TSTP Solution File: SEU304+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU304+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 : n010.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 26.09s 4.45s
% Output : Proof 27.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU304+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.34 % Computer : n010.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Wed Aug 23 17:46:21 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.16/0.63 ________ _____
% 0.16/0.63 ___ __ \_________(_)________________________________
% 0.16/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.63
% 0.16/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.63 (2023-06-19)
% 0.16/0.63
% 0.16/0.63 (c) Philipp Rümmer, 2009-2023
% 0.16/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.63 Amanda Stjerna.
% 0.16/0.63 Free software under BSD-3-Clause.
% 0.16/0.63
% 0.16/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.63
% 0.16/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.65 Running up to 7 provers in parallel.
% 0.16/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.52/1.29 Prover 1: Preprocessing ...
% 3.52/1.29 Prover 4: Preprocessing ...
% 3.52/1.34 Prover 2: Preprocessing ...
% 3.52/1.34 Prover 5: Preprocessing ...
% 3.52/1.35 Prover 6: Preprocessing ...
% 3.52/1.35 Prover 3: Preprocessing ...
% 3.52/1.35 Prover 0: Preprocessing ...
% 10.40/2.30 Prover 1: Warning: ignoring some quantifiers
% 10.40/2.34 Prover 3: Warning: ignoring some quantifiers
% 11.28/2.43 Prover 5: Proving ...
% 11.43/2.45 Prover 6: Proving ...
% 11.43/2.45 Prover 1: Constructing countermodel ...
% 11.43/2.46 Prover 3: Constructing countermodel ...
% 11.43/2.49 Prover 2: Proving ...
% 13.13/2.70 Prover 4: Warning: ignoring some quantifiers
% 13.58/2.86 Prover 4: Constructing countermodel ...
% 15.26/3.02 Prover 0: Proving ...
% 16.67/3.23 Prover 3: gave up
% 16.67/3.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.90/3.34 Prover 7: Preprocessing ...
% 17.90/3.55 Prover 7: Warning: ignoring some quantifiers
% 18.28/3.61 Prover 7: Constructing countermodel ...
% 21.63/3.90 Prover 1: gave up
% 21.63/3.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.33/3.97 Prover 8: Preprocessing ...
% 23.32/4.30 Prover 8: Warning: ignoring some quantifiers
% 23.87/4.33 Prover 8: Constructing countermodel ...
% 25.39/4.44 Prover 7: Found proof (size 89)
% 25.39/4.44 Prover 7: proved (1208ms)
% 25.39/4.44 Prover 5: stopped
% 25.39/4.44 Prover 6: stopped
% 25.39/4.44 Prover 2: stopped
% 25.39/4.44 Prover 8: stopped
% 25.39/4.44 Prover 4: stopped
% 25.39/4.44 Prover 0: proved (3791ms)
% 25.39/4.44
% 26.09/4.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.09/4.45
% 26.09/4.47 % SZS output start Proof for theBenchmark
% 26.09/4.48 Assumptions after simplification:
% 26.09/4.48 ---------------------------------
% 26.09/4.48
% 26.09/4.48 (commutativity_k4_lattices)
% 26.26/4.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (meet_commut(v0,
% 26.26/4.52 v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.26/4.52 meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ?
% 26.26/4.52 [v4: $i] : ? [v5: $i] : ((v5 = v3 & meet_commut(v0, v1, v2) = v3 & $i(v3))
% 26.26/4.52 | (the_carrier(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ element(v1,
% 26.26/4.52 v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 26.26/4.52 ~ (meet_commut(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.26/4.52 meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ?
% 26.26/4.52 [v4: $i] : ? [v5: $i] : ((v5 = v3 & meet_commut(v0, v2, v1) = v3 & $i(v3))
% 26.26/4.52 | (the_carrier(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ element(v1,
% 26.26/4.52 v4)))))
% 26.26/4.52
% 26.26/4.52 (d1_lattices)
% 26.26/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (the_L_join(v0) = v1) | ~ $i(v0) | ~
% 26.26/4.53 join_semilatt_str(v0) | empty_carrier(v0) | ? [v2: $i] : (the_carrier(v0) =
% 26.26/4.53 v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 26.26/4.53 (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ $i(v4) | ~
% 26.26/4.53 $i(v3) | ~ element(v4, v2) | ~ element(v3, v2) | (join(v0, v3, v4) =
% 26.26/4.53 v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 26.26/4.53 (join(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v2) |
% 26.26/4.53 ~ element(v3, v2) | (apply_binary_as_element(v2, v2, v2, v1, v3, v4) =
% 26.26/4.53 v5 & $i(v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) =
% 26.26/4.53 v1) | ~ $i(v0) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2:
% 26.26/4.53 $i] : (the_L_join(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.26/4.53 $i] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~
% 26.26/4.53 $i(v4) | ~ $i(v3) | ~ element(v4, v1) | ~ element(v3, v1) | (join(v0,
% 26.26/4.53 v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 26.26/4.53 ( ~ (join(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v1) |
% 26.26/4.53 ~ element(v3, v1) | (apply_binary_as_element(v1, v1, v1, v2, v3, v4) =
% 26.26/4.53 v5 & $i(v5)))))
% 26.26/4.53
% 26.26/4.53 (d2_lattices)
% 26.50/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (the_L_meet(v0) = v1) | ~ $i(v0) | ~
% 26.50/4.54 meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2: $i] : (the_carrier(v0) =
% 26.50/4.54 v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (meet(v0, v3,
% 26.50/4.54 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~
% 26.50/4.54 element(v3, v2) | (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5
% 26.50/4.54 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 26.50/4.54 (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ $i(v4) | ~
% 26.50/4.54 $i(v3) | ~ element(v4, v2) | ~ element(v3, v2) | (meet(v0, v3, v4) =
% 26.50/4.54 v5 & $i(v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) =
% 26.50/4.54 v1) | ~ $i(v0) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2:
% 26.50/4.54 $i] : (the_L_meet(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.50/4.54 $i] : ( ~ (meet(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 26.50/4.54 element(v4, v1) | ~ element(v3, v1) | (apply_binary_as_element(v1, v1,
% 26.50/4.54 v1, v2, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : !
% 26.50/4.54 [v5: $i] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~
% 26.50/4.54 $i(v4) | ~ $i(v3) | ~ element(v4, v1) | ~ element(v3, v1) | (meet(v0,
% 26.50/4.55 v3, v4) = v5 & $i(v5)))))
% 26.50/4.55
% 26.50/4.55 (d3_lattices)
% 26.55/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 26.55/4.55 | ~ (join(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ $i(v3) | ~
% 26.55/4.55 $i(v2) | ~ $i(v0) | ~ below(v0, v2, v3) | ~ join_semilatt_str(v0) | ~
% 26.55/4.55 element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) & ! [v0: $i] : !
% 26.55/4.55 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (join(v0, v2, v3) = v3) | ~
% 26.55/4.55 (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 26.55/4.55 join_semilatt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | below(v0,
% 26.55/4.55 v2, v3) | empty_carrier(v0))
% 26.55/4.55
% 26.55/4.55 (d8_lattices)
% 26.55/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 26.55/4.55 (meet(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2)
% 26.55/4.55 | ~ $i(v0) | ~ meet_absorbing(v0) | ~ latt_str(v0) | ~ element(v3, v1) |
% 26.55/4.55 ~ element(v2, v1) | join(v0, v4, v3) = v3 | empty_carrier(v0)) & ! [v0:
% 26.55/4.55 $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ latt_str(v0)
% 26.55/4.55 | meet_absorbing(v0) | empty_carrier(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 26.55/4.55 [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & meet(v0, v2, v3) = v4 & join(v0,
% 26.55/4.55 v4, v3) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & element(v3, v1) &
% 26.55/4.55 element(v2, v1)))
% 26.55/4.55
% 26.55/4.55 (dt_k4_lattices)
% 26.55/4.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (meet_commut(v0,
% 26.55/4.56 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.55/4.56 meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ?
% 26.55/4.56 [v4: $i] : (the_carrier(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~
% 26.55/4.56 element(v1, v4) | element(v3, v4))))
% 26.55/4.56
% 26.55/4.56 (dt_l3_lattices)
% 26.55/4.56 ! [v0: $i] : ( ~ $i(v0) | ~ latt_str(v0) | join_semilatt_str(v0)) & ! [v0:
% 26.55/4.56 $i] : ( ~ $i(v0) | ~ latt_str(v0) | meet_semilatt_str(v0))
% 26.55/4.56
% 26.55/4.56 (dt_u1_lattices)
% 26.55/4.56 ! [v0: $i] : ! [v1: $i] : ( ~ (the_L_meet(v0) = v1) | ~ $i(v0) | ~
% 26.55/4.56 meet_semilatt_str(v0) | function(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 26.55/4.56 (the_L_meet(v0) = v1) | ~ $i(v0) | ~ meet_semilatt_str(v0) | ? [v2: $i] :
% 26.55/4.56 ? [v3: $i] : (cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 &
% 26.55/4.56 $i(v3) & $i(v2) & relation_of2_as_subset(v1, v3, v2) & quasi_total(v1, v3,
% 26.55/4.56 v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~
% 26.55/4.56 $i(v0) | ~ meet_semilatt_str(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.55/4.56 (cartesian_product2(v1, v1) = v3 & the_L_meet(v0) = v2 & $i(v3) & $i(v2) &
% 26.55/4.56 relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3, v1) &
% 26.55/4.56 function(v2)))
% 26.55/4.56
% 26.55/4.56 (dt_u2_lattices)
% 26.55/4.58 ! [v0: $i] : ! [v1: $i] : ( ~ (the_L_join(v0) = v1) | ~ $i(v0) | ~
% 26.55/4.58 join_semilatt_str(v0) | function(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 26.55/4.58 (the_L_join(v0) = v1) | ~ $i(v0) | ~ join_semilatt_str(v0) | ? [v2: $i] :
% 26.55/4.58 ? [v3: $i] : (cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 &
% 26.55/4.58 $i(v3) & $i(v2) & relation_of2_as_subset(v1, v3, v2) & quasi_total(v1, v3,
% 26.55/4.58 v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~
% 26.55/4.58 $i(v0) | ~ join_semilatt_str(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.55/4.58 (cartesian_product2(v1, v1) = v3 & the_L_join(v0) = v2 & $i(v3) & $i(v2) &
% 26.55/4.58 relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3, v1) &
% 26.55/4.58 function(v2)))
% 26.55/4.58
% 26.55/4.58 (redefinition_k4_lattices)
% 26.55/4.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (meet(v0, v1, v2)
% 26.55/4.58 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ meet_semilatt_str(v0) | ~
% 26.55/4.58 meet_commutative(v0) | empty_carrier(v0) | ? [v4: $i] : ? [v5: $i] : ((v5
% 26.55/4.58 = v3 & meet_commut(v0, v1, v2) = v3 & $i(v3)) | (the_carrier(v0) = v4 &
% 26.55/4.58 $i(v4) & ( ~ element(v2, v4) | ~ element(v1, v4))))) & ! [v0: $i] : !
