TSTP Solution File: SEU361+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU361+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 : n003.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 8.62s 2.05s
% Output : Proof 11.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU361+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 : n003.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 19:12:22 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,
% 0.20/0.61 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/sandbox2/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
% 2.52/1.09 Prover 4: Preprocessing ...
% 2.52/1.09 Prover 1: Preprocessing ...
% 2.52/1.13 Prover 6: Preprocessing ...
% 2.52/1.13 Prover 0: Preprocessing ...
% 2.52/1.13 Prover 2: Preprocessing ...
% 2.52/1.13 Prover 3: Preprocessing ...
% 2.52/1.14 Prover 5: Preprocessing ...
% 5.14/1.54 Prover 1: Warning: ignoring some quantifiers
% 5.78/1.55 Prover 2: Proving ...
% 5.78/1.55 Prover 1: Constructing countermodel ...
% 5.78/1.56 Prover 5: Proving ...
% 5.78/1.56 Prover 6: Proving ...
% 5.78/1.58 Prover 3: Warning: ignoring some quantifiers
% 6.07/1.60 Prover 3: Constructing countermodel ...
% 8.27/1.90 Prover 3: gave up
% 8.27/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.27/1.92 Prover 4: Warning: ignoring some quantifiers
% 8.62/1.95 Prover 7: Preprocessing ...
% 8.62/1.99 Prover 4: Constructing countermodel ...
% 8.62/2.04 Prover 5: proved (1413ms)
% 8.62/2.04
% 8.62/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.62/2.05
% 8.62/2.05 Prover 2: stopped
% 8.62/2.05 Prover 6: stopped
% 9.11/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.11/2.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.11/2.07 Prover 7: Warning: ignoring some quantifiers
% 9.11/2.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.11/2.08 Prover 7: Constructing countermodel ...
% 9.11/2.10 Prover 0: Proving ...
% 9.11/2.10 Prover 0: stopped
% 9.11/2.11 Prover 8: Preprocessing ...
% 9.11/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.86/2.12 Prover 11: Preprocessing ...
% 9.86/2.13 Prover 10: Preprocessing ...
% 9.86/2.14 Prover 13: Preprocessing ...
% 10.24/2.17 Prover 10: Warning: ignoring some quantifiers
% 10.24/2.18 Prover 1: gave up
% 10.24/2.21 Prover 10: Constructing countermodel ...
% 10.24/2.21 Prover 8: Warning: ignoring some quantifiers
% 10.24/2.21 Prover 8: Constructing countermodel ...
% 10.24/2.21 Prover 13: Warning: ignoring some quantifiers
% 10.24/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.24/2.21 Prover 13: Constructing countermodel ...
% 10.24/2.23 Prover 16: Preprocessing ...
% 10.85/2.27 Prover 7: Found proof (size 30)
% 10.85/2.27 Prover 7: proved (350ms)
% 10.85/2.27 Prover 10: stopped
% 10.85/2.27 Prover 4: stopped
% 10.85/2.27 Prover 8: stopped
% 10.85/2.27 Prover 13: stopped
% 10.85/2.28 Prover 16: Warning: ignoring some quantifiers
% 11.06/2.28 Prover 16: Constructing countermodel ...
% 11.06/2.28 Prover 16: stopped
% 11.39/2.37 Prover 11: Warning: ignoring some quantifiers
% 11.39/2.38 Prover 11: Constructing countermodel ...
