TSTP Solution File: SEU097+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU097+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 17:42:30 EDT 2023
% Result : Theorem 10.71s 2.19s
% Output : Proof 15.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU097+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 : n005.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 : Wed Aug 23 13:09:38 EDT 2023
% 0.13/0.35 % 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
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 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 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 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
% 3.19/1.13 Prover 1: Preprocessing ...
% 3.19/1.13 Prover 4: Preprocessing ...
% 3.19/1.17 Prover 0: Preprocessing ...
% 3.19/1.17 Prover 6: Preprocessing ...
% 3.19/1.17 Prover 2: Preprocessing ...
% 3.19/1.17 Prover 3: Preprocessing ...
% 3.19/1.18 Prover 5: Preprocessing ...
% 7.01/1.70 Prover 5: Proving ...
% 7.01/1.70 Prover 2: Proving ...
% 7.67/1.73 Prover 1: Warning: ignoring some quantifiers
% 7.67/1.74 Prover 3: Warning: ignoring some quantifiers
% 7.67/1.77 Prover 1: Constructing countermodel ...
% 7.67/1.77 Prover 3: Constructing countermodel ...
% 7.67/1.78 Prover 6: Proving ...
% 8.07/1.78 Prover 4: Warning: ignoring some quantifiers
% 8.07/1.83 Prover 4: Constructing countermodel ...
% 8.61/1.87 Prover 0: Proving ...
% 10.71/2.18 Prover 5: proved (1546ms)
% 10.71/2.19
% 10.71/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.71/2.19
% 10.71/2.19 Prover 3: stopped
% 10.71/2.19 Prover 0: stopped
% 10.71/2.19 Prover 2: stopped
% 10.71/2.19 Prover 6: stopped
% 10.71/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.71/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.71/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.71/2.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.71/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.71/2.30 Prover 7: Preprocessing ...
% 10.71/2.31 Prover 8: Preprocessing ...
% 11.23/2.32 Prover 10: Preprocessing ...
% 11.23/2.34 Prover 13: Preprocessing ...
% 11.23/2.35 Prover 11: Preprocessing ...
% 12.39/2.40 Prover 7: Warning: ignoring some quantifiers
% 12.71/2.44 Prover 7: Constructing countermodel ...
% 12.71/2.44 Prover 10: Warning: ignoring some quantifiers
% 12.71/2.47 Prover 10: Constructing countermodel ...
% 12.71/2.48 Prover 13: Warning: ignoring some quantifiers
% 12.71/2.49 Prover 13: Constructing countermodel ...
% 13.21/2.50 Prover 8: Warning: ignoring some quantifiers
% 13.21/2.52 Prover 8: Constructing countermodel ...
% 13.69/2.60 Prover 10: gave up
% 13.69/2.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.69/2.63 Prover 11: Warning: ignoring some quantifiers
% 13.69/2.65 Prover 11: Constructing countermodel ...
% 14.43/2.67 Prover 16: Preprocessing ...
% 14.70/2.70 Prover 13: gave up
% 14.70/2.72 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 15.04/2.74 Prover 16: Warning: ignoring some quantifiers
% 15.04/2.75 Prover 19: Preprocessing ...
% 15.04/2.75 Prover 16: Constructing countermodel ...
% 15.04/2.79 Prover 7: Found proof (size 14)
% 15.04/2.79 Prover 7: proved (590ms)
% 15.04/2.79 Prover 16: stopped
% 15.04/2.79 Prover 1: stopped
% 15.04/2.79 Prover 11: stopped
% 15.04/2.79 Prover 8: stopped
% 15.04/2.79 Prover 4: stopped
% 15.04/2.86 Prover 19: Warning: ignoring some quantifiers
% 15.04/2.87 Prover 19: Constructing countermodel ...
