TSTP Solution File: SET878+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET878+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 : n032.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 15:26:53 EDT 2023
% Result : Theorem 3.92s 1.29s
% Output : Proof 5.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET878+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.31 % Computer : n032.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Sat Aug 26 09:46:28 EDT 2023
% 0.13/0.31 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.53 Running up to 7 provers in parallel.
% 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.37/0.86 Prover 4: Preprocessing ...
% 1.37/0.87 Prover 1: Preprocessing ...
% 1.97/0.91 Prover 2: Preprocessing ...
% 1.97/0.91 Prover 6: Preprocessing ...
% 1.97/0.91 Prover 3: Preprocessing ...
% 1.97/0.91 Prover 0: Preprocessing ...
% 1.97/0.91 Prover 5: Preprocessing ...
% 3.15/1.09 Prover 3: Warning: ignoring some quantifiers
% 3.15/1.10 Prover 6: Proving ...
% 3.19/1.10 Prover 5: Proving ...
% 3.23/1.11 Prover 1: Warning: ignoring some quantifiers
% 3.23/1.11 Prover 3: Constructing countermodel ...
% 3.23/1.11 Prover 1: Constructing countermodel ...
% 3.23/1.12 Prover 4: Warning: ignoring some quantifiers
% 3.23/1.12 Prover 0: Proving ...
% 3.23/1.13 Prover 4: Constructing countermodel ...
% 3.23/1.14 Prover 2: Proving ...
% 3.92/1.28 Prover 3: proved (741ms)
% 3.92/1.28
% 3.92/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.29
% 3.92/1.29 Prover 0: proved (755ms)
% 3.92/1.29
% 3.92/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.29
% 3.92/1.29 Prover 5: stopped
% 3.92/1.29 Prover 6: stopped
% 3.92/1.29 Prover 2: proved (755ms)
% 3.92/1.29
% 3.92/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.29
% 4.59/1.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.59/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.59/1.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.59/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.59/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.59/1.32 Prover 13: Preprocessing ...
% 4.59/1.32 Prover 10: Preprocessing ...
% 4.59/1.33 Prover 7: Preprocessing ...
% 4.59/1.33 Prover 8: Preprocessing ...
% 4.59/1.34 Prover 11: Preprocessing ...
% 4.59/1.35 Prover 1: Found proof (size 19)
% 4.59/1.35 Prover 4: Found proof (size 20)
% 4.59/1.35 Prover 1: proved (810ms)
% 4.59/1.35 Prover 4: proved (805ms)
% 4.59/1.35 Prover 11: stopped
% 4.59/1.37 Prover 10: Warning: ignoring some quantifiers
% 4.59/1.37 Prover 7: Warning: ignoring some quantifiers
% 4.59/1.37 Prover 8: Warning: ignoring some quantifiers
% 4.59/1.38 Prover 10: Constructing countermodel ...
% 4.59/1.38 Prover 13: Warning: ignoring some quantifiers
% 4.59/1.38 Prover 7: Constructing countermodel ...
% 4.59/1.38 Prover 10: stopped
% 4.59/1.38 Prover 8: Constructing countermodel ...
% 4.59/1.38 Prover 7: stopped
% 4.59/1.38 Prover 13: Constructing countermodel ...
% 4.59/1.39 Prover 8: stopped
% 4.59/1.39 Prover 13: stopped
% 4.59/1.39
% 4.59/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.59/1.39
% 5.22/1.39 % SZS output start Proof for theBenchmark
% 5.22/1.39 Assumptions after simplification:
% 5.22/1.39 ---------------------------------
% 5.22/1.39
% 5.22/1.39 (commutativity_k2_tarski)
% 5.22/1.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 5.22/1.42 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 5.22/1.42
% 5.22/1.42 (commutativity_k3_xboole_0)
% 5.22/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 5.22/1.43 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 5.22/1.43
% 5.22/1.43 (d2_tarski)
% 5.22/1.43 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 5.22/1.43 (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 5.22/1.43 $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 =
% 5.22/1.43 v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0: $i]
% 5.22/1.43 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) |
% 5.22/1.43 ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3,
% 5.22/1.43 v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3: $i]
% 5.22/1.43 : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0) | ~ $i(v3))))
% 5.22/1.43
% 5.22/1.43 (l32_zfmisc_1)
% 5.22/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 5.22/1.44 (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v1) | ~
% 5.22/1.44 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 5.22/1.44
% 5.22/1.44 (t19_zfmisc_1)
% 5.22/1.44 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 5.22/1.44 = v2) & singleton(v0) = v2 & set_intersection2(v2, v3) = v4 &