% 26.55/4.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~
% 26.55/4.58 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ meet_semilatt_str(v0) | ~
% 26.55/4.58 meet_commutative(v0) | empty_carrier(v0) | ? [v4: $i] : ? [v5: $i] : ((v5
% 26.55/4.58 = v3 & meet(v0, v1, v2) = v3 & $i(v3)) | (the_carrier(v0) = v4 & $i(v4)
% 26.55/4.58 & ( ~ element(v2, v4) | ~ element(v1, v4)))))
% 26.55/4.58
% 26.55/4.58 (t23_lattices)
% 26.55/4.58 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 26.55/4.58 (the_carrier(v0) = v1 & meet_commut(v0, v2, v3) = v4 & $i(v4) & $i(v3) &
% 26.55/4.58 $i(v2) & $i(v1) & $i(v0) & meet_absorbing(v0) & latt_str(v0) & element(v3,
% 26.55/4.58 v1) & element(v2, v1) & meet_commutative(v0) & ~ below(v0, v4, v2) & ~
% 26.55/4.58 empty_carrier(v0))
% 26.55/4.58
% 26.55/4.58 (function-axioms)
% 26.55/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.55/4.59 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (apply_binary_as_element(v7,
% 26.55/4.59 v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4,
% 26.55/4.59 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 26.55/4.59 ! [v4: $i] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~
% 26.55/4.59 (apply_binary(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 26.55/4.59 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~
% 26.55/4.59 (meet(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 26.55/4.59 $i] : ! [v4: $i] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3,
% 26.55/4.59 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 26.55/4.59 [v4: $i] : (v1 = v0 | ~ (meet_commut(v4, v3, v2) = v1) | ~ (meet_commut(v4,
% 26.55/4.59 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 26.55/4.59 (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3,
% 26.55/4.59 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.55/4.59 (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 26.55/4.59 ! [v2: $i] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0)) &
% 26.55/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_L_join(v2) = v1)
% 26.55/4.59 | ~ (the_L_join(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 26.55/4.59 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 26.55/4.59
% 26.55/4.59 Further assumptions not needed in the proof:
% 26.55/4.59 --------------------------------------------
% 26.55/4.59 antisymmetry_r2_hidden, cc1_finsub_1, cc2_finsub_1, dt_k1_binop_1,
% 26.55/4.59 dt_k1_lattices, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_lattices,
% 26.55/4.59 dt_k2_zfmisc_1, dt_l1_lattices, dt_l1_struct_0, dt_l2_lattices, dt_m1_relset_1,
% 26.55/4.59 dt_m1_subset_1, dt_m2_relset_1, dt_u1_struct_0, existence_l1_lattices,
% 26.55/4.59 existence_l1_struct_0, existence_l2_lattices, existence_l3_lattices,
% 26.55/4.59 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 26.55/4.59 fc1_finsub_1, fc1_struct_0, rc3_struct_0, rc5_struct_0, redefinition_k2_binop_1,
% 26.55/4.59 redefinition_m2_relset_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 26.55/4.59 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 26.55/4.59
% 26.55/4.59 Those formulas are unsatisfiable:
% 26.55/4.59 ---------------------------------
% 26.55/4.59
% 26.55/4.59 Begin of proof
% 26.55/4.59 |
% 26.55/4.59 | ALPHA: (commutativity_k4_lattices) implies:
% 26.55/4.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 26.55/4.59 | (meet_commut(v0, v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 26.55/4.59 | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0)
% 26.55/4.59 | | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & meet_commut(v0, v1, v2) =
% 26.55/4.59 | v3 & $i(v3)) | (the_carrier(v0) = v4 & $i(v4) & ( ~ element(v2,
% 26.55/4.59 | v4) | ~ element(v1, v4)))))
% 26.55/4.59 |
% 26.55/4.59 | ALPHA: (d1_lattices) implies:
% 26.55/4.60 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 26.55/4.60 | join_semilatt_str(v0) | empty_carrier(v0) | ? [v2: $i] :
% 26.55/4.60 | (the_L_join(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.55/4.60 | $i] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5)
% 26.55/4.60 | | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v1) | ~ element(v3, v1)
% 26.55/4.60 | | (join(v0, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] :
% 26.55/4.60 | ! [v5: $i] : ( ~ (join(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 26.55/4.60 | ~ element(v4, v1) | ~ element(v3, v1) |
% 26.55/4.60 | (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5 &
% 26.55/4.60 | $i(v5)))))
% 26.55/4.60 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (the_L_join(v0) = v1) | ~ $i(v0) | ~
% 26.55/4.60 | join_semilatt_str(v0) | empty_carrier(v0) | ? [v2: $i] :
% 26.55/4.60 | (the_carrier(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.55/4.60 | $i] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5)
% 26.55/4.60 | | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~ element(v3, v2)
% 26.55/4.60 | | (join(v0, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] :
% 26.55/4.60 | ! [v5: $i] : ( ~ (join(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 26.55/4.60 | ~ element(v4, v2) | ~ element(v3, v2) |
% 26.55/4.60 | (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5 &
% 26.55/4.60 | $i(v5)))))
% 26.55/4.60 |
% 26.55/4.60 | ALPHA: (d2_lattices) implies:
% 26.55/4.60 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 26.55/4.60 | meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2: $i] :
% 26.55/4.60 | (the_L_meet(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.55/4.60 | $i] : ( ~ (meet(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 26.55/4.60 | element(v4, v1) | ~ element(v3, v1) |
% 26.55/4.60 | (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5 & $i(v5)))
% 26.55/4.60 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 26.55/4.60 | (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~
% 26.55/4.60 | $i(v4) | ~ $i(v3) | ~ element(v4, v1) | ~ element(v3, v1) |
% 26.55/4.60 | (meet(v0, v3, v4) = v5 & $i(v5)))))
% 26.55/4.61 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (the_L_meet(v0) = v1) | ~ $i(v0) | ~