% 11.39/2.39 Prover 11: stopped
% 11.39/2.39
% 11.39/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.39/2.39
% 11.39/2.40 % SZS output start Proof for theBenchmark
% 11.39/2.40 Assumptions after simplification:
% 11.39/2.40 ---------------------------------
% 11.39/2.40
% 11.39/2.40 (d11_yellow_0)
% 11.74/2.43 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (join_on_relstr(v0, empty_set)
% 11.74/2.43 = v1) | ~ $i(v0) | ~ rel_str(v0) | (bottom_of_relstr(v0) = v1 & $i(v1)))
% 11.74/2.43 & ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0) | ~
% 11.74/2.43 rel_str(v0) | (join_on_relstr(v0, empty_set) = v1 & $i(v1)))
% 11.74/2.43
% 11.74/2.43 (dt_k3_yellow_0)
% 11.74/2.43 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 11.74/2.43 rel_str(v0) | ? [v2: $i] : (bottom_of_relstr(v0) = v2 & $i(v2) &
% 11.74/2.43 element(v2, v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0)
% 11.74/2.43 = v1) | ~ $i(v0) | ~ rel_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 &
% 11.74/2.43 $i(v2) & element(v1, v2)))
% 11.74/2.43
% 11.74/2.43 (rc1_xboole_0)
% 11.74/2.43 ? [v0: $i] : ($i(v0) & empty(v0))
% 11.74/2.43
% 11.74/2.43 (t30_yellow_0)
% 11.74/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 11.74/2.44 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v4) | ~ $i(v3) |
% 11.74/2.44 ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v3, v2) | ~
% 11.74/2.44 antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | ? [v5: $i]
% 11.74/2.44 : ($i(v5) & relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~
% 11.74/2.44 related(v0, v2, v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.74/2.44 $i] : ! [v4: $i] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3)
% 11.74/2.44 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v3,
% 11.74/2.44 v2) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) |
% 11.74/2.44 ex_sup_of_relstr_set(v0, v3) | ? [v5: $i] : ($i(v5) &
% 11.74/2.44 relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~ related(v0, v2,
% 11.74/2.44 v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 11.74/2.44 $i] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~
% 11.74/2.44 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v3,
% 11.74/2.44 v4) | ~ ex_sup_of_relstr_set(v0, v3) | ~ antisymmetric_relstr(v0) | ~
% 11.74/2.44 element(v4, v1) | ~ element(v2, v1) | ~ rel_str(v0) | related(v0, v2, v4))
% 11.74/2.44 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0)
% 11.74/2.44 = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 11.74/2.44 $i(v0) | ~ ex_sup_of_relstr_set(v0, v3) | ~ antisymmetric_relstr(v0) | ~
% 11.74/2.44 element(v2, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, v3, v2))
% 11.74/2.44
% 11.74/2.44 (t42_yellow_0)
% 11.74/2.44 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~
% 11.74/2.44 $i(v0) | ~ lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~
% 11.74/2.44 rel_str(v0) | ex_inf_of_relstr_set(v0, v1) | empty_carrier(v0)) & ! [v0:
% 11.74/2.44 $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 11.74/2.44 lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0) |
% 11.74/2.44 ex_sup_of_relstr_set(v0, empty_set) | empty_carrier(v0))
% 11.74/2.44
% 11.74/2.44 (t44_yellow_0)
% 11.74/2.44 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v1
% 11.74/2.44 & bottom_of_relstr(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 11.74/2.44 lower_bounded_relstr(v0) & antisymmetric_relstr(v0) & element(v3, v1) &
% 11.74/2.44 rel_str(v0) & ~ related(v0, v2, v3) & ~ empty_carrier(v0))
% 11.74/2.44
% 11.74/2.44 (t6_boole)
% 11.74/2.44 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 11.74/2.44
% 11.74/2.44 (t6_yellow_0)
% 11.74/2.44 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0)
% 11.74/2.44 = v1) | ~ $i(v2) | ~ $i(v0) | ~ element(v2, v1) | ~ rel_str(v0) |
% 11.74/2.44 relstr_element_smaller(v0, empty_set, v2)) & ! [v0: $i] : ! [v1: $i] : !
