TSTP Solution File: SEU357+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU357+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 : n031.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 17:44:16 EDT 2023
% Result : Theorem 8.38s 1.91s
% Output : Proof 11.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU357+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:16:50 EDT 2023
% 0.13/0.35 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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
% 2.37/0.99 Prover 1: Preprocessing ...
% 2.37/0.99 Prover 4: Preprocessing ...
% 2.37/1.02 Prover 5: Preprocessing ...
% 2.37/1.02 Prover 2: Preprocessing ...
% 2.37/1.02 Prover 0: Preprocessing ...
% 2.37/1.02 Prover 6: Preprocessing ...
% 2.37/1.03 Prover 3: Preprocessing ...
% 4.34/1.37 Prover 2: Proving ...
% 4.34/1.37 Prover 3: Warning: ignoring some quantifiers
% 4.34/1.37 Prover 5: Proving ...
% 4.34/1.38 Prover 6: Proving ...
% 4.34/1.39 Prover 3: Constructing countermodel ...
% 4.34/1.39 Prover 1: Warning: ignoring some quantifiers
% 4.34/1.40 Prover 1: Constructing countermodel ...
% 6.57/1.63 Prover 4: Warning: ignoring some quantifiers
% 6.90/1.67 Prover 4: Constructing countermodel ...
% 6.90/1.73 Prover 0: Proving ...
% 8.38/1.90 Prover 2: proved (1274ms)
% 8.38/1.91
% 8.38/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.38/1.91
% 8.38/1.91 Prover 0: stopped
% 8.38/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.38/1.91 Prover 3: stopped
% 8.38/1.91 Prover 6: stopped
% 8.38/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.38/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.38/1.91 Prover 5: stopped
% 8.38/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.38/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.38/1.95 Prover 10: Preprocessing ...
% 8.38/1.97 Prover 7: Preprocessing ...
% 8.38/1.98 Prover 8: Preprocessing ...
% 8.38/1.98 Prover 13: Preprocessing ...
% 9.26/1.99 Prover 11: Preprocessing ...
% 9.65/2.03 Prover 10: Warning: ignoring some quantifiers
% 9.65/2.04 Prover 10: Constructing countermodel ...
% 9.65/2.05 Prover 13: Warning: ignoring some quantifiers
% 9.65/2.06 Prover 13: Constructing countermodel ...
% 9.65/2.07 Prover 7: Warning: ignoring some quantifiers
% 9.65/2.07 Prover 7: Constructing countermodel ...
% 10.29/2.14 Prover 8: Warning: ignoring some quantifiers
% 10.29/2.16 Prover 8: Constructing countermodel ...
% 10.77/2.22 Prover 10: Found proof (size 28)
% 10.77/2.22 Prover 10: proved (306ms)
% 10.77/2.22 Prover 1: stopped
% 10.77/2.22 Prover 4: stopped
% 10.77/2.22 Prover 8: stopped
% 10.77/2.22 Prover 7: stopped
% 10.77/2.22 Prover 13: stopped
% 11.23/2.27 Prover 11: Warning: ignoring some quantifiers
% 11.27/2.28 Prover 11: Constructing countermodel ...