% 26.55/4.61 | meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2: $i] :
% 26.55/4.61 | (the_carrier(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 26.55/4.61 | $i] : ( ~ (meet(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 26.55/4.61 | element(v4, v2) | ~ element(v3, v2) |
% 26.55/4.61 | (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5 & $i(v5)))
% 26.55/4.61 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 26.81/4.61 | (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~
% 26.81/4.61 | $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~ element(v3, v2) |
% 26.81/4.61 | (meet(v0, v3, v4) = v5 & $i(v5)))))
% 26.81/4.61 |
% 26.81/4.61 | ALPHA: (d3_lattices) implies:
% 26.81/4.61 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (join(v0,
% 26.81/4.61 | v2, v3) = v3) | ~ (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2)
% 26.81/4.61 | | ~ $i(v0) | ~ join_semilatt_str(v0) | ~ element(v3, v1) | ~
% 26.81/4.61 | element(v2, v1) | below(v0, v2, v3) | empty_carrier(v0))
% 26.81/4.61 |
% 26.81/4.61 | ALPHA: (d8_lattices) implies:
% 26.81/4.61 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 26.81/4.61 | ~ (meet(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ $i(v3) |
% 26.81/4.61 | ~ $i(v2) | ~ $i(v0) | ~ meet_absorbing(v0) | ~ latt_str(v0) | ~
% 26.81/4.61 | element(v3, v1) | ~ element(v2, v1) | join(v0, v4, v3) = v3 |
% 26.81/4.61 | empty_carrier(v0))
% 26.81/4.61 |
% 26.81/4.61 | ALPHA: (dt_l3_lattices) implies:
% 26.81/4.61 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ latt_str(v0) | meet_semilatt_str(v0))
% 26.81/4.61 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ latt_str(v0) | join_semilatt_str(v0))
% 26.81/4.61 |
% 26.81/4.61 | ALPHA: (dt_u1_lattices) implies:
% 26.81/4.61 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) |
% 26.81/4.61 | ~ meet_semilatt_str(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.81/4.61 | (cartesian_product2(v1, v1) = v3 & the_L_meet(v0) = v2 & $i(v3) &
% 26.81/4.61 | $i(v2) & relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3,
% 26.81/4.61 | v1) & function(v2)))
% 26.81/4.61 |
% 26.81/4.61 | ALPHA: (dt_u2_lattices) implies:
% 26.81/4.61 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) |
% 26.81/4.61 | ~ join_semilatt_str(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.81/4.61 | (cartesian_product2(v1, v1) = v3 & the_L_join(v0) = v2 & $i(v3) &
% 26.81/4.61 | $i(v2) & relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3,
% 26.81/4.61 | v1) & function(v2)))
% 26.81/4.61 |
% 26.81/4.61 | ALPHA: (redefinition_k4_lattices) implies:
% 26.81/4.62 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 26.81/4.62 | (meet_commut(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 26.81/4.62 | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) |
% 26.81/4.62 | empty_carrier(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & meet(v0,
% 26.81/4.62 | v1, v2) = v3 & $i(v3)) | (the_carrier(v0) = v4 & $i(v4) & ( ~
% 26.81/4.62 | element(v2, v4) | ~ element(v1, v4)))))
% 26.81/4.62 |
% 26.81/4.62 | ALPHA: (function-axioms) implies:
% 26.81/4.62 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.81/4.62 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 26.81/4.62 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.81/4.62 | (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0))
% 26.81/4.62 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.81/4.62 | (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0))
% 26.81/4.62 |
% 26.81/4.62 | DELTA: instantiating (t23_lattices) with fresh symbols all_50_0, all_50_1,
% 26.81/4.62 | all_50_2, all_50_3, all_50_4 gives:
% 26.81/4.62 | (16) the_carrier(all_50_4) = all_50_3 & meet_commut(all_50_4, all_50_2,
% 26.81/4.62 | all_50_1) = all_50_0 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) &
% 26.81/4.62 | $i(all_50_3) & $i(all_50_4) & meet_absorbing(all_50_4) &
% 26.81/4.62 | latt_str(all_50_4) & element(all_50_1, all_50_3) & element(all_50_2,
% 26.81/4.62 | all_50_3) & meet_commutative(all_50_4) & ~ below(all_50_4,
% 26.81/4.62 | all_50_0, all_50_2) & ~ empty_carrier(all_50_4)
% 26.81/4.62 |
% 26.81/4.62 | ALPHA: (16) implies:
% 26.81/4.62 | (17) ~ empty_carrier(all_50_4)
% 26.81/4.62 | (18) ~ below(all_50_4, all_50_0, all_50_2)
% 26.81/4.62 | (19) meet_commutative(all_50_4)
% 26.81/4.62 | (20) element(all_50_2, all_50_3)
% 26.81/4.62 | (21) element(all_50_1, all_50_3)
% 26.81/4.62 | (22) latt_str(all_50_4)
% 26.81/4.62 | (23) meet_absorbing(all_50_4)
% 26.81/4.62 | (24) $i(all_50_4)
% 26.81/4.62 | (25) $i(all_50_2)
% 26.81/4.62 | (26) $i(all_50_1)
% 26.81/4.62 | (27) meet_commut(all_50_4, all_50_2, all_50_1) = all_50_0
% 26.81/4.62 | (28) the_carrier(all_50_4) = all_50_3
% 26.81/4.62 |
% 26.81/4.62 | GROUND_INST: instantiating (9) with all_50_4, simplifying with (22), (24)
% 26.81/4.62 | gives:
% 26.81/4.62 | (29) join_semilatt_str(all_50_4)
% 26.81/4.62 |
% 26.81/4.62 | GROUND_INST: instantiating (8) with all_50_4, simplifying with (22), (24)
% 26.81/4.62 | gives:
% 26.81/4.62 | (30) meet_semilatt_str(all_50_4)
% 26.81/4.62 |
% 26.81/4.63 | GROUND_INST: instantiating (1) with all_50_4, all_50_1, all_50_2, all_50_0,
% 26.81/4.63 | simplifying with (17), (19), (24), (25), (26), (27), (30) gives:
% 26.81/4.63 | (31) ? [v0: $i] : ? [v1: int] : ((v1 = all_50_0 & meet_commut(all_50_4,
% 26.81/4.63 | all_50_1, all_50_2) = all_50_0 & $i(all_50_0)) |
% 26.81/4.63 | (the_carrier(all_50_4) = v0 & $i(v0) & ( ~ element(all_50_1, v0) |
% 26.81/4.63 | ~ element(all_50_2, v0))))
% 26.81/4.63 |
% 26.81/4.63 | GROUND_INST: instantiating (dt_k4_lattices) with all_50_4, all_50_2, all_50_1,
% 26.81/4.63 | all_50_0, simplifying with (17), (19), (24), (25), (26), (27),
% 26.81/4.63 | (30) gives:
% 26.81/4.63 | (32) ? [v0: $i] : (the_carrier(all_50_4) = v0 & $i(v0) & ( ~
% 26.81/4.63 | element(all_50_1, v0) | ~ element(all_50_2, v0) |
% 26.81/4.63 | element(all_50_0, v0)))
% 26.81/4.63 |
% 26.81/4.63 | GROUND_INST: instantiating (4) with all_50_4, all_50_3, simplifying with (17),
% 26.81/4.63 | (24), (28), (30) gives:
% 26.81/4.63 | (33) ? [v0: $i] : (the_L_meet(all_50_4) = v0 & $i(v0) & ! [v1: $i] : !