% 11.74/2.44 [v2: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ element(v2,
% 11.74/2.44 v1) | ~ rel_str(v0) | relstr_set_smaller(v0, empty_set, v2))
% 11.74/2.44
% 11.74/2.44 (function-axioms)
% 11.74/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.74/2.44 (join_on_relstr(v3, v2) = v1) | ~ (join_on_relstr(v3, v2) = v0)) & ! [v0:
% 11.74/2.44 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~
% 11.74/2.44 (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.74/2.44 | ~ (bottom_of_relstr(v2) = v1) | ~ (bottom_of_relstr(v2) = v0))
% 11.74/2.44
% 11.74/2.44 Further assumptions not needed in the proof:
% 11.74/2.44 --------------------------------------------
% 11.74/2.44 antisymmetry_r2_hidden, cc1_finset_1, dt_k1_xboole_0, dt_k1_yellow_0,
% 11.74/2.44 dt_l1_orders_2, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0,
% 11.74/2.44 existence_l1_orders_2, existence_l1_struct_0, existence_m1_subset_1,
% 11.74/2.44 fc1_struct_0, fc1_xboole_0, rc1_finset_1, rc2_xboole_0, rc3_struct_0, t1_subset,
% 11.74/2.44 t2_subset, t7_boole, t8_boole
% 11.74/2.44
% 11.74/2.44 Those formulas are unsatisfiable:
% 11.74/2.44 ---------------------------------
% 11.74/2.44
% 11.74/2.44 Begin of proof
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (d11_yellow_0) implies:
% 11.74/2.45 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0)
% 11.74/2.45 | | ~ rel_str(v0) | (join_on_relstr(v0, empty_set) = v1 & $i(v1)))
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (dt_k3_yellow_0) implies:
% 11.74/2.45 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0)
% 11.74/2.45 | | ~ rel_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 & $i(v2) &
% 11.74/2.45 | element(v1, v2)))
% 11.74/2.45 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 11.74/2.45 | rel_str(v0) | ? [v2: $i] : (bottom_of_relstr(v0) = v2 & $i(v2) &
% 11.74/2.45 | element(v2, v1)))
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (t30_yellow_0) implies:
% 11.74/2.45 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 11.74/2.45 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~
% 11.74/2.45 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 11.74/2.45 | relstr_set_smaller(v0, v3, v4) | ~ ex_sup_of_relstr_set(v0, v3) | ~
% 11.74/2.45 | antisymmetric_relstr(v0) | ~ element(v4, v1) | ~ element(v2, v1) |
% 11.74/2.45 | ~ rel_str(v0) | related(v0, v2, v4))
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (t42_yellow_0) implies:
% 11.74/2.45 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 11.74/2.45 | lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~
% 11.74/2.45 | rel_str(v0) | ex_sup_of_relstr_set(v0, empty_set) |
% 11.74/2.45 | empty_carrier(v0))
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (t6_boole) implies:
% 11.74/2.45 | (6) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (t6_yellow_0) implies:
% 11.74/2.45 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v1) |
% 11.74/2.45 | ~ $i(v2) | ~ $i(v0) | ~ element(v2, v1) | ~ rel_str(v0) |
% 11.74/2.45 | relstr_set_smaller(v0, empty_set, v2))
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (function-axioms) implies:
% 11.74/2.45 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.74/2.45 | (bottom_of_relstr(v2) = v1) | ~ (bottom_of_relstr(v2) = v0))
% 11.74/2.45 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.74/2.45 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 11.74/2.45 |
% 11.74/2.45 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_25_0 gives:
% 11.74/2.45 | (10) $i(all_25_0) & empty(all_25_0)
% 11.74/2.45 |
% 11.74/2.45 | ALPHA: (10) implies:
% 11.74/2.46 | (11) empty(all_25_0)
% 11.74/2.46 | (12) $i(all_25_0)
% 11.74/2.46 |
% 11.74/2.46 | DELTA: instantiating (t44_yellow_0) with fresh symbols all_32_0, all_32_1,
% 11.74/2.46 | all_32_2, all_32_3 gives:
% 11.74/2.46 | (13) the_carrier(all_32_3) = all_32_2 & bottom_of_relstr(all_32_3) =
% 11.74/2.46 | all_32_1 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) &
% 11.74/2.46 | lower_bounded_relstr(all_32_3) & antisymmetric_relstr(all_32_3) &
