TSTP Solution File: SET891+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET891+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 : n013.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 15:26:56 EDT 2023
% Result : Theorem 3.82s 1.36s
% Output : Proof 5.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n013.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 12:51:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.92/0.97 Prover 4: Preprocessing ...
% 1.92/0.97 Prover 1: Preprocessing ...
% 2.42/1.02 Prover 6: Preprocessing ...
% 2.42/1.02 Prover 5: Preprocessing ...
% 2.42/1.02 Prover 3: Preprocessing ...
% 2.42/1.02 Prover 2: Preprocessing ...
% 2.42/1.02 Prover 0: Preprocessing ...
% 3.55/1.19 Prover 1: Warning: ignoring some quantifiers
% 3.55/1.20 Prover 3: Warning: ignoring some quantifiers
% 3.55/1.21 Prover 1: Constructing countermodel ...
% 3.55/1.21 Prover 4: Constructing countermodel ...
% 3.55/1.21 Prover 3: Constructing countermodel ...
% 3.55/1.21 Prover 6: Proving ...
% 3.73/1.22 Prover 5: Proving ...
% 3.82/1.25 Prover 2: Proving ...
% 3.82/1.25 Prover 0: Proving ...
% 3.82/1.36 Prover 0: proved (736ms)
% 3.82/1.36
% 3.82/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.82/1.36
% 3.82/1.36 Prover 5: proved (732ms)
% 3.82/1.36
% 3.82/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.82/1.36
% 3.82/1.36 Prover 3: stopped
% 3.82/1.37 Prover 2: stopped
% 3.82/1.37 Prover 6: stopped
% 3.82/1.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.82/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.82/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.82/1.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.82/1.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.82/1.39 Prover 7: Preprocessing ...
% 3.82/1.39 Prover 8: Preprocessing ...
% 4.72/1.42 Prover 10: Preprocessing ...
% 4.72/1.42 Prover 11: Preprocessing ...
% 4.72/1.43 Prover 13: Preprocessing ...
% 4.72/1.46 Prover 4: Found proof (size 19)
% 4.72/1.46 Prover 8: Warning: ignoring some quantifiers
% 4.72/1.47 Prover 10: Constructing countermodel ...
% 4.72/1.47 Prover 8: Constructing countermodel ...
% 4.72/1.47 Prover 4: proved (833ms)
% 4.72/1.47 Prover 1: stopped
% 4.72/1.47 Prover 10: stopped
% 4.72/1.48 Prover 8: stopped
% 5.40/1.48 Prover 11: Constructing countermodel ...
% 5.40/1.48 Prover 7: Constructing countermodel ...
% 5.40/1.49 Prover 11: stopped
% 5.40/1.49 Prover 7: stopped
% 5.40/1.50 Prover 13: Warning: ignoring some quantifiers
% 5.40/1.50 Prover 13: Constructing countermodel ...
% 5.40/1.51 Prover 13: stopped
% 5.40/1.51
% 5.40/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.40/1.51
% 5.40/1.51 % SZS output start Proof for theBenchmark
% 5.40/1.52 Assumptions after simplification:
% 5.40/1.52 ---------------------------------
% 5.40/1.52
% 5.40/1.52 (l52_zfmisc_1)
% 5.40/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 5.40/1.55 $i(v1) | ~ $i(v0) | ? [v3: $i] : (union(v3) = v2 & unordered_pair(v0, v1)
% 5.40/1.55 = v3 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 5.40/1.55 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 5.40/1.55 (union(v2) = v3 & set_union2(v0, v1) = v3 & $i(v3)))
% 5.40/1.55
% 5.40/1.55 (t32_zfmisc_1)
% 5.40/1.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.40/1.55 $i] : ? [v6: $i] : ( ~ (v6 = v5) & singleton(v1) = v3 & singleton(v0) = v2
% 5.40/1.55 & union(v4) = v5 & unordered_pair(v2, v3) = v4 & unordered_pair(v0, v1) = v6
% 5.40/1.55 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.40/1.55
% 5.40/1.55 (t41_enumset1)
% 5.40/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 5.40/1.56 (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v3) =
% 5.40/1.56 v4) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v4 & $i(v4))) & !
