TSTP Solution File: SET978+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET978+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 : n028.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 15:27:16 EDT 2023
% Result : Theorem 3.88s 1.31s
% Output : Proof 5.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET978+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n028.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 08:29:37 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.02/0.95 Prover 1: Preprocessing ...
% 2.02/0.95 Prover 4: Preprocessing ...
% 2.02/0.99 Prover 6: Preprocessing ...
% 2.02/0.99 Prover 0: Preprocessing ...
% 2.02/0.99 Prover 5: Preprocessing ...
% 2.02/0.99 Prover 2: Preprocessing ...
% 2.02/0.99 Prover 3: Preprocessing ...
% 3.21/1.12 Prover 1: Constructing countermodel ...
% 3.21/1.13 Prover 5: Proving ...
% 3.21/1.13 Prover 2: Proving ...
% 3.21/1.13 Prover 3: Constructing countermodel ...
% 3.21/1.13 Prover 4: Constructing countermodel ...
% 3.21/1.13 Prover 0: Proving ...
% 3.21/1.13 Prover 6: Constructing countermodel ...
% 3.88/1.30 Prover 5: proved (691ms)
% 3.88/1.31
% 3.88/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.88/1.31
% 3.88/1.31 Prover 3: stopped
% 3.88/1.31 Prover 0: stopped
% 3.88/1.31 Prover 2: stopped
% 3.88/1.32 Prover 6: stopped
% 3.88/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.88/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.88/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.88/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.88/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.88/1.34 Prover 7: Preprocessing ...
% 3.88/1.34 Prover 8: Preprocessing ...
% 4.76/1.34 Prover 13: Preprocessing ...
% 4.76/1.35 Prover 11: Preprocessing ...
% 4.76/1.35 Prover 10: Preprocessing ...
% 4.76/1.37 Prover 7: Constructing countermodel ...
% 4.76/1.38 Prover 4: Found proof (size 30)
% 4.76/1.38 Prover 4: proved (772ms)
% 4.76/1.38 Prover 1: stopped
% 4.76/1.39 Prover 7: stopped
% 4.76/1.40 Prover 13: Warning: ignoring some quantifiers
% 4.76/1.40 Prover 8: Warning: ignoring some quantifiers
% 4.76/1.40 Prover 10: Constructing countermodel ...
% 4.76/1.40 Prover 13: Constructing countermodel ...
% 4.76/1.40 Prover 8: Constructing countermodel ...
% 4.76/1.40 Prover 11: Constructing countermodel ...
% 4.76/1.40 Prover 10: stopped
% 4.76/1.41 Prover 13: stopped
% 4.76/1.41 Prover 8: stopped
% 4.76/1.41 Prover 11: stopped
% 4.76/1.41
% 4.76/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.76/1.41
% 4.76/1.41 % SZS output start Proof for theBenchmark
% 4.76/1.42 Assumptions after simplification:
% 4.76/1.42 ---------------------------------
% 4.76/1.42
% 4.76/1.42 (t127_zfmisc_1)
% 5.47/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 5.47/1.44 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~
% 5.47/1.44 (cartesian_product2(v0, v2) = v4) | ~ (disjoint(v4, v5) = v6) | ~ $i(v3) |
% 5.47/1.44 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ( ~ (v8 =
% 5.47/1.44 0) & ~ (v7 = 0) & disjoint(v2, v3) = v8 & disjoint(v0, v1) = v7))
% 5.47/1.44
% 5.47/1.45 (t131_zfmisc_1)
% 5.47/1.45 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.47/1.45 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i]
% 5.47/1.45 : ? [v11: any] : ( ~ (v1 = v0) & singleton(v1) = v6 & singleton(v0) = v4 &
% 5.47/1.45 cartesian_product2(v6, v3) = v7 & cartesian_product2(v4, v2) = v5 &
% 5.47/1.45 cartesian_product2(v3, v6) = v10 & cartesian_product2(v2, v4) = v9 &
% 5.47/1.45 disjoint(v9, v10) = v11 & disjoint(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7)
% 5.47/1.45 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v11 =
