TSTP Solution File: SET917+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET917+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 : n027.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 15:27:02 EDT 2023
% Result : Theorem 3.85s 1.39s
% Output : Proof 5.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET917+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n027.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 : Sat Aug 26 12:36:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.67 ________ _____
% 0.21/0.67 ___ __ \_________(_)________________________________
% 0.21/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.67
% 0.21/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.67 (2023-06-19)
% 0.21/0.67
% 0.21/0.67 (c) Philipp Rümmer, 2009-2023
% 0.21/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.67 Amanda Stjerna.
% 0.21/0.67 Free software under BSD-3-Clause.
% 0.21/0.67
% 0.21/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.67
% 0.21/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.69 Running up to 7 provers in parallel.
% 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.94/1.08 Prover 1: Preprocessing ...
% 1.94/1.08 Prover 4: Preprocessing ...
% 2.51/1.12 Prover 3: Preprocessing ...
% 2.51/1.12 Prover 0: Preprocessing ...
% 2.51/1.12 Prover 5: Preprocessing ...
% 2.51/1.12 Prover 2: Preprocessing ...
% 2.51/1.12 Prover 6: Preprocessing ...
% 3.02/1.25 Prover 1: Warning: ignoring some quantifiers
% 3.02/1.26 Prover 6: Proving ...
% 3.02/1.26 Prover 1: Constructing countermodel ...
% 3.02/1.27 Prover 5: Proving ...
% 3.02/1.27 Prover 3: Warning: ignoring some quantifiers
% 3.02/1.27 Prover 2: Proving ...
% 3.72/1.28 Prover 3: Constructing countermodel ...
% 3.85/1.30 Prover 4: Constructing countermodel ...
% 3.85/1.30 Prover 0: Proving ...
% 3.85/1.39 Prover 3: proved (690ms)
% 3.85/1.39
% 3.85/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.85/1.39
% 3.85/1.40 Prover 2: stopped
% 3.85/1.40 Prover 0: stopped
% 3.85/1.40 Prover 6: stopped
% 3.85/1.42 Prover 5: stopped
% 3.85/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.85/1.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.85/1.44 Prover 8: Preprocessing ...
% 3.85/1.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.85/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.85/1.44 Prover 10: Preprocessing ...
% 4.75/1.44 Prover 1: Found proof (size 18)
% 4.75/1.44 Prover 11: Preprocessing ...
% 4.75/1.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.75/1.44 Prover 7: Preprocessing ...
% 4.75/1.45 Prover 1: proved (754ms)
% 4.75/1.45 Prover 13: Preprocessing ...
% 4.75/1.45 Prover 4: stopped
% 4.92/1.45 Prover 11: stopped
% 4.92/1.46 Prover 10: Warning: ignoring some quantifiers
% 4.92/1.46 Prover 13: stopped
% 4.92/1.47 Prover 10: Constructing countermodel ...
% 4.92/1.47 Prover 7: Warning: ignoring some quantifiers
% 4.92/1.47 Prover 10: stopped
% 4.92/1.47 Prover 7: Constructing countermodel ...
% 4.92/1.47 Prover 7: stopped
% 4.92/1.47 Prover 8: Warning: ignoring some quantifiers
% 4.92/1.48 Prover 8: Constructing countermodel ...
% 4.92/1.49 Prover 8: stopped
% 4.92/1.49
% 4.92/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.49
% 4.92/1.49 % SZS output start Proof for theBenchmark
% 4.92/1.49 Assumptions after simplification:
% 4.92/1.49 ---------------------------------
% 4.92/1.49
% 4.92/1.49 (commutativity_k3_xboole_0)
% 4.92/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 4.92/1.52 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 4.92/1.52
% 4.92/1.52 (l28_zfmisc_1)
% 4.92/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.92/1.52 (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) |
% 4.92/1.52 in(v0, v1) = 0)
% 4.92/1.52
% 4.92/1.52 (l32_zfmisc_1)
% 4.92/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 4.92/1.53 (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v1) | ~
% 4.92/1.53 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.92/1.53
% 4.92/1.53 (t58_zfmisc_1)
% 5.38/1.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ( ~ (v4
% 5.38/1.53 = v2) & ~ (v3 = 0) & singleton(v0) = v2 & disjoint(v2, v1) = v3 &
% 5.38/1.53 set_intersection2(v2, v1) = v4 & $i(v4) & $i(v2) & $i(v1) & $i(v0))
% 5.38/1.53
% 5.38/1.53 (function-axioms)
