TSTP Solution File: SWV041+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV041+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 : n003.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 22:54:41 EDT 2023
% Result : Theorem 15.84s 2.77s
% Output : Proof 19.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV041+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.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 08:27:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.53/0.61 ________ _____
% 0.53/0.61 ___ __ \_________(_)________________________________
% 0.53/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.53/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.53/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.53/0.61
% 0.53/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.53/0.61 (2023-06-19)
% 0.53/0.61
% 0.53/0.61 (c) Philipp Rümmer, 2009-2023
% 0.53/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.53/0.61 Amanda Stjerna.
% 0.53/0.61 Free software under BSD-3-Clause.
% 0.53/0.61
% 0.53/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.53/0.61
% 0.53/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.62 Running up to 7 provers in parallel.
% 0.53/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.53/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.53/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.53/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.53/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.53/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.53/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.61/1.29 Prover 1: Preprocessing ...
% 4.61/1.29 Prover 4: Preprocessing ...
% 4.86/1.33 Prover 2: Preprocessing ...
% 4.86/1.33 Prover 6: Preprocessing ...
% 4.86/1.33 Prover 5: Preprocessing ...
% 4.86/1.33 Prover 0: Preprocessing ...
% 4.93/1.33 Prover 3: Preprocessing ...
% 10.00/2.07 Prover 1: Warning: ignoring some quantifiers
% 10.90/2.11 Prover 3: Warning: ignoring some quantifiers
% 10.90/2.14 Prover 1: Constructing countermodel ...
% 10.90/2.14 Prover 6: Proving ...
% 10.90/2.15 Prover 3: Constructing countermodel ...
% 10.90/2.20 Prover 4: Warning: ignoring some quantifiers
% 11.61/2.27 Prover 4: Constructing countermodel ...
% 11.61/2.28 Prover 0: Proving ...
% 11.61/2.28 Prover 5: Proving ...
% 12.32/2.32 Prover 2: Proving ...
% 15.84/2.77 Prover 3: proved (2138ms)
% 15.84/2.77
% 15.84/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.84/2.77
% 15.84/2.77 Prover 2: stopped
% 15.84/2.78 Prover 6: stopped
% 15.84/2.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.84/2.78 Prover 0: stopped
% 15.84/2.78 Prover 5: stopped
% 15.84/2.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.84/2.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.84/2.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.84/2.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.66/2.95 Prover 8: Preprocessing ...
% 16.66/2.97 Prover 10: Preprocessing ...
% 16.66/2.97 Prover 13: Preprocessing ...
% 16.66/2.98 Prover 11: Preprocessing ...
% 17.60/3.00 Prover 7: Preprocessing ...
% 18.05/3.06 Prover 1: Found proof (size 33)
% 18.05/3.06 Prover 1: proved (2426ms)
% 18.05/3.06 Prover 10: stopped
% 18.05/3.06 Prover 4: stopped
% 18.05/3.07 Prover 7: stopped
% 18.42/3.09 Prover 11: stopped
% 18.42/3.10 Prover 13: stopped
% 18.73/3.16 Prover 8: Warning: ignoring some quantifiers
% 18.79/3.17 Prover 8: Constructing countermodel ...
