TSTP Solution File: SWV203+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV203+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 : n002.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 22:55:20 EDT 2023
% Result : Theorem 22.21s 3.69s
% Output : Proof 30.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV203+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 04:57:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.07/1.34 Prover 1: Preprocessing ...
% 4.07/1.34 Prover 4: Preprocessing ...
% 4.07/1.37 Prover 2: Preprocessing ...
% 4.07/1.37 Prover 0: Preprocessing ...
% 4.07/1.37 Prover 3: Preprocessing ...
% 4.07/1.38 Prover 5: Preprocessing ...
% 4.07/1.38 Prover 6: Preprocessing ...
% 11.24/2.22 Prover 1: Warning: ignoring some quantifiers
% 11.24/2.27 Prover 4: Warning: ignoring some quantifiers
% 11.71/2.29 Prover 3: Warning: ignoring some quantifiers
% 11.71/2.31 Prover 1: Constructing countermodel ...
% 11.71/2.32 Prover 3: Constructing countermodel ...
% 11.71/2.34 Prover 6: Proving ...
% 11.71/2.35 Prover 4: Constructing countermodel ...
% 12.33/2.37 Prover 0: Proving ...
% 12.43/2.41 Prover 5: Proving ...
% 13.46/2.60 Prover 2: Proving ...
% 22.21/3.69 Prover 0: proved (3071ms)
% 22.21/3.69
% 22.21/3.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.21/3.69
% 22.21/3.69 Prover 3: stopped
% 22.21/3.69 Prover 6: stopped
% 22.21/3.69 Prover 2: stopped
% 22.55/3.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.55/3.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.55/3.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.55/3.73 Prover 5: stopped
% 22.55/3.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.55/3.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.11/3.97 Prover 11: Preprocessing ...
% 24.11/3.98 Prover 13: Preprocessing ...
% 24.11/3.98 Prover 10: Preprocessing ...
% 24.11/3.99 Prover 8: Preprocessing ...
% 24.11/3.99 Prover 7: Preprocessing ...
% 25.93/4.20 Prover 10: Warning: ignoring some quantifiers
% 25.93/4.20 Prover 7: Warning: ignoring some quantifiers
% 25.93/4.21 Prover 10: Constructing countermodel ...
% 25.93/4.23 Prover 7: Constructing countermodel ...
% 26.61/4.26 Prover 8: Warning: ignoring some quantifiers
% 26.92/4.29 Prover 11: Warning: ignoring some quantifiers
% 26.92/4.29 Prover 8: Constructing countermodel ...
% 26.92/4.31 Prover 11: Constructing countermodel ...
% 26.92/4.33 Prover 13: Warning: ignoring some quantifiers
% 27.36/4.35 Prover 13: Constructing countermodel ...
% 29.89/4.68 Prover 10: Found proof (size 38)
% 29.89/4.68 Prover 10: proved (984ms)
% 29.89/4.68 Prover 8: stopped
% 29.89/4.68 Prover 13: stopped
% 29.89/4.68 Prover 7: stopped
% 29.89/4.68 Prover 4: stopped
% 29.89/4.68 Prover 11: stopped
% 29.89/4.68 Prover 1: stopped
% 29.89/4.69
% 29.89/4.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.89/4.69
% 29.89/4.69 % SZS output start Proof for theBenchmark
% 29.89/4.69 Assumptions after simplification:
% 29.89/4.69 ---------------------------------
% 29.89/4.70
% 29.89/4.70 (finite_domain_2)
% 29.89/4.70 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 29.89/4.70 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 29.89/4.70
% 29.89/4.70 (leq_gt2)
% 29.89/4.70 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 29.89/4.70 | gt(v1, v0))
% 29.89/4.70
% 29.89/4.70 (leq_gt_pred)
% 29.89/4.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 29.89/4.72 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.89/4.72 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 29.89/4.72 v2))
% 29.89/4.72
% 29.89/4.72 (quaternion_ds1_inuse_0014)
% 30.19/4.73 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 30.19/4.73 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 30.19/4.73 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 30.19/4.73 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 30.19/4.73 a_select3(z_defuse, v1, v2) = v3 & a_select3(u_defuse, n2, n0) = use &
% 30.19/4.73 a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 30.19/4.73 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 30.19/4.73 = use & a_select2(xinit_noise_defuse, n3) = use &
% 30.19/4.73 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 30.19/4.73 = use & a_select2(xinit_noise_defuse, n0) = use &
% 30.19/4.73 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 30.19/4.73 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 30.19/4.73 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 30.19/4.73 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 30.19/4.73 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 30.19/4.73 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 30.19/4.73 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 30.19/4.73 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 30.19/4.73 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 30.19/4.73 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & $i(v3) & $i(v2) & $i(v1)
% 30.19/4.73 & $i(v0) & leq(v2, pv5) & leq(v1, n2) & leq(pv5, n998) & leq(n0, v2) &
% 30.19/4.73 leq(n0, v1) & leq(n0, pv5) & gt(pv5, n0) & ! [v4: $i] : ! [v5: $i] : !
