TSTP Solution File: SEU359+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU359+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 : 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 17:44:17 EDT 2023
% Result : Theorem 9.01s 2.09s
% Output : Proof 12.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU359+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % 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 15:47:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.10/1.04 Prover 1: Preprocessing ...
% 2.10/1.04 Prover 4: Preprocessing ...
% 2.69/1.08 Prover 5: Preprocessing ...
% 2.69/1.08 Prover 2: Preprocessing ...
% 2.69/1.08 Prover 6: Preprocessing ...
% 2.69/1.08 Prover 3: Preprocessing ...
% 2.69/1.08 Prover 0: Preprocessing ...
% 4.67/1.46 Prover 2: Proving ...
% 4.67/1.46 Prover 5: Proving ...
% 4.67/1.46 Prover 1: Warning: ignoring some quantifiers
% 4.67/1.47 Prover 6: Proving ...
% 4.67/1.47 Prover 3: Warning: ignoring some quantifiers
% 4.67/1.48 Prover 3: Constructing countermodel ...
% 4.67/1.48 Prover 1: Constructing countermodel ...
% 6.28/1.62 Prover 4: Warning: ignoring some quantifiers
% 6.28/1.64 Prover 4: Constructing countermodel ...
% 6.78/1.71 Prover 0: Proving ...
% 9.01/2.08 Prover 3: proved (1450ms)
% 9.01/2.09
% 9.01/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.01/2.09
% 9.01/2.09 Prover 6: stopped
% 9.01/2.09 Prover 0: stopped
% 9.01/2.09 Prover 5: stopped
% 9.01/2.10 Prover 2: stopped
% 9.01/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.01/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.01/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.01/2.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.01/2.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.01/2.13 Prover 10: Preprocessing ...
% 9.01/2.13 Prover 11: Preprocessing ...
% 9.01/2.16 Prover 7: Preprocessing ...
% 9.01/2.17 Prover 8: Preprocessing ...
% 9.01/2.18 Prover 13: Preprocessing ...
% 10.71/2.22 Prover 7: Warning: ignoring some quantifiers
% 10.71/2.23 Prover 10: Warning: ignoring some quantifiers
% 10.71/2.23 Prover 7: Constructing countermodel ...
% 10.96/2.26 Prover 10: Constructing countermodel ...
% 10.96/2.28 Prover 13: Warning: ignoring some quantifiers
% 10.96/2.29 Prover 13: Constructing countermodel ...
% 10.96/2.29 Prover 8: Warning: ignoring some quantifiers
% 10.96/2.31 Prover 8: Constructing countermodel ...
% 11.99/2.40 Prover 11: Warning: ignoring some quantifiers
% 11.99/2.41 Prover 10: Found proof (size 34)
% 11.99/2.41 Prover 10: proved (318ms)
% 11.99/2.41 Prover 7: stopped
% 11.99/2.41 Prover 1: stopped
% 11.99/2.41 Prover 4: stopped
% 11.99/2.41 Prover 8: stopped
% 11.99/2.41 Prover 13: stopped
% 11.99/2.42 Prover 11: Constructing countermodel ...
