TSTP Solution File: SEU230+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 17:43:30 EDT 2023
% Result : Theorem 8.29s 1.87s
% Output : Proof 10.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Wed Aug 23 12:41:38 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.03 Prover 1: Preprocessing ...
% 2.44/1.03 Prover 4: Preprocessing ...
% 2.94/1.07 Prover 6: Preprocessing ...
% 2.94/1.07 Prover 5: Preprocessing ...
% 2.94/1.07 Prover 2: Preprocessing ...
% 2.94/1.07 Prover 3: Preprocessing ...
% 2.94/1.07 Prover 0: Preprocessing ...
% 5.03/1.45 Prover 1: Warning: ignoring some quantifiers
% 5.62/1.48 Prover 4: Warning: ignoring some quantifiers
% 5.62/1.48 Prover 3: Warning: ignoring some quantifiers
% 5.62/1.49 Prover 6: Proving ...
% 5.62/1.50 Prover 2: Proving ...
% 5.62/1.50 Prover 1: Constructing countermodel ...
% 5.62/1.50 Prover 3: Constructing countermodel ...
% 5.62/1.50 Prover 5: Proving ...
% 5.91/1.51 Prover 4: Constructing countermodel ...
% 5.91/1.54 Prover 0: Proving ...
% 7.74/1.77 Prover 3: gave up
% 7.74/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.05/1.84 Prover 1: gave up
% 8.05/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.29/1.85 Prover 7: Preprocessing ...
% 8.29/1.87 Prover 8: Preprocessing ...
% 8.29/1.87 Prover 0: proved (1245ms)
% 8.29/1.87
% 8.29/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.29/1.87
% 8.29/1.87 Prover 5: stopped
% 8.29/1.87 Prover 2: stopped
% 8.29/1.87 Prover 6: stopped
% 8.29/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.29/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.29/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.29/1.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.29/1.92 Prover 11: Preprocessing ...
% 8.29/1.92 Prover 13: Preprocessing ...
% 8.29/1.93 Prover 16: Preprocessing ...
% 8.95/1.95 Prover 10: Preprocessing ...
% 8.95/1.96 Prover 7: Warning: ignoring some quantifiers
% 8.95/1.97 Prover 7: Constructing countermodel ...
% 9.32/2.03 Prover 8: Warning: ignoring some quantifiers
% 9.32/2.03 Prover 10: Warning: ignoring some quantifiers
% 9.32/2.04 Prover 10: Constructing countermodel ...
% 9.32/2.04 Prover 16: Warning: ignoring some quantifiers
% 9.32/2.05 Prover 16: Constructing countermodel ...
% 9.32/2.08 Prover 8: Constructing countermodel ...
% 9.32/2.10 Prover 13: Warning: ignoring some quantifiers
% 9.32/2.11 Prover 13: Constructing countermodel ...
% 9.32/2.14 Prover 7: Found proof (size 14)
% 9.32/2.14 Prover 7: proved (375ms)
% 9.32/2.14 Prover 8: stopped
% 9.32/2.15 Prover 16: stopped
% 9.32/2.15 Prover 13: stopped
% 9.32/2.15 Prover 10: gave up
% 9.32/2.15 Prover 4: stopped
% 9.32/2.16 Prover 11: Warning: ignoring some quantifiers
% 10.58/2.17 Prover 11: Constructing countermodel ...
% 10.58/2.18 Prover 11: stopped
% 10.58/2.18
% 10.58/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.58/2.18
% 10.64/2.18 % SZS output start Proof for theBenchmark
% 10.64/2.19 Assumptions after simplification:
% 10.64/2.19 ---------------------------------
% 10.64/2.19
% 10.64/2.19 (commutativity_k2_xboole_0)
% 10.64/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 10.64/2.21 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 10.64/2.21 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 10.64/2.21 | (set_union2(v1, v0) = v2 & $i(v2)))
% 10.64/2.21
% 10.64/2.21 (d1_ordinal1)
% 10.64/2.22 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 10.64/2.22 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 10.64/2.22 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 10.64/2.22 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 10.64/2.22
% 10.64/2.22 (d1_tarski)
% 10.64/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 10.64/2.22 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 10.64/2.22 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 10.64/2.22 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 10.64/2.22 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 10.64/2.22 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 10.64/2.22
% 10.64/2.22 (d2_xboole_0)
% 10.86/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0,
% 10.86/2.23 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3,
% 10.86/2.23 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 10.86/2.23 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 10.86/2.23 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i]