% 11.27/2.29 Prover 11: stopped
% 11.27/2.29
% 11.27/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.27/2.29
% 11.27/2.29 % SZS output start Proof for theBenchmark
% 11.27/2.29 Assumptions after simplification:
% 11.27/2.29 ---------------------------------
% 11.27/2.29
% 11.27/2.29 (d8_yellow_0)
% 11.43/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) =
% 11.43/2.32 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relstr_element_smaller(v0,
% 11.43/2.32 v2, v3) | ~ element(v3, v1) | ~ rel_str(v0) | ex_inf_of_relstr_set(v0,
% 11.43/2.32 v2) | ? [v4: $i] : ($i(v4) & (( ~ (v4 = v3) & relstr_element_smaller(v0,
% 11.43/2.32 v2, v4) & element(v4, v1) & ! [v5: $i] : ( ~ $i(v5) | ~
% 11.43/2.32 relstr_element_smaller(v0, v2, v5) | ~ element(v5, v1) |
% 11.43/2.32 related(v0, v5, v4))) | (relstr_element_smaller(v0, v2, v4) &
% 11.43/2.32 element(v4, v1) & ~ related(v0, v4, v3))))) & ! [v0: $i] : ! [v1:
% 11.43/2.32 $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 11.43/2.32 ex_inf_of_relstr_set(v0, v2) | ~ rel_str(v0) | ? [v3: $i] : ($i(v3) &
% 11.43/2.32 relstr_element_smaller(v0, v2, v3) & element(v3, v1) & ! [v4: $i] : (v4 =
% 11.43/2.32 v3 | ~ $i(v4) | ~ relstr_element_smaller(v0, v2, v4) | ~ element(v4,
% 11.43/2.32 v1) | ? [v5: $i] : ($i(v5) & relstr_element_smaller(v0, v2, v5) &
% 11.43/2.32 element(v5, v1) & ~ related(v0, v5, v4))) & ! [v4: $i] : ( ~ $i(v4)
% 11.43/2.32 | ~ relstr_element_smaller(v0, v2, v4) | ~ element(v4, v1) |
% 11.43/2.32 related(v0, v4, v3))))
% 11.43/2.32
% 11.43/2.32 (t16_yellow_0)
% 11.43/2.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v1
% 11.43/2.33 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & antisymmetric_relstr(v0) & rel_str(v0)
% 11.43/2.33 & ((relstr_element_smaller(v0, v2, v3) & element(v3, v1) & ~
% 11.43/2.33 ex_inf_of_relstr_set(v0, v2) & ! [v4: $i] : ( ~ $i(v4) | ~
% 11.43/2.33 relstr_element_smaller(v0, v2, v4) | ~ element(v4, v1) | related(v0,
% 11.43/2.33 v4, v3))) | (ex_inf_of_relstr_set(v0, v2) & ! [v4: $i] : ( ~ $i(v4)
% 11.43/2.33 | ~ relstr_element_smaller(v0, v2, v4) | ~ element(v4, v1) | ? [v5:
% 11.43/2.33 $i] : ($i(v5) & relstr_element_smaller(v0, v2, v5) & element(v5, v1)
% 11.43/2.33 & ~ related(v0, v5, v4))))))
% 11.43/2.33
% 11.43/2.33 (t25_orders_2)
% 11.55/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 11.55/2.33 (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 11.55/2.33 antisymmetric_relstr(v0) | ~ related(v0, v3, v2) | ~ related(v0, v2, v3) |
% 11.55/2.33 ~ element(v3, v1) | ~ element(v2, v1) | ~ rel_str(v0))
% 11.55/2.33
% 11.55/2.33 Further assumptions not needed in the proof:
% 11.55/2.33 --------------------------------------------
% 11.55/2.33 dt_l1_orders_2, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0,
% 11.55/2.33 existence_l1_orders_2, existence_l1_struct_0, existence_m1_subset_1
% 11.55/2.33
% 11.55/2.33 Those formulas are unsatisfiable:
% 11.55/2.33 ---------------------------------
% 11.55/2.33
% 11.55/2.33 Begin of proof
% 11.55/2.33 |
% 11.55/2.33 | ALPHA: (d8_yellow_0) implies:
% 11.55/2.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v1) |
% 11.55/2.33 | ~ $i(v2) | ~ $i(v0) | ~ ex_inf_of_relstr_set(v0, v2) | ~
