TSTP Solution File: SEU151+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU151+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 : n005.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 17:42:48 EDT 2023
% Result : Theorem 5.54s 1.68s
% Output : Proof 7.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU151+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 13:14:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.64 ________ _____
% 0.18/0.64 ___ __ \_________(_)________________________________
% 0.18/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.64
% 0.18/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.64 (2023-06-19)
% 0.18/0.64
% 0.18/0.64 (c) Philipp Rümmer, 2009-2023
% 0.18/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.64 Amanda Stjerna.
% 0.18/0.64 Free software under BSD-3-Clause.
% 0.18/0.64
% 0.18/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.64
% 0.18/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.65 Running up to 7 provers in parallel.
% 0.18/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/1.08 Prover 1: Preprocessing ...
% 2.12/1.08 Prover 4: Preprocessing ...
% 2.35/1.15 Prover 3: Preprocessing ...
% 2.35/1.15 Prover 5: Preprocessing ...
% 2.35/1.15 Prover 0: Preprocessing ...
% 2.35/1.15 Prover 6: Preprocessing ...
% 2.35/1.15 Prover 2: Preprocessing ...
% 3.39/1.29 Prover 1: Warning: ignoring some quantifiers
% 3.39/1.33 Prover 1: Constructing countermodel ...
% 3.39/1.34 Prover 4: Warning: ignoring some quantifiers
% 3.39/1.35 Prover 4: Constructing countermodel ...
% 3.39/1.35 Prover 6: Proving ...
% 3.39/1.35 Prover 5: Proving ...
% 3.39/1.35 Prover 3: Warning: ignoring some quantifiers
% 3.39/1.36 Prover 3: Constructing countermodel ...
% 3.39/1.36 Prover 2: Proving ...
% 3.39/1.37 Prover 0: Proving ...
% 5.54/1.68 Prover 2: proved (1005ms)
% 5.54/1.68
% 5.54/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.54/1.68
% 5.54/1.68 Prover 5: stopped
% 5.54/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.54/1.69 Prover 0: stopped
% 5.54/1.69 Prover 6: stopped
% 5.54/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.54/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.54/1.69 Prover 3: stopped
% 5.54/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.54/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.54/1.71 Prover 10: Preprocessing ...
% 6.22/1.72 Prover 8: Preprocessing ...
% 6.22/1.73 Prover 13: Preprocessing ...
% 6.22/1.73 Prover 7: Preprocessing ...
% 6.22/1.76 Prover 11: Preprocessing ...
% 6.22/1.76 Prover 10: Warning: ignoring some quantifiers
% 6.22/1.76 Prover 10: Constructing countermodel ...
% 6.79/1.80 Prover 8: Warning: ignoring some quantifiers
% 6.79/1.81 Prover 7: Warning: ignoring some quantifiers
% 6.79/1.82 Prover 13: Warning: ignoring some quantifiers
% 6.79/1.82 Prover 7: Constructing countermodel ...
% 6.79/1.82 Prover 8: Constructing countermodel ...
% 6.79/1.84 Prover 13: Constructing countermodel ...
% 6.79/1.84 Prover 11: Warning: ignoring some quantifiers
% 6.79/1.85 Prover 11: Constructing countermodel ...