% 10.86/2.23 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~
% 10.86/2.23 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] :
% 10.86/2.23 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) =
% 10.86/2.23 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 10.86/2.23 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 10.86/2.23 | in(v4, v0))))
% 10.86/2.23
% 10.86/2.23 (t10_ordinal1)
% 10.86/2.23 ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1) & $i(v0) & ~ in(v0, v1))
% 10.86/2.23
% 10.86/2.23 Further assumptions not needed in the proof:
% 10.86/2.23 --------------------------------------------
% 10.86/2.23 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k1_ordinal1,
% 10.86/2.23 dt_k1_tarski, dt_k1_xboole_0, dt_k2_xboole_0, dt_m1_subset_1,
% 10.86/2.23 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_relat_1,
% 10.86/2.23 fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, rc1_funct_1,
% 10.86/2.23 rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1,
% 10.86/2.23 rc3_relat_1, rc4_funct_1, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole,
% 10.86/2.23 t8_boole
% 10.86/2.23
% 10.86/2.23 Those formulas are unsatisfiable:
% 10.86/2.23 ---------------------------------
% 10.86/2.23
% 10.86/2.23 Begin of proof
% 10.86/2.23 |
% 10.86/2.23 | ALPHA: (commutativity_k2_xboole_0) implies:
% 10.86/2.23 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 10.86/2.23 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 10.86/2.23 |
% 10.86/2.23 | ALPHA: (d1_ordinal1) implies:
% 10.86/2.23 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 10.86/2.23 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 10.86/2.23 | $i(v1)))
% 10.86/2.23 |
% 10.86/2.23 | ALPHA: (d1_tarski) implies:
% 10.86/2.23 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 10.86/2.23 | $i(v0) | in(v0, v1))
% 10.86/2.23 |
% 10.86/2.23 | ALPHA: (d2_xboole_0) implies:
% 10.86/2.24 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.86/2.24 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.86/2.24 | $i(v0) | ~ in(v3, v0) | in(v3, v2))
% 10.86/2.24 |
% 10.86/2.24 | DELTA: instantiating (t10_ordinal1) with fresh symbols all_38_0, all_38_1
% 10.86/2.24 | gives:
% 10.86/2.24 | (5) succ(all_38_1) = all_38_0 & $i(all_38_0) & $i(all_38_1) & ~
% 10.86/2.24 | in(all_38_1, all_38_0)
% 10.86/2.24 |
% 10.86/2.24 | ALPHA: (5) implies:
% 10.86/2.24 | (6) ~ in(all_38_1, all_38_0)
% 10.86/2.24 | (7) $i(all_38_1)
% 10.86/2.24 | (8) succ(all_38_1) = all_38_0
% 10.86/2.24 |
% 10.86/2.24 | GROUND_INST: instantiating (2) with all_38_1, all_38_0, simplifying with (7),
% 10.86/2.24 | (8) gives:
% 10.86/2.24 | (9) ? [v0: $i] : (singleton(all_38_1) = v0 & set_union2(all_38_1, v0) =
% 10.86/2.24 | all_38_0 & $i(v0) & $i(all_38_0))
% 10.86/2.24 |
% 10.86/2.24 | DELTA: instantiating (9) with fresh symbol all_58_0 gives:
% 10.86/2.24 | (10) singleton(all_38_1) = all_58_0 & set_union2(all_38_1, all_58_0) =
% 10.86/2.24 | all_38_0 & $i(all_58_0) & $i(all_38_0)
% 10.86/2.24 |
% 10.86/2.24 | ALPHA: (10) implies:
% 10.93/2.24 | (11) $i(all_58_0)
% 10.93/2.24 | (12) set_union2(all_38_1, all_58_0) = all_38_0
% 10.93/2.24 | (13) singleton(all_38_1) = all_58_0
% 10.93/2.24 |
% 10.93/2.24 | GROUND_INST: instantiating (1) with all_58_0, all_38_1, all_38_0, simplifying
% 10.93/2.24 | with (7), (11), (12) gives:
% 10.93/2.24 | (14) set_union2(all_58_0, all_38_1) = all_38_0 & $i(all_38_0)
% 10.93/2.24 |
% 10.93/2.24 | ALPHA: (14) implies:
% 10.93/2.24 | (15) $i(all_38_0)
% 10.93/2.24 | (16) set_union2(all_58_0, all_38_1) = all_38_0
% 10.93/2.24 |
% 10.93/2.24 | GROUND_INST: instantiating (3) with all_38_1, all_58_0, simplifying with (7),
% 10.93/2.24 | (11), (13) gives:
% 10.93/2.24 | (17) in(all_38_1, all_58_0)
% 10.93/2.24 |
% 10.93/2.24 | GROUND_INST: instantiating (4) with all_58_0, all_38_1, all_38_0, all_38_1,
% 10.93/2.24 | simplifying with (6), (7), (11), (15), (16), (17) gives:
% 10.93/2.24 | (18) $false
% 10.93/2.25 |
% 10.93/2.25 | CLOSE: (18) is inconsistent.
% 10.93/2.25 |
% 10.93/2.25 End of proof
% 10.93/2.25 % SZS output end Proof for theBenchmark
% 10.93/2.25
% 10.93/2.25 1637ms
%------------------------------------------------------------------------------