% 26.81/4.63 | [v2: $i] : ! [v3: $i] : ( ~ (meet(all_50_4, v1, v2) = v3) | ~
% 26.81/4.63 | $i(v2) | ~ $i(v1) | ~ element(v2, all_50_3) | ~ element(v1,
% 26.81/4.63 | all_50_3) | (apply_binary_as_element(all_50_3, all_50_3,
% 26.81/4.63 | all_50_3, v0, v1, v2) = v3 & $i(v3))) & ! [v1: $i] : ! [v2:
% 26.81/4.63 | $i] : ! [v3: $i] : ( ~ (apply_binary_as_element(all_50_3,
% 26.81/4.63 | all_50_3, all_50_3, v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 26.81/4.63 | | ~ element(v2, all_50_3) | ~ element(v1, all_50_3) |
% 26.81/4.63 | (meet(all_50_4, v1, v2) = v3 & $i(v3))))
% 26.81/4.63 |
% 26.81/4.63 | GROUND_INST: instantiating (10) with all_50_4, all_50_3, simplifying with
% 26.81/4.63 | (24), (28), (30) gives:
% 26.81/4.63 | (34) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_50_3, all_50_3) =
% 26.81/4.63 | v1 & the_L_meet(all_50_4) = v0 & $i(v1) & $i(v0) &
% 26.81/4.63 | relation_of2_as_subset(v0, v1, all_50_3) & quasi_total(v0, v1,
% 26.81/4.63 | all_50_3) & function(v0))
% 26.81/4.63 |
% 26.81/4.63 | GROUND_INST: instantiating (2) with all_50_4, all_50_3, simplifying with (17),
% 26.81/4.63 | (24), (28), (29) gives:
% 26.81/4.64 | (35) ? [v0: $i] : (the_L_join(all_50_4) = v0 & $i(v0) & ! [v1: $i] : !
% 26.81/4.64 | [v2: $i] : ! [v3: $i] : ( ~ (apply_binary_as_element(all_50_3,
% 26.81/4.64 | all_50_3, all_50_3, v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 26.81/4.64 | | ~ element(v2, all_50_3) | ~ element(v1, all_50_3) |
% 26.81/4.64 | (join(all_50_4, v1, v2) = v3 & $i(v3))) & ! [v1: $i] : ! [v2:
% 26.81/4.64 | $i] : ! [v3: $i] : ( ~ (join(all_50_4, v1, v2) = v3) | ~ $i(v2)
% 26.81/4.64 | | ~ $i(v1) | ~ element(v2, all_50_3) | ~ element(v1, all_50_3)
% 26.81/4.64 | | (apply_binary_as_element(all_50_3, all_50_3, all_50_3, v0, v1,
% 26.81/4.64 | v2) = v3 & $i(v3))))
% 26.81/4.64 |
% 26.81/4.64 | GROUND_INST: instantiating (11) with all_50_4, all_50_3, simplifying with
% 26.81/4.64 | (24), (28), (29) gives:
% 26.81/4.64 | (36) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_50_3, all_50_3) =
% 26.81/4.64 | v1 & the_L_join(all_50_4) = v0 & $i(v1) & $i(v0) &
% 26.81/4.64 | relation_of2_as_subset(v0, v1, all_50_3) & quasi_total(v0, v1,
% 26.81/4.64 | all_50_3) & function(v0))
% 26.81/4.64 |
% 26.81/4.64 | DELTA: instantiating (32) with fresh symbol all_64_0 gives:
% 26.81/4.64 | (37) the_carrier(all_50_4) = all_64_0 & $i(all_64_0) & ( ~
% 26.81/4.64 | element(all_50_1, all_64_0) | ~ element(all_50_2, all_64_0) |
% 26.81/4.64 | element(all_50_0, all_64_0))
% 26.81/4.64 |
% 26.81/4.64 | ALPHA: (37) implies:
% 26.81/4.64 | (38) the_carrier(all_50_4) = all_64_0
% 26.81/4.64 | (39) ~ element(all_50_1, all_64_0) | ~ element(all_50_2, all_64_0) |
% 26.81/4.64 | element(all_50_0, all_64_0)
% 26.81/4.64 |
% 26.81/4.64 | DELTA: instantiating (34) with fresh symbols all_66_0, all_66_1 gives:
% 26.81/4.64 | (40) cartesian_product2(all_50_3, all_50_3) = all_66_0 &
% 26.81/4.64 | the_L_meet(all_50_4) = all_66_1 & $i(all_66_0) & $i(all_66_1) &
% 26.81/4.64 | relation_of2_as_subset(all_66_1, all_66_0, all_50_3) &
% 26.81/4.64 | quasi_total(all_66_1, all_66_0, all_50_3) & function(all_66_1)
% 26.81/4.64 |
% 26.81/4.64 | ALPHA: (40) implies:
% 26.81/4.64 | (41) the_L_meet(all_50_4) = all_66_1
% 26.81/4.64 |
% 26.81/4.64 | DELTA: instantiating (36) with fresh symbols all_68_0, all_68_1 gives:
% 26.81/4.64 | (42) cartesian_product2(all_50_3, all_50_3) = all_68_0 &
% 26.81/4.64 | the_L_join(all_50_4) = all_68_1 & $i(all_68_0) & $i(all_68_1) &
% 26.81/4.64 | relation_of2_as_subset(all_68_1, all_68_0, all_50_3) &
% 26.81/4.64 | quasi_total(all_68_1, all_68_0, all_50_3) & function(all_68_1)
% 26.81/4.64 |
% 26.81/4.64 | ALPHA: (42) implies:
% 26.81/4.64 | (43) the_L_join(all_50_4) = all_68_1
% 26.81/4.64 |
% 26.81/4.64 | DELTA: instantiating (31) with fresh symbols all_71_0, all_71_1 gives:
% 26.81/4.64 | (44) (all_71_0 = all_50_0 & meet_commut(all_50_4, all_50_1, all_50_2) =
% 26.81/4.64 | all_50_0 & $i(all_50_0)) | (the_carrier(all_50_4) = all_71_1 &
% 26.81/4.64 | $i(all_71_1) & ( ~ element(all_50_1, all_71_1) | ~
% 26.81/4.64 | element(all_50_2, all_71_1)))
% 26.81/4.64 |
% 26.81/4.64 | DELTA: instantiating (35) with fresh symbol all_72_0 gives:
% 26.81/4.65 | (45) the_L_join(all_50_4) = all_72_0 & $i(all_72_0) & ! [v0: $i] : ! [v1:
% 26.81/4.65 | $i] : ! [v2: $i] : ( ~ (apply_binary_as_element(all_50_3, all_50_3,
% 26.81/4.65 | all_50_3, all_72_0, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.81/4.65 | element(v1, all_50_3) | ~ element(v0, all_50_3) | (join(all_50_4,
% 26.81/4.65 | v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 26.81/4.65 | $i] : ( ~ (join(all_50_4, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.81/4.65 | element(v1, all_50_3) | ~ element(v0, all_50_3) |