% 11.74/2.46 | element(all_32_0, all_32_2) & rel_str(all_32_3) & ~ related(all_32_3,
% 11.74/2.46 | all_32_1, all_32_0) & ~ empty_carrier(all_32_3)
% 11.74/2.46 |
% 11.74/2.46 | ALPHA: (13) implies:
% 11.74/2.46 | (14) ~ empty_carrier(all_32_3)
% 11.74/2.46 | (15) ~ related(all_32_3, all_32_1, all_32_0)
% 11.74/2.46 | (16) rel_str(all_32_3)
% 11.74/2.46 | (17) element(all_32_0, all_32_2)
% 11.74/2.46 | (18) antisymmetric_relstr(all_32_3)
% 11.74/2.46 | (19) lower_bounded_relstr(all_32_3)
% 11.74/2.46 | (20) $i(all_32_3)
% 11.74/2.46 | (21) $i(all_32_0)
% 11.74/2.46 | (22) bottom_of_relstr(all_32_3) = all_32_1
% 11.74/2.46 | (23) the_carrier(all_32_3) = all_32_2
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (6) with all_25_0, simplifying with (11), (12)
% 11.74/2.46 | gives:
% 11.74/2.46 | (24) all_25_0 = empty_set
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (2) with all_32_3, all_32_1, simplifying with (16),
% 11.74/2.46 | (20), (22) gives:
% 11.74/2.46 | (25) ? [v0: $i] : (the_carrier(all_32_3) = v0 & $i(v0) & element(all_32_1,
% 11.74/2.46 | v0))
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (1) with all_32_3, all_32_1, simplifying with (16),
% 11.74/2.46 | (20), (22) gives:
% 11.74/2.46 | (26) join_on_relstr(all_32_3, empty_set) = all_32_1 & $i(all_32_1)
% 11.74/2.46 |
% 11.74/2.46 | ALPHA: (26) implies:
% 11.74/2.46 | (27) join_on_relstr(all_32_3, empty_set) = all_32_1
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (7) with all_32_3, all_32_2, all_32_0, simplifying
% 11.74/2.46 | with (16), (17), (20), (21), (23) gives:
% 11.74/2.46 | (28) relstr_set_smaller(all_32_3, empty_set, all_32_0)
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (5) with all_32_3, all_32_2, simplifying with (14),
% 11.74/2.46 | (16), (18), (19), (20), (23) gives:
% 11.74/2.46 | (29) ex_sup_of_relstr_set(all_32_3, empty_set)
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (3) with all_32_3, all_32_2, simplifying with (16),
% 11.74/2.46 | (20), (23) gives:
% 11.74/2.46 | (30) ? [v0: $i] : (bottom_of_relstr(all_32_3) = v0 & $i(v0) & element(v0,
% 11.74/2.46 | all_32_2))
% 11.74/2.46 |
% 11.74/2.46 | DELTA: instantiating (30) with fresh symbol all_44_0 gives:
% 11.74/2.46 | (31) bottom_of_relstr(all_32_3) = all_44_0 & $i(all_44_0) &
% 11.74/2.46 | element(all_44_0, all_32_2)
% 11.74/2.46 |
% 11.74/2.46 | ALPHA: (31) implies:
% 11.74/2.46 | (32) $i(all_44_0)
% 11.74/2.46 | (33) bottom_of_relstr(all_32_3) = all_44_0
% 11.74/2.46 |
% 11.74/2.46 | DELTA: instantiating (25) with fresh symbol all_46_0 gives:
% 11.74/2.46 | (34) the_carrier(all_32_3) = all_46_0 & $i(all_46_0) & element(all_32_1,
% 11.74/2.46 | all_46_0)
% 11.74/2.46 |
% 11.74/2.46 | ALPHA: (34) implies:
% 11.74/2.46 | (35) element(all_32_1, all_46_0)
% 11.74/2.46 | (36) the_carrier(all_32_3) = all_46_0
% 11.74/2.46 |
% 11.74/2.46 | REDUCE: (12), (24) imply:
% 11.74/2.46 | (37) $i(empty_set)
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (8) with all_32_1, all_44_0, all_32_3, simplifying
% 11.74/2.46 | with (22), (33) gives:
% 11.74/2.46 | (38) all_44_0 = all_32_1
% 11.74/2.46 |
% 11.74/2.46 | GROUND_INST: instantiating (9) with all_32_2, all_46_0, all_32_3, simplifying
% 11.74/2.46 | with (23), (36) gives:
% 11.74/2.46 | (39) all_46_0 = all_32_2
% 11.74/2.46 |
% 11.74/2.46 | REDUCE: (32), (38) imply:
% 11.74/2.46 | (40) $i(all_32_1)
% 11.74/2.46 |
% 11.74/2.47 | REDUCE: (35), (39) imply:
% 11.74/2.47 | (41) element(all_32_1, all_32_2)
% 11.74/2.47 |
% 11.74/2.47 | GROUND_INST: instantiating (4) with all_32_3, all_32_2, all_32_1, empty_set,
% 11.74/2.47 | all_32_0, simplifying with (15), (16), (17), (18), (20), (21),
% 11.74/2.47 | (23), (27), (28), (29), (37), (40), (41) gives:
% 11.74/2.47 | (42) $false
% 11.99/2.47 |
% 11.99/2.47 | CLOSE: (42) is inconsistent.
% 11.99/2.47 |
% 11.99/2.47 End of proof
% 11.99/2.47 % SZS output end Proof for theBenchmark
% 11.99/2.47
% 11.99/2.47 1863ms
%------------------------------------------------------------------------------