TSTP Solution File: SWV055+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV055+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 22:54:43 EDT 2023
% Result : Theorem 18.50s 3.30s
% Output : Proof 21.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV055+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 06:44:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.60/1.36 Prover 1: Preprocessing ...
% 4.60/1.38 Prover 4: Preprocessing ...
% 4.60/1.40 Prover 5: Preprocessing ...
% 4.60/1.40 Prover 6: Preprocessing ...
% 4.60/1.40 Prover 3: Preprocessing ...
% 4.60/1.40 Prover 0: Preprocessing ...
% 4.60/1.41 Prover 2: Preprocessing ...
% 10.56/2.26 Prover 1: Warning: ignoring some quantifiers
% 11.39/2.30 Prover 3: Warning: ignoring some quantifiers
% 11.74/2.33 Prover 6: Proving ...
% 11.74/2.35 Prover 1: Constructing countermodel ...
% 11.74/2.35 Prover 3: Constructing countermodel ...
% 11.74/2.36 Prover 4: Warning: ignoring some quantifiers
% 12.32/2.43 Prover 4: Constructing countermodel ...
% 12.32/2.45 Prover 5: Proving ...
% 12.32/2.52 Prover 0: Proving ...
% 12.89/2.58 Prover 2: Proving ...
% 18.50/3.30 Prover 3: proved (2628ms)
% 18.50/3.30
% 18.50/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.50/3.30
% 18.50/3.30 Prover 0: stopped
% 18.50/3.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.50/3.30 Prover 5: stopped
% 18.88/3.31 Prover 2: stopped
% 18.88/3.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.88/3.31 Prover 6: stopped
% 18.88/3.33 Prover 1: Found proof (size 102)
% 18.88/3.33 Prover 1: proved (2641ms)
% 18.88/3.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.88/3.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.88/3.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.88/3.34 Prover 4: stopped
% 19.98/3.45 Prover 7: Preprocessing ...
% 19.98/3.45 Prover 8: Preprocessing ...
% 19.98/3.46 Prover 11: Preprocessing ...
% 19.98/3.47 Prover 10: Preprocessing ...
% 19.98/3.49 Prover 13: Preprocessing ...
% 20.36/3.54 Prover 7: stopped
% 20.79/3.55 Prover 10: stopped
% 20.83/3.58 Prover 11: stopped
% 21.16/3.60 Prover 13: stopped
% 21.16/3.64 Prover 8: Warning: ignoring some quantifiers
% 21.37/3.65 Prover 8: Constructing countermodel ...
% 21.37/3.67 Prover 8: stopped
% 21.37/3.67
% 21.37/3.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.37/3.67
% 21.37/3.70 % SZS output start Proof for theBenchmark
% 21.37/3.71 Assumptions after simplification:
% 21.37/3.71 ---------------------------------
% 21.37/3.71
% 21.37/3.71 (cl5_nebula_norm_0037)
% 21.80/3.75 $i(x) & $i(center) & $i(q) & $i(n135300) & $i(pv10) & $i(n5) & $i(n1) & $i(n0)
% 21.80/3.75 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.80/3.75 (minus(n135300, n1) = v0 & minus(pv10, n1) = v1 & minus(n5, n1) = v2 &
% 21.80/3.75 minus(n0, n1) = v3 & a_select2(x, pv10) = v4 & leq(pv10, v0) = 0 & leq(n0,
% 21.80/3.75 pv10) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : !
% 21.80/3.75 [v6: $i] : ! [v7: $i] : ( ~ (a_select3(q, v5, v6) = v7) | ~ $i(v6) | ~
% 21.80/3.75 $i(v5) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : (sum(n0, v2, v7) =
% 21.80/3.75 v10 & leq(v5, v1) = v9 & leq(n0, v5) = v8 & $i(v10) & ( ~ (v9 = 0) | ~
% 21.80/3.75 (v8 = 0) | v10 = n1))) & ( ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 21.80/3.75 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 21.80/3.75 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : (
% 21.80/3.75 ~ (v17 = v7) & times(v13, v13) = v14 & times(v9, v9) = v10 & sqrt(v14) =
% 21.80/3.75 v15 & sqrt(v10) = v11 & divide(v11, v16) = v17 & minus(v12, v4) = v13 &
% 21.80/3.75 minus(v8, v4) = v9 & sum(n0, v2, v15) = v16 & a_select3(center, v6, n0)
% 21.80/3.75 = v12 & a_select3(center, v5, n0) = v8 & a_select3(q, pv10, v5) = v7 &
% 21.80/3.75 leq(v5, v3) = 0 & leq(n0, v5) = 0 & $i(v17) & $i(v16) & $i(v15) &
% 21.80/3.75 $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 21.80/3.75 $i(v7) & $i(v6) & $i(v5)) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 21.80/3.75 [v8: $i] : ( ~ (v8 = n1) & sum(n0, v2, v7) = v8 & a_select3(q, v5, v6) =
% 21.80/3.75 v7 & leq(v5, v1) = 0 & leq(n0, v5) = 0 & $i(v8) & $i(v7) & $i(v6) &
% 21.80/3.75 $i(v5))))
% 21.80/3.75
% 21.80/3.75 (finite_domain_0)
% 21.80/3.75 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 21.80/3.75 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 21.80/3.75
% 21.80/3.75 (gt_3_tptp_minus_1)
% 21.80/3.75 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1)
% 21.80/3.75
% 21.80/3.75 (irreflexivity_gt)
% 21.80/3.75 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0))
% 21.80/3.75
% 21.80/3.75 (leq_gt1)
% 21.80/3.75 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 21.80/3.75 leq(v0, v1) = 0)