% 15.04/2.88 Prover 19: stopped
% 15.04/2.88
% 15.04/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.04/2.88
% 15.04/2.88 % SZS output start Proof for theBenchmark
% 15.04/2.89 Assumptions after simplification:
% 15.04/2.89 ---------------------------------
% 15.04/2.89
% 15.04/2.89 (commutativity_k2_xboole_0)
% 15.75/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 15.75/2.92 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 15.75/2.92 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 15.75/2.92 | (set_union2(v1, v0) = v2 & $i(v2)))
% 15.75/2.92
% 15.75/2.92 (d6_xboole_0)
% 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) |
% 15.75/2.93 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (set_difference(v0, v1) =
% 15.75/2.93 v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3 & $i(v4)
% 15.75/2.93 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.75/2.93 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 15.75/2.93 [v4: $i] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3
% 15.75/2.93 & set_union2(v2, v4) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i]
% 15.75/2.93 : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~
% 15.75/2.93 $i(v0) | ? [v3: $i] : ? [v4: $i] : (set_difference(v1, v0) = v4 &
% 15.75/2.93 set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2 & $i(v4) & $i(v3) &
% 15.75/2.93 $i(v2)))
% 15.75/2.93
% 15.75/2.93 (fc12_finset_1)
% 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 15.75/2.93 ~ $i(v1) | ~ $i(v0) | ~ finite(v0) | finite(v2))
% 15.75/2.93
% 15.75/2.93 (fc9_finset_1)
% 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 15.75/2.93 $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 15.75/2.93
% 15.75/2.93 (l3_finset_1)
% 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 15.75/2.94 $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 15.75/2.94
% 15.75/2.94 (t16_finset_1)
% 15.75/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 15.75/2.94 ~ $i(v1) | ~ $i(v0) | ~ finite(v0) | finite(v2))
% 15.75/2.94
% 15.75/2.94 (t28_finset_1)
% 15.75/2.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (symmetric_difference(v0, v1) = v2 &
% 15.75/2.94 $i(v2) & $i(v1) & $i(v0) & finite(v1) & finite(v0) & ~ finite(v2))
% 15.75/2.94
% 15.75/2.94 Further assumptions not needed in the proof:
% 15.75/2.94 --------------------------------------------
% 15.75/2.94 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 15.75/2.94 cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 15.75/2.94 cc4_arytm_3, commutativity_k5_xboole_0, existence_m1_subset_1, fc12_relat_1,
% 15.75/2.94 fc1_subset_1, fc1_xboole_0, fc2_ordinal1, fc2_relat_1, fc2_xboole_0,
% 15.75/2.94 fc3_relat_1, fc3_xboole_0, fc4_relat_1, fc8_arytm_3, idempotence_k2_xboole_0,
% 15.75/2.94 rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1,
% 15.75/2.94 rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3,
% 15.75/2.94 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1,
% 15.75/2.94 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1,
% 15.75/2.94 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1,
% 15.75/2.94 reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, t3_boole, t3_subset,
% 15.75/2.94 t4_boole, t4_subset, t5_boole, t5_subset, t6_boole, t7_boole, t8_boole
% 15.75/2.94
% 15.75/2.94 Those formulas are unsatisfiable:
% 15.75/2.94 ---------------------------------
% 15.75/2.94
% 15.75/2.94 Begin of proof
