TSTP Solution File: SEU306+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU306+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 : n026.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 17:43:58 EDT 2023
% Result : Theorem 7.66s 2.07s
% Output : Proof 11.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU306+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 22:31:01 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.64 ________ _____
% 0.19/0.64 ___ __ \_________(_)________________________________
% 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.64
% 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.64 (2023-06-19)
% 0.19/0.64
% 0.19/0.64 (c) Philipp Rümmer, 2009-2023
% 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.64 Amanda Stjerna.
% 0.19/0.64 Free software under BSD-3-Clause.
% 0.19/0.64
% 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.64
% 0.19/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.66 Running up to 7 provers in parallel.
% 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.04/1.19 Prover 1: Preprocessing ...
% 3.04/1.19 Prover 4: Preprocessing ...
% 3.04/1.23 Prover 5: Preprocessing ...
% 3.04/1.23 Prover 6: Preprocessing ...
% 3.04/1.23 Prover 3: Preprocessing ...
% 3.04/1.23 Prover 0: Preprocessing ...
% 3.04/1.23 Prover 2: Preprocessing ...
% 6.24/1.80 Prover 5: Proving ...
% 6.76/1.84 Prover 1: Warning: ignoring some quantifiers
% 6.76/1.86 Prover 2: Proving ...
% 6.76/1.87 Prover 1: Constructing countermodel ...
% 7.12/1.90 Prover 3: Warning: ignoring some quantifiers
% 7.12/1.92 Prover 6: Proving ...
% 7.12/1.92 Prover 3: Constructing countermodel ...
% 7.66/2.07 Prover 5: proved (1396ms)
% 7.66/2.07
% 7.66/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.66/2.07
% 7.66/2.08 Prover 3: stopped
% 7.66/2.09 Prover 6: stopped
% 7.66/2.09 Prover 2: stopped
% 7.66/2.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.66/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.66/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.66/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.12/2.18 Prover 10: Preprocessing ...
% 9.12/2.19 Prover 7: Preprocessing ...
% 9.12/2.19 Prover 11: Preprocessing ...
% 9.12/2.20 Prover 8: Preprocessing ...
% 9.65/2.25 Prover 4: Warning: ignoring some quantifiers
% 9.65/2.28 Prover 10: Warning: ignoring some quantifiers
% 9.65/2.31 Prover 7: Warning: ignoring some quantifiers
% 9.65/2.31 Prover 10: Constructing countermodel ...
% 10.19/2.32 Prover 4: Constructing countermodel ...
% 10.19/2.33 Prover 7: Constructing countermodel ...
% 10.19/2.33 Prover 0: Proving ...
% 10.19/2.34 Prover 0: stopped
% 10.19/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.56/2.39 Prover 8: Warning: ignoring some quantifiers
% 10.56/2.40 Prover 1: Found proof (size 15)
% 10.56/2.40 Prover 1: proved (1735ms)
% 10.56/2.40 Prover 4: stopped
% 10.56/2.40 Prover 7: stopped
% 10.56/2.40 Prover 8: Constructing countermodel ...
% 10.56/2.40 Prover 13: Preprocessing ...
% 10.56/2.40 Prover 10: stopped
% 10.56/2.41 Prover 8: stopped
% 10.56/2.43 Prover 13: stopped
% 11.23/2.52 Prover 11: Warning: ignoring some quantifiers
% 11.48/2.53 Prover 11: Constructing countermodel ...
% 11.48/2.54 Prover 11: stopped
% 11.48/2.54
% 11.48/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.48/2.54
% 11.58/2.55 % SZS output start Proof for theBenchmark
% 11.58/2.55 Assumptions after simplification:
% 11.58/2.55 ---------------------------------
% 11.58/2.55
% 11.58/2.55 (d3_pre_topc)
% 11.58/2.58 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 11.58/2.58 any] : ? [v3: $i] : (cast_as_carrier_subset(v0) = v3 & one_sorted_str(v0)
% 11.58/2.58 = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 11.58/2.58
% 11.58/2.58 (t12_pre_topc)
% 11.58/2.58 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 11.58/2.58 cast_as_carrier_subset(v0) = v1 & the_carrier(v0) = v2 & one_sorted_str(v0)
% 11.58/2.58 = 0 & $i(v2) & $i(v1) & $i(v0))
% 11.58/2.58
% 11.58/2.58 (function-axioms)
% 11.58/2.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.58/2.59 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 11.58/2.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.58/2.59 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 11.58/2.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.58/2.59 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 11.58/2.59 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1)
% 11.58/2.59 | ~ (cast_as_carrier_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 11.58/2.59 [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) &
% 11.58/2.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 11.58/2.59 v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0:
% 11.58/2.59 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 11.58/2.59 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.58/2.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~
% 11.58/2.59 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.58/2.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~
% 11.58/2.59 (v1_int_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.58/2.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~
% 11.58/2.59 (v1_rat_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.58/2.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~
% 11.58/2.59 (v1_xreal_0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.58/2.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~
% 11.58/2.59 (v1_xcmplx_0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.58/2.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 11.58/2.59 (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 11.58/2.59 : ! [v2: $i] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) =
% 11.58/2.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.58/2.59 $i] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0)) & !