% 11.99/2.42 Prover 11: stopped
% 11.99/2.42
% 11.99/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.99/2.42
% 11.99/2.43 % SZS output start Proof for theBenchmark
% 11.99/2.43 Assumptions after simplification:
% 11.99/2.43 ---------------------------------
% 11.99/2.43
% 11.99/2.43 (d9_yellow_0)
% 12.42/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 12.42/2.46 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v4) | ~ $i(v3) |
% 12.42/2.46 ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v2, v3) | ~
% 12.42/2.46 ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~ rel_str(v0) | ? [v5:
% 12.42/2.46 $i] : ($i(v5) & relstr_set_smaller(v0, v2, v5) & element(v5, v1) & ~
% 12.42/2.46 related(v0, v3, v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.42/2.46 $i] : ! [v4: $i] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2)
% 12.42/2.46 = v3) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 12.42/2.46 relstr_set_smaller(v0, v2, v4) | ~ ex_sup_of_relstr_set(v0, v2) | ~
% 12.42/2.46 element(v4, v1) | ~ element(v3, v1) | ~ rel_str(v0) | related(v0, v3, v4))
% 12.42/2.46 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0)
% 12.42/2.46 = v1) | ~ (join_on_relstr(v0, v2) = v3) | ~ $i(v3) | ~ $i(v2) | ~
% 12.42/2.46 $i(v0) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~
% 12.42/2.46 rel_str(v0) | relstr_set_smaller(v0, v2, v3))
% 12.42/2.46
% 12.42/2.46 (t15_yellow_0)
% 12.50/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) =
% 12.50/2.46 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ antisymmetric_relstr(v0) | ~
% 12.50/2.46 relstr_set_smaller(v0, v2, v3) | ~ element(v3, v1) | ~ rel_str(v0) |
% 12.50/2.46 ex_sup_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) &
% 12.50/2.46 relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v3,
% 12.50/2.46 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) =
% 12.50/2.46 v1) | ~ $i(v2) | ~ $i(v0) | ~ antisymmetric_relstr(v0) | ~
% 12.50/2.46 ex_sup_of_relstr_set(v0, v2) | ~ rel_str(v0) | ? [v3: $i] : ($i(v3) &
% 12.50/2.46 relstr_set_smaller(v0, v2, v3) & element(v3, v1) & ! [v4: $i] : ( ~
% 12.50/2.46 $i(v4) | ~ relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) |
% 12.50/2.46 related(v0, v3, v4))))
% 12.50/2.46
% 12.50/2.46 (t30_yellow_0)
% 12.50/2.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 12.50/2.47 $i] : (the_carrier(v0) = v1 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 12.50/2.47 antisymmetric_relstr(v0) & element(v2, v1) & rel_str(v0) & ((v4 = v2 &
% 12.50/2.47 join_on_relstr(v0, v3) = v2 & ex_sup_of_relstr_set(v0, v3) & ( ~
% 12.50/2.47 relstr_set_smaller(v0, v3, v2) | (relstr_set_smaller(v0, v3, v5) &
% 12.50/2.47 element(v5, v1) & ~ related(v0, v2, v5)))) |
% 12.50/2.47 (relstr_set_smaller(v0, v3, v2) & ! [v6: $i] : ( ~ $i(v6) | ~
% 12.50/2.47 relstr_set_smaller(v0, v3, v6) | ~ element(v6, v1) | related(v0, v2,
% 12.50/2.47 v6)) & ( ~ ex_sup_of_relstr_set(v0, v3) | ( ~ (v4 = v2) &
% 12.50/2.47 join_on_relstr(v0, v3) = v4 & $i(v4))))))
% 12.50/2.47
% 12.50/2.47 Further assumptions not needed in the proof:
% 12.50/2.47 --------------------------------------------
% 12.50/2.47 dt_k1_yellow_0, dt_l1_orders_2, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0,
% 12.50/2.47 existence_l1_orders_2, existence_l1_struct_0, existence_m1_subset_1
% 12.50/2.47
% 12.50/2.47 Those formulas are unsatisfiable:
% 12.50/2.47 ---------------------------------
% 12.50/2.47
% 12.50/2.47 Begin of proof
% 12.50/2.47 |
% 12.50/2.47 | ALPHA: (d9_yellow_0) implies:
% 12.50/2.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.50/2.47 | (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v3) | ~ $i(v3)
% 12.50/2.47 | | ~ $i(v2) | ~ $i(v0) | ~ ex_sup_of_relstr_set(v0, v2) | ~
% 12.50/2.47 | element(v3, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, v2, v3))
% 12.50/2.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 12.50/2.47 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v3) | ~
% 12.50/2.47 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 12.50/2.47 | relstr_set_smaller(v0, v2, v4) | ~ ex_sup_of_relstr_set(v0, v2) | ~
% 12.50/2.47 | element(v4, v1) | ~ element(v3, v1) | ~ rel_str(v0) | related(v0,
% 12.50/2.47 | v3, v4))
% 12.50/2.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.50/2.47 | (v4 = v3 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v4)
% 12.50/2.47 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v2,
% 12.50/2.47 | v3) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~
% 12.50/2.47 | rel_str(v0) | ? [v5: $i] : ($i(v5) & relstr_set_smaller(v0, v2, v5)
% 12.50/2.47 | & element(v5, v1) & ~ related(v0, v3, v5)))
% 12.50/2.47 |
% 12.50/2.47 | ALPHA: (t15_yellow_0) implies:
% 12.50/2.47 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.50/2.47 | (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 12.50/2.47 | antisymmetric_relstr(v0) | ~ relstr_set_smaller(v0, v2, v3) | ~
% 12.50/2.47 | element(v3, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v2) | ?
