TSTP Solution File: ITP334_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 04:11:47 EDT 2023
% Result : Theorem 37.77s 5.91s
% Output : Proof 53.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 11:59:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 14.56/2.82 Prover 4: Preprocessing ...
% 14.56/2.85 Prover 1: Preprocessing ...
% 16.04/3.03 Prover 2: Preprocessing ...
% 16.04/3.03 Prover 3: Preprocessing ...
% 16.04/3.04 Prover 0: Preprocessing ...
% 16.69/3.07 Prover 6: Preprocessing ...
% 17.04/3.14 Prover 5: Preprocessing ...
% 34.65/5.48 Prover 1: Warning: ignoring some quantifiers
% 35.09/5.66 Prover 3: Warning: ignoring some quantifiers
% 35.09/5.70 Prover 3: Constructing countermodel ...
% 35.09/5.71 Prover 1: Constructing countermodel ...
% 36.19/5.77 Prover 6: Proving ...
% 37.77/5.90 Prover 3: proved (5258ms)
% 37.77/5.90
% 37.77/5.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.77/5.91
% 37.77/5.91 Prover 6: stopped
% 37.77/5.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 37.77/5.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 38.48/5.98 Prover 4: Warning: ignoring some quantifiers
% 40.12/6.19 Prover 4: Constructing countermodel ...
% 40.88/6.36 Prover 5: Proving ...
% 40.88/6.36 Prover 5: stopped
% 40.88/6.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 40.88/6.44 Prover 0: Proving ...
% 40.88/6.44 Prover 0: stopped
% 40.88/6.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 43.29/6.65 Prover 2: Proving ...
% 43.29/6.65 Prover 2: stopped
% 43.78/6.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 44.79/6.81 Prover 1: Found proof (size 108)
% 44.79/6.81 Prover 1: proved (6179ms)
% 44.79/6.81 Prover 4: stopped
% 46.06/7.02 Prover 8: Preprocessing ...
% 46.81/7.19 Prover 7: Preprocessing ...
% 48.61/7.38 Prover 10: Preprocessing ...
% 49.36/7.47 Prover 7: stopped
% 49.36/7.48 Prover 13: Preprocessing ...
% 49.89/7.50 Prover 11: Preprocessing ...
% 50.43/7.59 Prover 10: stopped
% 50.81/7.78 Prover 11: stopped
% 50.81/7.81 Prover 13: stopped
% 51.89/7.86 Prover 8: Warning: ignoring some quantifiers
% 52.34/7.91 Prover 8: Constructing countermodel ...
% 52.34/7.93 Prover 8: stopped
% 52.34/7.93
% 52.34/7.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.34/7.93
% 52.34/7.97 % SZS output start Proof for theBenchmark
% 52.65/8.00 Assumptions after simplification:
% 52.65/8.00 ---------------------------------
% 52.65/8.00
% 52.65/8.00 (axiom12)
% 52.65/8.01 Nat_int_fun$(of_nat$) & Rows_option_set$(top$b) &
% 52.65/8.01 Rows_option_option_set$(top$a) & ? [v0: Nat$] : ? [v1: int] : ? [v2: Nat$]
% 52.65/8.01 : (card$a(top$a) = v0 & card$b(top$b) = v2 & fun_app$h(of_nat$, v2) = $sum(v1,
% 52.65/8.01 -1) & fun_app$h(of_nat$, v0) = v1 & Nat$(v2) & Nat$(v0))
% 52.65/8.01
% 52.65/8.01 (axiom136)
% 52.65/8.01 Nat_int_fun$(of_nat$) & Rows_option_set$(top$b) & ? [v0: Nat$] : ? [v1: int]
% 52.65/8.01 : ($lesseq(1, v1) & card$b(top$b) = v0 & fun_app$h(of_nat$, v0) = v1 &
% 52.65/8.01 Nat$(v0))
% 52.65/8.01
% 52.65/8.01 (axiom139)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 52.65/8.02 ($lesseq(1, v1) & card$(top$) = v0 & fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom15)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_option_set$(top$b) & Rows_set$(top$) & ? [v0:
% 52.65/8.02 Nat$] : ? [v1: int] : ? [v2: Nat$] : (card$(top$) = v2 & card$b(top$b) =
% 52.65/8.02 v0 & fun_app$h(of_nat$, v2) = $sum(v1, -1) & fun_app$h(of_nat$, v0) = v1 &
% 52.65/8.02 Nat$(v2) & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom362)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_option_set$(top$b) & ? [v0: Nat$] : ? [v1: int]
% 52.65/8.02 : ($lesseq(1, v1) & card$b(top$b) = v0 & fun_app$h(of_nat$, v0) = v1 &
% 52.65/8.02 Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom365)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 52.65/8.02 ($lesseq(1, v1) & card$(top$) = v0 & fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom588)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 52.65/8.02 ($lesseq(2, v1) & card$(top$) = v0 & fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom589)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 52.65/8.02 ($lesseq(1, v1) & card$(top$) = v0 & fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom595)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_set$(top$) & Rows$(zero$) & ? [v0: Nat$] : ?
% 52.65/8.02 [v1: int] : (abs$(v1) = zero$ & card$(top$) = v0 & fun_app$h(of_nat$, v0) = v1
% 52.65/8.02 & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (axiom606)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_option_set$(top$b) & Rows_set$(top$) & ? [v0:
% 52.65/8.02 Nat$] : ? [v1: int] : ? [v2: Nat$] : ? [v3: int] : (card$(top$) = v0 &
% 52.65/8.02 card$b(top$b) = v2 & fun_app$h(of_nat$, v2) = v3 & fun_app$h(of_nat$, v0) =
% 52.65/8.02 v1 & Nat$(v2) & Nat$(v0) & ( ~ (v1 = 0) | v3 = 0) & ($difference(v3, v1) = 1
% 52.65/8.02 | v1 = 0))
% 52.65/8.02
% 52.65/8.02 (conjecture7)
% 52.65/8.02 Nat_int_fun$(of_nat$) & Rows_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 52.65/8.02 ($lesseq(v1, 0)card$(top$) = v0 & fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.02
% 52.65/8.02 (function-axioms)
% 52.65/8.05 ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 =
% 52.65/8.05 v0 | ~ (fun_app$z(v3, v2) = v1) | ~ (fun_app$z(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Num1_set$] : !