% 21.80/3.75
% 21.80/3.75 (leq_gt_pred)
% 21.80/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 21.80/3.76 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 21.80/3.76 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 21.80/3.76 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)
% 21.80/3.76 | gt(v1, v0) = 0)
% 21.80/3.76
% 21.80/3.76 (pred_minus_1)
% 21.80/3.76 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 21.80/3.76 (pred(v0) = v1 & $i(v1)))
% 21.80/3.76
% 21.80/3.76 (pred_succ)
% 21.80/3.76 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 21.80/3.76
% 21.80/3.76 (succ_tptp_minus_1)
% 21.80/3.76 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0)
% 21.80/3.76
% 21.80/3.76 (successor_1)
% 21.80/3.76 succ(n0) = n1 & $i(n1) & $i(n0)
% 21.80/3.76
% 21.80/3.76 (successor_2)
% 21.80/3.76 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 21.80/3.76
% 21.80/3.76 (successor_3)
% 21.80/3.76 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 21.80/3.76 succ(n0) = v0 & $i(v1) & $i(v0))
% 21.80/3.76
% 21.80/3.76 (successor_4)
% 21.80/3.76 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 21.80/3.76 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 21.80/3.76
% 21.80/3.76 (successor_5)
% 21.80/3.76 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 21.80/3.76 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 21.80/3.76 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.80/3.76
% 21.80/3.76 (function-axioms)
% 21.80/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.80/3.77 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 21.80/3.77 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 21.80/3.77 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 21.80/3.77 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.80/3.77 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 21.80/3.77 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 21.80/3.77 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 21.80/3.77 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.80/3.77 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 21.80/3.77 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.80/3.77 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3,
% 21.80/3.77 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 21.80/3.77 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] :
% 21.80/3.77 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) |
% 21.80/3.77 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 21.80/3.77 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0:
% 21.80/3.77 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3,
% 21.80/3.77 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 21.80/3.77 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~
% 21.80/3.77 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 21.80/3.77 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) =
% 21.80/3.77 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 21.80/3.77 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 21.80/3.77 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~
% 21.80/3.77 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 21.80/3.77 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2)
% 21.80/3.77 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 21.80/3.77 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) &
% 21.80/3.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 21.80/3.77 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 21.80/3.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.80/3.77 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 21.80/3.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.80/3.77 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 21.80/3.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.80/3.77 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 21.80/3.77 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) &
% 21.80/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 21.80/3.77 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.80/3.77 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.80/3.77 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 21.80/3.77 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 21.80/3.77 v0))
% 21.80/3.77
% 21.80/3.77 Further assumptions not needed in the proof:
% 21.80/3.77 --------------------------------------------
% 21.80/3.77 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 21.80/3.77 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 21.80/3.77 gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2, gt_135300_3,
