TSTP Solution File: SEU118+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU118+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 : n005.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 17:42:34 EDT 2023
% Result : Theorem 8.47s 1.91s
% Output : Proof 11.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 12:57:39 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.88/1.09 Prover 4: Preprocessing ...
% 2.88/1.09 Prover 1: Preprocessing ...
% 2.88/1.13 Prover 2: Preprocessing ...
% 2.88/1.13 Prover 3: Preprocessing ...
% 2.88/1.13 Prover 6: Preprocessing ...
% 2.88/1.13 Prover 0: Preprocessing ...
% 2.88/1.14 Prover 5: Preprocessing ...
% 5.05/1.51 Prover 2: Proving ...
% 5.05/1.51 Prover 5: Proving ...
% 5.05/1.55 Prover 1: Warning: ignoring some quantifiers
% 5.05/1.61 Prover 1: Constructing countermodel ...
% 6.52/1.63 Prover 6: Proving ...
% 6.63/1.65 Prover 3: Warning: ignoring some quantifiers
% 6.79/1.68 Prover 3: Constructing countermodel ...
% 6.79/1.71 Prover 4: Warning: ignoring some quantifiers
% 7.28/1.72 Prover 0: Proving ...
% 7.28/1.74 Prover 4: Constructing countermodel ...
% 8.47/1.91 Prover 5: proved (1300ms)
% 8.47/1.91
% 8.47/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.47/1.91
% 8.47/1.92 Prover 2: stopped
% 8.47/1.92 Prover 0: stopped
% 8.47/1.92 Prover 6: stopped
% 8.47/1.92 Prover 3: stopped
% 8.47/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.47/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.47/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.47/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.92/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.06/1.98 Prover 13: Preprocessing ...
% 9.06/2.02 Prover 10: Preprocessing ...
% 9.43/2.02 Prover 11: Preprocessing ...
% 9.43/2.02 Prover 7: Preprocessing ...
% 9.43/2.03 Prover 8: Preprocessing ...
% 9.75/2.09 Prover 13: Warning: ignoring some quantifiers
% 9.75/2.10 Prover 10: Warning: ignoring some quantifiers
% 9.75/2.10 Prover 13: Constructing countermodel ...
% 9.75/2.12 Prover 10: Constructing countermodel ...
% 9.75/2.13 Prover 7: Warning: ignoring some quantifiers
% 9.75/2.14 Prover 7: Constructing countermodel ...
% 9.75/2.17 Prover 8: Warning: ignoring some quantifiers
% 9.75/2.20 Prover 8: Constructing countermodel ...
% 9.75/2.26 Prover 11: Warning: ignoring some quantifiers
% 9.75/2.27 Prover 11: Constructing countermodel ...
% 9.75/2.30 Prover 13: Found proof (size 11)
% 11.35/2.30 Prover 13: proved (377ms)
% 11.35/2.30 Prover 7: stopped
% 11.35/2.30 Prover 8: stopped
% 11.35/2.30 Prover 11: stopped
% 11.35/2.30 Prover 10: stopped
% 11.35/2.30 Prover 4: stopped
% 11.35/2.30 Prover 1: stopped
% 11.35/2.30
% 11.35/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.35/2.30
% 11.35/2.31 % SZS output start Proof for theBenchmark
% 11.35/2.31 Assumptions after simplification:
% 11.35/2.31 ---------------------------------
% 11.35/2.31
% 11.35/2.31 (cc2_finset_1)
% 11.35/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v2)
% 11.35/2.33 | ~ $i(v0) | ~ element(v2, v1) | ~ finite(v0) | finite(v2))
% 11.35/2.33
% 11.35/2.33 (d5_finsub_1)
% 11.64/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (finite_subsets(v0) =
% 11.64/2.34 v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ? [v3: $i] : ($i(v3) &
% 11.64/2.34 ( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (in(v3, v1) |
% 11.64/2.34 (subset(v3, v0) & finite(v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.64/2.34 $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 11.64/2.34 subset(v2, v0) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1)) & ! [v0:
% 11.64/2.34 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v2)
% 11.64/2.34 | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2,
% 11.64/2.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) =
% 11.64/2.34 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ~ in(v2,
% 11.64/2.34 v1) | finite(v2))
% 11.64/2.34
% 11.64/2.34 (fc2_finsub_1)
% 11.64/2.34 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ~
% 11.64/2.34 empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~
% 11.64/2.34 $i(v0) | diff_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.64/2.34 (finite_subsets(v0) = v1) | ~ $i(v0) | cup_closed(v1)) & ! [v0: $i] : !
% 11.64/2.34 [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | preboolean(v1)) & ?
