_17_1
% 7.13/1.71 | (12) (all_17_0 = all_17_1 & ~ (all_17_3 = all_17_4)) | (all_17_3 =
% 7.13/1.71 | all_17_4 & ~ (all_17_0 = all_17_1))
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (maddux1_join_commutativity) with all_17_5,
% 7.13/1.71 | all_17_4, all_17_3, simplifying with (4), (5), (8) gives:
% 7.13/1.71 | (13) join(all_17_4, all_17_5) = all_17_3 & $i(all_17_3)
% 7.13/1.71 |
% 7.13/1.71 | ALPHA: (13) implies:
% 7.13/1.71 | (14) join(all_17_4, all_17_5) = all_17_3
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (maddux1_join_commutativity) with all_17_2,
% 7.13/1.71 | all_17_1, all_17_0, simplifying with (6), (7), (9) gives:
% 7.13/1.71 | (15) join(all_17_1, all_17_2) = all_17_0 & $i(all_17_0)
% 7.13/1.71 |
% 7.13/1.71 | ALPHA: (15) implies:
% 7.13/1.71 | (16) join(all_17_1, all_17_2) = all_17_0
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (converse_idempotence) with all_17_5, all_17_2,
% 7.13/1.71 | simplifying with (4), (10) gives:
% 7.13/1.71 | (17) converse(all_17_2) = all_17_5
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (converse_additivity) with all_17_5, all_17_4,
% 7.13/1.71 | all_17_2, all_17_1, all_17_0, simplifying with (4), (5), (9),
% 7.13/1.71 | (10), (11) gives:
% 7.13/1.71 | (18) ? [v0: $i] : (converse(v0) = all_17_0 & join(all_17_5, all_17_4) = v0
% 7.13/1.71 | & $i(v0) & $i(all_17_0))
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (converse_idempotence) with all_17_4, all_17_1,
% 7.13/1.71 | simplifying with (5), (11) gives:
% 7.13/1.71 | (19) converse(all_17_1) = all_17_4
% 7.13/1.71 |
% 7.13/1.71 | DELTA: instantiating (18) with fresh symbol all_25_0 gives:
% 7.13/1.71 | (20) converse(all_25_0) = all_17_0 & join(all_17_5, all_17_4) = all_25_0 &
% 7.13/1.71 | $i(all_25_0) & $i(all_17_0)
% 7.13/1.71 |
% 7.13/1.71 | ALPHA: (20) implies:
% 7.13/1.71 | (21) join(all_17_5, all_17_4) = all_25_0
% 7.13/1.71 | (22) converse(all_25_0) = all_17_0
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (2) with all_17_3, all_25_0, all_17_4, all_17_5,
% 7.13/1.71 | simplifying with (8), (21) gives:
% 7.13/1.71 | (23) all_25_0 = all_17_3
% 7.13/1.71 |
% 7.13/1.71 | REDUCE: (22), (23) imply:
% 7.13/1.71 | (24) converse(all_17_3) = all_17_0
% 7.13/1.71 |
% 7.13/1.71 | GROUND_INST: instantiating (converse_additivity) with all_17_1, all_17_2,
% 7.13/1.71 | all_17_4, all_17_5, all_17_3, simplifying with (6), (7), (14),
% 7.13/1.71 | (17), (19) gives:
% 7.13/1.72 | (25) ? [v0: $i] : (converse(v0) = all_17_3 & join(all_17_1, all_17_2) = v0
% 7.13/1.72 | & $i(v0) & $i(all_17_3))
% 7.13/1.72 |
% 7.13/1.72 | DELTA: instantiating (25) with fresh symbol all_37_0 gives:
% 7.13/1.72 | (26) converse(all_37_0) = all_17_3 & join(all_17_1, all_17_2) = all_37_0 &
% 7.13/1.72 | $i(all_37_0) & $i(all_17_3)
% 7.13/1.72 |
% 7.13/1.72 | ALPHA: (26) implies:
% 7.13/1.72 | (27) join(all_17_1, all_17_2) = all_37_0
% 7.13/1.72 | (28) converse(all_37_0) = all_17_3
% 7.13/1.72 |
% 7.13/1.72 | GROUND_INST: instantiating (2) with all_17_0, all_37_0, all_17_2, all_17_1,
% 7.13/1.72 | simplifying with (16), (27) gives:
% 7.13/1.72 | (29) all_37_0 = all_17_0
% 7.13/1.72 |
% 7.13/1.72 | REDUCE: (28), (29) imply:
% 7.13/1.72 | (30) converse(all_17_0) = all_17_3
% 7.13/1.72 |
% 7.13/1.72 | BETA: splitting (12) gives:
% 7.13/1.72 |
% 7.13/1.72 | Case 1:
% 7.13/1.72 | |
% 7.13/1.72 | | (31) all_17_0 = all_17_1 & ~ (all_17_3 = all_17_4)
% 7.13/1.72 | |
% 7.13/1.72 | | ALPHA: (31) implies:
% 7.13/1.72 | | (32) all_17_0 = all_17_1
% 7.13/1.72 | | (33) ~ (all_17_3 = all_17_4)
% 7.13/1.72 | |
% 7.13/1.72 | | REDUCE: (30), (32) imply:
% 7.13/1.72 | | (34) converse(all_17_1) = all_17_3
% 7.13/1.72 | |
% 7.13/1.72 | | GROUND_INST: instantiating (1) with all_17_4, all_17_3, all_17_1,
% 7.13/1.72 | | simplifying with (19), (34) gives:
% 7.13/1.72 | | (35) all_17_3 = all_17_4
% 7.13/1.72 | |
% 7.13/1.72 | | REDUCE: (33), (35) imply:
% 7.13/1.72 | | (36) $false
% 7.13/1.72 | |
% 7.13/1.72 | | CLOSE: (36) is inconsistent.
% 7.13/1.72 | |
% 7.13/1.72 | Case 2:
% 7.13/1.72 | |
% 7.13/1.72 | | (37) all_17_3 = all_17_4 & ~ (all_17_0 = all_17_1)
% 7.13/1.72 | |
% 7.13/1.72 | | ALPHA: (37) implies:
% 7.13/1.72 | | (38) all_17_3 = all_17_4
% 7.13/1.72 | | (39) ~ (all_17_0 = all_17_1)
% 7.13/1.72 | |
% 7.13/1.72 | | REDUCE: (24), (38) imply:
% 7.13/1.72 | | (40) converse(all_17_4) = all_17_0
% 7.13/1.72 | |
% 7.13/1.72 | | GROUND_INST: instantiating (1) with all_17_1, all_17_0, all_17_4,
% 7.13/1.72 | | simplifying with (11), (40) gives:
% 7.13/1.72 | | (41) all_17_0 = all_17_1
% 7.13/1.72 | |
% 7.13/1.72 | | REDUCE: (39), (41) imply:
% 7.13/1.72 | | (42) $false
% 7.13/1.72 | |
% 7.13/1.72 | | CLOSE: (42) is inconsistent.
% 7.13/1.72 | |
% 7.13/1.72 | End of split
% 7.13/1.72 |
% 7.13/1.72 End of proof
% 7.26/1.72 % SZS output end Proof for theBenchmark
% 7.26/1.72
% 7.26/1.72 1118ms
%------------------------------------------------------------------------------