% 11.58/2.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 11.58/2.59 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0)) & ! [v0:
% 11.58/2.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.58/2.59 ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) & ! [v0:
% 11.58/2.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.58/2.59 ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0))
% 11.58/2.59
% 11.58/2.59 Further assumptions not needed in the proof:
% 11.58/2.59 --------------------------------------------
% 11.58/2.59 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered,
% 11.58/2.59 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 11.58/2.59 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered,
% 11.58/2.59 cc3_membered, cc4_membered, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_pre_topc,
% 11.58/2.59 dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, existence_l1_struct_0,
% 11.58/2.59 existence_m1_subset_1, fc1_subset_1, fc6_membered, rc1_membered, rc1_subset_1,
% 11.58/2.59 rc2_subset_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset,
% 11.58/2.59 t5_subset, t6_boole, t7_boole, t8_boole
% 11.58/2.59
% 11.58/2.59 Those formulas are unsatisfiable:
% 11.58/2.59 ---------------------------------
% 11.58/2.59
% 11.58/2.59 Begin of proof
% 11.58/2.59 |
% 11.58/2.59 | ALPHA: (function-axioms) implies:
% 11.58/2.60 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.58/2.60 | (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 11.58/2.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.58/2.60 | (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) =
% 11.58/2.60 | v0))
% 11.58/2.60 |
% 11.58/2.60 | DELTA: instantiating (t12_pre_topc) with fresh symbols all_38_0, all_38_1,
% 11.58/2.60 | all_38_2 gives:
% 11.58/2.60 | (3) ~ (all_38_0 = all_38_1) & cast_as_carrier_subset(all_38_2) = all_38_1
% 11.58/2.60 | & the_carrier(all_38_2) = all_38_0 & one_sorted_str(all_38_2) = 0 &
% 11.58/2.60 | $i(all_38_0) & $i(all_38_1) & $i(all_38_2)
% 11.58/2.60 |
% 11.58/2.60 | ALPHA: (3) implies:
% 11.58/2.60 | (4) ~ (all_38_0 = all_38_1)
% 11.58/2.60 | (5) $i(all_38_2)
% 11.58/2.60 | (6) one_sorted_str(all_38_2) = 0
% 11.58/2.60 | (7) the_carrier(all_38_2) = all_38_0
% 11.58/2.60 | (8) cast_as_carrier_subset(all_38_2) = all_38_1
% 11.58/2.60 |
% 11.58/2.60 | GROUND_INST: instantiating (d3_pre_topc) with all_38_2, all_38_0, simplifying
% 11.58/2.60 | with (5), (7) gives:
% 11.58/2.60 | (9) ? [v0: any] : ? [v1: $i] : (cast_as_carrier_subset(all_38_2) = v1 &
% 11.58/2.60 | one_sorted_str(all_38_2) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 11.58/2.60 | all_38_0))
% 11.58/2.60 |
% 11.58/2.60 | DELTA: instantiating (9) with fresh symbols all_63_0, all_63_1 gives:
% 11.58/2.60 | (10) cast_as_carrier_subset(all_38_2) = all_63_0 & one_sorted_str(all_38_2)
% 11.58/2.60 | = all_63_1 & $i(all_63_0) & ( ~ (all_63_1 = 0) | all_63_0 = all_38_0)
% 11.58/2.60 |
% 11.58/2.60 | ALPHA: (10) implies:
% 11.58/2.60 | (11) one_sorted_str(all_38_2) = all_63_1
% 11.58/2.60 | (12) cast_as_carrier_subset(all_38_2) = all_63_0
% 11.58/2.60 | (13) ~ (all_63_1 = 0) | all_63_0 = all_38_0
% 11.58/2.60 |
% 11.58/2.60 | GROUND_INST: instantiating (1) with 0, all_63_1, all_38_2, simplifying with
% 11.58/2.60 | (6), (11) gives:
% 11.58/2.60 | (14) all_63_1 = 0
% 11.58/2.60 |
% 11.58/2.60 | GROUND_INST: instantiating (2) with all_38_1, all_63_0, all_38_2, simplifying
% 11.58/2.60 | with (8), (12) gives:
% 11.58/2.60 | (15) all_63_0 = all_38_1
% 11.58/2.60 |
% 11.58/2.60 | BETA: splitting (13) gives:
% 11.58/2.60 |
% 11.58/2.60 | Case 1:
% 11.58/2.60 | |
% 11.58/2.60 | | (16) ~ (all_63_1 = 0)
% 11.58/2.60 | |
% 11.58/2.60 | | REDUCE: (14), (16) imply:
% 11.58/2.60 | | (17) $false
% 11.58/2.61 | |
% 11.58/2.61 | | CLOSE: (17) is inconsistent.
% 11.58/2.61 | |
% 11.58/2.61 | Case 2:
% 11.58/2.61 | |
% 11.58/2.61 | | (18) all_63_0 = all_38_0
% 11.58/2.61 | |
% 11.58/2.61 | | COMBINE_EQS: (15), (18) imply:
% 11.58/2.61 | | (19) all_38_0 = all_38_1
% 11.58/2.61 | |
% 11.58/2.61 | | SIMP: (19) implies:
% 11.58/2.61 | | (20) all_38_0 = all_38_1
% 11.58/2.61 | |
% 11.58/2.61 | | REDUCE: (4), (20) imply:
% 11.58/2.61 | | (21) $false
% 11.58/2.61 | |
% 11.58/2.61 | | CLOSE: (21) is inconsistent.
% 11.58/2.61 | |
% 11.58/2.61 | End of split
% 11.58/2.61 |
% 11.58/2.61 End of proof
% 11.58/2.61 % SZS output end Proof for theBenchmark
% 11.58/2.61
% 11.58/2.61 1961ms
%------------------------------------------------------------------------------