% 5.40/1.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~
% 5.40/1.56 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v1) = v4 &
% 5.40/1.56 singleton(v0) = v3 & set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2)))
% 5.40/1.56
% 5.40/1.56 (function-axioms)
% 5.40/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.40/1.56 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 5.40/1.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 5.40/1.56 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.40/1.56 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & !
% 5.40/1.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~
% 5.40/1.56 (union(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 5.40/1.56 : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.40/1.56
% 5.40/1.56 Further assumptions not needed in the proof:
% 5.40/1.56 --------------------------------------------
% 5.40/1.56 commutativity_k2_tarski, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 5.40/1.56 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0
% 5.40/1.56
% 5.40/1.56 Those formulas are unsatisfiable:
% 5.40/1.56 ---------------------------------
% 5.40/1.56
% 5.40/1.56 Begin of proof
% 5.85/1.57 |
% 5.85/1.57 | ALPHA: (l52_zfmisc_1) implies:
% 5.85/1.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 5.85/1.57 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (union(v2) = v3 &
% 5.85/1.57 | set_union2(v0, v1) = v3 & $i(v3)))
% 5.85/1.57 |
% 5.85/1.57 | ALPHA: (t41_enumset1) implies:
% 5.85/1.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 5.85/1.57 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 5.85/1.57 | (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2 &
% 5.85/1.57 | $i(v4) & $i(v3) & $i(v2)))
% 5.85/1.57 |
% 5.85/1.57 | ALPHA: (function-axioms) implies:
% 5.85/1.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) =
% 5.85/1.57 | v1) | ~ (union(v2) = v0))
% 5.85/1.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 5.85/1.57 | = v1) | ~ (singleton(v2) = v0))
% 5.85/1.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.85/1.57 | (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 5.85/1.57 |
% 5.85/1.58 | DELTA: instantiating (t32_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 5.85/1.58 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6 gives:
% 5.85/1.58 | (6) ~ (all_14_0 = all_14_1) & singleton(all_14_5) = all_14_3 &
% 5.85/1.58 | singleton(all_14_6) = all_14_4 & union(all_14_2) = all_14_1 &
% 5.85/1.58 | unordered_pair(all_14_4, all_14_3) = all_14_2 &
% 5.85/1.58 | unordered_pair(all_14_6, all_14_5) = all_14_0 & $i(all_14_0) &
% 5.85/1.58 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) &
% 5.85/1.58 | $i(all_14_5) & $i(all_14_6)
% 5.85/1.58 |
% 5.85/1.58 | ALPHA: (6) implies:
% 5.85/1.58 | (7) ~ (all_14_0 = all_14_1)
% 5.85/1.58 | (8) $i(all_14_6)
% 5.85/1.58 | (9) $i(all_14_5)
% 5.85/1.58 | (10) $i(all_14_4)
% 5.85/1.58 | (11) $i(all_14_3)
% 5.85/1.58 | (12) unordered_pair(all_14_6, all_14_5) = all_14_0