% 7.43/1.88 Prover 10: Found proof (size 29)
% 7.43/1.88 Prover 10: proved (190ms)
% 7.43/1.88 Prover 11: stopped
% 7.43/1.88 Prover 4: stopped
% 7.43/1.88 Prover 7: stopped
% 7.43/1.88 Prover 8: stopped
% 7.43/1.88 Prover 13: stopped
% 7.43/1.88 Prover 1: stopped
% 7.43/1.88
% 7.43/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.43/1.89
% 7.43/1.90 % SZS output start Proof for theBenchmark
% 7.57/1.90 Assumptions after simplification:
% 7.57/1.90 ---------------------------------
% 7.57/1.90
% 7.57/1.90 (commutativity_k2_tarski)
% 7.67/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 7.67/1.95 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 7.67/1.95
% 7.67/1.95 (d2_tarski)
% 7.67/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 7.67/1.96 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.67/1.96 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.67/1.96 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 7.67/1.96 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~
% 7.67/1.96 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1:
% 7.67/1.96 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~
% 7.67/1.96 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 7.67/1.96 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0,
% 7.67/1.96 v2))
% 7.67/1.96
% 7.67/1.96 (t10_zfmisc_1)
% 7.67/1.97 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3
% 7.67/1.97 = v0) & ~ (v2 = v0) & unordered_pair(v2, v3) = v4 & unordered_pair(v0,
% 7.67/1.97 v1) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.67/1.97
% 7.67/1.97 Further assumptions not needed in the proof:
% 7.67/1.97 --------------------------------------------
% 7.67/1.97 antisymmetry_r2_hidden, dt_k2_tarski
% 7.67/1.97
% 7.67/1.97 Those formulas are unsatisfiable:
% 7.67/1.97 ---------------------------------
% 7.67/1.97
% 7.67/1.97 Begin of proof
% 7.67/1.97 |
% 7.67/1.97 | ALPHA: (d2_tarski) implies:
% 7.67/1.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 7.67/1.97 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2))
% 7.67/1.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 7.67/1.98 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v2))
% 7.67/1.98 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 =
% 7.67/1.98 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 7.67/1.98 | $i(v1) | ~ $i(v0) | ~ in(v3, v2))
% 7.67/1.98 |
% 7.67/1.98 | DELTA: instantiating (t10_zfmisc_1) with fresh symbols all_6_0, all_6_1,
% 7.67/1.98 | all_6_2, all_6_3, all_6_4 gives:
% 7.67/1.98 | (4) ~ (all_6_1 = all_6_4) & ~ (all_6_2 = all_6_4) &
% 7.67/1.98 | unordered_pair(all_6_2, all_6_1) = all_6_0 & unordered_pair(all_6_4,
% 7.67/1.98 | all_6_3) = all_6_0 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) &
% 7.67/1.98 | $i(all_6_3) & $i(all_6_4)
% 7.67/1.98 |
% 7.67/1.98 | ALPHA: (4) implies:
% 7.67/1.99 | (5) ~ (all_6_2 = all_6_4)
% 7.67/1.99 | (6) ~ (all_6_1 = all_6_4)
% 7.67/1.99 | (7) $i(all_6_4)
% 7.67/1.99 | (8) $i(all_6_3)
% 7.67/1.99 | (9) $i(all_6_2)
% 7.67/1.99 | (10) $i(all_6_1)
% 7.67/1.99 | (11) $i(all_6_0)
% 7.67/1.99 | (12) unordered_pair(all_6_4, all_6_3) = all_6_0
% 7.67/1.99 | (13) unordered_pair(all_6_2, all_6_1) = all_6_0
% 7.67/1.99 |
% 7.67/1.99 | GROUND_INST: instantiating (1) with all_6_4, all_6_3, all_6_0, simplifying
% 7.67/1.99 | with (7), (8), (11), (12) gives:
% 7.67/1.99 | (14) in(all_6_4, all_6_0)
% 7.67/1.99 |
% 7.67/1.99 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_6_4, all_6_3,
% 7.67/1.99 | all_6_0, simplifying with (7), (8), (12) gives:
% 7.67/1.99 | (15) unordered_pair(all_6_3, all_6_4) = all_6_0 & $i(all_6_0)
% 7.67/1.99 |
% 7.67/1.99 | ALPHA: (15) implies:
% 7.67/2.00 | (16) unordered_pair(all_6_3, all_6_4) = all_6_0
% 7.67/2.00 |
% 7.67/2.00 | GROUND_INST: instantiating (2) with all_6_2, all_6_1, all_6_0, simplifying
% 7.67/2.00 | with (9), (10), (11), (13) gives:
% 7.67/2.00 | (17) in(all_6_1, all_6_0)
% 7.67/2.00 |
% 7.67/2.00 | GROUND_INST: instantiating (1) with all_6_2, all_6_1, all_6_0, simplifying
% 7.67/2.00 | with (9), (10), (11), (13) gives:
% 7.67/2.00 | (18) in(all_6_2, all_6_0)
% 7.67/2.00 |
% 7.67/2.00 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_6_2, all_6_1,
% 7.67/2.00 | all_6_0, simplifying with (9), (10), (13) gives:
% 7.67/2.00 | (19) unordered_pair(all_6_1, all_6_2) = all_6_0 & $i(all_6_0)
% 7.67/2.00 |
% 7.67/2.00 | ALPHA: (19) implies:
% 7.67/2.00 | (20) unordered_pair(all_6_1, all_6_2) = all_6_0
% 7.67/2.00 |
% 7.67/2.00 | GROUND_INST: instantiating (3) with all_6_3, all_6_4, all_6_0, all_6_1,
% 7.67/2.00 | simplifying with (7), (8), (10), (11), (16), (17) gives:
% 7.67/2.00 | (21) all_6_1 = all_6_3 | all_6_1 = all_6_4
% 7.67/2.00 |
% 7.67/2.00 | GROUND_INST: instantiating (3) with all_6_3, all_6_4, all_6_0, all_6_2,
% 7.67/2.00 | simplifying with (7), (8), (9), (11), (16), (18) gives:
% 7.67/2.01 | (22) all_6_2 = all_6_3 | all_6_2 = all_6_4
% 7.67/2.01 |
% 7.67/2.01 | GROUND_INST: instantiating (3) with all_6_1, all_6_2, all_6_0, all_6_4,
% 7.67/2.01 | simplifying with (7), (9), (10), (11), (14), (20) gives:
% 7.67/2.01 | (23) all_6_1 = all_6_4 | all_6_2 = all_6_4
% 7.67/2.01 |
% 7.67/2.01 | BETA: splitting (21) gives:
% 7.67/2.01 |
% 7.67/2.01 | Case 1:
% 7.67/2.01 | |
% 7.67/2.01 | | (24) all_6_1 = all_6_3
% 7.67/2.01 | |
% 7.67/2.01 | | BETA: splitting (22) gives:
% 7.67/2.01 | |
% 7.67/2.01 | | Case 1:
% 7.67/2.01 | | |
% 7.67/2.01 | | | (25) all_6_2 = all_6_3
% 7.67/2.01 | | |
% 7.67/2.01 | | | REDUCE: (5), (25) imply:
% 7.67/2.01 | | | (26) ~ (all_6_3 = all_6_4)
% 7.67/2.01 | | |
% 7.67/2.01 | | | BETA: splitting (23) gives:
% 7.67/2.01 | | |
% 7.67/2.01 | | | Case 1:
% 7.67/2.01 | | | |
% 7.67/2.01 | | | | (27) all_6_1 = all_6_4
% 7.67/2.01 | | | |
% 7.67/2.01 | | | | COMBINE_EQS: (24), (27) imply:
% 7.67/2.01 | | | | (28) all_6_3 = all_6_4
% 7.67/2.01 | | | |
% 7.67/2.01 | | | | REDUCE: (26), (28) imply:
% 7.67/2.01 | | | | (29) $false
% 7.67/2.01 | | | |
% 7.67/2.01 | | | | CLOSE: (29) is inconsistent.
% 7.67/2.01 | | | |
% 7.67/2.01 | | | Case 2:
% 7.67/2.01 | | | |
% 7.67/2.01 | | | | (30) all_6_2 = all_6_4
% 7.67/2.01 | | | |
% 7.67/2.01 | | | | COMBINE_EQS: (25), (30) imply:
% 7.67/2.02 | | | | (31) all_6_3 = all_6_4
% 7.67/2.02 | | | |
% 7.67/2.02 | | | | SIMP: (31) implies:
% 7.67/2.02 | | | | (32) all_6_3 = all_6_4
% 7.67/2.02 | | | |
% 7.67/2.02 | | | | REDUCE: (26), (32) imply:
% 7.67/2.02 | | | | (33) $false
% 7.67/2.02 | | | |
% 7.67/2.02 | | | | CLOSE: (33) is inconsistent.
% 7.67/2.02 | | | |
% 7.67/2.02 | | | End of split
% 7.67/2.02 | | |
% 7.67/2.02 | | Case 2:
% 7.67/2.02 | | |
% 7.67/2.02 | | | (34) all_6_2 = all_6_4
% 7.67/2.02 | | |
% 7.67/2.02 | | | REDUCE: (5), (34) imply:
% 7.67/2.02 | | | (35) $false
% 7.67/2.02 | | |
% 7.67/2.02 | | | CLOSE: (35) is inconsistent.
% 7.67/2.02 | | |
% 7.67/2.02 | | End of split
% 7.67/2.02 | |
% 7.67/2.02 | Case 2:
% 7.67/2.02 | |
% 7.67/2.02 | | (36) all_6_1 = all_6_4
% 7.67/2.02 | |
% 7.67/2.02 | | REDUCE: (6), (36) imply:
% 7.67/2.02 | | (37) $false
% 7.67/2.02 | |
% 7.67/2.02 | | CLOSE: (37) is inconsistent.
% 7.67/2.02 | |
% 7.67/2.02 | End of split
% 7.67/2.02 |
% 7.67/2.02 End of proof
% 7.67/2.02 % SZS output end Proof for theBenchmark
% 7.67/2.02
% 7.67/2.02 1381ms
%------------------------------------------------------------------------------