% 30.19/4.73 [v6: $i] : (v6 = use | ~ (a_select3(z_defuse, v4, v5) = v6) | ~ $i(v5) |
% 30.19/4.73 ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, n2) | ~ leq(n0, v5) | ~ leq(n0,
% 30.19/4.73 v4)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = use | ~
% 30.19/4.73 (a_select3(u_defuse, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5,
% 30.19/4.73 v0) | ~ leq(v4, n2) | ~ leq(n0, v5) | ~ leq(n0, v4)) & ( ~ (v2 = pv5)
% 30.19/4.73 | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1
% 30.19/4.73 = n0)))
% 30.19/4.73
% 30.19/4.73 Further assumptions not needed in the proof:
% 30.19/4.73 --------------------------------------------
% 30.19/4.73 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 30.19/4.73 finite_domain_1, finite_domain_3, finite_domain_4, finite_domain_5,
% 30.19/4.73 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 30.19/4.73 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,
% 30.19/4.73 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,
% 30.19/4.73 gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1,
% 30.19/4.73 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt,
% 30.19/4.73 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 30.19/4.73 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 30.19/4.73 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 30.19/4.73 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 30.19/4.73 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 30.19/4.73 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 30.19/4.73 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 30.19/4.73 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 30.19/4.73 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 30.19/4.73 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 30.19/4.73
% 30.19/4.73 Those formulas are unsatisfiable:
% 30.19/4.73 ---------------------------------
% 30.19/4.73
% 30.19/4.73 Begin of proof
% 30.19/4.73 |
% 30.19/4.73 | ALPHA: (leq_gt_pred) implies:
% 30.19/4.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 30.19/4.73 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 30.19/4.73 |
% 30.19/4.73 | ALPHA: (finite_domain_2) implies:
% 30.19/4.74 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2)
% 30.19/4.74 | | ~ leq(n0, v0))
% 30.19/4.74 |
% 30.19/4.74 | ALPHA: (quaternion_ds1_inuse_0014) implies:
% 30.19/4.74 | (3) $i(pv5)
% 30.19/4.74 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use)
% 30.19/4.74 | & a_select3(z_defuse, v1, v2) = v3 & a_select3(u_defuse, n2, n0) =
% 30.19/4.74 | use & a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0)
% 30.19/4.74 | = use & a_select2(xinit_noise_defuse, n5) = use &
% 30.19/4.74 | a_select2(xinit_noise_defuse, n4) = use &
% 30.19/4.74 | a_select2(xinit_noise_defuse, n3) = use &
% 30.19/4.74 | a_select2(xinit_noise_defuse, n2) = use &
% 30.19/4.74 | a_select2(xinit_noise_defuse, n1) = use &
% 30.19/4.74 | a_select2(xinit_noise_defuse, n0) = use &
% 30.19/4.74 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 30.19/4.74 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 30.19/4.74 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 30.19/4.74 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 30.19/4.74 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 30.19/4.74 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 30.19/4.74 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 30.19/4.74 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 30.19/4.74 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 30.19/4.74 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 30.19/4.74 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & $i(v3) & $i(v2) &