% 52.65/8.05 [v3: Num1_set$] : (v1 = v0 | ~ (less_eq$d(v3, v2) = v1) | ~ (less_eq$d(v3,
% 52.65/8.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 52.65/8.05 ! [v2: Num0_set$] : ! [v3: Num0_set$] : (v1 = v0 | ~ (less_eq$c(v3, v2) =
% 52.65/8.05 v1) | ~ (less_eq$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Literal_set$] : ! [v3: Literal_set$] : (v1 =
% 52.65/8.05 v0 | ~ (less_eq$b(v3, v2) = v1) | ~ (less_eq$b(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : !
% 52.65/8.05 [v3: Nat_set$] : (v1 = v0 | ~ (less_eq$a(v3, v2) = v1) | ~ (less_eq$a(v3,
% 52.65/8.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 52.65/8.05 ! [v2: Rows_set$] : ! [v3: Rows_set$] : (v1 = v0 | ~ (less_eq$(v3, v2) = v1)
% 52.65/8.05 | ~ (less_eq$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Rows_bool_fun$] : ! [v3: Rows_bool_fun$] : (v1
% 52.65/8.05 = v0 | ~ (less$i(v3, v2) = v1) | ~ (less$i(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_bool_fun$] :
% 52.65/8.05 ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (less$h(v3, v2) = v1) | ~ (less$h(v3,
% 52.65/8.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 52.65/8.05 ! [v2: Literal_bool_fun$] : ! [v3: Literal_bool_fun$] : (v1 = v0 | ~
% 52.65/8.05 (less$g(v3, v2) = v1) | ~ (less$g(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Num0_bool_fun$] :
% 52.65/8.05 ! [v3: Num0_bool_fun$] : (v1 = v0 | ~ (less$f(v3, v2) = v1) | ~ (less$f(v3,
% 52.65/8.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 52.65/8.05 ! [v2: Num1_bool_fun$] : ! [v3: Num1_bool_fun$] : (v1 = v0 | ~ (less$e(v3,
% 52.65/8.05 v2) = v1) | ~ (less$e(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 52.65/8.05 [v2: Num1_set$] : ! [v3: Num1_set_int_fun$] : (v1 = v0 | ~ (fun_app$y(v3,
% 52.65/8.05 v2) = v1) | ~ (fun_app$y(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] :
% 52.65/8.05 ! [v2: Num0_set$] : ! [v3: Num0_set_int_fun$] : (v1 = v0 | ~ (fun_app$x(v3,
% 52.65/8.05 v2) = v1) | ~ (fun_app$x(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] :
% 52.65/8.05 ! [v2: Literal_set$] : ! [v3: Literal_set_int_fun$] : (v1 = v0 | ~
% 52.65/8.05 (fun_app$w(v3, v2) = v1) | ~ (fun_app$w(v3, v2) = v0)) & ! [v0: int] : !
% 52.65/8.05 [v1: int] : ! [v2: Nat_set$] : ! [v3: Nat_set_int_fun$] : (v1 = v0 | ~
% 52.65/8.05 (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! [v0: int] : !
% 52.65/8.05 [v1: int] : ! [v2: Rows_set$] : ! [v3: Rows_set_int_fun$] : (v1 = v0 | ~
% 52.65/8.05 (fun_app$u(v3, v2) = v1) | ~ (fun_app$u(v3, v2) = v0)) & ! [v0: Num1_set$]
% 52.65/8.05 : ! [v1: Num1_set$] : ! [v2: int] : ! [v3: Int_num1_set_fun$] : (v1 = v0 |
% 52.65/8.05 ~ (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 Num0_set$] : ! [v1: Num0_set$] : ! [v2: int] : ! [v3: Int_num0_set_fun$]
% 52.65/8.05 : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | ~ (fun_app$s(v3, v2) = v0)) & !
% 52.65/8.05 [v0: Literal_set$] : ! [v1: Literal_set$] : ! [v2: int] : ! [v3:
% 52.65/8.05 Int_literal_set_fun$] : (v1 = v0 | ~ (fun_app$r(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$r(v3, v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2:
% 52.65/8.05 int] : ! [v3: Int_nat_set_fun$] : (v1 = v0 | ~ (fun_app$q(v3, v2) = v1) |
% 52.65/8.05 ~ (fun_app$q(v3, v2) = v0)) & ! [v0: Rows_set$] : ! [v1: Rows_set$] : !
% 52.65/8.05 [v2: int] : ! [v3: Int_rows_set_fun$] : (v1 = v0 | ~ (fun_app$p(v3, v2) =
% 52.65/8.05 v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: Num1_set$] : ! [v1:
% 52.65/8.05 Num1_set$] : ! [v2: Nat$] : ! [v3: Nat_num1_set_fun$] : (v1 = v0 | ~
% 52.65/8.05 (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Num1_set$] : !
% 52.65/8.05 [v3: Num1_set$] : (v1 = v0 | ~ (less$d(v3, v2) = v1) | ~ (less$d(v3, v2) =
% 52.65/8.05 v0)) & ! [v0: Num0_set$] : ! [v1: Num0_set$] : ! [v2: Nat$] : ! [v3:
% 52.65/8.05 Nat_num0_set_fun$] : (v1 = v0 | ~ (fun_app$n(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$n(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Num0_set$] : ! [v3: Num0_set$] : (v1 = v0 | ~
% 52.65/8.05 (less$c(v3, v2) = v1) | ~ (less$c(v3, v2) = v0)) & ! [v0: Literal_set$] :
% 52.65/8.05 ! [v1: Literal_set$] : ! [v2: Nat$] : ! [v3: Nat_literal_set_fun$] : (v1 =
% 52.65/8.05 v0 | ~ (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Literal_set$] : !
% 52.65/8.05 [v3: Literal_set$] : (v1 = v0 | ~ (less$b(v3, v2) = v1) | ~ (less$b(v3, v2)
% 52.65/8.05 = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat$] : ! [v3:
% 52.65/8.05 Nat_nat_set_fun$] : (v1 = v0 | ~ (fun_app$l(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$l(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat_set$] : (v1 = v0 | ~
% 52.65/8.05 (less$a(v3, v2) = v1) | ~ (less$a(v3, v2) = v0)) & ! [v0: Rows_set$] : !
% 52.65/8.05 [v1: Rows_set$] : ! [v2: Nat$] : ! [v3: Nat_rows_set_fun$] : (v1 = v0 | ~
% 52.65/8.05 (fun_app$k(v3, v2) = v1) | ~ (fun_app$k(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Rows_set$] : !
% 52.65/8.05 [v3: Rows_set$] : (v1 = v0 | ~ (less$(v3, v2) = v1) | ~ (less$(v3, v2) =
% 52.65/8.05 v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat$] :
% 52.65/8.05 ! [v3: Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$j(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$j(v3, v2) = v0)) & ! [v0: Rows$] : ! [v1: Rows$] : ! [v2: Rows$]
% 52.65/8.05 : ! [v3: Rows_rows_fun$] : (v1 = v0 | ~ (fun_app$i(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$i(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : !
% 52.65/8.05 [v3: Nat_int_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$h(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Rows$] : ! [v3: Rows_bool_fun$] : (v1 = v0 |
% 52.65/8.05 ~ (fun_app$g(v3, v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Rows_set$] : !
% 52.65/8.05 [v3: Rows$] : (v1 = v0 | ~ (member$d(v3, v2) = v1) | ~ (member$d(v3, v2) =
% 52.65/8.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 52.65/8.05 Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat$] : (v1 = v0 | ~
% 52.65/8.05 (member$c(v3, v2) = v1) | ~ (member$c(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Literal$] : !
% 52.65/8.05 [v3: Literal_bool_fun$] : (v1 = v0 | ~ (fun_app$e(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$e(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Literal_set$] : ! [v3: Literal$] : (v1 = v0 |
% 52.65/8.05 ~ (member$b(v3, v2) = v1) | ~ (member$b(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Num0$] : ! [v3:
% 52.65/8.05 Num0_bool_fun$] : (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3,
% 52.65/8.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 52.65/8.05 ! [v2: Num0_set$] : ! [v3: Num0$] : (v1 = v0 | ~ (member$a(v3, v2) = v1) |
% 52.65/8.05 ~ (member$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: Num1$] : ! [v3: Num1_bool_fun$] : (v1 = v0 |
% 52.65/8.05 ~ (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0:
% 52.65/8.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Num1_set$] : !
% 52.65/8.05 [v3: Num1$] : (v1 = v0 | ~ (member$(v3, v2) = v1) | ~ (member$(v3, v2) =
% 52.65/8.05 v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$]
% 52.65/8.05 : (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & !
% 52.65/8.05 [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! [v3:
% 52.65/8.05 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~
% 52.65/8.05 (fun_app$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.65/8.05 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~
% 52.65/8.05 (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0: Nat$] : !
% 52.65/8.05 [v1: Nat$] : ! [v2: Nat_option_set$] : (v1 = v0 | ~ (card$l(v2) = v1) | ~
% 52.65/8.05 (card$l(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 52.65/8.05 Literal_option_set$] : (v1 = v0 | ~ (card$k(v2) = v1) | ~ (card$k(v2) =
% 52.65/8.05 v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Num0_option_set$] : (v1 =
% 52.65/8.05 v0 | ~ (card$j(v2) = v1) | ~ (card$j(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 52.65/8.05 Nat$] : ! [v2: Unit_set$] : (v1 = v0 | ~ (card$i(v2) = v1) | ~
% 52.65/8.05 (card$i(v2) = v0)) & ! [v0: Rows$] : ! [v1: Rows$] : ! [v2: int] : (v1 =
% 52.65/8.05 v0 | ~ (abs$(v2) = v1) | ~ (abs$(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 52.65/8.05 Nat$] : ! [v2: Num0_set$] : (v1 = v0 | ~ (card$h(v2) = v1) | ~
% 52.65/8.05 (card$h(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0
% 52.65/8.05 | ~ (nat$(v2) = v1) | ~ (nat$(v2) = v0)) & ! [v0: Num1_set$] : ! [v1:
% 52.65/8.05 Num1_set$] : ! [v2: Num1_bool_fun$] : (v1 = v0 | ~ (collect$d(v2) = v1) |
% 52.65/8.05 ~ (collect$d(v2) = v0)) & ! [v0: Num0_set$] : ! [v1: Num0_set$] : ! [v2:
% 52.65/8.05 Num0_bool_fun$] : (v1 = v0 | ~ (collect$c(v2) = v1) | ~ (collect$c(v2) =
% 52.65/8.05 v0)) & ! [v0: Literal_set$] : ! [v1: Literal_set$] : ! [v2:
% 52.65/8.05 Literal_bool_fun$] : (v1 = v0 | ~ (collect$b(v2) = v1) | ~ (collect$b(v2)
% 52.65/8.05 = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat_bool_fun$] :
% 52.65/8.05 (v1 = v0 | ~ (collect$a(v2) = v1) | ~ (collect$a(v2) = v0)) & ! [v0:
% 52.65/8.05 Rows_set$] : ! [v1: Rows_set$] : ! [v2: Rows_bool_fun$] : (v1 = v0 | ~
% 52.65/8.05 (collect$(v2) = v1) | ~ (collect$(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 52.65/8.05 Nat$] : ! [v2: Literal_set$] : (v1 = v0 | ~ (card$g(v2) = v1) | ~
% 52.65/8.05 (card$g(v2) = v0)) & ! [v0: Rows_rows_fun$] : ! [v1: Rows_rows_fun$] : !
% 52.65/8.05 [v2: Rows$] : (v1 = v0 | ~ (minus$(v2) = v1) | ~ (minus$(v2) = v0)) & !
% 52.65/8.05 [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_set$] : (v1 = v0 | ~ (card$f(v2) =
% 52.65/8.05 v1) | ~ (card$f(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 52.65/8.05 Rows_set$] : (v1 = v0 | ~ (card$(v2) = v1) | ~ (card$(v2) = v0)) & ! [v0:
% 52.65/8.05 Nat$] : ! [v1: Nat$] : ! [v2: Num1_set$] : (v1 = v0 | ~ (card$e(v2) = v1)
% 52.65/8.05 | ~ (card$e(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 52.65/8.05 Num1_option_option_set$] : (v1 = v0 | ~ (card$c(v2) = v1) | ~ (card$c(v2)
% 52.65/8.05 = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Num1_option_set$] : (v1 =
% 52.65/8.05 v0 | ~ (card$d(v2) = v1) | ~ (card$d(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 52.65/8.05 Nat$] : ! [v2: Rows_option_option_set$] : (v1 = v0 | ~ (card$a(v2) = v1) |
% 52.65/8.05 ~ (card$a(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 52.65/8.05 Rows_option_set$] : (v1 = v0 | ~ (card$b(v2) = v1) | ~ (card$b(v2) = v0))
% 52.65/8.05 & ! [v0: Rows_bool_fun$] : ! [v1: Rows_bool_fun$] : ! [v2: Rows_set$] : (v1
% 52.65/8.05 = v0 | ~ (uua$(v2) = v1) | ~ (uua$(v2) = v0)) & ! [v0: Nat_bool_fun$] :
% 52.65/8.05 ! [v1: Nat_bool_fun$] : ! [v2: Nat_set$] : (v1 = v0 | ~ (uub$(v2) = v1) | ~
% 52.65/8.05 (uub$(v2) = v0)) & ! [v0: Literal_bool_fun$] : ! [v1: Literal_bool_fun$] :
% 52.65/8.05 ! [v2: Literal_set$] : (v1 = v0 | ~ (uuc$(v2) = v1) | ~ (uuc$(v2) = v0)) &
% 52.65/8.05 ! [v0: Num0_bool_fun$] : ! [v1: Num0_bool_fun$] : ! [v2: Num0_set$] : (v1 =
% 52.65/8.05 v0 | ~ (uud$(v2) = v1) | ~ (uud$(v2) = v0)) & ! [v0: Num1_bool_fun$] : !