% 11.55/2.33 | rel_str(v0) | ? [v3: $i] : ($i(v3) & relstr_element_smaller(v0, v2,
% 11.55/2.34 | v3) & element(v3, v1) & ! [v4: $i] : (v4 = v3 | ~ $i(v4) | ~
% 11.55/2.34 | relstr_element_smaller(v0, v2, v4) | ~ element(v4, v1) | ? [v5:
% 11.55/2.34 | $i] : ($i(v5) & relstr_element_smaller(v0, v2, v5) &
% 11.55/2.34 | element(v5, v1) & ~ related(v0, v5, v4))) & ! [v4: $i] : ( ~
% 11.55/2.34 | $i(v4) | ~ relstr_element_smaller(v0, v2, v4) | ~ element(v4,
% 11.55/2.34 | v1) | related(v0, v4, v3))))
% 11.55/2.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.55/2.34 | (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 11.55/2.34 | relstr_element_smaller(v0, v2, v3) | ~ element(v3, v1) | ~
% 11.55/2.34 | rel_str(v0) | ex_inf_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) &
% 11.55/2.34 | (( ~ (v4 = v3) & relstr_element_smaller(v0, v2, v4) & element(v4,
% 11.55/2.34 | v1) & ! [v5: $i] : ( ~ $i(v5) | ~
% 11.55/2.34 | relstr_element_smaller(v0, v2, v5) | ~ element(v5, v1) |
% 11.55/2.34 | related(v0, v5, v4))) | (relstr_element_smaller(v0, v2, v4) &
% 11.55/2.34 | element(v4, v1) & ~ related(v0, v4, v3)))))
% 11.55/2.34 |
% 11.55/2.34 | DELTA: instantiating (t16_yellow_0) with fresh symbols all_11_0, all_11_1,
% 11.55/2.34 | all_11_2, all_11_3 gives:
% 11.55/2.34 | (3) the_carrier(all_11_3) = all_11_2 & $i(all_11_0) & $i(all_11_1) &
% 11.55/2.34 | $i(all_11_2) & $i(all_11_3) & antisymmetric_relstr(all_11_3) &
% 11.55/2.34 | rel_str(all_11_3) & ((relstr_element_smaller(all_11_3, all_11_1,
% 11.55/2.34 | all_11_0) & element(all_11_0, all_11_2) & ~
% 11.55/2.34 | ex_inf_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0)
% 11.55/2.34 | | ~ relstr_element_smaller(all_11_3, all_11_1, v0) | ~
% 11.55/2.34 | element(v0, all_11_2) | related(all_11_3, v0, all_11_0))) |
% 11.55/2.34 | (ex_inf_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0)
% 11.55/2.34 | | ~ relstr_element_smaller(all_11_3, all_11_1, v0) | ~
% 11.55/2.34 | element(v0, all_11_2) | ? [v1: $i] : ($i(v1) &
% 11.55/2.34 | relstr_element_smaller(all_11_3, all_11_1, v1) & element(v1,
% 11.55/2.34 | all_11_2) & ~ related(all_11_3, v1, v0)))))
% 11.55/2.34 |
% 11.55/2.34 | ALPHA: (3) implies:
% 11.55/2.34 | (4) rel_str(all_11_3)
% 11.55/2.34 | (5) antisymmetric_relstr(all_11_3)
% 11.55/2.34 | (6) $i(all_11_3)
% 11.55/2.34 | (7) $i(all_11_1)
% 11.55/2.34 | (8) $i(all_11_0)
% 11.55/2.34 | (9) the_carrier(all_11_3) = all_11_2
% 11.55/2.35 | (10) (relstr_element_smaller(all_11_3, all_11_1, all_11_0) &
% 11.55/2.35 | element(all_11_0, all_11_2) & ~ ex_inf_of_relstr_set(all_11_3,
% 11.55/2.35 | all_11_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 11.55/2.35 | relstr_element_smaller(all_11_3, all_11_1, v0) | ~ element(v0,
% 11.55/2.35 | all_11_2) | related(all_11_3, v0, all_11_0))) |
% 11.55/2.35 | (ex_inf_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0) |
% 11.55/2.35 | ~ relstr_element_smaller(all_11_3, all_11_1, v0) | ~ element(v0,
% 11.55/2.35 | all_11_2) | ? [v1: $i] : ($i(v1) &
% 11.55/2.35 | relstr_element_smaller(all_11_3, all_11_1, v1) & element(v1,
% 11.55/2.35 | all_11_2) & ~ related(all_11_3, v1, v0))))
% 11.55/2.35 |