% 30.19/4.74 | $i(v1) & $i(v0) & leq(v2, pv5) & leq(v1, n2) & leq(pv5, n998) &
% 30.19/4.74 | leq(n0, v2) & leq(n0, v1) & leq(n0, pv5) & gt(pv5, n0) & ! [v4: $i]
% 30.19/4.74 | : ! [v5: $i] : ! [v6: $i] : (v6 = use | ~ (a_select3(z_defuse, v4,
% 30.19/4.74 | v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4,
% 30.19/4.74 | n2) | ~ leq(n0, v5) | ~ leq(n0, v4)) & ! [v4: $i] : ! [v5:
% 30.19/4.74 | $i] : ! [v6: $i] : (v6 = use | ~ (a_select3(u_defuse, v4, v5) =
% 30.19/4.74 | v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, n2) |
% 30.19/4.74 | ~ leq(n0, v5) | ~ leq(n0, v4)) & ( ~ (v2 = pv5) | ~ (v1 = n2)) &
% 30.19/4.74 | ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 = n0)))
% 30.19/4.74 |
% 30.19/4.74 | DELTA: instantiating (4) with fresh symbols all_71_0, all_71_1, all_71_2,
% 30.19/4.74 | all_71_3 gives:
% 30.19/4.75 | (5) ~ (all_71_0 = use) & a_select3(z_defuse, all_71_2, all_71_1) =
% 30.19/4.75 | all_71_0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 30.19/4.75 | n0) = use & a_select3(u_defuse, n0, n0) = use &
% 30.19/4.75 | a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse,
% 30.19/4.75 | n4) = use & a_select2(xinit_noise_defuse, n3) = use &
% 30.19/4.75 | a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse,
% 30.19/4.75 | n1) = use & a_select2(xinit_noise_defuse, n0) = use &
% 30.19/4.75 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 30.19/4.75 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 30.19/4.75 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 30.19/4.75 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 30.19/4.75 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use &
% 30.19/4.75 | a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 30.19/4.75 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 30.19/4.75 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 30.19/4.75 | a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 30.19/4.75 | a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use &
% 30.19/4.75 | pred(pv5) = all_71_3 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) &
% 30.19/4.75 | $i(all_71_3) & leq(all_71_1, pv5) & leq(all_71_2, n2) & leq(pv5, n998)
% 30.19/4.75 | & leq(n0, all_71_1) & leq(n0, all_71_2) & leq(n0, pv5) & gt(pv5, n0) &
% 30.19/4.75 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~
% 30.19/4.75 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 30.19/4.75 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 30.19/4.75 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~
% 30.19/4.75 | (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 30.19/4.75 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 30.19/4.75 | & ( ~ (all_71_1 = pv5) | ~ (all_71_2 = n2)) & ( ~ (all_71_1 = pv5) |
% 30.19/4.75 | ~ (all_71_2 = n1)) & ( ~ (all_71_1 = pv5) | ~ (all_71_2 = n0))
% 30.19/4.75 |
% 30.19/4.75 | ALPHA: (5) implies:
% 30.19/4.75 | (6) ~ (all_71_0 = use)
% 30.19/4.75 | (7) leq(n0, all_71_2)
% 30.19/4.75 | (8) leq(n0, all_71_1)
% 30.19/4.75 | (9) leq(all_71_2, n2)
% 30.19/4.75 | (10) leq(all_71_1, pv5)
