TSTP Solution File: SET885+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET885+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 : n021.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 15:26:54 EDT 2023
% Result : Theorem 5.62s 1.56s
% Output : Proof 7.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET885+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 : n021.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 13:13:42 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.82/0.98 Prover 4: Preprocessing ...
% 1.82/0.98 Prover 1: Preprocessing ...
% 2.24/1.03 Prover 5: Preprocessing ...
% 2.24/1.03 Prover 3: Preprocessing ...
% 2.24/1.03 Prover 2: Preprocessing ...
% 2.24/1.03 Prover 0: Preprocessing ...
% 2.24/1.04 Prover 6: Preprocessing ...
% 3.91/1.25 Prover 1: Warning: ignoring some quantifiers
% 3.91/1.25 Prover 4: Warning: ignoring some quantifiers
% 3.91/1.25 Prover 3: Warning: ignoring some quantifiers
% 3.91/1.26 Prover 6: Proving ...
% 3.91/1.26 Prover 5: Proving ...
% 3.91/1.27 Prover 2: Proving ...
% 3.91/1.28 Prover 4: Constructing countermodel ...
% 3.91/1.28 Prover 1: Constructing countermodel ...
% 3.91/1.28 Prover 3: Constructing countermodel ...
% 4.34/1.30 Prover 0: Proving ...
% 4.84/1.52 Prover 3: gave up
% 4.84/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.62/1.56 Prover 2: proved (928ms)
% 5.62/1.56
% 5.62/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.62/1.56
% 5.62/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.62/1.56 Prover 0: stopped
% 5.62/1.56 Prover 6: stopped
% 6.18/1.58 Prover 5: stopped
% 6.18/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.18/1.59 Prover 1: gave up
% 6.18/1.59 Prover 10: Preprocessing ...
% 6.18/1.59 Prover 7: Preprocessing ...
% 6.18/1.59 Prover 8: Preprocessing ...
% 6.18/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.18/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.18/1.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.18/1.60 Prover 4: gave up
% 6.18/1.61 Prover 16: Preprocessing ...
% 6.18/1.61 Prover 11: Preprocessing ...
% 6.18/1.61 Prover 13: Preprocessing ...
% 6.18/1.62 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.18/1.63 Prover 19: Preprocessing ...
% 6.18/1.65 Prover 16: Warning: ignoring some quantifiers
% 6.18/1.65 Prover 10: Warning: ignoring some quantifiers
% 6.18/1.65 Prover 8: Warning: ignoring some quantifiers
% 6.18/1.66 Prover 16: Constructing countermodel ...
% 6.18/1.66 Prover 10: Constructing countermodel ...
% 6.84/1.66 Prover 7: Warning: ignoring some quantifiers
% 6.84/1.66 Prover 8: Constructing countermodel ...
% 6.84/1.67 Prover 13: Warning: ignoring some quantifiers
% 6.84/1.67 Prover 7: Constructing countermodel ...
% 6.84/1.67 Prover 13: Constructing countermodel ...
% 7.03/1.72 Prover 11: Warning: ignoring some quantifiers
% 7.34/1.74 Prover 11: Constructing countermodel ...
% 7.34/1.74 Prover 19: Warning: ignoring some quantifiers
% 7.34/1.74 Prover 19: Constructing countermodel ...
% 7.34/1.76 Prover 10: Found proof (size 17)
% 7.34/1.76 Prover 10: proved (194ms)
% 7.34/1.76 Prover 13: stopped
% 7.34/1.76 Prover 8: stopped
% 7.34/1.76 Prover 11: stopped
% 7.34/1.76 Prover 16: stopped
% 7.34/1.76 Prover 7: stopped
% 7.34/1.76 Prover 19: stopped
% 7.34/1.76
% 7.34/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.34/1.76
% 7.34/1.76 % SZS output start Proof for theBenchmark
% 7.34/1.77 Assumptions after simplification:
% 7.34/1.77 ---------------------------------
% 7.34/1.77
% 7.34/1.77 (commutativity_k2_tarski)
% 7.34/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 7.34/1.79 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 7.34/1.79
% 7.34/1.79 (d1_tarski)
% 7.34/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 7.34/1.80 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 7.34/1.80 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 7.34/1.80 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 7.34/1.80 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 7.34/1.80 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 7.34/1.80
% 7.34/1.80 (d2_tarski)
% 7.34/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 7.34/1.80 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.34/1.80 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.34/1.80 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 7.34/1.80 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~
% 7.34/1.80 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1:
% 7.34/1.80 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~
% 7.34/1.80 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 7.34/1.80 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0,
% 7.34/1.80 v2))
% 7.34/1.80
% 7.34/1.80 (d3_tarski)
% 7.78/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 7.78/1.81 ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0: $i] : ? [v1: $i]
% 7.78/1.81 : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & in(v2, v0)
% 7.78/1.81 & ~ in(v2, v1)))
% 7.78/1.81
% 7.78/1.81 (t26_zfmisc_1)
% 7.78/1.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v2
% 7.78/1.81 = v0) & singleton(v2) = v4 & unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3)
% 7.78/1.81 & $i(v2) & $i(v1) & $i(v0) & subset(v3, v4))
% 7.78/1.81
% 7.78/1.81 Further assumptions not needed in the proof:
% 7.78/1.81 --------------------------------------------
% 7.78/1.81 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 7.78/1.81
% 7.78/1.81 Those formulas are unsatisfiable:
% 7.78/1.81 ---------------------------------
% 7.78/1.81
% 7.78/1.81 Begin of proof
% 7.78/1.81 |
% 7.78/1.81 | ALPHA: (d1_tarski) implies:
% 7.78/1.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 7.78/1.81 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 7.78/1.81 |
% 7.78/1.81 | ALPHA: (d2_tarski) implies:
% 7.78/1.81 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 7.78/1.81 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2))
% 7.78/1.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 7.78/1.81 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v2))
% 7.78/1.81 |
% 7.78/1.81 | ALPHA: (d3_tarski) implies:
% 7.78/1.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 7.78/1.82 | $i(v0) | ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 7.78/1.82 |
% 7.78/1.82 | DELTA: instantiating (t26_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 7.78/1.82 | all_14_2, all_14_3, all_14_4 gives:
% 7.78/1.82 | (5) ~ (all_14_2 = all_14_4) & singleton(all_14_2) = all_14_0 &
% 7.78/1.82 | unordered_pair(all_14_4, all_14_3) = all_14_1 & $i(all_14_0) &
% 7.78/1.82 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) &
% 7.78/1.82 | subset(all_14_1, all_14_0)
% 7.78/1.82 |
% 7.78/1.82 | ALPHA: (5) implies:
% 7.78/1.82 | (6) ~ (all_14_2 = all_14_4)
% 7.78/1.82 | (7) subset(all_14_1, all_14_0)
% 7.78/1.82 | (8) $i(all_14_4)
% 7.78/1.82 | (9) $i(all_14_3)
% 7.78/1.82 | (10) $i(all_14_2)
% 7.78/1.82 | (11) $i(all_14_1)
% 7.78/1.82 | (12) $i(all_14_0)
% 7.78/1.82 | (13) unordered_pair(all_14_4, all_14_3) = all_14_1
% 7.78/1.82 | (14) singleton(all_14_2) = all_14_0
% 7.78/1.82 |
% 7.78/1.82 | GROUND_INST: instantiating (3) with all_14_4, all_14_3, all_14_1, simplifying
% 7.78/1.82 | with (8), (9), (11), (13) gives:
% 7.78/1.82 | (15) in(all_14_3, all_14_1)
% 7.78/1.82 |
% 7.78/1.82 | GROUND_INST: instantiating (2) with all_14_4, all_14_3, all_14_1, simplifying
% 7.78/1.82 | with (8), (9), (11), (13) gives:
% 7.78/1.82 | (16) in(all_14_4, all_14_1)
% 7.78/1.82 |
% 7.78/1.82 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_14_4, all_14_3,
% 7.78/1.82 | all_14_1, simplifying with (8), (9), (13) gives:
% 7.78/1.82 | (17) unordered_pair(all_14_3, all_14_4) = all_14_1 & $i(all_14_1)
% 7.78/1.82 |
% 7.78/1.82 | GROUND_INST: instantiating (4) with all_14_1, all_14_0, all_14_4, simplifying
% 7.78/1.82 | with (7), (8), (11), (12), (16) gives:
% 7.78/1.83 | (18) in(all_14_4, all_14_0)
% 7.78/1.83 |
% 7.78/1.83 | GROUND_INST: instantiating (4) with all_14_1, all_14_0, all_14_3, simplifying
% 7.78/1.83 | with (7), (9), (11), (12), (15) gives:
% 7.78/1.83 | (19) in(all_14_3, all_14_0)
% 7.78/1.83 |
% 7.78/1.83 | GROUND_INST: instantiating (1) with all_14_2, all_14_0, all_14_4, simplifying
% 7.78/1.83 | with (8), (10), (12), (14), (18) gives:
% 7.78/1.83 | (20) all_14_2 = all_14_4
% 7.78/1.83 |
% 7.78/1.83 | GROUND_INST: instantiating (1) with all_14_2, all_14_0, all_14_3, simplifying
% 7.78/1.83 | with (9), (10), (12), (14), (19) gives:
% 7.78/1.83 | (21) all_14_2 = all_14_3
% 7.78/1.83 |
% 7.78/1.83 | COMBINE_EQS: (20), (21) imply:
% 7.78/1.83 | (22) all_14_3 = all_14_4
% 7.78/1.83 |
% 7.78/1.83 | REDUCE: (6), (20) imply:
% 7.78/1.83 | (23) $false
% 7.78/1.83 |
% 7.78/1.83 | CLOSE: (23) is inconsistent.
% 7.78/1.83 |
% 7.78/1.83 End of proof
% 7.78/1.83 % SZS output end Proof for theBenchmark
% 7.78/1.83
% 7.78/1.83 1220ms
%------------------------------------------------------------------------------