TSTP Solution File: SET904+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET904+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 : n019.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 15:26:58 EDT 2023
% Result : Theorem 4.53s 1.31s
% Output : Proof 4.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 11:19:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.91/0.98 Prover 4: Preprocessing ...
% 1.91/0.99 Prover 1: Preprocessing ...
% 2.40/1.03 Prover 0: Preprocessing ...
% 2.40/1.03 Prover 3: Preprocessing ...
% 2.40/1.03 Prover 6: Preprocessing ...
% 2.40/1.03 Prover 2: Preprocessing ...
% 2.40/1.03 Prover 5: Preprocessing ...
% 3.62/1.19 Prover 1: Warning: ignoring some quantifiers
% 3.62/1.19 Prover 3: Warning: ignoring some quantifiers
% 3.62/1.20 Prover 6: Proving ...
% 3.62/1.20 Prover 5: Proving ...
% 3.62/1.21 Prover 4: Constructing countermodel ...
% 3.62/1.21 Prover 2: Proving ...
% 3.62/1.21 Prover 1: Constructing countermodel ...
% 3.62/1.21 Prover 3: Constructing countermodel ...
% 3.62/1.21 Prover 0: Proving ...
% 4.04/1.31 Prover 5: proved (683ms)
% 4.53/1.31
% 4.53/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.53/1.31
% 4.53/1.31 Prover 3: stopped
% 4.53/1.31 Prover 2: stopped
% 4.53/1.31 Prover 0: stopped
% 4.53/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.53/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.53/1.32 Prover 6: stopped
% 4.53/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.53/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.53/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.53/1.34 Prover 8: Preprocessing ...
% 4.53/1.34 Prover 11: Preprocessing ...
% 4.53/1.35 Prover 7: Preprocessing ...
% 4.53/1.35 Prover 10: Preprocessing ...
% 4.53/1.36 Prover 13: Preprocessing ...
% 4.92/1.39 Prover 7: Warning: ignoring some quantifiers
% 4.92/1.39 Prover 1: Found proof (size 7)
% 4.92/1.39 Prover 1: proved (769ms)
% 4.92/1.39 Prover 7: Constructing countermodel ...
% 4.92/1.39 Prover 13: stopped
% 4.92/1.39 Prover 7: stopped
% 4.92/1.39 Prover 8: Warning: ignoring some quantifiers
% 4.92/1.40 Prover 4: stopped
% 4.92/1.40 Prover 8: Constructing countermodel ...
% 4.92/1.40 Prover 10: Warning: ignoring some quantifiers
% 4.92/1.40 Prover 8: stopped
% 4.92/1.41 Prover 10: Constructing countermodel ...
% 4.92/1.41 Prover 10: stopped
% 4.92/1.41 Prover 11: Constructing countermodel ...
% 4.92/1.42 Prover 11: stopped
% 4.92/1.42
% 4.92/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.42
% 4.92/1.42 % SZS output start Proof for theBenchmark
% 4.92/1.43 Assumptions after simplification:
% 4.92/1.43 ---------------------------------
% 4.92/1.43
% 4.92/1.43 (l21_zfmisc_1)
% 4.92/1.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v0) =
% 4.92/1.46 v2) | ~ (subset(v3, v1) = 0) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) |
% 4.92/1.46 ~ $i(v0) | in(v0, v1) = 0)
% 4.92/1.46
% 4.92/1.46 (t45_zfmisc_1)
% 4.92/1.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 4.92/1.46 = 0) & singleton(v0) = v2 & in(v0, v1) = v4 & subset(v3, v1) = 0 &
% 4.92/1.46 set_union2(v2, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 4.92/1.46
% 4.92/1.46 (function-axioms)
% 4.92/1.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.92/1.47 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.92/1.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.92/1.47 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 4.92/1.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.92/1.47 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 4.92/1.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 4.92/1.47 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.92/1.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 4.92/1.47 (empty(v2) = v0))
% 4.92/1.47
% 4.92/1.47 Further assumptions not needed in the proof:
% 4.92/1.47 --------------------------------------------
% 4.92/1.47 antisymmetry_r2_hidden, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 4.92/1.47 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 4.92/1.47
% 4.92/1.47 Those formulas are unsatisfiable:
% 4.92/1.47 ---------------------------------
% 4.92/1.47
% 4.92/1.47 Begin of proof
% 4.92/1.47 |
% 4.92/1.47 | ALPHA: (function-axioms) implies:
% 4.92/1.47 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.92/1.47 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.92/1.47 |
% 4.92/1.47 | DELTA: instantiating (t45_zfmisc_1) with fresh symbols all_16_0, all_16_1,
% 4.92/1.47 | all_16_2, all_16_3, all_16_4 gives:
% 4.92/1.47 | (2) ~ (all_16_0 = 0) & singleton(all_16_4) = all_16_2 & in(all_16_4,
% 4.92/1.47 | all_16_3) = all_16_0 & subset(all_16_1, all_16_3) = 0 &
% 4.92/1.47 | set_union2(all_16_2, all_16_3) = all_16_1 & $i(all_16_1) & $i(all_16_2)
% 4.92/1.47 | & $i(all_16_3) & $i(all_16_4)
% 4.92/1.47 |
% 4.92/1.47 | ALPHA: (2) implies:
% 4.92/1.48 | (3) ~ (all_16_0 = 0)
% 4.92/1.48 | (4) $i(all_16_4)
% 4.92/1.48 | (5) $i(all_16_3)
% 4.92/1.48 | (6) set_union2(all_16_2, all_16_3) = all_16_1
% 4.92/1.48 | (7) subset(all_16_1, all_16_3) = 0
% 4.92/1.48 | (8) in(all_16_4, all_16_3) = all_16_0
% 4.92/1.48 | (9) singleton(all_16_4) = all_16_2
% 4.92/1.48 |
% 4.92/1.48 | GROUND_INST: instantiating (l21_zfmisc_1) with all_16_4, all_16_3, all_16_2,
% 4.92/1.48 | all_16_1, simplifying with (4), (5), (6), (7), (9) gives:
% 4.92/1.48 | (10) in(all_16_4, all_16_3) = 0
% 4.92/1.48 |
% 4.92/1.48 | GROUND_INST: instantiating (1) with all_16_0, 0, all_16_3, all_16_4,
% 4.92/1.48 | simplifying with (8), (10) gives:
% 4.92/1.48 | (11) all_16_0 = 0
% 4.92/1.48 |
% 4.92/1.48 | REDUCE: (3), (11) imply:
% 4.92/1.48 | (12) $false
% 4.92/1.48 |
% 4.92/1.48 | CLOSE: (12) is inconsistent.
% 4.92/1.48 |
% 4.92/1.48 End of proof
% 4.92/1.48 % SZS output end Proof for theBenchmark
% 4.92/1.48
% 4.92/1.48 879ms
%------------------------------------------------------------------------------