% 15.75/2.94 |
% 15.75/2.94 | ALPHA: (commutativity_k2_xboole_0) implies:
% 15.75/2.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 15.75/2.94 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 15.75/2.94 |
% 15.75/2.94 | ALPHA: (d6_xboole_0) implies:
% 15.75/2.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0,
% 15.75/2.94 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 15.75/2.94 | (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 &
% 15.75/2.94 | set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2)))
% 15.75/2.94 |
% 15.75/2.94 | DELTA: instantiating (t28_finset_1) with fresh symbols all_85_0, all_85_1,
% 15.75/2.94 | all_85_2 gives:
% 15.75/2.94 | (3) symmetric_difference(all_85_2, all_85_1) = all_85_0 & $i(all_85_0) &
% 15.75/2.94 | $i(all_85_1) & $i(all_85_2) & finite(all_85_1) & finite(all_85_2) & ~
% 15.75/2.94 | finite(all_85_0)
% 15.75/2.94 |
% 15.75/2.94 | ALPHA: (3) implies:
% 15.75/2.95 | (4) ~ finite(all_85_0)
% 15.75/2.95 | (5) finite(all_85_2)
% 15.75/2.95 | (6) finite(all_85_1)
% 15.75/2.95 | (7) $i(all_85_2)
% 15.75/2.95 | (8) $i(all_85_1)
% 15.75/2.95 | (9) symmetric_difference(all_85_2, all_85_1) = all_85_0
% 15.75/2.95 |
% 15.75/2.95 | GROUND_INST: instantiating (2) with all_85_2, all_85_1, all_85_0, simplifying
% 15.75/2.95 | with (7), (8), (9) gives:
% 15.75/2.95 | (10) ? [v0: $i] : ? [v1: $i] : (set_difference(all_85_1, all_85_2) = v1 &
% 15.75/2.95 | set_difference(all_85_2, all_85_1) = v0 & set_union2(v0, v1) =
% 15.75/2.95 | all_85_0 & $i(v1) & $i(v0) & $i(all_85_0))
% 15.75/2.95 |
% 15.75/2.95 | DELTA: instantiating (10) with fresh symbols all_101_0, all_101_1 gives:
% 15.75/2.95 | (11) set_difference(all_85_1, all_85_2) = all_101_0 &
% 15.75/2.95 | set_difference(all_85_2, all_85_1) = all_101_1 & set_union2(all_101_1,
% 15.75/2.95 | all_101_0) = all_85_0 & $i(all_101_0) & $i(all_101_1) & $i(all_85_0)
% 15.75/2.95 |
% 15.75/2.95 | ALPHA: (11) implies:
% 15.75/2.95 | (12) $i(all_101_1)
% 15.75/2.95 | (13) $i(all_101_0)
% 15.75/2.95 | (14) set_union2(all_101_1, all_101_0) = all_85_0
% 15.75/2.95 | (15) set_difference(all_85_2, all_85_1) = all_101_1
% 15.75/2.95 | (16) set_difference(all_85_1, all_85_2) = all_101_0
% 15.75/2.95 |
% 15.75/2.95 | GROUND_INST: instantiating (1) with all_101_0, all_101_1, all_85_0,
% 15.75/2.95 | simplifying with (12), (13), (14) gives:
% 15.75/2.95 | (17) set_union2(all_101_0, all_101_1) = all_85_0 & $i(all_85_0)
% 15.75/2.95 |
% 15.75/2.95 | ALPHA: (17) implies:
% 15.75/2.95 | (18) set_union2(all_101_0, all_101_1) = all_85_0
% 15.75/2.95 |
% 15.75/2.95 | GROUND_INST: instantiating (t16_finset_1) with all_85_2, all_85_1, all_101_1,
% 15.75/2.95 | simplifying with (5), (7), (8), (15) gives:
% 15.75/2.95 | (19) finite(all_101_1)
% 15.75/2.95 |
% 15.75/2.95 | GROUND_INST: instantiating (t16_finset_1) with all_85_1, all_85_2, all_101_0,
% 15.75/2.95 | simplifying with (6), (7), (8), (16) gives:
% 15.75/2.95 | (20) finite(all_101_0)
% 15.75/2.95 |
% 15.75/2.95 | GROUND_INST: instantiating (l3_finset_1) with all_101_0, all_101_1, all_85_0,
% 15.75/2.95 | simplifying with (4), (12), (13), (18), (19), (20) gives:
% 15.75/2.95 | (21) $false
% 15.75/2.95 |
% 15.75/2.95 | CLOSE: (21) is inconsistent.
% 15.75/2.95 |
% 15.75/2.95 End of proof
% 15.75/2.95 % SZS output end Proof for theBenchmark
% 15.75/2.95
% 15.75/2.95 2348ms
%------------------------------------------------------------------------------