% 12.50/2.47 | [v4: $i] : ($i(v4) & relstr_set_smaller(v0, v2, v4) & element(v4, v1)
% 12.50/2.47 | & ~ related(v0, v3, v4)))
% 12.50/2.47 |
% 12.50/2.47 | DELTA: instantiating (t30_yellow_0) with fresh symbols all_12_0, all_12_1,
% 12.50/2.47 | all_12_2, all_12_3, all_12_4, all_12_5 gives:
% 12.50/2.48 | (5) the_carrier(all_12_5) = all_12_4 & $i(all_12_0) & $i(all_12_2) &
% 12.50/2.48 | $i(all_12_3) & $i(all_12_4) & $i(all_12_5) &
% 12.50/2.48 | antisymmetric_relstr(all_12_5) & element(all_12_3, all_12_4) &
% 12.50/2.48 | rel_str(all_12_5) & ((all_12_1 = all_12_3 & join_on_relstr(all_12_5,
% 12.50/2.48 | all_12_2) = all_12_3 & ex_sup_of_relstr_set(all_12_5, all_12_2) &
% 12.50/2.48 | ( ~ relstr_set_smaller(all_12_5, all_12_2, all_12_3) |
% 12.50/2.48 | (relstr_set_smaller(all_12_5, all_12_2, all_12_0) &
% 12.50/2.48 | element(all_12_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.48 | all_12_0)))) | (relstr_set_smaller(all_12_5, all_12_2,
% 12.50/2.48 | all_12_3) & ! [v0: $i] : ( ~ $i(v0) | ~
% 12.50/2.48 | relstr_set_smaller(all_12_5, all_12_2, v0) | ~ element(v0,
% 12.50/2.48 | all_12_4) | related(all_12_5, all_12_3, v0)) & ( ~
% 12.50/2.48 | ex_sup_of_relstr_set(all_12_5, all_12_2) | ( ~ (all_12_1 =
% 12.50/2.48 | all_12_3) & join_on_relstr(all_12_5, all_12_2) = all_12_1 &
% 12.50/2.48 | $i(all_12_1)))))
% 12.50/2.48 |
% 12.50/2.48 | ALPHA: (5) implies:
% 12.50/2.48 | (6) rel_str(all_12_5)
% 12.50/2.48 | (7) element(all_12_3, all_12_4)
% 12.50/2.48 | (8) antisymmetric_relstr(all_12_5)
% 12.50/2.48 | (9) $i(all_12_5)
% 12.50/2.48 | (10) $i(all_12_3)
% 12.50/2.48 | (11) $i(all_12_2)
% 12.50/2.48 | (12) $i(all_12_0)
% 12.50/2.48 | (13) the_carrier(all_12_5) = all_12_4
% 12.50/2.48 | (14) (all_12_1 = all_12_3 & join_on_relstr(all_12_5, all_12_2) = all_12_3 &
% 12.50/2.48 | ex_sup_of_relstr_set(all_12_5, all_12_2) & ( ~
% 12.50/2.48 | relstr_set_smaller(all_12_5, all_12_2, all_12_3) |
% 12.50/2.48 | (relstr_set_smaller(all_12_5, all_12_2, all_12_0) &
% 12.50/2.48 | element(all_12_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.48 | all_12_0)))) | (relstr_set_smaller(all_12_5, all_12_2,
% 12.50/2.48 | all_12_3) & ! [v0: $i] : ( ~ $i(v0) | ~
% 12.50/2.48 | relstr_set_smaller(all_12_5, all_12_2, v0) | ~ element(v0,
% 12.50/2.48 | all_12_4) | related(all_12_5, all_12_3, v0)) & ( ~
% 12.50/2.48 | ex_sup_of_relstr_set(all_12_5, all_12_2) | ( ~ (all_12_1 =
% 12.50/2.48 | all_12_3) & join_on_relstr(all_12_5, all_12_2) = all_12_1 &