% 26.81/4.65 | (apply_binary_as_element(all_50_3, all_50_3, all_50_3, all_72_0, v0,
% 26.81/4.65 | v1) = v2 & $i(v2)))
% 26.81/4.65 |
% 26.81/4.65 | ALPHA: (45) implies:
% 26.81/4.65 | (46) the_L_join(all_50_4) = all_72_0
% 26.81/4.65 |
% 26.81/4.65 | DELTA: instantiating (33) with fresh symbol all_75_0 gives:
% 26.81/4.65 | (47) the_L_meet(all_50_4) = all_75_0 & $i(all_75_0) & ! [v0: $i] : ! [v1:
% 26.81/4.65 | $i] : ! [v2: $i] : ( ~ (meet(all_50_4, v0, v1) = v2) | ~ $i(v1) |
% 26.81/4.65 | ~ $i(v0) | ~ element(v1, all_50_3) | ~ element(v0, all_50_3) |
% 26.81/4.65 | (apply_binary_as_element(all_50_3, all_50_3, all_50_3, all_75_0, v0,
% 26.81/4.65 | v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 26.81/4.65 | ( ~ (apply_binary_as_element(all_50_3, all_50_3, all_50_3, all_75_0,
% 26.81/4.65 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, all_50_3)
% 26.81/4.65 | | ~ element(v0, all_50_3) | (meet(all_50_4, v0, v1) = v2 & $i(v2)))
% 26.81/4.65 |
% 26.81/4.65 | ALPHA: (47) implies:
% 26.81/4.65 | (48) the_L_meet(all_50_4) = all_75_0
% 26.81/4.65 | (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (meet(all_50_4, v0, v1)
% 26.81/4.65 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, all_50_3) | ~
% 26.81/4.65 | element(v0, all_50_3) | (apply_binary_as_element(all_50_3, all_50_3,
% 26.81/4.65 | all_50_3, all_75_0, v0, v1) = v2 & $i(v2)))
% 26.81/4.65 |
% 26.81/4.65 | GROUND_INST: instantiating (13) with all_50_3, all_64_0, all_50_4, simplifying
% 26.81/4.65 | with (28), (38) gives:
% 26.81/4.65 | (50) all_64_0 = all_50_3
% 26.81/4.65 |
% 26.81/4.65 | GROUND_INST: instantiating (14) with all_68_1, all_72_0, all_50_4, simplifying
% 26.81/4.65 | with (43), (46) gives:
% 26.81/4.65 | (51) all_72_0 = all_68_1
% 26.81/4.65 |
% 26.81/4.65 | GROUND_INST: instantiating (15) with all_66_1, all_75_0, all_50_4, simplifying
% 26.81/4.65 | with (41), (48) gives:
% 26.81/4.65 | (52) all_75_0 = all_66_1
% 26.81/4.65 |
% 26.81/4.65 | BETA: splitting (39) gives:
% 26.81/4.65 |
% 26.81/4.65 | Case 1:
% 26.81/4.65 | |
% 26.81/4.65 | | (53) ~ element(all_50_1, all_64_0)
% 26.81/4.65 | |
% 26.81/4.65 | | REDUCE: (50), (53) imply:
% 26.81/4.65 | | (54) ~ element(all_50_1, all_50_3)
% 26.81/4.65 | |
% 26.81/4.65 | | PRED_UNIFY: (21), (54) imply:
% 26.81/4.65 | | (55) $false
% 26.81/4.66 | |
% 26.81/4.66 | | CLOSE: (55) is inconsistent.
% 26.81/4.66 | |
% 26.81/4.66 | Case 2:
% 26.81/4.66 | |
% 26.81/4.66 | | (56) element(all_50_1, all_64_0)
% 26.81/4.66 | | (57) ~ element(all_50_2, all_64_0) | element(all_50_0, all_64_0)
% 26.81/4.66 | |
% 26.81/4.66 | | BETA: splitting (57) gives:
% 26.81/4.66 | |
% 26.81/4.66 | | Case 1:
% 26.81/4.66 | | |
% 26.81/4.66 | | | (58) ~ element(all_50_2, all_64_0)
% 26.81/4.66 | | |
% 26.81/4.66 | | | REDUCE: (50), (58) imply:
% 26.81/4.66 | | | (59) ~ element(all_50_2, all_50_3)
% 26.81/4.66 | | |
% 26.81/4.66 | | | PRED_UNIFY: (20), (59) imply:
% 26.81/4.66 | | | (60) $false
% 26.81/4.66 | | |
% 26.81/4.66 | | | CLOSE: (60) is inconsistent.
% 26.81/4.66 | | |
% 26.81/4.66 | | Case 2:
% 26.81/4.66 | | |
% 27.05/4.66 | | | (61) element(all_50_2, all_64_0)
% 27.05/4.66 | | | (62) element(all_50_0, all_64_0)
% 27.05/4.66 | | |
% 27.05/4.66 | | | REDUCE: (50), (62) imply:
% 27.05/4.66 | | | (63) element(all_50_0, all_50_3)
% 27.05/4.66 | | |
% 27.05/4.66 | | | BETA: splitting (44) gives:
% 27.05/4.66 | | |
% 27.05/4.66 | | | Case 1:
% 27.05/4.66 | | | |
% 27.05/4.66 | | | | (64) all_71_0 = all_50_0 & meet_commut(all_50_4, all_50_1, all_50_2)
% 27.05/4.66 | | | | = all_50_0 & $i(all_50_0)
% 27.05/4.66 | | | |
% 27.05/4.66 | | | | ALPHA: (64) implies:
% 27.05/4.66 | | | | (65) meet_commut(all_50_4, all_50_1, all_50_2) = all_50_0
% 27.05/4.66 | | | |
% 27.05/4.66 | | | | GROUND_INST: instantiating (12) with all_50_4, all_50_1, all_50_2,
% 27.05/4.66 | | | | all_50_0, simplifying with (17), (19), (24), (25), (26),
% 27.05/4.66 | | | | (30), (65) gives:
% 27.05/4.66 | | | | (66) ? [v0: $i] : ? [v1: int] : ((v1 = all_50_0 & meet(all_50_4,
% 27.05/4.66 | | | | all_50_1, all_50_2) = all_50_0 & $i(all_50_0)) |
% 27.05/4.66 | | | | (the_carrier(all_50_4) = v0 & $i(v0) & ( ~ element(all_50_1,
% 27.05/4.66 | | | | v0) | ~ element(all_50_2, v0))))
% 27.05/4.66 | | | |
% 27.05/4.66 | | | | GROUND_INST: instantiating (3) with all_50_4, all_68_1, simplifying with
% 27.05/4.66 | | | | (17), (24), (29), (43) gives:
% 27.05/4.67 | | | | (67) ? [v0: $i] : (the_carrier(all_50_4) = v0 & $i(v0) & ! [v1: $i]
% 27.05/4.67 | | | | : ! [v2: $i] : ! [v3: $i] : ( ~ (apply_binary_as_element(v0,
% 27.05/4.67 | | | | v0, v0, all_68_1, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 27.05/4.67 | | | | | ~ element(v2, v0) | ~ element(v1, v0) | (join(all_50_4,
% 27.05/4.67 | | | | v1, v2) = v3 & $i(v3))) & ! [v1: $i] : ! [v2: $i] : !