% 5.47/1.45 0) | ~ (v8 = 0)))
% 5.47/1.45
% 5.47/1.45 (t17_zfmisc_1)
% 5.47/1.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.47/1.45 | v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~
% 5.47/1.45 (disjoint(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0))
% 5.47/1.45
% 5.47/1.45 Further assumptions not needed in the proof:
% 5.47/1.45 --------------------------------------------
% 5.47/1.45 rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0
% 5.47/1.45
% 5.47/1.45 Those formulas are unsatisfiable:
% 5.47/1.45 ---------------------------------
% 5.47/1.45
% 5.47/1.45 Begin of proof
% 5.47/1.45 |
% 5.47/1.45 | DELTA: instantiating (t131_zfmisc_1) with fresh symbols all_10_0, all_10_1,
% 5.47/1.45 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8,
% 5.47/1.45 | all_10_9, all_10_10, all_10_11 gives:
% 5.47/1.46 | (1) ~ (all_10_10 = all_10_11) & singleton(all_10_10) = all_10_5 &
% 5.47/1.46 | singleton(all_10_11) = all_10_7 & cartesian_product2(all_10_5,
% 5.47/1.46 | all_10_8) = all_10_4 & cartesian_product2(all_10_7, all_10_9) =
% 5.47/1.46 | all_10_6 & cartesian_product2(all_10_8, all_10_5) = all_10_1 &
% 5.47/1.46 | cartesian_product2(all_10_9, all_10_7) = all_10_2 & disjoint(all_10_2,
% 5.47/1.46 | all_10_1) = all_10_0 & disjoint(all_10_6, all_10_4) = all_10_3 &
% 5.47/1.46 | $i(all_10_1) & $i(all_10_2) & $i(all_10_4) & $i(all_10_5) &
% 5.47/1.46 | $i(all_10_6) & $i(all_10_7) & $i(all_10_8) & $i(all_10_9) &
% 5.47/1.46 | $i(all_10_10) & $i(all_10_11) & ( ~ (all_10_0 = 0) | ~ (all_10_3 = 0))
% 5.47/1.46 |
% 5.47/1.46 | ALPHA: (1) implies:
% 5.47/1.46 | (2) ~ (all_10_10 = all_10_11)
% 5.47/1.46 | (3) $i(all_10_11)
% 5.47/1.46 | (4) $i(all_10_10)
% 5.47/1.46 | (5) $i(all_10_9)
% 5.47/1.46 | (6) $i(all_10_8)
% 5.47/1.46 | (7) $i(all_10_7)
% 5.47/1.46 | (8) $i(all_10_5)
% 5.47/1.46 | (9) disjoint(all_10_6, all_10_4) = all_10_3
% 5.47/1.46 | (10) disjoint(all_10_2, all_10_1) = all_10_0
% 5.47/1.46 | (11) cartesian_product2(all_10_9, all_10_7) = all_10_2
% 5.47/1.46 | (12) cartesian_product2(all_10_8, all_10_5) = all_10_1
% 5.47/1.46 | (13) cartesian_product2(all_10_7, all_10_9) = all_10_6
% 5.47/1.46 | (14) cartesian_product2(all_10_5, all_10_8) = all_10_4
% 5.47/1.46 | (15) singleton(all_10_11) = all_10_7
% 5.47/1.46 | (16) singleton(all_10_10) = all_10_5
% 5.47/1.46 | (17) ~ (all_10_0 = 0) | ~ (all_10_3 = 0)
% 5.47/1.46 |
% 5.47/1.47 | GROUND_INST: instantiating (t127_zfmisc_1) with all_10_9, all_10_8, all_10_7,
% 5.47/1.47 | all_10_5, all_10_2, all_10_1, all_10_0, simplifying with (5),
% 5.47/1.47 | (6), (7), (8), (10), (11), (12) gives:
% 5.47/1.47 | (18) all_10_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 5.47/1.47 | 0) & disjoint(all_10_7, all_10_5) = v1 & disjoint(all_10_9,
% 5.47/1.47 | all_10_8) = v0)
% 5.47/1.47 |
% 5.47/1.47 | GROUND_INST: instantiating (t127_zfmisc_1) with all_10_7, all_10_5, all_10_9,
% 5.47/1.47 | all_10_8, all_10_6, all_10_4, all_10_3, simplifying with (5),
% 5.47/1.47 | (6), (7), (8), (9), (13), (14) gives:
% 5.47/1.47 | (19) all_10_3 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 5.47/1.47 | 0) & disjoint(all_10_7, all_10_5) = v0 & disjoint(all_10_9,
% 5.47/1.47 | all_10_8) = v1)
% 5.47/1.47 |
% 5.47/1.47 | BETA: splitting (17) gives:
% 5.47/1.47 |
% 5.47/1.47 | Case 1:
% 5.47/1.47 | |
% 5.47/1.47 | | (20) ~ (all_10_0 = 0)
% 5.47/1.47 | |
% 5.47/1.47 | | BETA: splitting (18) gives:
% 5.47/1.47 | |
% 5.47/1.47 | | Case 1:
% 5.47/1.47 | | |
% 5.47/1.47 | | | (21) all_10_0 = 0
% 5.47/1.47 | | |
% 5.47/1.47 | | | REDUCE: (20), (21) imply:
% 5.47/1.47 | | | (22) $false
% 5.47/1.47 | | |
% 5.47/1.47 | | | CLOSE: (22) is inconsistent.