% 11.55/2.35 | BETA: splitting (10) gives:
% 11.55/2.35 |
% 11.55/2.35 | Case 1:
% 11.55/2.35 | |
% 11.55/2.35 | | (11) relstr_element_smaller(all_11_3, all_11_1, all_11_0) &
% 11.55/2.35 | | element(all_11_0, all_11_2) & ~ ex_inf_of_relstr_set(all_11_3,
% 11.55/2.35 | | all_11_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 11.55/2.35 | | relstr_element_smaller(all_11_3, all_11_1, v0) | ~ element(v0,
% 11.55/2.35 | | all_11_2) | related(all_11_3, v0, all_11_0))
% 11.55/2.35 | |
% 11.55/2.35 | | ALPHA: (11) implies:
% 11.55/2.35 | | (12) ~ ex_inf_of_relstr_set(all_11_3, all_11_1)
% 11.55/2.35 | | (13) element(all_11_0, all_11_2)
% 11.55/2.35 | | (14) relstr_element_smaller(all_11_3, all_11_1, all_11_0)
% 11.55/2.35 | | (15) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_element_smaller(all_11_3,
% 11.55/2.35 | | all_11_1, v0) | ~ element(v0, all_11_2) | related(all_11_3, v0,
% 11.55/2.35 | | all_11_0))
% 11.55/2.35 | |
% 11.55/2.35 | | GROUND_INST: instantiating (2) with all_11_3, all_11_2, all_11_1, all_11_0,
% 11.55/2.35 | | simplifying with (4), (6), (7), (8), (9), (12), (13), (14)
% 11.55/2.35 | | gives:
% 11.55/2.35 | | (16) ? [v0: $i] : ($i(v0) & (( ~ (v0 = all_11_0) &
% 11.55/2.35 | | relstr_element_smaller(all_11_3, all_11_1, v0) & element(v0,
% 11.55/2.35 | | all_11_2) & ! [v1: $i] : ( ~ $i(v1) | ~
% 11.55/2.35 | | relstr_element_smaller(all_11_3, all_11_1, v1) | ~
% 11.55/2.35 | | element(v1, all_11_2) | related(all_11_3, v1, v0))) |
% 11.55/2.35 | | (relstr_element_smaller(all_11_3, all_11_1, v0) & element(v0,
% 11.55/2.35 | | all_11_2) & ~ related(all_11_3, v0, all_11_0))))
% 11.55/2.35 | |
% 11.55/2.35 | | DELTA: instantiating (16) with fresh symbol all_40_0 gives:
% 11.55/2.35 | | (17) $i(all_40_0) & (( ~ (all_40_0 = all_11_0) &
% 11.55/2.35 | | relstr_element_smaller(all_11_3, all_11_1, all_40_0) &
% 11.55/2.35 | | element(all_40_0, all_11_2) & ! [v0: $i] : ( ~ $i(v0) | ~
% 11.55/2.35 | | relstr_element_smaller(all_11_3, all_11_1, v0) | ~
% 11.55/2.35 | | element(v0, all_11_2) | related(all_11_3, v0, all_40_0))) |
% 11.55/2.35 | | (relstr_element_smaller(all_11_3, all_11_1, all_40_0) &
% 11.55/2.35 | | element(all_40_0, all_11_2) & ~ related(all_11_3, all_40_0,
% 11.55/2.35 | | all_11_0)))
% 11.55/2.35 | |
% 11.55/2.35 | | ALPHA: (17) implies:
% 11.55/2.35 | | (18) $i(all_40_0)
% 11.55/2.36 | | (19) ( ~ (all_40_0 = all_11_0) & relstr_element_smaller(all_11_3,
% 11.55/2.36 | | all_11_1, all_40_0) & element(all_40_0, all_11_2) & ! [v0: $i]
% 11.55/2.36 | | : ( ~ $i(v0) | ~ relstr_element_smaller(all_11_3, all_11_1, v0) |
% 11.55/2.36 | | ~ element(v0, all_11_2) | related(all_11_3, v0, all_40_0))) |
% 11.55/2.36 | | (relstr_element_smaller(all_11_3, all_11_1, all_40_0) &
% 11.55/2.36 | | element(all_40_0, all_11_2) & ~ related(all_11_3, all_40_0,
% 11.55/2.36 | | all_11_0))
% 11.55/2.36 | |
% 11.55/2.36 | | BETA: splitting (19) gives:
% 11.55/2.36 | |
% 11.55/2.36 | | Case 1:
% 11.55/2.36 | | |
% 11.55/2.36 | | | (20) ~ (all_40_0 = all_11_0) & relstr_element_smaller(all_11_3,
% 11.55/2.36 | | | all_11_1, all_40_0) & element(all_40_0, all_11_2) & ! [v0: $i]
% 11.55/2.36 | | | : ( ~ $i(v0) | ~ relstr_element_smaller(all_11_3, all_11_1, v0) |