% 11.64/2.34 [v0: $i] : ( ~ $i(v0) | ? [v1: $i] : (finite_subsets(v0) = v1 & $i(v1) &
% 11.64/2.34 preboolean(v1)))
% 11.64/2.34
% 11.64/2.34 (t1_subset)
% 11.64/2.34 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v0, v1) |
% 11.64/2.34 element(v0, v1))
% 11.64/2.34
% 11.64/2.34 (t34_finsub_1)
% 11.64/2.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (finite_subsets(v0) =
% 11.64/2.35 v3 & powerset(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v1, v2)
% 11.64/2.35 & finite(v0) & ~ element(v1, v3))
% 11.64/2.35
% 11.64/2.35 (t3_subset)
% 11.64/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1)
% 11.64/2.35 | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0: $i] : ! [v1:
% 11.64/2.35 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 11.64/2.35 element(v0, v2) | subset(v0, v1))
% 11.64/2.35
% 11.64/2.35 Further assumptions not needed in the proof:
% 11.64/2.35 --------------------------------------------
% 11.64/2.35 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finsub_1, cc3_finsub_1,
% 11.64/2.35 dt_k5_finsub_1, existence_m1_subset_1, fc1_finsub_1, fc1_subset_1, fc1_xboole_0,
% 11.64/2.35 rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0, rc2_finset_1,
% 11.64/2.35 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc4_finset_1, reflexivity_r1_tarski,
% 11.64/2.35 t13_finset_1, t2_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 11.64/2.35
% 11.64/2.35 Those formulas are unsatisfiable:
% 11.64/2.35 ---------------------------------
% 11.64/2.35
% 11.64/2.35 Begin of proof
% 11.64/2.35 |
% 11.64/2.35 | ALPHA: (d5_finsub_1) implies:
% 11.64/2.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v1)
% 11.64/2.35 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v2, v0) | ~
% 11.64/2.35 | preboolean(v1) | ~ finite(v2) | in(v2, v1))
% 11.64/2.35 |
% 11.64/2.35 | ALPHA: (fc2_finsub_1) implies:
% 11.64/2.35 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) |
% 11.64/2.35 | preboolean(v1))
% 11.64/2.35 |
% 11.64/2.35 | ALPHA: (t3_subset) implies:
% 11.64/2.35 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~
% 11.64/2.35 | $i(v1) | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1))
% 11.64/2.35 |
% 11.64/2.35 | DELTA: instantiating (t34_finsub_1) with fresh symbols all_41_0, all_41_1,
% 11.64/2.35 | all_41_2, all_41_3 gives:
% 11.64/2.35 | (4) finite_subsets(all_41_3) = all_41_0 & powerset(all_41_3) = all_41_1 &
% 11.64/2.35 | $i(all_41_0) & $i(all_41_1) & $i(all_41_2) & $i(all_41_3) &
% 11.64/2.35 | element(all_41_2, all_41_1) & finite(all_41_3) & ~ element(all_41_2,
% 11.64/2.35 | all_41_0)
% 11.64/2.35 |
% 11.64/2.35 | ALPHA: (4) implies:
% 11.64/2.35 | (5) ~ element(all_41_2, all_41_0)
% 11.64/2.36 | (6) finite(all_41_3)
% 11.64/2.36 | (7) element(all_41_2, all_41_1)
% 11.64/2.36 | (8) $i(all_41_3)
% 11.64/2.36 | (9) $i(all_41_2)
% 11.64/2.36 | (10) $i(all_41_0)
% 11.64/2.36 | (11) powerset(all_41_3) = all_41_1
% 11.64/2.36 | (12) finite_subsets(all_41_3) = all_41_0
% 11.64/2.36 |
% 11.64/2.36 | GROUND_INST: instantiating (cc2_finset_1) with all_41_3, all_41_1, all_41_2,
% 11.64/2.36 | simplifying with (6), (7), (8), (9), (11) gives:
% 11.64/2.36 | (13) finite(all_41_2)
% 11.64/2.36 |
% 11.64/2.36 | GROUND_INST: instantiating (3) with all_41_2, all_41_3, all_41_1, simplifying
% 11.64/2.36 | with (7), (8), (9), (11) gives:
% 11.64/2.36 | (14) subset(all_41_2, all_41_3)
% 11.64/2.36 |
% 11.64/2.36 | GROUND_INST: instantiating (2) with all_41_3, all_41_0, simplifying with (8),
% 11.64/2.36 | (12) gives:
% 11.64/2.36 | (15) preboolean(all_41_0)
% 11.64/2.36 |
% 11.64/2.36 | GROUND_INST: instantiating (1) with all_41_3, all_41_0, all_41_2, simplifying
% 11.64/2.36 | with (8), (9), (10), (12), (13), (14), (15) gives:
% 11.64/2.36 | (16) in(all_41_2, all_41_0)
% 11.64/2.36 |
% 11.64/2.36 | GROUND_INST: instantiating (t1_subset) with all_41_2, all_41_0, simplifying
% 11.64/2.36 | with (5), (9), (10), (16) gives:
% 11.64/2.36 | (17) $false
% 11.64/2.36 |
% 11.64/2.36 | CLOSE: (17) is inconsistent.
% 11.64/2.36 |
% 11.64/2.36 End of proof
% 11.64/2.36 % SZS output end Proof for theBenchmark
% 11.64/2.36
% 11.64/2.36 1778ms
%------------------------------------------------------------------------------