% 27.05/4.67 | | | | [v3: $i] : ( ~ (join(all_50_4, v1, v2) = v3) | ~ $i(v2) | ~
% 27.05/4.67 | | | | $i(v1) | ~ element(v2, v0) | ~ element(v1, v0) |
% 27.05/4.67 | | | | (apply_binary_as_element(v0, v0, v0, all_68_1, v1, v2) = v3
% 27.05/4.67 | | | | & $i(v3))))
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | GROUND_INST: instantiating (5) with all_50_4, all_66_1, simplifying with
% 27.05/4.67 | | | | (17), (24), (30), (41) gives:
% 27.05/4.67 | | | | (68) ? [v0: $i] : (the_carrier(all_50_4) = v0 & $i(v0) & ! [v1: $i]
% 27.05/4.67 | | | | : ! [v2: $i] : ! [v3: $i] : ( ~ (meet(all_50_4, v1, v2) =
% 27.05/4.67 | | | | v3) | ~ $i(v2) | ~ $i(v1) | ~ element(v2, v0) | ~
% 27.05/4.67 | | | | element(v1, v0) | (apply_binary_as_element(v0, v0, v0,
% 27.05/4.67 | | | | all_66_1, v1, v2) = v3 & $i(v3))) & ! [v1: $i] : !
% 27.05/4.67 | | | | [v2: $i] : ! [v3: $i] : ( ~ (apply_binary_as_element(v0, v0,
% 27.05/4.67 | | | | v0, all_66_1, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 27.05/4.67 | | | | element(v2, v0) | ~ element(v1, v0) | (meet(all_50_4, v1,
% 27.05/4.67 | | | | v2) = v3 & $i(v3))))
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | DELTA: instantiating (66) with fresh symbols all_106_0, all_106_1 gives:
% 27.05/4.67 | | | | (69) (all_106_0 = all_50_0 & meet(all_50_4, all_50_1, all_50_2) =
% 27.05/4.67 | | | | all_50_0 & $i(all_50_0)) | (the_carrier(all_50_4) = all_106_1
% 27.05/4.67 | | | | & $i(all_106_1) & ( ~ element(all_50_1, all_106_1) | ~
% 27.05/4.67 | | | | element(all_50_2, all_106_1)))
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | DELTA: instantiating (68) with fresh symbol all_107_0 gives:
% 27.05/4.67 | | | | (70) the_carrier(all_50_4) = all_107_0 & $i(all_107_0) & ! [v0: $i]
% 27.05/4.67 | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ (meet(all_50_4, v0, v1) = v2)
% 27.05/4.67 | | | | | ~ $i(v1) | ~ $i(v0) | ~ element(v1, all_107_0) | ~
% 27.05/4.67 | | | | element(v0, all_107_0) | (apply_binary_as_element(all_107_0,
% 27.05/4.67 | | | | all_107_0, all_107_0, all_66_1, v0, v1) = v2 & $i(v2))) &
% 27.05/4.67 | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 27.05/4.67 | | | | (apply_binary_as_element(all_107_0, all_107_0, all_107_0,
% 27.05/4.67 | | | | all_66_1, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.05/4.67 | | | | element(v1, all_107_0) | ~ element(v0, all_107_0) |
% 27.05/4.67 | | | | (meet(all_50_4, v0, v1) = v2 & $i(v2)))
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | ALPHA: (70) implies:
% 27.05/4.67 | | | | (71) the_carrier(all_50_4) = all_107_0
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | DELTA: instantiating (67) with fresh symbol all_110_0 gives:
% 27.05/4.67 | | | | (72) the_carrier(all_50_4) = all_110_0 & $i(all_110_0) & ! [v0: $i]
% 27.05/4.67 | | | | : ! [v1: $i] : ! [v2: $i] : ( ~
% 27.05/4.67 | | | | (apply_binary_as_element(all_110_0, all_110_0, all_110_0,
% 27.05/4.67 | | | | all_68_1, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.05/4.67 | | | | element(v1, all_110_0) | ~ element(v0, all_110_0) |
% 27.05/4.67 | | | | (join(all_50_4, v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 27.05/4.67 | | | | [v1: $i] : ! [v2: $i] : ( ~ (join(all_50_4, v0, v1) = v2) | ~
% 27.05/4.67 | | | | $i(v1) | ~ $i(v0) | ~ element(v1, all_110_0) | ~
% 27.05/4.67 | | | | element(v0, all_110_0) | (apply_binary_as_element(all_110_0,
% 27.05/4.67 | | | | all_110_0, all_110_0, all_68_1, v0, v1) = v2 & $i(v2)))
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | ALPHA: (72) implies:
% 27.05/4.67 | | | | (73) the_carrier(all_50_4) = all_110_0
% 27.05/4.67 | | | |
% 27.05/4.67 | | | | GROUND_INST: instantiating (13) with all_50_3, all_110_0, all_50_4,
% 27.05/4.67 | | | | simplifying with (28), (73) gives:
% 27.05/4.68 | | | | (74) all_110_0 = all_50_3
% 27.05/4.68 | | | |
% 27.05/4.68 | | | | GROUND_INST: instantiating (13) with all_107_0, all_110_0, all_50_4,
% 27.05/4.68 | | | | simplifying with (71), (73) gives:
% 27.05/4.68 | | | | (75) all_110_0 = all_107_0
% 27.05/4.68 | | | |
% 27.05/4.68 | | | | COMBINE_EQS: (74), (75) imply:
% 27.05/4.68 | | | | (76) all_107_0 = all_50_3
% 27.05/4.68 | | | |
% 27.05/4.68 | | | | BETA: splitting (69) gives:
% 27.05/4.68 | | | |
% 27.05/4.68 | | | | Case 1:
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | (77) all_106_0 = all_50_0 & meet(all_50_4, all_50_1, all_50_2) =
% 27.05/4.68 | | | | | all_50_0 & $i(all_50_0)
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | ALPHA: (77) implies:
% 27.05/4.68 | | | | | (78) meet(all_50_4, all_50_1, all_50_2) = all_50_0
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | GROUND_INST: instantiating (7) with all_50_4, all_50_3, all_50_1,
% 27.05/4.68 | | | | | all_50_2, all_50_0, simplifying with (17), (20), (21),
% 27.05/4.68 | | | | | (22), (23), (24), (25), (26), (28), (78) gives:
% 27.05/4.68 | | | | | (79) join(all_50_4, all_50_0, all_50_2) = all_50_2