% 11.55/2.36 | | | ~ element(v0, all_11_2) | related(all_11_3, v0, all_40_0))
% 11.55/2.36 | | |
% 11.55/2.36 | | | ALPHA: (20) implies:
% 11.55/2.36 | | | (21) ~ (all_40_0 = all_11_0)
% 11.55/2.36 | | | (22) element(all_40_0, all_11_2)
% 11.55/2.36 | | | (23) relstr_element_smaller(all_11_3, all_11_1, all_40_0)
% 11.55/2.36 | | | (24) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_element_smaller(all_11_3,
% 11.55/2.36 | | | all_11_1, v0) | ~ element(v0, all_11_2) | related(all_11_3,
% 11.55/2.36 | | | v0, all_40_0))
% 11.55/2.36 | | |
% 11.55/2.36 | | | GROUND_INST: instantiating (24) with all_11_0, simplifying with (8), (13),
% 11.55/2.36 | | | (14) gives:
% 11.55/2.36 | | | (25) related(all_11_3, all_11_0, all_40_0)
% 11.55/2.36 | | |
% 11.55/2.36 | | | GROUND_INST: instantiating (15) with all_40_0, simplifying with (18),
% 11.55/2.36 | | | (22), (23) gives:
% 11.55/2.36 | | | (26) related(all_11_3, all_40_0, all_11_0)
% 11.55/2.36 | | |
% 11.55/2.36 | | | GROUND_INST: instantiating (t25_orders_2) with all_11_3, all_11_2,
% 11.55/2.36 | | | all_11_0, all_40_0, simplifying with (4), (5), (6), (8), (9),
% 11.55/2.36 | | | (13), (18), (22), (25), (26) gives:
% 11.55/2.36 | | | (27) all_40_0 = all_11_0
% 11.55/2.36 | | |
% 11.55/2.36 | | | REDUCE: (21), (27) imply:
% 11.55/2.36 | | | (28) $false
% 11.55/2.36 | | |
% 11.55/2.36 | | | CLOSE: (28) is inconsistent.
% 11.55/2.36 | | |
% 11.55/2.36 | | Case 2:
% 11.55/2.36 | | |
% 11.55/2.36 | | | (29) relstr_element_smaller(all_11_3, all_11_1, all_40_0) &
% 11.55/2.36 | | | element(all_40_0, all_11_2) & ~ related(all_11_3, all_40_0,
% 11.55/2.36 | | | all_11_0)
% 11.55/2.36 | | |
% 11.55/2.36 | | | ALPHA: (29) implies:
% 11.55/2.36 | | | (30) ~ related(all_11_3, all_40_0, all_11_0)
% 11.55/2.36 | | | (31) element(all_40_0, all_11_2)
% 11.55/2.36 | | | (32) relstr_element_smaller(all_11_3, all_11_1, all_40_0)
% 11.55/2.36 | | |
% 11.55/2.36 | | | GROUND_INST: instantiating (15) with all_40_0, simplifying with (18),
% 11.55/2.36 | | | (30), (31), (32) gives:
% 11.55/2.36 | | | (33) $false
% 11.55/2.36 | | |
% 11.55/2.36 | | | CLOSE: (33) is inconsistent.
% 11.55/2.36 | | |
% 11.55/2.36 | | End of split
% 11.55/2.36 | |
% 11.55/2.36 | Case 2:
% 11.55/2.36 | |
% 11.55/2.36 | | (34) ex_inf_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0)
% 11.55/2.36 | | | ~ relstr_element_smaller(all_11_3, all_11_1, v0) | ~
% 11.55/2.36 | | element(v0, all_11_2) | ? [v1: $i] : ($i(v1) &
% 11.55/2.36 | | relstr_element_smaller(all_11_3, all_11_1, v1) & element(v1,
% 11.55/2.36 | | all_11_2) & ~ related(all_11_3, v1, v0)))
% 11.55/2.36 | |
% 11.55/2.36 | | ALPHA: (34) implies:
% 11.55/2.37 | | (35) ex_inf_of_relstr_set(all_11_3, all_11_1)
% 11.55/2.37 | | (36) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_element_smaller(all_11_3,
% 11.55/2.37 | | all_11_1, v0) | ~ element(v0, all_11_2) | ? [v1: $i] : ($i(v1)
% 11.55/2.37 | | & relstr_element_smaller(all_11_3, all_11_1, v1) & element(v1,
% 11.55/2.37 | | all_11_2) & ~ related(all_11_3, v1, v0)))
% 11.55/2.37 | |
% 11.55/2.37 | | GROUND_INST: instantiating (1) with all_11_3, all_11_2, all_11_1,