% 5.38/1.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.38/1.53 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 5.38/1.53 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.38/1.53 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 5.38/1.53 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 5.38/1.53 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 5.38/1.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 5.38/1.53 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.38/1.54 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.38/1.54
% 5.38/1.54 Further assumptions not needed in the proof:
% 5.38/1.54 --------------------------------------------
% 5.38/1.54 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 5.38/1.54 symmetry_r1_xboole_0
% 5.38/1.54
% 5.38/1.54 Those formulas are unsatisfiable:
% 5.38/1.54 ---------------------------------
% 5.38/1.54
% 5.38/1.54 Begin of proof
% 5.38/1.54 |
% 5.38/1.54 | ALPHA: (function-axioms) implies:
% 5.38/1.54 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.38/1.54 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.38/1.54 |
% 5.38/1.54 | DELTA: instantiating (t58_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 5.38/1.54 | all_14_2, all_14_3, all_14_4 gives:
% 5.38/1.54 | (2) ~ (all_14_0 = all_14_2) & ~ (all_14_1 = 0) & singleton(all_14_4) =
% 5.38/1.54 | all_14_2 & disjoint(all_14_2, all_14_3) = all_14_1 &
% 5.38/1.54 | set_intersection2(all_14_2, all_14_3) = all_14_0 & $i(all_14_0) &
% 5.38/1.54 | $i(all_14_2) & $i(all_14_3) & $i(all_14_4)
% 5.38/1.54 |
% 5.38/1.54 | ALPHA: (2) implies:
% 5.38/1.54 | (3) ~ (all_14_1 = 0)
% 5.38/1.54 | (4) ~ (all_14_0 = all_14_2)
% 5.38/1.54 | (5) $i(all_14_4)
% 5.38/1.54 | (6) $i(all_14_3)
% 5.38/1.54 | (7) $i(all_14_2)
% 5.38/1.54 | (8) set_intersection2(all_14_2, all_14_3) = all_14_0
% 5.38/1.54 | (9) disjoint(all_14_2, all_14_3) = all_14_1
% 5.38/1.54 | (10) singleton(all_14_4) = all_14_2
% 5.38/1.54 |
% 5.38/1.55 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_2,
% 5.38/1.55 | all_14_3, all_14_0, simplifying with (6), (7), (8) gives:
% 5.38/1.55 | (11) set_intersection2(all_14_3, all_14_2) = all_14_0 & $i(all_14_0)
% 5.38/1.55 |
% 5.38/1.55 | ALPHA: (11) implies:
% 5.38/1.55 | (12) set_intersection2(all_14_3, all_14_2) = all_14_0
% 5.38/1.55 |
% 5.38/1.55 | GROUND_INST: instantiating (l28_zfmisc_1) with all_14_4, all_14_3, all_14_2,
% 5.38/1.55 | all_14_1, simplifying with (5), (6), (9), (10) gives:
% 5.38/1.55 | (13) all_14_1 = 0 | in(all_14_4, all_14_3) = 0
% 5.38/1.55 |
% 5.38/1.55 | BETA: splitting (13) gives:
% 5.38/1.55 |
% 5.38/1.55 | Case 1:
% 5.38/1.55 | |
% 5.38/1.55 | | (14) in(all_14_4, all_14_3) = 0
% 5.38/1.55 | |
% 5.38/1.55 | | GROUND_INST: instantiating (l32_zfmisc_1) with all_14_4, all_14_3, all_14_2,
% 5.38/1.55 | | all_14_0, simplifying with (5), (6), (10), (12) gives:
% 5.38/1.55 | | (15) all_14_0 = all_14_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4,
% 5.38/1.55 | | all_14_3) = v0)
% 5.38/1.55 | |
% 5.38/1.55 | | BETA: splitting (15) gives:
% 5.38/1.55 | |
% 5.38/1.55 | | Case 1:
% 5.38/1.55 | | |
% 5.38/1.55 | | | (16) all_14_0 = all_14_2
% 5.38/1.55 | | |
% 5.38/1.55 | | | REDUCE: (4), (16) imply:
% 5.38/1.55 | | | (17) $false
% 5.38/1.55 | | |
% 5.38/1.55 | | | CLOSE: (17) is inconsistent.
% 5.38/1.55 | | |
% 5.38/1.55 | | Case 2:
% 5.38/1.55 | | |
% 5.38/1.55 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, all_14_3) = v0)
% 5.38/1.55 | | |
% 5.38/1.55 | | | DELTA: instantiating (18) with fresh symbol all_37_0 gives:
% 5.38/1.55 | | | (19) ~ (all_37_0 = 0) & in(all_14_4, all_14_3) = all_37_0
% 5.38/1.55 | | |
% 5.38/1.55 | | | ALPHA: (19) implies:
% 5.38/1.55 | | | (20) ~ (all_37_0 = 0)
% 5.38/1.55 | | | (21) in(all_14_4, all_14_3) = all_37_0
% 5.38/1.55 | | |
% 5.38/1.55 | | | GROUND_INST: instantiating (1) with 0, all_37_0, all_14_3, all_14_4,
% 5.38/1.55 | | | simplifying with (14), (21) gives:
% 5.38/1.55 | | | (22) all_37_0 = 0
% 5.38/1.55 | | |
% 5.38/1.55 | | | REDUCE: (20), (22) imply:
% 5.38/1.55 | | | (23) $false
% 5.38/1.55 | | |
% 5.38/1.55 | | | CLOSE: (23) is inconsistent.
% 5.38/1.55 | | |
% 5.38/1.55 | | End of split
% 5.38/1.55 | |
% 5.38/1.55 | Case 2:
% 5.38/1.55 | |
% 5.38/1.55 | | (24) all_14_1 = 0
% 5.38/1.55 | |
% 5.38/1.55 | | REDUCE: (3), (24) imply:
% 5.38/1.55 | | (25) $false
% 5.38/1.55 | |
% 5.38/1.55 | | CLOSE: (25) is inconsistent.
% 5.38/1.55 | |
% 5.38/1.55 | End of split
% 5.38/1.55 |
% 5.38/1.55 End of proof
% 5.38/1.55 % SZS output end Proof for theBenchmark
% 5.38/1.55
% 5.38/1.55 880ms
%------------------------------------------------------------------------------