% 52.65/8.05 [v1: Num1_bool_fun$] : ! [v2: Num1_set$] : (v1 = v0 | ~ (uue$(v2) = v1) | ~
% 52.65/8.05 (uue$(v2) = v0)) & ! [v0: Int_int_fun$] : ! [v1: Int_int_fun$] : ! [v2:
% 52.65/8.05 int] : (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0))
% 52.65/8.05
% 52.65/8.05 Further assumptions not needed in the proof:
% 52.65/8.05 --------------------------------------------
% 52.65/8.05 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104,
% 52.65/8.05 axiom105, axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111,
% 52.65/8.05 axiom112, axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119,
% 52.65/8.05 axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127,
% 52.65/8.05 axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, axiom134,
% 52.65/8.05 axiom135, axiom137, axiom138, axiom14, axiom140, axiom141, axiom142, axiom143,
% 52.65/8.05 axiom144, axiom145, axiom146, axiom147, axiom148, axiom149, axiom150, axiom151,
% 52.65/8.05 axiom152, axiom153, axiom154, axiom155, axiom156, axiom157, axiom158, axiom159,
% 52.65/8.05 axiom16, axiom160, axiom161, axiom162, axiom163, axiom164, axiom165, axiom166,
% 52.65/8.05 axiom167, axiom168, axiom169, axiom17, axiom170, axiom171, axiom172, axiom173,
% 52.65/8.05 axiom174, axiom175, axiom176, axiom177, axiom178, axiom179, axiom18, axiom180,
% 52.65/8.05 axiom181, axiom182, axiom183, axiom184, axiom185, axiom186, axiom187, axiom188,
% 52.65/8.05 axiom189, axiom19, axiom190, axiom191, axiom192, axiom193, axiom194, axiom195,
% 52.65/8.05 axiom196, axiom197, axiom198, axiom199, axiom2, axiom20, axiom200, axiom201,
% 52.65/8.05 axiom202, axiom203, axiom204, axiom205, axiom206, axiom207, axiom208, axiom209,
% 52.65/8.05 axiom21, axiom210, axiom211, axiom212, axiom213, axiom214, axiom215, axiom216,
% 52.65/8.05 axiom217, axiom218, axiom219, axiom22, axiom220, axiom221, axiom222, axiom223,
% 52.65/8.05 axiom224, axiom225, axiom226, axiom227, axiom228, axiom229, axiom23, axiom230,
% 52.65/8.05 axiom231, axiom232, axiom233, axiom234, axiom235, axiom236, axiom237, axiom238,
% 52.65/8.05 axiom239, axiom24, axiom240, axiom241, axiom242, axiom243, axiom244, axiom245,
% 52.65/8.05 axiom246, axiom247, axiom248, axiom249, axiom25, axiom250, axiom251, axiom252,
% 52.65/8.05 axiom253, axiom254, axiom255, axiom256, axiom257, axiom258, axiom259, axiom26,
% 52.65/8.05 axiom260, axiom261, axiom262, axiom263, axiom264, axiom265, axiom266, axiom267,
% 52.65/8.05 axiom268, axiom269, axiom27, axiom270, axiom271, axiom272, axiom273, axiom274,
% 52.65/8.05 axiom275, axiom276, axiom277, axiom278, axiom279, axiom28, axiom280, axiom281,
% 52.65/8.05 axiom282, axiom283, axiom284, axiom285, axiom286, axiom287, axiom288, axiom289,
% 52.65/8.05 axiom29, axiom290, axiom291, axiom292, axiom293, axiom294, axiom295, axiom296,
% 52.65/8.05 axiom297, axiom298, axiom299, axiom3, axiom30, axiom300, axiom301, axiom302,
% 52.65/8.05 axiom303, axiom304, axiom305, axiom306, axiom307, axiom308, axiom309, axiom31,
% 52.65/8.05 axiom310, axiom311, axiom312, axiom313, axiom314, axiom315, axiom316, axiom317,
% 52.65/8.05 axiom318, axiom319, axiom32, axiom320, axiom321, axiom322, axiom323, axiom324,
% 52.65/8.05 axiom325, axiom326, axiom327, axiom328, axiom329, axiom33, axiom330, axiom331,
% 52.65/8.05 axiom332, axiom333, axiom334, axiom335, axiom336, axiom337, axiom338, axiom339,
% 52.65/8.05 axiom34, axiom340, axiom341, axiom342, axiom343, axiom344, axiom345, axiom346,
% 52.65/8.05 axiom347, axiom348, axiom349, axiom35, axiom350, axiom351, axiom352, axiom353,
% 52.65/8.05 axiom354, axiom355, axiom356, axiom357, axiom358, axiom359, axiom36, axiom360,
% 52.65/8.05 axiom361, axiom363, axiom364, axiom366, axiom367, axiom368, axiom369, axiom37,
% 52.65/8.05 axiom370, axiom371, axiom372, axiom373, axiom374, axiom375, axiom376, axiom377,
% 52.65/8.05 axiom378, axiom379, axiom38, axiom380, axiom381, axiom382, axiom383, axiom384,
% 52.65/8.05 axiom385, axiom386, axiom387, axiom388, axiom389, axiom39, axiom390, axiom391,
% 52.65/8.05 axiom392, axiom393, axiom394, axiom395, axiom396, axiom397, axiom398, axiom399,
% 52.65/8.05 axiom4, axiom40, axiom400, axiom401, axiom402, axiom403, axiom404, axiom405,
% 52.65/8.05 axiom406, axiom407, axiom408, axiom409, axiom41, axiom410, axiom411, axiom412,
% 52.65/8.05 axiom413, axiom414, axiom415, axiom416, axiom417, axiom418, axiom419, axiom42,
% 52.65/8.05 axiom420, axiom421, axiom422, axiom423, axiom424, axiom425, axiom426, axiom427,
% 52.65/8.05 axiom428, axiom429, axiom43, axiom430, axiom431, axiom432, axiom433, axiom434,
% 52.65/8.05 axiom435, axiom436, axiom437, axiom438, axiom439, axiom44, axiom440, axiom441,
% 52.65/8.05 axiom442, axiom443, axiom444, axiom445, axiom446, axiom447, axiom448, axiom449,
% 52.65/8.05 axiom45, axiom450, axiom451, axiom452, axiom453, axiom454, axiom455, axiom456,
% 52.65/8.05 axiom457, axiom458, axiom459, axiom46, axiom460, axiom461, axiom462, axiom463,