% 21.80/3.77 gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1,
% 21.80/3.77 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_4_0, gt_4_1,
% 21.80/3.77 gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4,
% 21.80/3.77 gt_5_tptp_minus_1, gt_succ, leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt,
% 21.80/3.77 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 21.80/3.77 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 21.80/3.77 matrix_symm_trans, matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1,
% 21.80/3.77 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 21.80/3.77 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 21.80/3.77 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 21.80/3.77 succ_pred, sum_plus_base, sum_plus_base_float, totality, transitivity_gt,
% 21.80/3.77 transitivity_leq, ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 21.80/3.77
% 21.80/3.77 Those formulas are unsatisfiable:
% 21.80/3.77 ---------------------------------
% 21.80/3.77
% 21.80/3.77 Begin of proof
% 21.80/3.77 |
% 21.80/3.77 | ALPHA: (leq_gt_pred) implies:
% 21.80/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 21.80/3.77 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0)
% 21.80/3.77 |
% 21.80/3.77 | ALPHA: (succ_tptp_minus_1) implies:
% 21.80/3.77 | (2) succ(tptp_minus_1) = n0
% 21.80/3.77 |
% 21.80/3.77 | ALPHA: (pred_minus_1) implies:
% 21.80/3.77 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 21.80/3.77 | (pred(v0) = v1 & $i(v1)))
% 21.80/3.77 |
% 21.80/3.77 | ALPHA: (gt_3_tptp_minus_1) implies:
% 21.80/3.77 | (4) $i(tptp_minus_1)
% 21.80/3.77 |
% 21.80/3.77 | ALPHA: (finite_domain_0) implies:
% 21.80/3.77 | (5) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 21.80/3.77 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 21.80/3.77 |
% 21.80/3.77 | ALPHA: (successor_4) implies:
% 21.80/3.78 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 21.80/3.78 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 21.80/3.78 |
% 21.80/3.78 | ALPHA: (successor_5) implies:
% 21.80/3.78 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 21.80/3.78 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 21.80/3.78 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.80/3.78 |
% 21.80/3.78 | ALPHA: (successor_1) implies:
% 21.80/3.78 | (8) succ(n0) = n1
% 21.80/3.78 |
% 21.80/3.78 | ALPHA: (successor_2) implies:
% 21.80/3.78 | (9) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 21.80/3.78 |
% 21.80/3.78 | ALPHA: (successor_3) implies:
% 21.80/3.78 | (10) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 21.80/3.78 | = v0 & $i(v1) & $i(v0))
% 21.80/3.78 |
% 21.80/3.78 | ALPHA: (cl5_nebula_norm_0037) implies:
% 21.80/3.78 | (11) $i(n0)
% 21.80/3.78 | (12) $i(n5)
% 21.80/3.78 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.80/3.78 | (minus(n135300, n1) = v0 & minus(pv10, n1) = v1 & minus(n5, n1) = v2 &
% 21.80/3.78 | minus(n0, n1) = v3 & a_select2(x, pv10) = v4 & leq(pv10, v0) = 0 &
% 21.80/3.78 | leq(n0, pv10) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 21.80/3.78 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (a_select3(q, v5, v6) =
% 21.80/3.78 | v7) | ~ $i(v6) | ~ $i(v5) | ? [v8: any] : ? [v9: any] : ?
% 21.80/3.78 | [v10: $i] : (sum(n0, v2, v7) = v10 & leq(v5, v1) = v9 & leq(n0,
% 21.80/3.78 | v5) = v8 & $i(v10) & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = n1)))
% 21.80/3.78 | & ( ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 21.80/3.78 | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i]
% 21.80/3.78 | : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ( ~
% 21.80/3.78 | (v17 = v7) & times(v13, v13) = v14 & times(v9, v9) = v10 &
% 21.80/3.78 | sqrt(v14) = v15 & sqrt(v10) = v11 & divide(v11, v16) = v17 &
% 21.80/3.78 | minus(v12, v4) = v13 & minus(v8, v4) = v9 & sum(n0, v2, v15) =
% 21.80/3.78 | v16 & a_select3(center, v6, n0) = v12 & a_select3(center, v5,
% 21.80/3.78 | n0) = v8 & a_select3(q, pv10, v5) = v7 & leq(v5, v3) = 0 &
% 21.80/3.78 | leq(n0, v5) = 0 & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 21.80/3.78 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7)
% 21.80/3.78 | & $i(v6) & $i(v5)) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 21.80/3.78 | ? [v8: $i] : ( ~ (v8 = n1) & sum(n0, v2, v7) = v8 & a_select3(q,
% 21.80/3.78 | v5, v6) = v7 & leq(v5, v1) = 0 & leq(n0, v5) = 0 & $i(v8) &
% 21.80/3.78 | $i(v7) & $i(v6) & $i(v5))))
% 21.80/3.78 |
% 21.80/3.78 | ALPHA: (function-axioms) implies:
% 21.80/3.78 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) =
% 21.80/3.78 | v1) | ~ (pred(v2) = v0))
% 21.80/3.78 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 21.80/3.78 | v1) | ~ (succ(v2) = v0))
