TSTP Solution File: SEU123+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU123+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 : n016.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 17:42:36 EDT 2023
% Result : Theorem 4.01s 1.31s
% Output : Proof 5.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU123+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 21:33:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.90/0.99 Prover 4: Preprocessing ...
% 1.90/0.99 Prover 1: Preprocessing ...
% 2.50/1.04 Prover 5: Preprocessing ...
% 2.50/1.04 Prover 2: Preprocessing ...
% 2.50/1.04 Prover 3: Preprocessing ...
% 2.50/1.04 Prover 6: Preprocessing ...
% 2.50/1.04 Prover 0: Preprocessing ...
% 2.90/1.15 Prover 5: Proving ...
% 2.90/1.15 Prover 2: Proving ...
% 3.44/1.17 Prover 3: Warning: ignoring some quantifiers
% 3.44/1.18 Prover 3: Constructing countermodel ...
% 3.44/1.18 Prover 1: Warning: ignoring some quantifiers
% 3.44/1.19 Prover 6: Proving ...
% 3.44/1.19 Prover 1: Constructing countermodel ...
% 3.44/1.19 Prover 4: Constructing countermodel ...
% 3.76/1.23 Prover 0: Proving ...
% 4.01/1.31 Prover 0: proved (651ms)
% 4.01/1.31 Prover 2: proved (650ms)
% 4.01/1.31
% 4.01/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.31
% 4.01/1.31
% 4.01/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.31
% 4.01/1.32 Prover 5: proved (641ms)
% 4.01/1.32
% 4.01/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.32
% 4.01/1.32 Prover 3: proved (641ms)
% 4.01/1.32
% 4.01/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.32
% 4.01/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.01/1.32 Prover 6: stopped
% 4.01/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.01/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.01/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.01/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.67/1.34 Prover 7: Preprocessing ...
% 4.67/1.34 Prover 10: Preprocessing ...
% 4.67/1.35 Prover 4: Found proof (size 14)
% 4.67/1.35 Prover 4: proved (681ms)
% 4.67/1.35 Prover 1: Found proof (size 14)
% 4.67/1.35 Prover 1: proved (691ms)
% 4.67/1.35 Prover 8: Preprocessing ...
% 4.67/1.35 Prover 11: Preprocessing ...
% 4.67/1.35 Prover 13: Preprocessing ...
% 4.67/1.36 Prover 7: Warning: ignoring some quantifiers
% 4.67/1.37 Prover 7: Constructing countermodel ...
% 4.67/1.37 Prover 7: stopped
% 4.67/1.37 Prover 11: stopped
% 4.67/1.38 Prover 10: Warning: ignoring some quantifiers
% 4.67/1.38 Prover 10: Constructing countermodel ...
% 4.67/1.38 Prover 13: Warning: ignoring some quantifiers
% 5.06/1.39 Prover 13: Constructing countermodel ...
% 5.06/1.39 Prover 10: stopped
% 5.06/1.39 Prover 13: stopped
% 5.06/1.39 Prover 8: Warning: ignoring some quantifiers
% 5.06/1.40 Prover 8: Constructing countermodel ...