% 5.85/1.58 | (13) unordered_pair(all_14_4, all_14_3) = all_14_2
% 5.85/1.58 | (14) union(all_14_2) = all_14_1
% 5.85/1.58 | (15) singleton(all_14_6) = all_14_4
% 5.85/1.58 | (16) singleton(all_14_5) = all_14_3
% 5.85/1.58 |
% 5.94/1.58 | GROUND_INST: instantiating (2) with all_14_6, all_14_5, all_14_0, simplifying
% 5.94/1.58 | with (8), (9), (12) gives:
% 5.94/1.58 | (17) ? [v0: $i] : ? [v1: $i] : (singleton(all_14_5) = v1 &
% 5.94/1.58 | singleton(all_14_6) = v0 & set_union2(v0, v1) = all_14_0 & $i(v1) &
% 5.94/1.58 | $i(v0) & $i(all_14_0))
% 5.94/1.58 |
% 5.94/1.58 | GROUND_INST: instantiating (1) with all_14_4, all_14_3, all_14_2, simplifying
% 5.94/1.58 | with (10), (11), (13) gives:
% 5.94/1.59 | (18) ? [v0: $i] : (union(all_14_2) = v0 & set_union2(all_14_4, all_14_3) =
% 5.94/1.59 | v0 & $i(v0))
% 5.94/1.59 |
% 5.94/1.59 | DELTA: instantiating (18) with fresh symbol all_22_0 gives:
% 5.94/1.59 | (19) union(all_14_2) = all_22_0 & set_union2(all_14_4, all_14_3) = all_22_0
% 5.94/1.59 | & $i(all_22_0)
% 5.94/1.59 |
% 5.94/1.59 | ALPHA: (19) implies:
% 5.94/1.59 | (20) set_union2(all_14_4, all_14_3) = all_22_0
% 5.94/1.59 | (21) union(all_14_2) = all_22_0
% 5.94/1.59 |
% 5.94/1.59 | DELTA: instantiating (17) with fresh symbols all_28_0, all_28_1 gives:
% 5.94/1.59 | (22) singleton(all_14_5) = all_28_0 & singleton(all_14_6) = all_28_1 &
% 5.94/1.59 | set_union2(all_28_1, all_28_0) = all_14_0 & $i(all_28_0) &
% 5.94/1.59 | $i(all_28_1) & $i(all_14_0)
% 5.94/1.59 |
% 5.94/1.59 | ALPHA: (22) implies:
% 5.94/1.59 | (23) set_union2(all_28_1, all_28_0) = all_14_0
% 5.94/1.59 | (24) singleton(all_14_6) = all_28_1
% 5.94/1.59 | (25) singleton(all_14_5) = all_28_0
% 5.94/1.59 |
% 5.94/1.59 | GROUND_INST: instantiating (3) with all_14_1, all_22_0, all_14_2, simplifying
% 5.94/1.59 | with (14), (21) gives:
% 5.94/1.59 | (26) all_22_0 = all_14_1
% 5.94/1.59 |
% 5.94/1.59 | GROUND_INST: instantiating (4) with all_14_4, all_28_1, all_14_6, simplifying
% 5.94/1.59 | with (15), (24) gives:
% 5.94/1.59 | (27) all_28_1 = all_14_4
% 5.94/1.59 |
% 5.94/1.59 | GROUND_INST: instantiating (4) with all_14_3, all_28_0, all_14_5, simplifying
% 5.94/1.59 | with (16), (25) gives:
% 5.94/1.59 | (28) all_28_0 = all_14_3
% 5.94/1.59 |
% 5.94/1.59 | REDUCE: (23), (27), (28) imply:
% 5.94/1.59 | (29) set_union2(all_14_4, all_14_3) = all_14_0
% 5.94/1.59 |
% 5.94/1.59 | REDUCE: (20), (26) imply:
% 5.94/1.59 | (30) set_union2(all_14_4, all_14_3) = all_14_1
% 5.94/1.59 |
% 5.94/1.59 | GROUND_INST: instantiating (5) with all_14_1, all_14_0, all_14_3, all_14_4,
% 5.94/1.59 | simplifying with (29), (30) gives:
% 5.94/1.59 | (31) all_14_0 = all_14_1
% 5.94/1.59 |
% 5.94/1.59 | REDUCE: (7), (31) imply:
% 5.94/1.59 | (32) $false
% 5.94/1.59 |
% 5.94/1.59 | CLOSE: (32) is inconsistent.
% 5.94/1.59 |
% 5.94/1.59 End of proof
% 5.94/1.59 % SZS output end Proof for theBenchmark
% 5.94/1.59
% 5.94/1.59 990ms
%------------------------------------------------------------------------------