% 21.80/3.78 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 21.80/3.78 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 21.80/3.79 | v0))
% 21.80/3.79 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.80/3.79 | (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0))
% 21.80/3.79 |
% 21.80/3.79 | DELTA: instantiating (9) with fresh symbol all_49_0 gives:
% 21.80/3.79 | (18) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0)
% 21.80/3.79 |
% 21.80/3.79 | ALPHA: (18) implies:
% 21.80/3.79 | (19) succ(n0) = all_49_0
% 21.80/3.79 | (20) succ(all_49_0) = n2
% 21.80/3.79 |
% 21.80/3.79 | DELTA: instantiating (10) with fresh symbols all_51_0, all_51_1 gives:
% 21.80/3.79 | (21) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1
% 21.80/3.79 | & $i(all_51_0) & $i(all_51_1)
% 21.80/3.79 |
% 21.80/3.79 | ALPHA: (21) implies:
% 21.80/3.79 | (22) succ(n0) = all_51_1
% 21.80/3.79 | (23) succ(all_51_1) = all_51_0
% 21.80/3.79 | (24) succ(all_51_0) = n3
% 21.80/3.79 |
% 21.80/3.79 | DELTA: instantiating (6) with fresh symbols all_53_0, all_53_1, all_53_2
% 21.80/3.79 | gives:
% 21.80/3.79 | (25) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) =
% 21.80/3.79 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) &
% 21.80/3.79 | $i(all_53_2)
% 21.80/3.79 |
% 21.80/3.79 | ALPHA: (25) implies:
% 21.80/3.79 | (26) succ(n0) = all_53_2
% 21.80/3.79 | (27) succ(all_53_2) = all_53_1
% 21.80/3.80 | (28) succ(all_53_1) = all_53_0
% 21.80/3.80 | (29) succ(all_53_0) = n4
% 21.80/3.80 |
% 21.80/3.80 | DELTA: instantiating (7) with fresh symbols all_55_0, all_55_1, all_55_2,
% 21.80/3.80 | all_55_3 gives:
% 21.80/3.81 | (30) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) =
% 21.80/3.81 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 &
% 21.80/3.81 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3)
% 21.80/3.81 |
% 21.80/3.81 | ALPHA: (30) implies:
% 21.80/3.81 | (31) $i(all_55_0)
% 21.80/3.81 | (32) succ(n0) = all_55_3
% 21.80/3.81 | (33) succ(all_55_3) = all_55_2
% 21.80/3.81 | (34) succ(all_55_2) = all_55_1
% 21.80/3.81 | (35) succ(all_55_1) = all_55_0
% 21.80/3.81 | (36) succ(all_55_0) = n5
% 21.80/3.81 |
% 21.80/3.81 | DELTA: instantiating (13) with fresh symbols all_74_0, all_74_1, all_74_2,
% 21.80/3.81 | all_74_3, all_74_4 gives:
% 21.80/3.81 | (37) minus(n135300, n1) = all_74_4 & minus(pv10, n1) = all_74_3 & minus(n5,
% 21.80/3.81 | n1) = all_74_2 & minus(n0, n1) = all_74_1 & a_select2(x, pv10) =
% 21.80/3.81 | all_74_0 & leq(pv10, all_74_4) = 0 & leq(n0, pv10) = 0 & $i(all_74_0)
% 21.80/3.81 | & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) & $i(all_74_4) & ! [v0:
% 21.80/3.81 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q, v0, v1) = v2) |
% 21.80/3.81 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 21.80/3.81 | (sum(n0, all_74_2, v2) = v5 & leq(v0, all_74_3) = v4 & leq(n0, v0) =
% 21.80/3.81 | v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = n1))) & ( ? [v0:
% 21.80/3.81 | $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 21.80/3.81 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 21.80/3.81 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ( ~ (v12 = v2) &
% 21.80/3.81 | times(v8, v8) = v9 & times(v4, v4) = v5 & sqrt(v9) = v10 &
% 21.80/3.81 | sqrt(v5) = v6 & divide(v6, v11) = v12 & minus(v7, all_74_0) = v8 &
% 21.80/3.81 | minus(v3, all_74_0) = v4 & sum(n0, all_74_2, v10) = v11 &
% 21.80/3.81 | a_select3(center, v1, n0) = v7 & a_select3(center, v0, n0) = v3 &
% 21.80/3.81 | a_select3(q, pv10, v0) = v2 & leq(v0, all_74_1) = 0 & leq(n0, v0)
% 21.80/3.81 | = 0 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 21.80/3.81 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ?
% 21.80/3.81 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = n1) &
% 21.80/3.81 | sum(n0, all_74_2, v2) = v3 & a_select3(q, v0, v1) = v2 & leq(v0,
% 21.80/3.82 | all_74_3) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 21.80/3.82 | $i(v0)))
% 21.80/3.82 |
% 21.80/3.82 | ALPHA: (37) implies:
% 21.80/3.82 | (38) minus(n0, n1) = all_74_1
% 21.80/3.82 | (39) minus(n5, n1) = all_74_2
% 21.80/3.82 | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.80/3.82 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 21.80/3.82 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ( ~ (v12 = v2) & times(v8,
% 21.80/3.82 | v8) = v9 & times(v4, v4) = v5 & sqrt(v9) = v10 & sqrt(v5) = v6 &
% 21.80/3.82 | divide(v6, v11) = v12 & minus(v7, all_74_0) = v8 & minus(v3,
% 21.80/3.82 | all_74_0) = v4 & sum(n0, all_74_2, v10) = v11 & a_select3(center,
% 21.80/3.82 | v1, n0) = v7 & a_select3(center, v0, n0) = v3 & a_select3(q, pv10,