% 30.19/4.75 | (11) $i(all_71_2)
% 30.19/4.75 | (12) $i(all_71_1)
% 30.19/4.75 | (13) pred(pv5) = all_71_3
% 30.19/4.75 | (14) a_select3(z_defuse, all_71_2, all_71_1) = all_71_0
% 30.19/4.75 | (15) ~ (all_71_1 = pv5) | ~ (all_71_2 = n0)
% 30.19/4.75 | (16) ~ (all_71_1 = pv5) | ~ (all_71_2 = n1)
% 30.19/4.75 | (17) ~ (all_71_1 = pv5) | ~ (all_71_2 = n2)
% 30.19/4.75 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~
% 30.19/4.75 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 30.19/4.75 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0,
% 30.19/4.75 | v0))
% 30.19/4.75 |
% 30.19/4.75 | GROUND_INST: instantiating (2) with all_71_2, simplifying with (7), (9), (11)
% 30.19/4.75 | gives:
% 30.19/4.75 | (19) all_71_2 = n2 | all_71_2 = n1 | all_71_2 = n0
% 30.19/4.75 |
% 30.19/4.75 | GROUND_INST: instantiating (leq_gt2) with all_71_1, pv5, simplifying with (3),
% 30.19/4.75 | (10), (12) gives:
% 30.19/4.75 | (20) all_71_1 = pv5 | gt(pv5, all_71_1)
% 30.19/4.75 |
% 30.19/4.75 | BETA: splitting (15) gives:
% 30.19/4.75 |
% 30.19/4.75 | Case 1:
% 30.19/4.75 | |
% 30.19/4.75 | | (21) ~ (all_71_2 = n0)
% 30.19/4.75 | |
% 30.19/4.75 | | BETA: splitting (17) gives:
% 30.19/4.75 | |
% 30.19/4.75 | | Case 1:
% 30.19/4.75 | | |
% 30.19/4.75 | | | (22) ~ (all_71_1 = pv5)
% 30.19/4.75 | | |
% 30.30/4.75 | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (13), (14), (18),
% 30.30/4.75 | | | (20), (22) are inconsistent by sub-proof #1.
% 30.30/4.75 | | |
% 30.30/4.75 | | Case 2:
% 30.30/4.75 | | |
% 30.30/4.75 | | | (23) all_71_1 = pv5
% 30.30/4.75 | | | (24) ~ (all_71_2 = n2)
% 30.30/4.75 | | |
% 30.30/4.75 | | | BETA: splitting (16) gives:
% 30.30/4.75 | | |
% 30.30/4.75 | | | Case 1:
% 30.30/4.75 | | | |
% 30.30/4.76 | | | | (25) ~ (all_71_1 = pv5)
% 30.30/4.76 | | | |
% 30.30/4.76 | | | | REDUCE: (23), (25) imply:
% 30.30/4.76 | | | | (26) $false
% 30.30/4.76 | | | |
% 30.30/4.76 | | | | CLOSE: (26) is inconsistent.
% 30.30/4.76 | | | |
% 30.30/4.76 | | | Case 2:
% 30.30/4.76 | | | |
% 30.30/4.76 | | | | (27) ~ (all_71_2 = n1)
% 30.30/4.76 | | | |
% 30.30/4.76 | | | | BETA: splitting (19) gives:
% 30.30/4.76 | | | |
% 30.30/4.76 | | | | Case 1:
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | | (28) all_71_2 = n0
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | | REDUCE: (21), (28) imply:
% 30.30/4.76 | | | | | (29) $false
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | | CLOSE: (29) is inconsistent.
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | Case 2:
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | | (30) all_71_2 = n2 | all_71_2 = n1
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | | BETA: splitting (30) gives:
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | | Case 1:
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | | (31) all_71_2 = n2
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | | REDUCE: (24), (31) imply:
% 30.30/4.76 | | | | | | (32) $false
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | | CLOSE: (32) is inconsistent.
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | Case 2:
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | | (33) all_71_2 = n1
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | | REDUCE: (27), (33) imply:
% 30.30/4.76 | | | | | | (34) $false
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | | CLOSE: (34) is inconsistent.