% 12.50/2.48 | $i(all_12_1))))
% 12.50/2.48 |
% 12.50/2.48 | BETA: splitting (14) gives:
% 12.50/2.48 |
% 12.50/2.48 | Case 1:
% 12.50/2.48 | |
% 12.50/2.48 | | (15) all_12_1 = all_12_3 & join_on_relstr(all_12_5, all_12_2) = all_12_3
% 12.50/2.48 | | & ex_sup_of_relstr_set(all_12_5, all_12_2) & ( ~
% 12.50/2.48 | | relstr_set_smaller(all_12_5, all_12_2, all_12_3) |
% 12.50/2.48 | | (relstr_set_smaller(all_12_5, all_12_2, all_12_0) &
% 12.50/2.48 | | element(all_12_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.48 | | all_12_0)))
% 12.50/2.48 | |
% 12.50/2.48 | | ALPHA: (15) implies:
% 12.50/2.48 | | (16) ex_sup_of_relstr_set(all_12_5, all_12_2)
% 12.50/2.48 | | (17) join_on_relstr(all_12_5, all_12_2) = all_12_3
% 12.50/2.48 | | (18) ~ relstr_set_smaller(all_12_5, all_12_2, all_12_3) |
% 12.50/2.48 | | (relstr_set_smaller(all_12_5, all_12_2, all_12_0) &
% 12.50/2.48 | | element(all_12_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.48 | | all_12_0))
% 12.50/2.48 | |
% 12.50/2.48 | | GROUND_INST: instantiating (1) with all_12_5, all_12_4, all_12_2, all_12_3,
% 12.50/2.48 | | simplifying with (6), (7), (9), (10), (11), (13), (16), (17)
% 12.50/2.48 | | gives:
% 12.50/2.48 | | (19) relstr_set_smaller(all_12_5, all_12_2, all_12_3)
% 12.50/2.48 | |
% 12.50/2.48 | | BETA: splitting (18) gives:
% 12.50/2.48 | |
% 12.50/2.48 | | Case 1:
% 12.50/2.48 | | |
% 12.50/2.48 | | | (20) ~ relstr_set_smaller(all_12_5, all_12_2, all_12_3)
% 12.50/2.48 | | |
% 12.50/2.48 | | | PRED_UNIFY: (19), (20) imply:
% 12.50/2.48 | | | (21) $false
% 12.50/2.48 | | |
% 12.50/2.48 | | | CLOSE: (21) is inconsistent.
% 12.50/2.48 | | |
% 12.50/2.48 | | Case 2:
% 12.50/2.48 | | |
% 12.50/2.49 | | | (22) relstr_set_smaller(all_12_5, all_12_2, all_12_0) &
% 12.50/2.49 | | | element(all_12_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.49 | | | all_12_0)
% 12.50/2.49 | | |
% 12.50/2.49 | | | ALPHA: (22) implies:
% 12.50/2.49 | | | (23) ~ related(all_12_5, all_12_3, all_12_0)
% 12.50/2.49 | | | (24) element(all_12_0, all_12_4)
% 12.50/2.49 | | | (25) relstr_set_smaller(all_12_5, all_12_2, all_12_0)
% 12.50/2.49 | | |
% 12.50/2.49 | | | GROUND_INST: instantiating (2) with all_12_5, all_12_4, all_12_2,
% 12.50/2.49 | | | all_12_3, all_12_0, simplifying with (6), (7), (9), (10),
% 12.50/2.49 | | | (11), (12), (13), (16), (17), (23), (24), (25) gives:
% 12.50/2.49 | | | (26) $false
% 12.50/2.49 | | |
% 12.50/2.49 | | | CLOSE: (26) is inconsistent.
