TSTP Solution File: SWV190+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV190+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 : n014.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 22:55:17 EDT 2023
% Result : Theorem 14.00s 2.75s
% Output : Proof 17.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV190+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.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 04:01:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.86/1.33 Prover 1: Preprocessing ...
% 3.86/1.33 Prover 4: Preprocessing ...
% 3.86/1.37 Prover 5: Preprocessing ...
% 3.86/1.37 Prover 3: Preprocessing ...
% 3.86/1.37 Prover 2: Preprocessing ...
% 3.86/1.37 Prover 6: Preprocessing ...
% 3.86/1.37 Prover 0: Preprocessing ...
% 9.22/2.06 Prover 1: Warning: ignoring some quantifiers
% 9.80/2.15 Prover 3: Warning: ignoring some quantifiers
% 10.40/2.17 Prover 1: Constructing countermodel ...
% 10.40/2.22 Prover 3: Constructing countermodel ...
% 10.40/2.23 Prover 6: Proving ...
% 10.99/2.27 Prover 4: Warning: ignoring some quantifiers
% 11.85/2.37 Prover 4: Constructing countermodel ...
% 12.27/2.44 Prover 5: Proving ...
% 12.58/2.49 Prover 2: Proving ...
% 12.58/2.50 Prover 0: Proving ...
% 14.00/2.75 Prover 3: proved (2131ms)
% 14.00/2.75
% 14.00/2.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.00/2.75
% 14.00/2.75 Prover 6: stopped
% 14.00/2.76 Prover 5: stopped
% 14.00/2.76 Prover 0: stopped
% 14.00/2.77 Prover 2: stopped
% 14.00/2.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.00/2.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.00/2.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.00/2.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.00/2.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.81/2.89 Prover 7: Preprocessing ...
% 15.81/2.89 Prover 1: Found proof (size 21)
% 15.81/2.90 Prover 1: proved (2282ms)
% 15.81/2.90 Prover 4: stopped
% 15.81/2.90 Prover 8: Preprocessing ...
% 15.81/2.93 Prover 13: Preprocessing ...
% 16.23/2.95 Prover 10: Preprocessing ...
% 16.23/2.96 Prover 11: Preprocessing ...
% 16.23/2.96 Prover 7: stopped
% 16.23/3.00 Prover 10: stopped
% 16.69/3.02 Prover 13: stopped
% 16.69/3.02 Prover 11: stopped
% 16.96/3.09 Prover 8: Warning: ignoring some quantifiers
% 16.96/3.11 Prover 8: Constructing countermodel ...
% 16.96/3.13 Prover 8: stopped
% 16.96/3.13
% 16.96/3.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.96/3.13
% 16.96/3.13 % SZS output start Proof for theBenchmark
% 16.96/3.13 Assumptions after simplification:
% 16.96/3.13 ---------------------------------
% 16.96/3.13
% 16.96/3.14 (finite_domain_0)
% 17.40/3.16 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 17.40/3.16 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 17.40/3.16
% 17.40/3.16 (irreflexivity_gt)
% 17.40/3.16 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0))
% 17.40/3.16
% 17.40/3.16 (leq_gt1)
% 17.40/3.16 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 17.40/3.16 leq(v0, v1) = 0)
% 17.40/3.16
% 17.40/3.16 (leq_gt_pred)
% 17.40/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.40/3.16 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 17.40/3.16 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 17.40/3.16 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)
% 17.40/3.16 | gt(v1, v0) = 0)
% 17.40/3.16
% 17.40/3.16 (pred_succ)
% 17.40/3.16 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 17.40/3.16
% 17.40/3.16 (quaternion_ds1_inuse_0001)
% 17.40/3.17 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 17.40/3.17 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use &
% 17.40/3.17 a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, n3) =
% 17.40/3.17 use & a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse,
% 17.40/3.17 n1) = use & a_select2(xinit_noise_defuse, n0) = use &
% 17.40/3.17 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 17.40/3.17 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 17.40/3.17 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 17.40/3.17 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 17.40/3.17 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 17.40/3.17 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 17.40/3.17 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 17.40/3.17 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 17.40/3.17 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 17.40/3.17 a_select2(rho_defuse, n0) = use & $i(xinit_noise_defuse) &