% 30.30/4.76 | | | | | |
% 30.30/4.76 | | | | | End of split
% 30.30/4.76 | | | | |
% 30.30/4.76 | | | | End of split
% 30.30/4.76 | | | |
% 30.30/4.76 | | | End of split
% 30.30/4.76 | | |
% 30.30/4.76 | | End of split
% 30.30/4.76 | |
% 30.30/4.76 | Case 2:
% 30.30/4.76 | |
% 30.30/4.76 | | (35) ~ (all_71_1 = pv5)
% 30.30/4.76 | |
% 30.30/4.76 | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (13), (14), (18), (20),
% 30.30/4.76 | | (35) are inconsistent by sub-proof #1.
% 30.30/4.76 | |
% 30.30/4.76 | End of split
% 30.30/4.76 |
% 30.30/4.76 End of proof
% 30.30/4.76
% 30.30/4.76 Sub-proof #1 shows that the following formulas are inconsistent:
% 30.30/4.76 ----------------------------------------------------------------
% 30.30/4.76 (1) leq(all_71_2, n2)
% 30.30/4.76 (2) leq(n0, all_71_1)
% 30.30/4.76 (3) $i(pv5)
% 30.30/4.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1)
% 30.30/4.76 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 30.30/4.76 (5) a_select3(z_defuse, all_71_2, all_71_1) = all_71_0
% 30.30/4.76 (6) leq(n0, all_71_2)
% 30.30/4.76 (7) pred(pv5) = all_71_3
% 30.30/4.76 (8) ~ (all_71_1 = pv5)
% 30.30/4.76 (9) $i(all_71_1)
% 30.30/4.76 (10) ~ (all_71_0 = use)
% 30.30/4.76 (11) $i(all_71_2)
% 30.30/4.76 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~
% 30.30/4.76 (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 30.30/4.76 leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 30.30/4.76 (13) all_71_1 = pv5 | gt(pv5, all_71_1)
% 30.30/4.76
% 30.30/4.76 Begin of proof
% 30.30/4.76 |
% 30.30/4.76 | BETA: splitting (13) gives:
% 30.30/4.76 |
% 30.30/4.76 | Case 1:
% 30.30/4.76 | |
% 30.30/4.76 | | (14) gt(pv5, all_71_1)
% 30.30/4.76 | |
% 30.30/4.76 | | GROUND_INST: instantiating (4) with all_71_1, pv5, all_71_3, simplifying
% 30.30/4.76 | | with (3), (7), (9), (14) gives:
% 30.30/4.76 | | (15) leq(all_71_1, all_71_3)
% 30.30/4.76 | |
% 30.30/4.76 | | GROUND_INST: instantiating (12) with all_71_2, all_71_1, all_71_0,
% 30.30/4.76 | | simplifying with (1), (2), (5), (6), (9), (11), (15) gives:
% 30.30/4.76 | | (16) all_71_0 = use
% 30.30/4.76 | |
% 30.30/4.76 | | REDUCE: (10), (16) imply:
% 30.30/4.76 | | (17) $false
% 30.30/4.76 | |
% 30.30/4.76 | | CLOSE: (17) is inconsistent.
% 30.30/4.76 | |
% 30.30/4.76 | Case 2:
% 30.30/4.76 | |
% 30.30/4.76 | | (18) all_71_1 = pv5
% 30.30/4.76 | |
% 30.30/4.76 | | REDUCE: (8), (18) imply:
% 30.30/4.76 | | (19) $false
% 30.30/4.76 | |
% 30.30/4.76 | | CLOSE: (19) is inconsistent.
% 30.30/4.76 | |
% 30.30/4.76 | End of split
% 30.30/4.76 |
% 30.30/4.76 End of proof
% 30.30/4.76 % SZS output end Proof for theBenchmark
% 30.30/4.76
% 30.30/4.76 4166ms
%------------------------------------------------------------------------------