% 12.50/2.49 | | |
% 12.50/2.49 | | End of split
% 12.50/2.49 | |
% 12.50/2.49 | Case 2:
% 12.50/2.49 | |
% 12.50/2.49 | | (27) relstr_set_smaller(all_12_5, all_12_2, all_12_3) & ! [v0: $i] : ( ~
% 12.50/2.49 | | $i(v0) | ~ relstr_set_smaller(all_12_5, all_12_2, v0) | ~
% 12.50/2.49 | | element(v0, all_12_4) | related(all_12_5, all_12_3, v0)) & ( ~
% 12.50/2.49 | | ex_sup_of_relstr_set(all_12_5, all_12_2) | ( ~ (all_12_1 =
% 12.50/2.49 | | all_12_3) & join_on_relstr(all_12_5, all_12_2) = all_12_1 &
% 12.50/2.49 | | $i(all_12_1)))
% 12.50/2.49 | |
% 12.50/2.49 | | ALPHA: (27) implies:
% 12.50/2.49 | | (28) relstr_set_smaller(all_12_5, all_12_2, all_12_3)
% 12.50/2.49 | | (29) ~ ex_sup_of_relstr_set(all_12_5, all_12_2) | ( ~ (all_12_1 =
% 12.50/2.49 | | all_12_3) & join_on_relstr(all_12_5, all_12_2) = all_12_1 &
% 12.50/2.49 | | $i(all_12_1))
% 12.50/2.49 | | (30) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_12_5, all_12_2,
% 12.50/2.49 | | v0) | ~ element(v0, all_12_4) | related(all_12_5, all_12_3,
% 12.50/2.49 | | v0))
% 12.50/2.49 | |
% 12.50/2.49 | | GROUND_INST: instantiating (4) with all_12_5, all_12_4, all_12_2, all_12_3,
% 12.50/2.49 | | simplifying with (6), (7), (8), (9), (10), (11), (13), (28)
% 12.50/2.49 | | gives:
% 12.50/2.49 | | (31) ex_sup_of_relstr_set(all_12_5, all_12_2) | ? [v0: $i] : ($i(v0) &
% 12.50/2.49 | | relstr_set_smaller(all_12_5, all_12_2, v0) & element(v0, all_12_4)
% 12.50/2.49 | | & ~ related(all_12_5, all_12_3, v0))
% 12.50/2.49 | |
% 12.50/2.49 | | BETA: splitting (29) gives:
% 12.50/2.49 | |
% 12.50/2.49 | | Case 1:
% 12.50/2.49 | | |
% 12.50/2.49 | | | (32) ~ ex_sup_of_relstr_set(all_12_5, all_12_2)
% 12.50/2.49 | | |
% 12.50/2.49 | | | BETA: splitting (31) gives:
% 12.50/2.49 | | |
% 12.50/2.49 | | | Case 1:
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | (33) ex_sup_of_relstr_set(all_12_5, all_12_2)
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | PRED_UNIFY: (32), (33) imply:
% 12.50/2.49 | | | | (34) $false
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | CLOSE: (34) is inconsistent.
% 12.50/2.49 | | | |
% 12.50/2.49 | | | Case 2:
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | (35) ? [v0: $i] : ($i(v0) & relstr_set_smaller(all_12_5, all_12_2,
% 12.50/2.49 | | | | v0) & element(v0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.49 | | | | v0))
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | DELTA: instantiating (35) with fresh symbol all_52_0 gives:
% 12.50/2.49 | | | | (36) $i(all_52_0) & relstr_set_smaller(all_12_5, all_12_2, all_52_0)
% 12.50/2.49 | | | | & element(all_52_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.49 | | | | all_52_0)
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | ALPHA: (36) implies:
% 12.50/2.49 | | | | (37) ~ related(all_12_5, all_12_3, all_52_0)
% 12.50/2.49 | | | | (38) element(all_52_0, all_12_4)
% 12.50/2.49 | | | | (39) relstr_set_smaller(all_12_5, all_12_2, all_52_0)
% 12.50/2.49 | | | | (40) $i(all_52_0)
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | GROUND_INST: instantiating (30) with all_52_0, simplifying with (37),
% 12.50/2.49 | | | | (38), (39), (40) gives:
% 12.50/2.49 | | | | (41) $false
% 12.50/2.49 | | | |
% 12.50/2.49 | | | | CLOSE: (41) is inconsistent.