% 17.40/3.17 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 17.40/3.17 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) &
% 17.40/3.17 $i(tptp_minus_1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2
% 17.40/3.17 = use) & a_select3(u_defuse, v0, v1) = v2 & leq(v1, tptp_minus_1) = 0 &
% 17.40/3.17 leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) &
% 17.40/3.17 $i(v0))
% 17.40/3.17
% 17.40/3.17 (succ_tptp_minus_1)
% 17.40/3.17 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0)
% 17.40/3.17
% 17.40/3.17 (function-axioms)
% 17.40/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.40/3.18 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.40/3.18 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.40/3.18 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.40/3.18 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.40/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.40/3.18 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.40/3.18 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.40/3.18 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.40/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.40/3.18 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.40/3.18 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 17.40/3.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.40/3.18 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 17.40/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 17.40/3.18 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.40/3.18 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 17.40/3.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.40/3.18 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 17.40/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 17.40/3.18 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.40/3.18 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 17.40/3.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.40/3.18 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 17.40/3.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.40/3.18 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 17.40/3.18 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.40/3.18 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.40/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.40/3.18 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.40/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.40/3.18 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.40/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.40/3.18 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.40/3.18 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 17.40/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 17.40/3.18 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.40/3.18 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.40/3.18 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 17.40/3.18
% 17.40/3.18 Further assumptions not needed in the proof:
% 17.40/3.18 --------------------------------------------
% 17.40/3.18 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 17.40/3.18 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 17.40/3.18 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 17.40/3.18 gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 17.40/3.18 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1,
% 17.40/3.18 gt_succ, leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 17.40/3.18 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 17.40/3.18 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 17.40/3.18 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1,
% 17.40/3.18 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 17.40/3.18 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 17.40/3.18 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 17.40/3.18 succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5,