% 21.80/3.82 | v0) = v2 & leq(v0, all_74_1) = 0 & leq(n0, v0) = 0 & $i(v12) &
% 21.80/3.82 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 21.80/3.82 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1:
% 21.80/3.82 | $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = n1) & sum(n0, all_74_2,
% 21.80/3.82 | v2) = v3 & a_select3(q, v0, v1) = v2 & leq(v0, all_74_3) = 0 &
% 21.80/3.82 | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.80/3.82 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q, v0, v1) =
% 21.80/3.82 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 21.80/3.82 | [v5: $i] : (sum(n0, all_74_2, v2) = v5 & leq(v0, all_74_3) = v4 &
% 21.80/3.82 | leq(n0, v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 21.80/3.82 | n1)))
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with all_51_1, all_53_2, n0, simplifying with
% 21.80/3.82 | (22), (26) gives:
% 21.80/3.82 | (42) all_53_2 = all_51_1
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with all_49_0, all_53_2, n0, simplifying with
% 21.80/3.82 | (19), (26) gives:
% 21.80/3.82 | (43) all_53_2 = all_49_0
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with all_51_1, all_55_3, n0, simplifying with
% 21.80/3.82 | (22), (32) gives:
% 21.80/3.82 | (44) all_55_3 = all_51_1
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with n1, all_55_3, n0, simplifying with (8),
% 21.80/3.82 | (32) gives:
% 21.80/3.82 | (45) all_55_3 = n1
% 21.80/3.82 |
% 21.80/3.82 | COMBINE_EQS: (44), (45) imply:
% 21.80/3.82 | (46) all_51_1 = n1
% 21.80/3.82 |
% 21.80/3.82 | SIMP: (46) implies:
% 21.80/3.82 | (47) all_51_1 = n1
% 21.80/3.82 |
% 21.80/3.82 | COMBINE_EQS: (42), (43) imply:
% 21.80/3.82 | (48) all_51_1 = all_49_0
% 21.80/3.82 |
% 21.80/3.82 | SIMP: (48) implies:
% 21.80/3.82 | (49) all_51_1 = all_49_0
% 21.80/3.82 |
% 21.80/3.82 | COMBINE_EQS: (47), (49) imply:
% 21.80/3.82 | (50) all_49_0 = n1
% 21.80/3.82 |
% 21.80/3.82 | COMBINE_EQS: (43), (50) imply:
% 21.80/3.82 | (51) all_53_2 = n1
% 21.80/3.82 |
% 21.80/3.82 | REDUCE: (33), (45) imply:
% 21.80/3.82 | (52) succ(n1) = all_55_2
% 21.80/3.82 |
% 21.80/3.82 | REDUCE: (27), (51) imply:
% 21.80/3.82 | (53) succ(n1) = all_53_1
% 21.80/3.82 |
% 21.80/3.82 | REDUCE: (23), (47) imply:
% 21.80/3.82 | (54) succ(n1) = all_51_0
% 21.80/3.82 |
% 21.80/3.82 | REDUCE: (20), (50) imply:
% 21.80/3.82 | (55) succ(n1) = n2
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with all_51_0, all_53_1, n1, simplifying with
% 21.80/3.82 | (53), (54) gives:
% 21.80/3.82 | (56) all_53_1 = all_51_0
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with all_53_1, all_55_2, n1, simplifying with
% 21.80/3.82 | (52), (53) gives:
% 21.80/3.82 | (57) all_55_2 = all_53_1
% 21.80/3.82 |
% 21.80/3.82 | GROUND_INST: instantiating (15) with n2, all_55_2, n1, simplifying with (52),
% 21.80/3.82 | (55) gives:
% 21.80/3.82 | (58) all_55_2 = n2
% 21.80/3.82 |
% 21.80/3.82 | COMBINE_EQS: (57), (58) imply:
% 21.80/3.82 | (59) all_53_1 = n2
% 21.80/3.82 |
% 21.80/3.82 | SIMP: (59) implies:
% 21.80/3.83 | (60) all_53_1 = n2
% 21.80/3.83 |
% 21.80/3.83 | COMBINE_EQS: (56), (60) imply:
% 21.80/3.83 | (61) all_51_0 = n2
% 21.80/3.83 |
% 21.80/3.83 | SIMP: (61) implies:
% 21.80/3.83 | (62) all_51_0 = n2
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (34), (58) imply:
% 21.80/3.83 | (63) succ(n2) = all_55_1
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (28), (60) imply:
% 21.80/3.83 | (64) succ(n2) = all_53_0
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (24), (62) imply:
% 21.80/3.83 | (65) succ(n2) = n3
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (15) with all_53_0, all_55_1, n2, simplifying with
% 21.80/3.83 | (63), (64) gives:
% 21.80/3.83 | (66) all_55_1 = all_53_0
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (15) with n3, all_55_1, n2, simplifying with (63),
% 21.80/3.83 | (65) gives:
% 21.80/3.83 | (67) all_55_1 = n3
% 21.80/3.83 |
% 21.80/3.83 | COMBINE_EQS: (66), (67) imply:
% 21.80/3.83 | (68) all_53_0 = n3
% 21.80/3.83 |
% 21.80/3.83 | SIMP: (68) implies:
% 21.80/3.83 | (69) all_53_0 = n3
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (35), (67) imply:
% 21.80/3.83 | (70) succ(n3) = all_55_0
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (29), (69) imply:
% 21.80/3.83 | (71) succ(n3) = n4
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (15) with n4, all_55_0, n3, simplifying with (70),
% 21.80/3.83 | (71) gives:
% 21.80/3.83 | (72) all_55_0 = n4
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (36), (72) imply:
% 21.80/3.83 | (73) succ(n4) = n5
% 21.80/3.83 |
% 21.80/3.83 | REDUCE: (31), (72) imply:
% 21.80/3.83 | (74) $i(n4)
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with