% 11.55/2.37 | | simplifying with (4), (6), (7), (9), (35) gives:
% 11.55/2.37 | | (37) ? [v0: $i] : ($i(v0) & relstr_element_smaller(all_11_3, all_11_1,
% 11.55/2.37 | | v0) & element(v0, all_11_2) & ! [v1: $i] : (v1 = v0 | ~ $i(v1)
% 11.55/2.37 | | | ~ relstr_element_smaller(all_11_3, all_11_1, v1) | ~
% 11.55/2.37 | | element(v1, all_11_2) | ? [v2: $i] : ($i(v2) &
% 11.55/2.37 | | relstr_element_smaller(all_11_3, all_11_1, v2) & element(v2,
% 11.55/2.37 | | all_11_2) & ~ related(all_11_3, v2, v1))) & ! [v1: $i] : (
% 11.55/2.37 | | ~ $i(v1) | ~ relstr_element_smaller(all_11_3, all_11_1, v1) |
% 11.55/2.37 | | ~ element(v1, all_11_2) | related(all_11_3, v1, v0)))
% 11.55/2.37 | |
% 11.55/2.37 | | DELTA: instantiating (37) with fresh symbol all_39_0 gives:
% 11.55/2.37 | | (38) $i(all_39_0) & relstr_element_smaller(all_11_3, all_11_1, all_39_0)
% 11.55/2.37 | | & element(all_39_0, all_11_2) & ! [v0: any] : (v0 = all_39_0 | ~
% 11.55/2.37 | | $i(v0) | ~ relstr_element_smaller(all_11_3, all_11_1, v0) | ~
% 11.55/2.37 | | element(v0, all_11_2) | ? [v1: $i] : ($i(v1) &
% 11.55/2.37 | | relstr_element_smaller(all_11_3, all_11_1, v1) & element(v1,
% 11.55/2.37 | | all_11_2) & ~ related(all_11_3, v1, v0))) & ! [v0: $i] : ( ~
% 11.55/2.37 | | $i(v0) | ~ relstr_element_smaller(all_11_3, all_11_1, v0) | ~
% 11.55/2.37 | | element(v0, all_11_2) | related(all_11_3, v0, all_39_0))
% 11.55/2.37 | |
% 11.55/2.37 | | ALPHA: (38) implies:
% 11.55/2.37 | | (39) element(all_39_0, all_11_2)
% 11.55/2.37 | | (40) relstr_element_smaller(all_11_3, all_11_1, all_39_0)
% 11.55/2.37 | | (41) $i(all_39_0)
% 11.55/2.37 | | (42) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_element_smaller(all_11_3,
% 11.55/2.37 | | all_11_1, v0) | ~ element(v0, all_11_2) | related(all_11_3, v0,
% 11.55/2.37 | | all_39_0))
% 11.55/2.37 | |
% 11.55/2.37 | | GROUND_INST: instantiating (36) with all_39_0, simplifying with (39), (40),
% 11.55/2.37 | | (41) gives:
% 11.55/2.37 | | (43) ? [v0: $i] : ($i(v0) & relstr_element_smaller(all_11_3, all_11_1,
% 11.55/2.37 | | v0) & element(v0, all_11_2) & ~ related(all_11_3, v0,
% 11.55/2.37 | | all_39_0))
% 11.55/2.37 | |
% 11.55/2.37 | | DELTA: instantiating (43) with fresh symbol all_48_0 gives:
% 11.55/2.37 | | (44) $i(all_48_0) & relstr_element_smaller(all_11_3, all_11_1, all_48_0)
% 11.55/2.37 | | & element(all_48_0, all_11_2) & ~ related(all_11_3, all_48_0,
% 11.55/2.37 | | all_39_0)
% 11.55/2.37 | |
% 11.55/2.37 | | ALPHA: (44) implies:
% 11.55/2.37 | | (45) ~ related(all_11_3, all_48_0, all_39_0)
% 11.55/2.37 | | (46) element(all_48_0, all_11_2)
% 11.55/2.37 | | (47) relstr_element_smaller(all_11_3, all_11_1, all_48_0)
% 11.55/2.37 | | (48) $i(all_48_0)
% 11.55/2.37 | |
% 11.55/2.37 | | GROUND_INST: instantiating (42) with all_48_0, simplifying with (45), (46),
% 11.55/2.37 | | (47), (48) gives:
% 11.55/2.37 | | (49) $false
% 11.55/2.37 | |
% 11.55/2.37 | | CLOSE: (49) is inconsistent.
% 11.55/2.37 | |
% 11.55/2.37 | End of split
% 11.55/2.37 |
% 11.55/2.37 End of proof
% 11.55/2.37 % SZS output end Proof for theBenchmark
% 11.55/2.37
% 11.55/2.37 1762ms
%------------------------------------------------------------------------------