% 12.50/2.49 | | | |
% 12.50/2.49 | | | End of split
% 12.50/2.49 | | |
% 12.50/2.49 | | Case 2:
% 12.50/2.49 | | |
% 12.50/2.49 | | | (42) ex_sup_of_relstr_set(all_12_5, all_12_2)
% 12.50/2.49 | | | (43) ~ (all_12_1 = all_12_3) & join_on_relstr(all_12_5, all_12_2) =
% 12.50/2.49 | | | all_12_1 & $i(all_12_1)
% 12.50/2.49 | | |
% 12.50/2.49 | | | ALPHA: (43) implies:
% 12.50/2.49 | | | (44) ~ (all_12_1 = all_12_3)
% 12.50/2.50 | | | (45) join_on_relstr(all_12_5, all_12_2) = all_12_1
% 12.50/2.50 | | |
% 12.50/2.50 | | | GROUND_INST: instantiating (3) with all_12_5, all_12_4, all_12_2,
% 12.50/2.50 | | | all_12_3, all_12_1, simplifying with (6), (7), (9), (10),
% 12.50/2.50 | | | (11), (13), (28), (42), (45) gives:
% 12.50/2.50 | | | (46) all_12_1 = all_12_3 | ? [v0: $i] : ($i(v0) &
% 12.50/2.50 | | | relstr_set_smaller(all_12_5, all_12_2, v0) & element(v0,
% 12.50/2.50 | | | all_12_4) & ~ related(all_12_5, all_12_3, v0))
% 12.50/2.50 | | |
% 12.50/2.50 | | | BETA: splitting (46) gives:
% 12.50/2.50 | | |
% 12.50/2.50 | | | Case 1:
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | (47) all_12_1 = all_12_3
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | REDUCE: (44), (47) imply:
% 12.50/2.50 | | | | (48) $false
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | CLOSE: (48) is inconsistent.
% 12.50/2.50 | | | |
% 12.50/2.50 | | | Case 2:
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | (49) ? [v0: $i] : ($i(v0) & relstr_set_smaller(all_12_5, all_12_2,
% 12.50/2.50 | | | | v0) & element(v0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.50 | | | | v0))
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | DELTA: instantiating (49) with fresh symbol all_52_0 gives:
% 12.50/2.50 | | | | (50) $i(all_52_0) & relstr_set_smaller(all_12_5, all_12_2, all_52_0)
% 12.50/2.50 | | | | & element(all_52_0, all_12_4) & ~ related(all_12_5, all_12_3,
% 12.50/2.50 | | | | all_52_0)
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | ALPHA: (50) implies:
% 12.50/2.50 | | | | (51) ~ related(all_12_5, all_12_3, all_52_0)
% 12.50/2.50 | | | | (52) element(all_52_0, all_12_4)
% 12.50/2.50 | | | | (53) relstr_set_smaller(all_12_5, all_12_2, all_52_0)
% 12.50/2.50 | | | | (54) $i(all_52_0)
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | GROUND_INST: instantiating (30) with all_52_0, simplifying with (51),
% 12.50/2.50 | | | | (52), (53), (54) gives:
% 12.50/2.50 | | | | (55) $false
% 12.50/2.50 | | | |
% 12.50/2.50 | | | | CLOSE: (55) is inconsistent.
% 12.50/2.50 | | | |
% 12.50/2.50 | | | End of split
% 12.50/2.50 | | |
% 12.50/2.50 | | End of split
% 12.50/2.50 | |
% 12.50/2.50 | End of split
% 12.50/2.50 |
% 12.50/2.50 End of proof
% 12.50/2.50 % SZS output end Proof for theBenchmark
% 12.50/2.50
% 12.50/2.50 1888ms
%------------------------------------------------------------------------------