% 21.80/3.83 | (2), (4) gives:
% 21.80/3.83 | (75) pred(n0) = tptp_minus_1
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (73),
% 21.80/3.83 | (74) gives:
% 21.80/3.83 | (76) pred(n5) = n4
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (3) with n0, all_74_1, simplifying with (11), (38)
% 21.80/3.83 | gives:
% 21.80/3.83 | (77) pred(n0) = all_74_1 & $i(all_74_1)
% 21.80/3.83 |
% 21.80/3.83 | ALPHA: (77) implies:
% 21.80/3.83 | (78) pred(n0) = all_74_1
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (3) with n5, all_74_2, simplifying with (12), (39)
% 21.80/3.83 | gives:
% 21.80/3.83 | (79) pred(n5) = all_74_2 & $i(all_74_2)
% 21.80/3.83 |
% 21.80/3.83 | ALPHA: (79) implies:
% 21.80/3.83 | (80) pred(n5) = all_74_2
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (14) with tptp_minus_1, all_74_1, n0, simplifying
% 21.80/3.83 | with (75), (78) gives:
% 21.80/3.83 | (81) all_74_1 = tptp_minus_1
% 21.80/3.83 |
% 21.80/3.83 | GROUND_INST: instantiating (14) with n4, all_74_2, n5, simplifying with (76),
% 21.80/3.83 | (80) gives:
% 21.80/3.83 | (82) all_74_2 = n4
% 21.80/3.83 |
% 21.80/3.83 | BETA: splitting (40) gives:
% 21.80/3.83 |
% 21.80/3.83 | Case 1:
% 21.80/3.83 | |
% 21.80/3.83 | | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 21.80/3.83 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 21.80/3.83 | | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ( ~ (v12 = v2)
% 21.80/3.83 | | & times(v8, v8) = v9 & times(v4, v4) = v5 & sqrt(v9) = v10 &
% 21.80/3.83 | | sqrt(v5) = v6 & divide(v6, v11) = v12 & minus(v7, all_74_0) = v8 &
% 21.80/3.83 | | minus(v3, all_74_0) = v4 & sum(n0, all_74_2, v10) = v11 &
% 21.80/3.83 | | a_select3(center, v1, n0) = v7 & a_select3(center, v0, n0) = v3 &
% 21.80/3.83 | | a_select3(q, pv10, v0) = v2 & leq(v0, all_74_1) = 0 & leq(n0, v0)
% 21.80/3.83 | | = 0 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 21.80/3.83 | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.80/3.83 | |
% 21.80/3.83 | | DELTA: instantiating (83) with fresh symbols all_142_0, all_142_1,
% 21.80/3.83 | | all_142_2, all_142_3, all_142_4, all_142_5, all_142_6, all_142_7,
% 21.80/3.83 | | all_142_8, all_142_9, all_142_10, all_142_11, all_142_12 gives:
% 21.80/3.83 | | (84) ~ (all_142_0 = all_142_10) & times(all_142_4, all_142_4) =
% 21.80/3.83 | | all_142_3 & times(all_142_8, all_142_8) = all_142_7 &
% 21.80/3.83 | | sqrt(all_142_3) = all_142_2 & sqrt(all_142_7) = all_142_6 &
% 21.80/3.83 | | divide(all_142_6, all_142_1) = all_142_0 & minus(all_142_5,
% 21.80/3.83 | | all_74_0) = all_142_4 & minus(all_142_9, all_74_0) = all_142_8 &
% 21.80/3.83 | | sum(n0, all_74_2, all_142_2) = all_142_1 & a_select3(center,
% 21.80/3.83 | | all_142_11, n0) = all_142_5 & a_select3(center, all_142_12, n0) =
% 21.80/3.83 | | all_142_9 & a_select3(q, pv10, all_142_12) = all_142_10 &
% 21.80/3.83 | | leq(all_142_12, all_74_1) = 0 & leq(n0, all_142_12) = 0 &
% 21.80/3.83 | | $i(all_142_0) & $i(all_142_1) & $i(all_142_2) & $i(all_142_3) &
% 21.80/3.83 | | $i(all_142_4) & $i(all_142_5) & $i(all_142_6) & $i(all_142_7) &
% 21.80/3.83 | | $i(all_142_8) & $i(all_142_9) & $i(all_142_10) & $i(all_142_11) &
% 21.80/3.83 | | $i(all_142_12)
% 21.80/3.83 | |
% 21.80/3.83 | | ALPHA: (84) implies:
% 21.80/3.83 | | (85) $i(all_142_12)
% 21.80/3.83 | | (86) leq(n0, all_142_12) = 0
% 21.80/3.83 | | (87) leq(all_142_12, all_74_1) = 0
% 21.80/3.83 | |
% 21.80/3.83 | | REDUCE: (81), (87) imply:
% 21.80/3.83 | | (88) leq(all_142_12, tptp_minus_1) = 0
% 21.80/3.83 | |
% 21.80/3.83 | | GROUND_INST: instantiating (5) with all_142_12, simplifying with (85), (86)
% 21.80/3.83 | | gives:
% 21.80/3.83 | | (89) all_142_12 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_142_12, n0)
% 21.80/3.83 | | = v0)
% 21.80/3.83 | |
% 21.80/3.83 | | GROUND_INST: instantiating (1) with all_142_12, n0, tptp_minus_1,
% 21.80/3.83 | | simplifying with (11), (75), (85), (88) gives:
% 21.80/3.84 | | (90) gt(n0, all_142_12) = 0
% 21.80/3.84 | |
% 21.80/3.84 | | GROUND_INST: instantiating (leq_gt1) with all_142_12, n0, simplifying with
% 21.80/3.84 | | (11), (85), (90) gives:
% 21.80/3.84 | | (91) leq(all_142_12, n0) = 0
% 21.80/3.84 | |
% 21.80/3.84 | | BETA: splitting (89) gives:
% 21.80/3.84 | |
% 21.80/3.84 | | Case 1:
% 21.80/3.84 | | |
% 21.80/3.84 | | | (92) all_142_12 = n0
% 21.80/3.84 | | |
% 21.80/3.84 | | | REDUCE: (90), (92) imply:
% 21.80/3.84 | | | (93) gt(n0, n0) = 0
% 21.80/3.84 | | |
% 21.80/3.84 | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with
% 21.80/3.84 | | | (11), (93) gives:
% 21.80/3.84 | | | (94) $false
% 21.80/3.84 | | |
% 21.80/3.84 | | | CLOSE: (94) is inconsistent.