% 5.47/1.47 | | |
% 5.47/1.47 | | Case 2:
% 5.47/1.47 | | |
% 5.47/1.47 | | | (23) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 5.47/1.47 | | | disjoint(all_10_7, all_10_5) = v1 & disjoint(all_10_9, all_10_8)
% 5.47/1.47 | | | = v0)
% 5.47/1.47 | | |
% 5.47/1.47 | | | DELTA: instantiating (23) with fresh symbols all_28_0, all_28_1 gives:
% 5.47/1.47 | | | (24) ~ (all_28_0 = 0) & ~ (all_28_1 = 0) & disjoint(all_10_7,
% 5.47/1.47 | | | all_10_5) = all_28_0 & disjoint(all_10_9, all_10_8) = all_28_1
% 5.47/1.47 | | |
% 5.47/1.47 | | | ALPHA: (24) implies:
% 5.47/1.47 | | | (25) ~ (all_28_0 = 0)
% 5.47/1.47 | | | (26) disjoint(all_10_7, all_10_5) = all_28_0
% 5.47/1.47 | | |
% 5.47/1.47 | | | GROUND_INST: instantiating (t17_zfmisc_1) with all_10_11, all_10_10,
% 5.47/1.47 | | | all_10_7, all_10_5, all_28_0, simplifying with (3), (4),
% 5.47/1.47 | | | (15), (16), (26) gives:
% 5.47/1.47 | | | (27) all_28_0 = 0 | all_10_10 = all_10_11
% 5.47/1.47 | | |
% 5.47/1.47 | | | BETA: splitting (27) gives:
% 5.47/1.47 | | |
% 5.47/1.47 | | | Case 1:
% 5.47/1.47 | | | |
% 5.47/1.47 | | | | (28) all_28_0 = 0
% 5.47/1.47 | | | |
% 5.47/1.47 | | | | REDUCE: (25), (28) imply:
% 5.47/1.47 | | | | (29) $false
% 5.47/1.47 | | | |
% 5.47/1.47 | | | | CLOSE: (29) is inconsistent.
% 5.47/1.47 | | | |
% 5.47/1.47 | | | Case 2:
% 5.47/1.47 | | | |
% 5.47/1.48 | | | | (30) all_10_10 = all_10_11
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | REDUCE: (2), (30) imply:
% 5.47/1.48 | | | | (31) $false
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | CLOSE: (31) is inconsistent.
% 5.47/1.48 | | | |
% 5.47/1.48 | | | End of split
% 5.47/1.48 | | |
% 5.47/1.48 | | End of split
% 5.47/1.48 | |
% 5.47/1.48 | Case 2:
% 5.47/1.48 | |
% 5.47/1.48 | | (32) ~ (all_10_3 = 0)
% 5.47/1.48 | |
% 5.47/1.48 | | BETA: splitting (19) gives:
% 5.47/1.48 | |
% 5.47/1.48 | | Case 1:
% 5.47/1.48 | | |
% 5.47/1.48 | | | (33) all_10_3 = 0
% 5.47/1.48 | | |
% 5.47/1.48 | | | REDUCE: (32), (33) imply:
% 5.47/1.48 | | | (34) $false
% 5.47/1.48 | | |
% 5.47/1.48 | | | CLOSE: (34) is inconsistent.
% 5.47/1.48 | | |
% 5.47/1.48 | | Case 2:
% 5.47/1.48 | | |
% 5.47/1.48 | | | (35) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 5.47/1.48 | | | disjoint(all_10_7, all_10_5) = v0 & disjoint(all_10_9, all_10_8)
% 5.47/1.48 | | | = v1)
% 5.47/1.48 | | |
% 5.47/1.48 | | | DELTA: instantiating (35) with fresh symbols all_28_0, all_28_1 gives:
% 5.47/1.48 | | | (36) ~ (all_28_0 = 0) & ~ (all_28_1 = 0) & disjoint(all_10_7,
% 5.47/1.48 | | | all_10_5) = all_28_1 & disjoint(all_10_9, all_10_8) = all_28_0
% 5.47/1.48 | | |
% 5.47/1.48 | | | ALPHA: (36) implies:
% 5.47/1.48 | | | (37) ~ (all_28_1 = 0)
% 5.47/1.48 | | | (38) disjoint(all_10_7, all_10_5) = all_28_1
% 5.47/1.48 | | |
% 5.47/1.48 | | | GROUND_INST: instantiating (t17_zfmisc_1) with all_10_11, all_10_10,
% 5.47/1.48 | | | all_10_7, all_10_5, all_28_1, simplifying with (3), (4),
% 5.47/1.48 | | | (15), (16), (38) gives:
% 5.47/1.48 | | | (39) all_28_1 = 0 | all_10_10 = all_10_11
% 5.47/1.48 | | |
% 5.47/1.48 | | | BETA: splitting (39) gives:
% 5.47/1.48 | | |
% 5.47/1.48 | | | Case 1:
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | (40) all_28_1 = 0
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | REDUCE: (37), (40) imply:
% 5.47/1.48 | | | | (41) $false
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | CLOSE: (41) is inconsistent.
% 5.47/1.48 | | | |
% 5.47/1.48 | | | Case 2:
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | (42) all_10_10 = all_10_11
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | REDUCE: (2), (42) imply:
% 5.47/1.48 | | | | (43) $false
% 5.47/1.48 | | | |
% 5.47/1.48 | | | | CLOSE: (43) is inconsistent.
% 5.47/1.48 | | | |
% 5.47/1.48 | | | End of split
% 5.47/1.48 | | |
% 5.47/1.48 | | End of split
% 5.47/1.48 | |
% 5.47/1.48 | End of split
% 5.47/1.48 |
% 5.47/1.48 End of proof
% 5.47/1.48 % SZS output end Proof for theBenchmark
% 5.47/1.48
% 5.47/1.48 890ms
%------------------------------------------------------------------------------