% 5.06/1.40 Prover 8: stopped
% 5.06/1.40
% 5.06/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/1.41
% 5.06/1.41 % SZS output start Proof for theBenchmark
% 5.06/1.41 Assumptions after simplification:
% 5.06/1.41 ---------------------------------
% 5.06/1.41
% 5.06/1.41 (d10_xboole_0)
% 5.06/1.44 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) |
% 5.06/1.44 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i]
% 5.06/1.44 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 5.06/1.44 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1:
% 5.06/1.44 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 5.06/1.44
% 5.06/1.44 (t2_xboole_1)
% 5.06/1.44 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set,
% 5.06/1.44 v0) = v1) | ~ $i(v0))
% 5.06/1.44
% 5.06/1.44 (t3_xboole_1)
% 5.06/1.45 $i(empty_set) & ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0
% 5.06/1.45 & $i(v0))
% 5.06/1.45
% 5.06/1.45 Further assumptions not needed in the proof:
% 5.06/1.45 --------------------------------------------
% 5.06/1.45 antisymmetry_r2_hidden, dt_k1_xboole_0, fc1_xboole_0, rc1_xboole_0,
% 5.06/1.45 rc2_xboole_0, reflexivity_r1_tarski, t6_boole, t7_boole, t8_boole
% 5.06/1.45
% 5.06/1.45 Those formulas are unsatisfiable:
% 5.06/1.45 ---------------------------------
% 5.06/1.45
% 5.06/1.45 Begin of proof
% 5.06/1.45 |
% 5.06/1.45 | ALPHA: (d10_xboole_0) implies:
% 5.06/1.45 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~
% 5.06/1.45 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) =
% 5.06/1.45 | v2))
% 5.06/1.45 |
% 5.06/1.45 | ALPHA: (t2_xboole_1) implies:
% 5.06/1.45 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)
% 5.06/1.45 | | ~ $i(v0))
% 5.06/1.45 |
% 5.06/1.45 | ALPHA: (t3_xboole_1) implies:
% 5.06/1.45 | (3) $i(empty_set)
% 5.06/1.45 | (4) ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0 &
% 5.06/1.45 | $i(v0))
% 5.06/1.45 |
% 5.06/1.45 | DELTA: instantiating (4) with fresh symbol all_15_0 gives:
% 5.06/1.45 | (5) ~ (all_15_0 = empty_set) & subset(all_15_0, empty_set) = 0 &
% 5.06/1.45 | $i(all_15_0)
% 5.06/1.45 |
% 5.06/1.45 | ALPHA: (5) implies:
% 5.06/1.46 | (6) ~ (all_15_0 = empty_set)
% 5.06/1.46 | (7) $i(all_15_0)
% 5.06/1.46 | (8) subset(all_15_0, empty_set) = 0
% 5.06/1.46 |
% 5.06/1.46 | GROUND_INST: instantiating (1) with empty_set, all_15_0, simplifying with (3),
% 5.06/1.46 | (7), (8) gives:
% 5.06/1.46 | (9) all_15_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set,
% 5.06/1.46 | all_15_0) = v0)
% 5.06/1.46 |
% 5.06/1.46 | BETA: splitting (9) gives:
% 5.06/1.46 |
% 5.06/1.46 | Case 1:
% 5.06/1.46 | |
% 5.06/1.46 | | (10) all_15_0 = empty_set
% 5.06/1.46 | |
% 5.06/1.46 | | REDUCE: (6), (10) imply:
% 5.06/1.46 | | (11) $false
% 5.06/1.46 | |
% 5.06/1.46 | | CLOSE: (11) is inconsistent.
% 5.06/1.46 | |
% 5.06/1.46 | Case 2:
% 5.06/1.46 | |
% 5.06/1.46 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, all_15_0) = v0)
% 5.06/1.46 | |
% 5.06/1.46 | | DELTA: instantiating (12) with fresh symbol all_27_0 gives:
% 5.06/1.46 | | (13) ~ (all_27_0 = 0) & subset(empty_set, all_15_0) = all_27_0
% 5.06/1.46 | |
% 5.06/1.46 | | ALPHA: (13) implies:
% 5.06/1.46 | | (14) ~ (all_27_0 = 0)
% 5.06/1.46 | | (15) subset(empty_set, all_15_0) = all_27_0
% 5.06/1.46 | |
% 5.06/1.46 | | GROUND_INST: instantiating (2) with all_15_0, all_27_0, simplifying with
% 5.06/1.46 | | (7), (15) gives:
% 5.06/1.46 | | (16) all_27_0 = 0
% 5.06/1.46 | |
% 5.06/1.46 | | REDUCE: (14), (16) imply:
% 5.06/1.46 | | (17) $false
% 5.06/1.46 | |
% 5.06/1.46 | | CLOSE: (17) is inconsistent.
% 5.06/1.46 | |
% 5.06/1.46 | End of split
% 5.06/1.46 |
% 5.06/1.46 End of proof
% 5.06/1.46 % SZS output end Proof for theBenchmark
% 5.06/1.46
% 5.06/1.46 823ms
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