% 21.80/3.84 | | |
% 21.80/3.84 | | Case 2:
% 21.80/3.84 | | |
% 21.80/3.84 | | | (95) ? [v0: int] : ( ~ (v0 = 0) & leq(all_142_12, n0) = v0)
% 21.80/3.84 | | |
% 21.80/3.84 | | | DELTA: instantiating (95) with fresh symbol all_166_0 gives:
% 21.80/3.84 | | | (96) ~ (all_166_0 = 0) & leq(all_142_12, n0) = all_166_0
% 21.80/3.84 | | |
% 21.80/3.84 | | | ALPHA: (96) implies:
% 21.80/3.84 | | | (97) ~ (all_166_0 = 0)
% 21.80/3.84 | | | (98) leq(all_142_12, n0) = all_166_0
% 21.80/3.84 | | |
% 21.80/3.84 | | | GROUND_INST: instantiating (16) with 0, all_166_0, n0, all_142_12,
% 21.80/3.84 | | | simplifying with (91), (98) gives:
% 21.80/3.84 | | | (99) all_166_0 = 0
% 21.80/3.84 | | |
% 21.80/3.84 | | | REDUCE: (97), (99) imply:
% 21.80/3.84 | | | (100) $false
% 21.80/3.84 | | |
% 21.80/3.84 | | | CLOSE: (100) is inconsistent.
% 21.80/3.84 | | |
% 21.80/3.84 | | End of split
% 21.80/3.84 | |
% 21.80/3.84 | Case 2:
% 21.80/3.84 | |
% 21.80/3.84 | | (101) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 21.80/3.84 | | n1) & sum(n0, all_74_2, v2) = v3 & a_select3(q, v0, v1) = v2 &
% 21.80/3.84 | | leq(v0, all_74_3) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2) &
% 21.80/3.84 | | $i(v1) & $i(v0))
% 21.80/3.84 | |
% 21.80/3.84 | | DELTA: instantiating (101) with fresh symbols all_142_0, all_142_1,
% 21.80/3.84 | | all_142_2, all_142_3 gives:
% 21.80/3.84 | | (102) ~ (all_142_0 = n1) & sum(n0, all_74_2, all_142_1) = all_142_0 &
% 21.80/3.84 | | a_select3(q, all_142_3, all_142_2) = all_142_1 & leq(all_142_3,
% 21.80/3.84 | | all_74_3) = 0 & leq(n0, all_142_3) = 0 & $i(all_142_0) &
% 21.80/3.84 | | $i(all_142_1) & $i(all_142_2) & $i(all_142_3)
% 21.80/3.84 | |
% 21.80/3.84 | | ALPHA: (102) implies:
% 21.80/3.84 | | (103) ~ (all_142_0 = n1)
% 21.80/3.84 | | (104) $i(all_142_3)
% 21.80/3.84 | | (105) $i(all_142_2)
% 21.80/3.84 | | (106) leq(n0, all_142_3) = 0
% 21.80/3.84 | | (107) leq(all_142_3, all_74_3) = 0
% 21.80/3.84 | | (108) a_select3(q, all_142_3, all_142_2) = all_142_1
% 21.80/3.84 | | (109) sum(n0, all_74_2, all_142_1) = all_142_0
% 21.80/3.84 | |
% 21.80/3.84 | | REDUCE: (82), (109) imply:
% 21.80/3.84 | | (110) sum(n0, n4, all_142_1) = all_142_0
% 21.80/3.84 | |
% 21.80/3.84 | | GROUND_INST: instantiating (41) with all_142_3, all_142_2, all_142_1,
% 21.80/3.84 | | simplifying with (104), (105), (108) gives:
% 21.80/3.84 | | (111) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sum(n0, all_74_2,
% 21.80/3.84 | | all_142_1) = v2 & leq(all_142_3, all_74_3) = v1 & leq(n0,
% 21.80/3.84 | | all_142_3) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 =
% 21.80/3.84 | | n1))
% 21.80/3.84 | |
% 21.80/3.84 | | DELTA: instantiating (111) with fresh symbols all_150_0, all_150_1,
% 21.80/3.84 | | all_150_2 gives:
% 21.80/3.84 | | (112) sum(n0, all_74_2, all_142_1) = all_150_0 & leq(all_142_3, all_74_3)
% 21.80/3.84 | | = all_150_1 & leq(n0, all_142_3) = all_150_2 & $i(all_150_0) & ( ~
% 21.80/3.84 | | (all_150_1 = 0) | ~ (all_150_2 = 0) | all_150_0 = n1)
% 21.80/3.84 | |
% 21.80/3.84 | | ALPHA: (112) implies:
% 21.80/3.84 | | (113) leq(n0, all_142_3) = all_150_2
% 21.80/3.84 | | (114) leq(all_142_3, all_74_3) = all_150_1
% 21.80/3.84 | | (115) sum(n0, all_74_2, all_142_1) = all_150_0
% 21.80/3.84 | | (116) ~ (all_150_1 = 0) | ~ (all_150_2 = 0) | all_150_0 = n1
% 21.80/3.84 | |
% 21.80/3.84 | | REDUCE: (82), (115) imply:
% 21.80/3.84 | | (117) sum(n0, n4, all_142_1) = all_150_0
% 21.80/3.84 | |
% 21.80/3.84 | | GROUND_INST: instantiating (16) with 0, all_150_2, all_142_3, n0,
% 21.80/3.84 | | simplifying with (106), (113) gives:
% 21.80/3.84 | | (118) all_150_2 = 0
% 21.80/3.84 | |
% 21.80/3.84 | | GROUND_INST: instantiating (16) with 0, all_150_1, all_74_3, all_142_3,
% 21.80/3.84 | | simplifying with (107), (114) gives:
% 21.80/3.84 | | (119) all_150_1 = 0
% 21.80/3.84 | |
% 21.80/3.84 | | GROUND_INST: instantiating (17) with all_142_0, all_150_0, all_142_1, n4,
% 21.80/3.84 | | n0, simplifying with (110), (117) gives:
% 21.80/3.84 | | (120) all_150_0 = all_142_0
% 21.80/3.84 | |
% 21.80/3.84 | | BETA: splitting (116) gives:
% 21.80/3.84 | |
% 21.80/3.84 | | Case 1:
% 21.80/3.84 | | |
% 21.80/3.84 | | | (121) ~ (all_150_1 = 0)
% 21.80/3.84 | | |
% 21.80/3.84 | | | REDUCE: (119), (121) imply:
% 21.80/3.84 | | | (122) $false
% 21.80/3.84 | | |
% 21.80/3.84 | | | CLOSE: (122) is inconsistent.
% 21.80/3.84 | | |
% 21.80/3.84 | | Case 2:
% 21.80/3.84 | | |
% 21.80/3.84 | | | (123) ~ (all_150_2 = 0) | all_150_0 = n1
% 21.80/3.84 | | |
% 21.80/3.84 | | | BETA: splitting (123) gives:
% 21.80/3.84 | | |
% 21.80/3.84 | | | Case 1:
% 21.80/3.84 | | | |
% 21.80/3.84 | | | | (124) ~ (all_150_2 = 0)
% 21.80/3.84 | | | |
% 21.80/3.84 | | | | REDUCE: (118), (124) imply:
% 21.80/3.84 | | | | (125) $false
% 21.80/3.84 | | | |
% 21.80/3.84 | | | | CLOSE: (125) is inconsistent.
% 21.80/3.84 | | | |
% 21.80/3.84 | | | Case 2:
% 21.80/3.84 | | | |
% 21.80/3.84 | | | | (126) all_150_0 = n1
% 21.80/3.84 | | | |
% 21.80/3.84 | | | | COMBINE_EQS: (120), (126) imply:
% 21.80/3.84 | | | | (127) all_142_0 = n1
% 21.80/3.84 | | | |
% 21.80/3.84 | | | | REDUCE: (103), (127) imply:
% 21.80/3.85 | | | | (128) $false
% 21.80/3.85 | | | |
% 21.80/3.85 | | | | CLOSE: (128) is inconsistent.
% 21.80/3.85 | | | |
% 21.80/3.85 | | | End of split
% 21.80/3.85 | | |
% 21.80/3.85 | | End of split
% 21.80/3.85 | |
% 21.80/3.85 | End of split
% 21.80/3.85 |
% 21.80/3.85 End of proof
% 21.80/3.85 % SZS output end Proof for theBenchmark
% 21.80/3.85
% 21.80/3.85 3200ms
%------------------------------------------------------------------------------