% 17.40/3.18 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq,
% 17.40/3.18 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 17.40/3.18
% 17.40/3.18 Those formulas are unsatisfiable:
% 17.40/3.18 ---------------------------------
% 17.40/3.18
% 17.40/3.18 Begin of proof
% 17.40/3.18 |
% 17.40/3.18 | ALPHA: (leq_gt_pred) implies:
% 17.40/3.18 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 17.40/3.18 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0)
% 17.40/3.18 |
% 17.40/3.18 | ALPHA: (succ_tptp_minus_1) implies:
% 17.40/3.18 | (2) succ(tptp_minus_1) = n0
% 17.40/3.18 |
% 17.40/3.18 | ALPHA: (finite_domain_0) implies:
% 17.40/3.18 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 17.40/3.18 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 17.40/3.18 |
% 17.40/3.18 | ALPHA: (quaternion_ds1_inuse_0001) implies:
% 17.40/3.19 | (4) $i(n0)
% 17.40/3.19 | (5) $i(tptp_minus_1)
% 17.40/3.19 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) &
% 17.40/3.19 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, tptp_minus_1) = 0 &
% 17.40/3.19 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1)
% 17.40/3.19 | & $i(v0))
% 17.40/3.19 |
% 17.40/3.19 | ALPHA: (function-axioms) implies:
% 17.40/3.19 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.40/3.19 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 17.40/3.19 |
% 17.40/3.19 | DELTA: instantiating (6) with fresh symbols all_55_0, all_55_1, all_55_2
% 17.40/3.19 | gives:
% 17.61/3.19 | (8) ~ (all_55_0 = use) & a_select3(u_defuse, all_55_2, all_55_1) =
% 17.61/3.19 | all_55_0 & leq(all_55_1, tptp_minus_1) = 0 & leq(all_55_2, n2) = 0 &
% 17.61/3.19 | leq(n0, all_55_1) = 0 & leq(n0, all_55_2) = 0 & $i(all_55_0) &
% 17.61/3.19 | $i(all_55_1) & $i(all_55_2)
% 17.61/3.19 |
% 17.61/3.19 | ALPHA: (8) implies:
% 17.61/3.19 | (9) $i(all_55_1)
% 17.61/3.19 | (10) leq(n0, all_55_1) = 0
% 17.61/3.19 | (11) leq(all_55_1, tptp_minus_1) = 0
% 17.61/3.19 |
% 17.61/3.19 | GROUND_INST: instantiating (3) with all_55_1, simplifying with (9), (10)
% 17.61/3.19 | gives:
% 17.61/3.19 | (12) all_55_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_55_1, n0) = v0)
% 17.61/3.19 |
% 17.61/3.19 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with
% 17.61/3.19 | (2), (5) gives:
% 17.61/3.19 | (13) pred(n0) = tptp_minus_1
% 17.61/3.19 |
% 17.61/3.19 | GROUND_INST: instantiating (1) with all_55_1, n0, tptp_minus_1, simplifying
% 17.61/3.19 | with (4), (9), (11), (13) gives:
% 17.61/3.19 | (14) gt(n0, all_55_1) = 0
% 17.61/3.19 |
% 17.61/3.19 | GROUND_INST: instantiating (leq_gt1) with all_55_1, n0, simplifying with (4),
% 17.61/3.19 | (9), (14) gives:
% 17.61/3.19 | (15) leq(all_55_1, n0) = 0
% 17.61/3.19 |
% 17.61/3.19 | BETA: splitting (12) gives:
% 17.61/3.19 |
% 17.61/3.19 | Case 1:
% 17.61/3.19 | |
% 17.61/3.19 | | (16) all_55_1 = n0
% 17.61/3.19 | |
% 17.61/3.19 | | REDUCE: (14), (16) imply:
% 17.61/3.19 | | (17) gt(n0, n0) = 0
% 17.61/3.19 | |
% 17.61/3.19 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4),
% 17.61/3.19 | | (17) gives:
% 17.61/3.19 | | (18) $false
% 17.61/3.19 | |
% 17.61/3.19 | | CLOSE: (18) is inconsistent.
% 17.61/3.19 | |
% 17.61/3.19 | Case 2:
% 17.61/3.19 | |
% 17.61/3.19 | | (19) ? [v0: int] : ( ~ (v0 = 0) & leq(all_55_1, n0) = v0)
% 17.61/3.19 | |
% 17.61/3.19 | | DELTA: instantiating (19) with fresh symbol all_116_0 gives:
% 17.61/3.19 | | (20) ~ (all_116_0 = 0) & leq(all_55_1, n0) = all_116_0
% 17.61/3.19 | |
% 17.61/3.19 | | ALPHA: (20) implies:
% 17.61/3.20 | | (21) ~ (all_116_0 = 0)
% 17.61/3.20 | | (22) leq(all_55_1, n0) = all_116_0
% 17.61/3.20 | |
% 17.61/3.20 | | GROUND_INST: instantiating (7) with 0, all_116_0, n0, all_55_1, simplifying
% 17.61/3.20 | | with (15), (22) gives:
% 17.61/3.20 | | (23) all_116_0 = 0
% 17.61/3.20 | |
% 17.61/3.20 | | REDUCE: (21), (23) imply:
% 17.61/3.20 | | (24) $false
% 17.61/3.20 | |
% 17.61/3.20 | | CLOSE: (24) is inconsistent.
% 17.61/3.20 | |
% 17.61/3.20 | End of split
% 17.61/3.20 |
% 17.61/3.20 End of proof
% 17.61/3.20 % SZS output end Proof for theBenchmark
% 17.61/3.20
% 17.61/3.20 2600ms
%------------------------------------------------------------------------------