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | GROUND_INST: instantiating (49) with all_50_1, all_50_2, all_50_0,
% 27.05/4.68 | | | | | simplifying with (20), (21), (25), (26), (78) gives:
% 27.05/4.68 | | | | | (80) apply_binary_as_element(all_50_3, all_50_3, all_50_3,
% 27.05/4.68 | | | | | all_75_0, all_50_1, all_50_2) = all_50_0 & $i(all_50_0)
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | ALPHA: (80) implies:
% 27.05/4.68 | | | | | (81) $i(all_50_0)
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | GROUND_INST: instantiating (6) with all_50_4, all_50_3, all_50_0,
% 27.05/4.68 | | | | | all_50_2, simplifying with (17), (18), (20), (24), (25),
% 27.05/4.68 | | | | | (28), (29), (63), (79), (81) gives:
% 27.05/4.68 | | | | | (82) $false
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | CLOSE: (82) is inconsistent.
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | Case 2:
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | (83) the_carrier(all_50_4) = all_106_1 & $i(all_106_1) & ( ~
% 27.05/4.68 | | | | | element(all_50_1, all_106_1) | ~ element(all_50_2,
% 27.05/4.68 | | | | | all_106_1))
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | ALPHA: (83) implies:
% 27.05/4.68 | | | | | (84) the_carrier(all_50_4) = all_106_1
% 27.05/4.68 | | | | | (85) ~ element(all_50_1, all_106_1) | ~ element(all_50_2,
% 27.05/4.68 | | | | | all_106_1)
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | GROUND_INST: instantiating (13) with all_50_3, all_106_1, all_50_4,
% 27.05/4.68 | | | | | simplifying with (28), (84) gives:
% 27.05/4.68 | | | | | (86) all_106_1 = all_50_3
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | BETA: splitting (85) gives:
% 27.05/4.68 | | | | |
% 27.05/4.68 | | | | | Case 1:
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | (87) ~ element(all_50_1, all_106_1)
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | REDUCE: (86), (87) imply:
% 27.05/4.68 | | | | | | (88) ~ element(all_50_1, all_50_3)
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | PRED_UNIFY: (21), (88) imply:
% 27.05/4.68 | | | | | | (89) $false
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | CLOSE: (89) is inconsistent.
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | Case 2:
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | (90) ~ element(all_50_2, all_106_1)
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | REDUCE: (86), (90) imply:
% 27.05/4.68 | | | | | | (91) ~ element(all_50_2, all_50_3)
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | PRED_UNIFY: (20), (91) imply:
% 27.05/4.68 | | | | | | (92) $false
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | | CLOSE: (92) is inconsistent.
% 27.05/4.68 | | | | | |
% 27.05/4.68 | | | | | End of split
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | End of split
% 27.05/4.69 | | | |
% 27.05/4.69 | | | Case 2:
% 27.05/4.69 | | | |
% 27.05/4.69 | | | | (93) the_carrier(all_50_4) = all_71_1 & $i(all_71_1) & ( ~
% 27.05/4.69 | | | | element(all_50_1, all_71_1) | ~ element(all_50_2, all_71_1))
% 27.05/4.69 | | | |
% 27.05/4.69 | | | | ALPHA: (93) implies:
% 27.05/4.69 | | | | (94) the_carrier(all_50_4) = all_71_1
% 27.05/4.69 | | | | (95) ~ element(all_50_1, all_71_1) | ~ element(all_50_2, all_71_1)
% 27.05/4.69 | | | |
% 27.05/4.69 | | | | GROUND_INST: instantiating (13) with all_50_3, all_71_1, all_50_4,
% 27.05/4.69 | | | | simplifying with (28), (94) gives:
% 27.05/4.69 | | | | (96) all_71_1 = all_50_3
% 27.05/4.69 | | | |
% 27.05/4.69 | | | | BETA: splitting (95) gives:
% 27.05/4.69 | | | |
% 27.05/4.69 | | | | Case 1:
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | (97) ~ element(all_50_1, all_71_1)
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | REDUCE: (96), (97) imply:
% 27.05/4.69 | | | | | (98) ~ element(all_50_1, all_50_3)
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | PRED_UNIFY: (21), (98) imply:
% 27.05/4.69 | | | | | (99) $false
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | CLOSE: (99) is inconsistent.
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | Case 2:
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | (100) ~ element(all_50_2, all_71_1)
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | REDUCE: (96), (100) imply:
% 27.05/4.69 | | | | | (101) ~ element(all_50_2, all_50_3)
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | PRED_UNIFY: (20), (101) imply:
% 27.05/4.69 | | | | | (102) $false
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | | CLOSE: (102) is inconsistent.
% 27.05/4.69 | | | | |
% 27.05/4.69 | | | | End of split
% 27.05/4.69 | | | |
% 27.05/4.69 | | | End of split
% 27.05/4.69 | | |
% 27.05/4.69 | | End of split
% 27.05/4.69 | |
% 27.05/4.69 | End of split
% 27.05/4.69 |
% 27.05/4.69 End of proof
% 27.05/4.69 % SZS output end Proof for theBenchmark
% 27.05/4.69
% 27.05/4.69 4058ms
%------------------------------------------------------------------------------