TSTP Solution File: SET877+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET877+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 : n017.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 15:26:52 EDT 2023
% Result : Theorem 4.75s 1.38s
% Output : Proof 5.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n017.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:07:56 EDT 2023
% 0.13/0.35 % 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/sandbox/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 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 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 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 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
% 2.16/1.02 Prover 4: Preprocessing ...
% 2.16/1.02 Prover 1: Preprocessing ...
% 2.55/1.07 Prover 5: Preprocessing ...
% 2.55/1.07 Prover 6: Preprocessing ...
% 2.55/1.07 Prover 3: Preprocessing ...
% 2.55/1.07 Prover 2: Preprocessing ...
% 2.55/1.07 Prover 0: Preprocessing ...
% 3.47/1.21 Prover 1: Warning: ignoring some quantifiers
% 3.47/1.23 Prover 6: Proving ...
% 3.47/1.23 Prover 3: Warning: ignoring some quantifiers
% 3.47/1.23 Prover 0: Proving ...
% 3.47/1.23 Prover 1: Constructing countermodel ...
% 3.47/1.23 Prover 4: Warning: ignoring some quantifiers
% 3.47/1.24 Prover 3: Constructing countermodel ...
% 3.47/1.24 Prover 5: Proving ...
% 3.47/1.24 Prover 4: Constructing countermodel ...
% 3.47/1.28 Prover 2: Proving ...
% 4.75/1.38 Prover 3: proved (748ms)
% 4.75/1.38
% 4.75/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.38
% 4.75/1.38 Prover 0: stopped
% 4.75/1.38 Prover 6: stopped
% 4.75/1.40 Prover 2: stopped
% 4.75/1.40 Prover 5: stopped
% 4.75/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.75/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.75/1.40 Prover 7: Preprocessing ...
% 4.75/1.40 Prover 4: Found proof (size 10)
% 4.75/1.40 Prover 4: proved (768ms)
% 4.75/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.75/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.75/1.40 Prover 8: Preprocessing ...
% 4.75/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.75/1.40 Prover 1: stopped
% 4.75/1.41 Prover 7: stopped
% 4.75/1.42 Prover 11: Preprocessing ...
% 4.75/1.42 Prover 10: Preprocessing ...
% 4.75/1.42 Prover 13: Preprocessing ...
% 4.75/1.43 Prover 10: stopped
% 4.75/1.43 Prover 11: stopped
% 4.75/1.44 Prover 13: stopped
% 4.75/1.45 Prover 8: Warning: ignoring some quantifiers
% 4.75/1.45 Prover 8: Constructing countermodel ...
% 4.75/1.46 Prover 8: stopped
% 4.75/1.46
% 4.75/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.46
% 4.75/1.46 % SZS output start Proof for theBenchmark
% 5.37/1.46 Assumptions after simplification:
% 5.37/1.46 ---------------------------------
% 5.37/1.46
% 5.37/1.46 (commutativity_k3_xboole_0)
% 5.49/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 5.49/1.50 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 5.49/1.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 5.49/1.50 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 5.49/1.50
% 5.49/1.50 (d1_tarski)
% 5.49/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 5.49/1.50 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 5.49/1.50 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) =
% 5.49/1.50 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.49/1.50 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 5.49/1.50 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 =
% 5.49/1.50 0 | v3 = v1)))
% 5.49/1.50
% 5.49/1.50 (l30_zfmisc_1)
% 5.49/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, v0) = v2) | ~
% 5.49/1.51 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) &
% 5.49/1.51 singleton(v1) = v3 & set_intersection2(v0, v3) = v4 & $i(v4) & $i(v3))) &
% 5.49/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v1) = v2) | ~
% 5.49/1.51 (set_intersection2(v0, v2) = v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v0) = 0)
% 5.49/1.51
% 5.49/1.51 (t18_zfmisc_1)
% 5.49/1.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) &
% 5.49/1.51 singleton(v1) = v3 & singleton(v0) = v2 & set_intersection2(v2, v3) = v2 &
% 5.49/1.51 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.49/1.51
% 5.49/1.51 Further assumptions not needed in the proof:
% 5.49/1.51 --------------------------------------------
% 5.49/1.51 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 5.49/1.51
% 5.49/1.51 Those formulas are unsatisfiable:
% 5.49/1.51 ---------------------------------
% 5.49/1.51
% 5.49/1.51 Begin of proof
% 5.49/1.51 |
% 5.49/1.51 | ALPHA: (commutativity_k3_xboole_0) implies:
% 5.49/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 5.49/1.51 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 5.49/1.51 | v2 & $i(v2)))
% 5.49/1.51 |
% 5.49/1.51 | ALPHA: (d1_tarski) implies:
% 5.49/1.51 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 5.49/1.51 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 5.49/1.51 |
% 5.49/1.51 | ALPHA: (l30_zfmisc_1) implies:
% 5.49/1.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v1) = v2) | ~
% 5.49/1.52 | (set_intersection2(v0, v2) = v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v0)
% 5.49/1.52 | = 0)
% 5.49/1.52 |
% 5.49/1.52 | DELTA: instantiating (t18_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 5.49/1.52 | all_12_2, all_12_3 gives:
% 5.49/1.52 | (4) ~ (all_12_2 = all_12_3) & singleton(all_12_2) = all_12_0 &
% 5.49/1.52 | singleton(all_12_3) = all_12_1 & set_intersection2(all_12_1, all_12_0)
% 5.49/1.52 | = all_12_1 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & $i(all_12_3)
% 5.49/1.52 |
% 5.49/1.52 | ALPHA: (4) implies:
% 5.49/1.52 | (5) ~ (all_12_2 = all_12_3)
% 5.49/1.52 | (6) $i(all_12_3)
% 5.49/1.52 | (7) $i(all_12_2)
% 5.49/1.52 | (8) $i(all_12_1)
% 5.49/1.52 | (9) $i(all_12_0)
% 5.49/1.52 | (10) set_intersection2(all_12_1, all_12_0) = all_12_1
% 5.49/1.52 | (11) singleton(all_12_3) = all_12_1
% 5.49/1.52 | (12) singleton(all_12_2) = all_12_0
% 5.49/1.52 |
% 5.49/1.52 | GROUND_INST: instantiating (1) with all_12_0, all_12_1, all_12_1, simplifying
% 5.49/1.52 | with (8), (9), (10) gives:
% 5.49/1.52 | (13) set_intersection2(all_12_0, all_12_1) = all_12_1
% 5.49/1.52 |
% 5.66/1.52 | GROUND_INST: instantiating (3) with all_12_0, all_12_3, all_12_1, simplifying
% 5.66/1.52 | with (6), (9), (11), (13) gives:
% 5.66/1.52 | (14) in(all_12_3, all_12_0) = 0
% 5.66/1.52 |
% 5.66/1.53 | GROUND_INST: instantiating (2) with all_12_2, all_12_0, all_12_3, simplifying
% 5.66/1.53 | with (6), (7), (9), (12), (14) gives:
% 5.66/1.53 | (15) all_12_2 = all_12_3
% 5.66/1.53 |
% 5.66/1.53 | REDUCE: (5), (15) imply:
% 5.66/1.53 | (16) $false
% 5.66/1.53 |
% 5.66/1.53 | CLOSE: (16) is inconsistent.
% 5.66/1.53 |
% 5.66/1.53 End of proof
% 5.66/1.53 % SZS output end Proof for theBenchmark
% 5.66/1.53
% 5.66/1.53 917ms
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