% 52.65/8.05 axiom464, axiom465, axiom466, axiom467, axiom468, axiom469, axiom47, axiom470,
% 52.65/8.05 axiom471, axiom472, axiom473, axiom474, axiom475, axiom476, axiom477, axiom478,
% 52.65/8.05 axiom479, axiom48, axiom480, axiom481, axiom482, axiom483, axiom484, axiom485,
% 52.65/8.05 axiom486, axiom487, axiom488, axiom489, axiom49, axiom490, axiom491, axiom492,
% 52.65/8.05 axiom493, axiom494, axiom495, axiom496, axiom497, axiom498, axiom499, axiom5,
% 52.65/8.05 axiom50, axiom500, axiom501, axiom502, axiom503, axiom504, axiom505, axiom506,
% 52.65/8.05 axiom507, axiom508, axiom509, axiom51, axiom510, axiom511, axiom512, axiom513,
% 52.65/8.05 axiom514, axiom515, axiom516, axiom517, axiom518, axiom519, axiom52, axiom520,
% 52.65/8.05 axiom521, axiom522, axiom523, axiom524, axiom525, axiom526, axiom527, axiom528,
% 52.65/8.05 axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, axiom535,
% 52.65/8.05 axiom536, axiom537, axiom538, axiom539, axiom54, axiom540, axiom541, axiom542,
% 52.65/8.05 axiom543, axiom544, axiom545, axiom546, axiom547, axiom548, axiom549, axiom55,
% 52.65/8.05 axiom550, axiom551, axiom552, axiom553, axiom554, axiom555, axiom556, axiom557,
% 52.65/8.05 axiom558, axiom559, axiom56, axiom560, axiom561, axiom562, axiom563, axiom564,
% 52.65/8.05 axiom565, axiom566, axiom567, axiom568, axiom569, axiom57, axiom570, axiom571,
% 52.65/8.05 axiom572, axiom573, axiom574, axiom575, axiom576, axiom577, axiom578, axiom579,
% 52.65/8.05 axiom58, axiom580, axiom581, axiom582, axiom583, axiom584, axiom585, axiom586,
% 52.65/8.05 axiom587, axiom59, axiom590, axiom591, axiom592, axiom593, axiom594, axiom596,
% 52.65/8.05 axiom597, axiom598, axiom599, axiom6, axiom60, axiom600, axiom601, axiom602,
% 52.65/8.05 axiom603, axiom604, axiom605, axiom607, axiom608, axiom609, axiom61, axiom610,
% 52.65/8.05 axiom611, axiom612, axiom613, axiom614, axiom615, axiom616, axiom617, axiom618,
% 52.65/8.05 axiom619, axiom62, axiom63, axiom64, axiom65, axiom66, axiom67, axiom68,
% 52.65/8.05 axiom69, axiom70, axiom71, axiom72, axiom73, axiom74, axiom75, axiom76, axiom77,
% 52.65/8.05 axiom78, axiom79, axiom8, axiom80, axiom81, axiom82, axiom83, axiom84, axiom85,
% 52.65/8.05 axiom86, axiom87, axiom88, axiom89, axiom9, axiom90, axiom91, axiom92, axiom93,
% 52.65/8.05 axiom94, axiom95, axiom96, axiom97, axiom98, axiom99, formula_621, formula_622
% 52.65/8.05
% 52.65/8.05 Those formulas are unsatisfiable:
% 52.65/8.05 ---------------------------------
% 52.65/8.05
% 52.65/8.05 Begin of proof
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom12) implies:
% 52.65/8.06 | (1) ? [v0: Nat$] : ? [v1: int] : ? [v2: Nat$] : (card$a(top$a) = v0 &
% 52.65/8.06 | card$b(top$b) = v2 & fun_app$h(of_nat$, v2) = $sum(v1, -1) &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v2) & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom15) implies:
% 52.65/8.06 | (2) ? [v0: Nat$] : ? [v1: int] : ? [v2: Nat$] : (card$(top$) = v2 &
% 52.65/8.06 | card$b(top$b) = v0 & fun_app$h(of_nat$, v2) = $sum(v1, -1) &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v2) & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom362) implies:
% 52.65/8.06 | (3) ? [v0: Nat$] : ? [v1: int] : ($lesseq(1, v1) & card$b(top$b) = v0 &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom588) implies:
% 52.65/8.06 | (4) ? [v0: Nat$] : ? [v1: int] : ($lesseq(2, v1) & card$(top$) = v0 &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom589) implies:
% 52.65/8.06 | (5) ? [v0: Nat$] : ? [v1: int] : ($lesseq(1, v1) & card$(top$) = v0 &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom595) implies:
% 52.65/8.06 | (6) ? [v0: Nat$] : ? [v1: int] : (abs$(v1) = zero$ & card$(top$) = v0 &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (axiom606) implies:
% 52.65/8.06 | (7) ? [v0: Nat$] : ? [v1: int] : ? [v2: Nat$] : ? [v3: int] :
% 52.65/8.06 | (card$(top$) = v0 & card$b(top$b) = v2 & fun_app$h(of_nat$, v2) = v3 &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v2) & Nat$(v0) & ( ~ (v1 = 0) | v3
% 52.65/8.06 | = 0) & ($difference(v3, v1) = 1 | v1 = 0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (conjecture7) implies:
% 52.65/8.06 | (8) ? [v0: Nat$] : ? [v1: int] : ($lesseq(v1, 0)card$(top$) = v0 &
% 52.65/8.06 | fun_app$h(of_nat$, v0) = v1 & Nat$(v0))
% 52.65/8.06 |
% 52.65/8.06 | ALPHA: (function-axioms) implies:
% 52.65/8.06 | (9) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Rows_option_set$] : (v1 = v0 |
% 52.65/8.06 | ~ (card$b(v2) = v1) | ~ (card$b(v2) = v0))
% 52.65/8.06 | (10) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Rows_set$] : (v1 = v0 | ~
% 52.65/8.07 | (card$(v2) = v1) | ~ (card$(v2) = v0))
% 52.65/8.07 | (11) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] :
% 52.65/8.07 | (v1 = v0 | ~ (fun_app$h(v3, v2) = v1) | ~ (fun_app$h(v3, v2) = v0))
% 52.65/8.07 |
% 52.65/8.07 | DELTA: instantiating (5) with fresh symbols all_455_0, all_455_1 gives:
% 52.65/8.07 | (12) $lesseq(1, all_455_0) & card$(top$) = all_455_1 & fun_app$h(of_nat$,
% 52.65/8.07 | all_455_1) = all_455_0 & Nat$(all_455_1)
% 52.65/8.07 |
% 52.65/8.07 | ALPHA: (12) implies:
% 52.65/8.07 | (13) fun_app$h(of_nat$, all_455_1) = all_455_0
% 52.65/8.07 | (14) card$(top$) = all_455_1
% 52.65/8.07 |
% 52.65/8.07 | DELTA: instantiating (5) with fresh symbols all_458_0, all_458_1 gives:
% 52.65/8.07 | (15) $lesseq(1, all_458_0) & card$(top$) = all_458_1 & fun_app$h(of_nat$,
% 52.65/8.07 | all_458_1) = all_458_0 & Nat$(all_458_1)
% 52.65/8.07 |
% 52.65/8.07 | ALPHA: (15) implies:
% 52.65/8.07 | (16) card$(top$) = all_458_1
% 52.65/8.07 |
% 52.65/8.07 | DELTA: instantiating (3) with fresh symbols all_461_0, all_461_1 gives:
% 52.65/8.07 | (17) $lesseq(1, all_461_0) & card$b(top$b) = all_461_1 & fun_app$h(of_nat$,
% 52.65/8.07 | all_461_1) = all_461_0 & Nat$(all_461_1)
% 52.65/8.07 |
% 52.65/8.07 | ALPHA: (17) implies:
% 52.65/8.07 | (18) fun_app$h(of_nat$, all_461_1) = all_461_0
% 52.65/8.07 | (19) card$b(top$b) = all_461_1
% 52.65/8.07 |
% 52.65/8.07 | DELTA: instantiating (4) with fresh symbols all_464_0, all_464_1 gives:
% 52.65/8.07 | (20) $lesseq(2, all_464_0) & card$(top$) = all_464_1 & fun_app$h(of_nat$,
% 52.65/8.07 | all_464_1) = all_464_0 & Nat$(all_464_1)
% 52.65/8.07 |
% 52.65/8.07 | ALPHA: (20) implies:
% 53.08/8.07 | (21) $lesseq(2, all_464_0)
% 53.08/8.07 | (22) fun_app$h(of_nat$, all_464_1) = all_464_0
% 53.08/8.07 | (23) card$(top$) = all_464_1
% 53.08/8.07 |
% 53.08/8.07 | DELTA: instantiating (6) with fresh symbols all_467_0, all_467_1 gives:
% 53.08/8.07 | (24) abs$(all_467_0) = zero$ & card$(top$) = all_467_1 & fun_app$h(of_nat$,
% 53.08/8.07 | all_467_1) = all_467_0 & Nat$(all_467_1)
% 53.08/8.07 |
% 53.08/8.07 | ALPHA: (24) implies:
% 53.08/8.07 | (25) fun_app$h(of_nat$, all_467_1) = all_467_0
% 53.08/8.07 | (26) card$(top$) = all_467_1
% 53.08/8.07 |
% 53.08/8.07 | DELTA: instantiating (5) with fresh symbols all_475_0, all_475_1 gives:
% 53.08/8.07 | (27) $lesseq(1, all_475_0) & card$(top$) = all_475_1 & fun_app$h(of_nat$,
% 53.08/8.07 | all_475_1) = all_475_0 & Nat$(all_475_1)
% 53.08/8.07 |
% 53.08/8.07 | ALPHA: (27) implies:
% 53.08/8.07 | (28) fun_app$h(of_nat$, all_475_1) = all_475_0
% 53.08/8.07 | (29) card$(top$) = all_475_1
% 53.08/8.07 |
% 53.08/8.07 | DELTA: instantiating (8) with fresh symbols all_478_0, all_478_1 gives:
% 53.08/8.07 | (30) $lesseq(all_478_0, 0)card$(top$) = all_478_1 & fun_app$h(of_nat$,
% 53.08/8.07 | all_478_1) = all_478_0 & Nat$(all_478_1)
% 53.08/8.07 |
% 53.08/8.07 | ALPHA: (30) implies:
% 53.08/8.07 | (31) $lesseq(all_478_0, 0)
% 53.08/8.07 | (32) fun_app$h(of_nat$, all_478_1) = all_478_0
% 53.08/8.07 | (33) card$(top$) = all_478_1
% 53.08/8.07 |
% 53.08/8.07 | DELTA: instantiating (3) with fresh symbols all_486_0, all_486_1 gives:
% 53.08/8.07 | (34) $lesseq(1, all_486_0) & card$b(top$b) = all_486_1 & fun_app$h(of_nat$,
% 53.08/8.07 | all_486_1) = all_486_0 & Nat$(all_486_1)
% 53.08/8.07 |
% 53.08/8.07 | ALPHA: (34) implies:
% 53.08/8.07 | (35) fun_app$h(of_nat$, all_486_1) = all_486_0
% 53.08/8.07 | (36) card$b(top$b) = all_486_1
% 53.08/8.07 |
% 53.08/8.07 | DELTA: instantiating (1) with fresh symbols all_494_0, all_494_1, all_494_2
% 53.08/8.07 | gives:
% 53.08/8.07 | (37) card$a(top$a) = all_494_2 & card$b(top$b) = all_494_0 &
% 53.08/8.07 | fun_app$h(of_nat$, all_494_0) = $sum(all_494_1, -1) &
% 53.08/8.07 | fun_app$h(of_nat$, all_494_2) = all_494_1 & Nat$(all_494_0) &
% 53.08/8.07 | Nat$(all_494_2)
% 53.08/8.07 |
% 53.08/8.07 | ALPHA: (37) implies:
% 53.08/8.07 | (38) fun_app$h(of_nat$, all_494_0) = $sum(all_494_1, -1)
% 53.08/8.07 | (39) card$b(top$b) = all_494_0
% 53.08/8.07 |
% 53.08/8.07 | DELTA: instantiating (2) with fresh symbols all_496_0, all_496_1, all_496_2
% 53.08/8.07 | gives:
% 53.08/8.08 | (40) card$(top$) = all_496_0 & card$b(top$b) = all_496_2 &
% 53.08/8.08 | fun_app$h(of_nat$, all_496_0) = $sum(all_496_1, -1) &
% 53.08/8.08 | fun_app$h(of_nat$, all_496_2) = all_496_1 & Nat$(all_496_0) &
% 53.08/8.08 | Nat$(all_496_2)
% 53.08/8.08 |
% 53.08/8.08 | ALPHA: (40) implies:
% 53.08/8.08 | (41) fun_app$h(of_nat$, all_496_2) = all_496_1
% 53.08/8.08 | (42) fun_app$h(of_nat$, all_496_0) = $sum(all_496_1, -1)
% 53.08/8.08 | (43) card$b(top$b) = all_496_2
% 53.08/8.08 | (44) card$(top$) = all_496_0
% 53.08/8.08 |
% 53.08/8.08 | DELTA: instantiating (7) with fresh symbols all_516_0, all_516_1, all_516_2,
% 53.08/8.08 | all_516_3 gives:
% 53.08/8.08 | (45) card$(top$) = all_516_3 & card$b(top$b) = all_516_1 &
% 53.08/8.08 | fun_app$h(of_nat$, all_516_1) = all_516_0 & fun_app$h(of_nat$,
% 53.08/8.08 | all_516_3) = all_516_2 & Nat$(all_516_1) & Nat$(all_516_3) & ( ~
% 53.08/8.08 | (all_516_2 = 0) | all_516_0 = 0) & ($difference(all_516_0,
% 53.08/8.08 | all_516_2) = 1 | all_516_2 = 0)
% 53.08/8.08 |
% 53.08/8.08 | ALPHA: (45) implies:
% 53.08/8.08 | (46) fun_app$h(of_nat$, all_516_1) = all_516_0
% 53.08/8.08 | (47) card$b(top$b) = all_516_1
% 53.08/8.08 | (48) card$(top$) = all_516_3
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (9) with all_486_1, all_494_0, top$b, simplifying
% 53.08/8.08 | with (36), (39) gives:
% 53.08/8.08 | (49) all_494_0 = all_486_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (9) with all_496_2, all_516_1, top$b, simplifying
% 53.08/8.08 | with (43), (47) gives:
% 53.08/8.08 | (50) all_516_1 = all_496_2
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (9) with all_494_0, all_516_1, top$b, simplifying
% 53.08/8.08 | with (39), (47) gives:
% 53.08/8.08 | (51) all_516_1 = all_494_0
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (9) with all_461_1, all_516_1, top$b, simplifying
% 53.08/8.08 | with (19), (47) gives:
% 53.08/8.08 | (52) all_516_1 = all_461_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_458_1, all_475_1, top$, simplifying
% 53.08/8.08 | with (16), (29) gives:
% 53.08/8.08 | (53) all_475_1 = all_458_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_475_1, all_478_1, top$, simplifying
% 53.08/8.08 | with (29), (33) gives:
% 53.08/8.08 | (54) all_478_1 = all_475_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_467_1, all_478_1, top$, simplifying
% 53.08/8.08 | with (26), (33) gives:
% 53.08/8.08 | (55) all_478_1 = all_467_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_455_1, all_478_1, top$, simplifying
% 53.08/8.08 | with (14), (33) gives:
% 53.08/8.08 | (56) all_478_1 = all_455_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_496_0, all_516_3, top$, simplifying
% 53.08/8.08 | with (44), (48) gives:
% 53.08/8.08 | (57) all_516_3 = all_496_0
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_478_1, all_516_3, top$, simplifying
% 53.08/8.08 | with (33), (48) gives:
% 53.08/8.08 | (58) all_516_3 = all_478_1
% 53.08/8.08 |
% 53.08/8.08 | GROUND_INST: instantiating (10) with all_464_1, all_516_3, top$, simplifying
% 53.08/8.08 | with (23), (48) gives:
% 53.08/8.08 | (59) all_516_3 = all_464_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (50), (52) imply:
% 53.08/8.08 | (60) all_496_2 = all_461_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (50), (51) imply:
% 53.08/8.08 | (61) all_496_2 = all_494_0
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (57), (58) imply:
% 53.08/8.08 | (62) all_496_0 = all_478_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (57), (59) imply:
% 53.08/8.08 | (63) all_496_0 = all_464_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (62), (63) imply:
% 53.08/8.08 | (64) all_478_1 = all_464_1
% 53.08/8.08 |
% 53.08/8.08 | SIMP: (64) implies:
% 53.08/8.08 | (65) all_478_1 = all_464_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (60), (61) imply:
% 53.08/8.08 | (66) all_494_0 = all_461_1
% 53.08/8.08 |
% 53.08/8.08 | SIMP: (66) implies:
% 53.08/8.08 | (67) all_494_0 = all_461_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (49), (67) imply:
% 53.08/8.08 | (68) all_486_1 = all_461_1
% 53.08/8.08 |
% 53.08/8.08 | SIMP: (68) implies:
% 53.08/8.08 | (69) all_486_1 = all_461_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (55), (65) imply:
% 53.08/8.08 | (70) all_467_1 = all_464_1
% 53.08/8.08 |
% 53.08/8.08 | COMBINE_EQS: (54), (55) imply:
% 53.08/8.09 | (71) all_475_1 = all_467_1
% 53.08/8.09 |
% 53.08/8.09 | SIMP: (71) implies:
% 53.08/8.09 | (72) all_475_1 = all_467_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (55), (56) imply:
% 53.08/8.09 | (73) all_467_1 = all_455_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (53), (72) imply:
% 53.08/8.09 | (74) all_467_1 = all_458_1
% 53.08/8.09 |
% 53.08/8.09 | SIMP: (74) implies:
% 53.08/8.09 | (75) all_467_1 = all_458_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (70), (73) imply:
% 53.08/8.09 | (76) all_464_1 = all_455_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (70), (75) imply:
% 53.08/8.09 | (77) all_464_1 = all_458_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (76), (77) imply:
% 53.08/8.09 | (78) all_458_1 = all_455_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (53), (78) imply:
% 53.08/8.09 | (79) all_475_1 = all_455_1
% 53.08/8.09 |
% 53.08/8.09 | COMBINE_EQS: (63), (76) imply:
% 53.08/8.09 | (80) all_496_0 = all_455_1
% 53.08/8.09 |
% 53.08/8.09 | REDUCE: (46), (52) imply:
% 53.08/8.09 | (81) fun_app$h(of_nat$, all_461_1) = all_516_0
% 53.08/8.09 |
% 53.08/8.09 | REDUCE: (42), (80) imply:
% 53.08/8.09 | (82) fun_app$h(of_nat$, all_455_1) = $sum(all_496_1, -1)
% 53.08/8.09 |
% 53.08/8.09 | REDUCE: (41), (60) imply:
% 53.08/8.09 | (83) fun_app$h(of_nat$, all_461_1) = all_496_1
% 53.08/8.09 |
% 53.08/8.09 | REDUCE: (38), (67) imply:
% 53.08/8.09 | (84) fun_app$h(of_nat$, all_461_1) = $sum(all_494_1, -1)
% 53.08/8.09 |
% 53.17/8.09 | REDUCE: (35), (69) imply:
% 53.17/8.09 | (85) fun_app$h(of_nat$, all_461_1) = all_486_0
% 53.17/8.09 |
% 53.17/8.09 | REDUCE: (32), (56) imply:
% 53.17/8.09 | (86) fun_app$h(of_nat$, all_455_1) = all_478_0
% 53.17/8.09 |
% 53.17/8.09 | REDUCE: (28), (79) imply:
% 53.17/8.09 | (87) fun_app$h(of_nat$, all_455_1) = all_475_0
% 53.17/8.09 |
% 53.17/8.09 | REDUCE: (25), (73) imply:
% 53.17/8.09 | (88) fun_app$h(of_nat$, all_455_1) = all_467_0
% 53.17/8.09 |
% 53.17/8.09 | REDUCE: (22), (76) imply:
% 53.17/8.09 | (89) fun_app$h(of_nat$, all_455_1) = all_464_0
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_467_0, all_475_0, all_455_1, of_nat$,
% 53.17/8.09 | simplifying with (87), (88) gives:
% 53.17/8.09 | (90) all_475_0 = all_467_0
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_464_0, all_475_0, all_455_1, of_nat$,
% 53.17/8.09 | simplifying with (87), (89) gives:
% 53.17/8.09 | (91) all_475_0 = all_464_0
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_455_0, all_478_0, all_455_1, of_nat$,
% 53.17/8.09 | simplifying with (13), (86) gives:
% 53.17/8.09 | (92) all_478_0 = all_455_0
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_475_0, all_478_0, all_455_1, of_nat$,
% 53.17/8.09 | simplifying with (86), (87) gives:
% 53.17/8.09 | (93) all_478_0 = all_475_0
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_475_0, $sum(all_496_1, -1),
% 53.17/8.09 | all_455_1, of_nat$, simplifying with (82), (87) gives:
% 53.17/8.09 | (94) $difference(all_496_1, all_475_0) = 1
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_461_0, all_516_0, all_461_1, of_nat$,
% 53.17/8.09 | simplifying with (18), (81) gives:
% 53.17/8.09 | (95) all_516_0 = all_461_0
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_496_1, all_516_0, all_461_1, of_nat$,
% 53.17/8.09 | simplifying with (81), (83) gives:
% 53.17/8.09 | (96) all_516_0 = all_496_1
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with $sum(all_494_1, -1), all_516_0,
% 53.17/8.09 | all_461_1, of_nat$, simplifying with (81), (84) gives:
% 53.17/8.09 | (97) $difference(all_516_0, all_494_1) = -1
% 53.17/8.09 |
% 53.17/8.09 | GROUND_INST: instantiating (11) with all_486_0, all_516_0, all_461_1, of_nat$,
% 53.17/8.09 | simplifying with (81), (85) gives:
% 53.17/8.09 | (98) all_516_0 = all_486_0
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (95), (96) imply:
% 53.17/8.09 | (99) all_496_1 = all_461_0
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (96), (98) imply:
% 53.17/8.09 | (100) all_496_1 = all_486_0
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (96), (97) imply:
% 53.17/8.09 | (101) $difference(all_496_1, all_494_1) = -1
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (94), (101) imply:
% 53.17/8.09 | (102) $difference(all_494_1, all_475_0) = 2
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (99), (101) imply:
% 53.17/8.09 | (103) $difference(all_494_1, all_461_0) = 1
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (100), (101) imply:
% 53.17/8.09 | (104) $difference(all_494_1, all_486_0) = 1
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (103), (104) imply:
% 53.17/8.09 | (105) all_486_0 = all_461_0
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (102), (104) imply:
% 53.17/8.09 | (106) $difference(all_486_0, all_475_0) = 1
% 53.17/8.09 |
% 53.17/8.09 | COMBINE_EQS: (105), (106) imply:
% 53.17/8.09 | (107) $difference(all_475_0, all_461_0) = -1
% 53.17/8.09 |
% 53.17/8.09 | SIMP: (107) implies:
% 53.17/8.09 | (108) $difference(all_475_0, all_461_0) = -1
% 53.17/8.09 |
% 53.17/8.10 | COMBINE_EQS: (92), (93) imply:
% 53.17/8.10 | (109) all_475_0 = all_455_0
% 53.17/8.10 |
% 53.17/8.10 | SIMP: (109) implies:
% 53.17/8.10 | (110) all_475_0 = all_455_0
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_EQS: (90), (110) imply:
% 53.17/8.10 | (111) all_467_0 = all_455_0
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_EQS: (90), (108) imply:
% 53.17/8.10 | (112) $difference(all_467_0, all_461_0) = -1
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_EQS: (90), (91) imply:
% 53.17/8.10 | (113) all_467_0 = all_464_0
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_EQS: (112), (113) imply:
% 53.17/8.10 | (114) $difference(all_464_0, all_461_0) = -1
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_EQS: (111), (113) imply:
% 53.17/8.10 | (115) all_464_0 = all_455_0
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_EQS: (114), (115) imply:
% 53.17/8.10 | (116) $difference(all_461_0, all_455_0) = 1
% 53.17/8.10 |
% 53.17/8.10 | REDUCE: (31), (92) imply:
% 53.17/8.10 | (117) $lesseq(all_455_0, 0)
% 53.17/8.10 |
% 53.17/8.10 | REDUCE: (21), (115) imply:
% 53.17/8.10 | (118) $lesseq(2, all_455_0)
% 53.17/8.10 |
% 53.17/8.10 | COMBINE_INEQS: (117), (118) imply:
% 53.17/8.10 | (119) $false
% 53.17/8.10 |
% 53.17/8.10 | CLOSE: (119) is inconsistent.
% 53.17/8.10 |
% 53.17/8.10 End of proof
% 53.17/8.10 % SZS output end Proof for theBenchmark
% 53.17/8.10
% 53.17/8.10 7484ms
%------------------------------------------------------------------------------