% 5.22/1.44 unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.22/1.44
% 5.22/1.44 Further assumptions not needed in the proof:
% 5.22/1.44 --------------------------------------------
% 5.22/1.44 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 5.22/1.44
% 5.22/1.44 Those formulas are unsatisfiable:
% 5.22/1.44 ---------------------------------
% 5.22/1.44
% 5.22/1.44 Begin of proof
% 5.22/1.44 |
% 5.22/1.44 | ALPHA: (d2_tarski) implies:
% 5.22/1.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 5.22/1.44 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4:
% 5.22/1.44 | int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1)
% 5.22/1.44 | & ~ (v3 = v0))) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 5.22/1.44 | (in(v3, v2) = 0) | ~ $i(v3))))
% 5.22/1.44 |
% 5.22/1.44 | DELTA: instantiating (t19_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 5.22/1.44 | all_14_2, all_14_3, all_14_4 gives:
% 5.22/1.45 | (2) ~ (all_14_0 = all_14_2) & singleton(all_14_4) = all_14_2 &
% 5.22/1.45 | set_intersection2(all_14_2, all_14_1) = all_14_0 &
% 5.22/1.45 | unordered_pair(all_14_4, all_14_3) = all_14_1 & $i(all_14_0) &
% 5.22/1.45 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4)
% 5.22/1.45 |
% 5.22/1.45 | ALPHA: (2) implies:
% 5.22/1.45 | (3) ~ (all_14_0 = all_14_2)
% 5.22/1.45 | (4) $i(all_14_4)
% 5.22/1.45 | (5) $i(all_14_3)
% 5.22/1.45 | (6) $i(all_14_2)
% 5.22/1.45 | (7) unordered_pair(all_14_4, all_14_3) = all_14_1
% 5.22/1.45 | (8) set_intersection2(all_14_2, all_14_1) = all_14_0
% 5.22/1.45 | (9) singleton(all_14_4) = all_14_2
% 5.22/1.45 |
% 5.22/1.45 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_14_4, all_14_3,
% 5.22/1.45 | all_14_1, simplifying with (4), (5), (7) gives:
% 5.22/1.45 | (10) unordered_pair(all_14_3, all_14_4) = all_14_1 & $i(all_14_1)
% 5.22/1.45 |
% 5.22/1.45 | ALPHA: (10) implies:
% 5.22/1.45 | (11) $i(all_14_1)
% 5.22/1.45 | (12) unordered_pair(all_14_3, all_14_4) = all_14_1
% 5.22/1.45 |
% 5.22/1.45 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_2,
% 5.22/1.45 | all_14_1, all_14_0, simplifying with (6), (8), (11) gives:
% 5.22/1.45 | (13) set_intersection2(all_14_1, all_14_2) = all_14_0 & $i(all_14_0)
% 5.22/1.45 |
% 5.22/1.45 | ALPHA: (13) implies:
% 5.22/1.45 | (14) set_intersection2(all_14_1, all_14_2) = all_14_0
% 5.22/1.45 |
% 5.22/1.45 | GROUND_INST: instantiating (1) with all_14_3, all_14_4, all_14_1, simplifying
% 5.22/1.45 | with (4), (5), (11), (12) gives:
% 5.22/1.46 | (15) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_14_1) = v1) | ~
% 5.22/1.46 | $i(v0) | ( ~ (v0 = all_14_3) & ~ (v0 = all_14_4))) & ! [v0: any] :
% 5.22/1.46 | (v0 = all_14_3 | v0 = all_14_4 | ~ (in(v0, all_14_1) = 0) | ~
% 5.22/1.46 | $i(v0))
% 5.22/1.46 |
% 5.22/1.46 | ALPHA: (15) implies:
% 5.22/1.46 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_14_1) = v1) | ~
% 5.22/1.46 | $i(v0) | ( ~ (v0 = all_14_3) & ~ (v0 = all_14_4)))
% 5.22/1.46 |
% 5.22/1.46 | GROUND_INST: instantiating (l32_zfmisc_1) with all_14_4, all_14_1, all_14_2,
% 5.22/1.46 | all_14_0, simplifying with (4), (9), (11), (14) gives:
% 5.22/1.46 | (17) all_14_0 = all_14_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4,
% 5.22/1.46 | all_14_1) = v0)
% 5.22/1.46 |
% 5.22/1.46 | BETA: splitting (17) gives:
% 5.22/1.46 |
% 5.22/1.46 | Case 1:
% 5.22/1.46 | |
% 5.22/1.46 | | (18) all_14_0 = all_14_2
% 5.22/1.46 | |
% 5.22/1.46 | | REDUCE: (3), (18) imply:
% 5.22/1.46 | | (19) $false
% 5.22/1.46 | |
% 5.22/1.46 | | CLOSE: (19) is inconsistent.
% 5.22/1.46 | |
% 5.22/1.46 | Case 2:
% 5.22/1.46 | |
% 5.22/1.46 | | (20) ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, all_14_1) = v0)
% 5.22/1.46 | |
% 5.22/1.46 | | DELTA: instantiating (20) with fresh symbol all_39_0 gives:
% 5.22/1.46 | | (21) ~ (all_39_0 = 0) & in(all_14_4, all_14_1) = all_39_0
% 5.22/1.46 | |
% 5.22/1.46 | | ALPHA: (21) implies:
% 5.22/1.46 | | (22) ~ (all_39_0 = 0)
% 5.22/1.46 | | (23) in(all_14_4, all_14_1) = all_39_0
% 5.22/1.46 | |
% 5.22/1.46 | | GROUND_INST: instantiating (16) with all_14_4, all_39_0, simplifying with
% 5.22/1.46 | | (4), (23) gives:
% 5.22/1.46 | | (24) all_39_0 = 0
% 5.22/1.46 | |
% 5.22/1.46 | | REDUCE: (22), (24) imply:
% 5.22/1.46 | | (25) $false
% 5.22/1.46 | |
% 5.22/1.46 | | CLOSE: (25) is inconsistent.
% 5.22/1.46 | |
% 5.22/1.47 | End of split
% 5.22/1.47 |
% 5.22/1.47 End of proof
% 5.22/1.47 % SZS output end Proof for theBenchmark
% 5.22/1.47
% 5.22/1.47 946ms
%------------------------------------------------------------------------------