% 18.79/3.19 Prover 8: stopped
% 18.79/3.19
% 18.79/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.79/3.19
% 18.79/3.20 % SZS output start Proof for theBenchmark
% 18.79/3.20 Assumptions after simplification:
% 18.79/3.20 ---------------------------------
% 18.79/3.20
% 18.79/3.20 (finite_domain_0)
% 19.03/3.23 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 19.03/3.23 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 19.03/3.23
% 19.03/3.23 (gauss_init_0077)
% 19.03/3.23 $i(init) & $i(uninit) & $i(n410) & $i(n330) & $i(n3) & $i(n2) & $i(n1) &
% 19.03/3.23 $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.03/3.23 ? [v5: $i] : (minus(n410, n1) = v1 & minus(n330, n1) = v0 & minus(n0, n1) =
% 19.03/3.23 v2 & tptp_const_array2(v3, v4, uninit) = v5 & dim(n0, n3) = v3 & dim(n0, n2)
% 19.03/3.23 = v4 & geq(v1, n0) = 0 & geq(v0, n0) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 19.03/3.23 & $i(v1) & $i(v0) & ? [v6: $i] : (leq(v6, n2) = 0 & leq(n0, v6) = 0 &
% 19.03/3.23 $i(v6) & ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = init) & a_select3(v5, v7,
% 19.03/3.23 v6) = v8 & leq(v7, v2) = 0 & leq(n0, v7) = 0 & $i(v8) & $i(v7))))
% 19.03/3.23
% 19.03/3.23 (gt_3_tptp_minus_1)
% 19.03/3.23 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1)
% 19.03/3.23
% 19.03/3.23 (irreflexivity_gt)
% 19.03/3.23 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0))
% 19.03/3.23
% 19.03/3.23 (leq_gt1)
% 19.03/3.23 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 19.03/3.23 leq(v0, v1) = 0)
% 19.03/3.23
% 19.03/3.23 (leq_gt_pred)
% 19.03/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 19.03/3.24 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 19.03/3.24 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 19.03/3.24 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)
% 19.03/3.24 | gt(v1, v0) = 0)
% 19.03/3.24
% 19.03/3.24 (pred_minus_1)
% 19.03/3.24 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 19.03/3.24 (pred(v0) = v1 & $i(v1)))
% 19.03/3.24
% 19.03/3.24 (pred_succ)
% 19.03/3.24 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 19.03/3.24
% 19.03/3.24 (succ_tptp_minus_1)
% 19.03/3.24 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0)
% 19.03/3.24
% 19.03/3.24 (function-axioms)
% 19.03/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.03/3.25 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 19.03/3.25 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.03/3.25 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 19.03/3.25 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.03/3.25 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 19.03/3.25 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.03/3.25 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 19.03/3.25 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.21/3.25 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 19.21/3.25 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.21/3.25 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 19.21/3.25 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.21/3.25 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 19.21/3.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 19.21/3.25 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.21/3.25 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 19.21/3.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 19.21/3.25 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 19.21/3.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 19.21/3.25 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 19.21/3.25 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 19.21/3.25 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.21/3.25 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 19.21/3.25 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.21/3.25 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 19.21/3.25 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 19.21/3.25 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 19.21/3.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.21/3.25 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 19.21/3.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.21/3.25 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 19.21/3.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.21/3.25 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 19.21/3.25 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 19.21/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 19.21/3.25 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.21/3.25 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.21/3.25 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 19.21/3.25
% 19.21/3.25 Further assumptions not needed in the proof:
% 19.21/3.25 --------------------------------------------
% 19.21/3.25 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 19.21/3.25 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 19.21/3.25 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 19.21/3.25 gt_330_0, gt_330_1, gt_330_2, gt_330_3, gt_330_4, gt_330_5, gt_330_tptp_minus_1,
% 19.21/3.25 gt_3_0, gt_3_1, gt_3_2, gt_410_0, gt_410_1, gt_410_2, gt_410_3, gt_410_330,
% 19.21/3.25 gt_410_4, gt_410_5, gt_410_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 19.21/3.25 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,
% 19.21/3.25 gt_succ, leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 19.21/3.25 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 19.21/3.25 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 19.21/3.25 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2,
% 19.21/3.25 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l,
% 19.21/3.25 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r,
% 19.21/3.25 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred,
% 19.21/3.25 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 19.21/3.25 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 19.21/3.25 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 19.21/3.25
% 19.21/3.25 Those formulas are unsatisfiable:
% 19.21/3.25 ---------------------------------
% 19.21/3.25
% 19.21/3.25 Begin of proof
% 19.21/3.25 |
% 19.21/3.25 | ALPHA: (leq_gt_pred) implies:
% 19.21/3.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 19.21/3.25 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0)
% 19.21/3.25 |
% 19.21/3.25 | ALPHA: (succ_tptp_minus_1) implies:
% 19.21/3.25 | (2) succ(tptp_minus_1) = n0
% 19.21/3.25 |
% 19.21/3.25 | ALPHA: (pred_minus_1) implies:
% 19.21/3.25 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 19.21/3.25 | (pred(v0) = v1 & $i(v1)))
% 19.21/3.25 |
% 19.21/3.25 | ALPHA: (gt_3_tptp_minus_1) implies:
% 19.21/3.25 | (4) $i(tptp_minus_1)
% 19.21/3.25 |
% 19.21/3.25 | ALPHA: (finite_domain_0) implies:
% 19.21/3.25 | (5) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 19.21/3.25 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 19.21/3.25 |
% 19.21/3.25 | ALPHA: (gauss_init_0077) implies:
% 19.21/3.25 | (6) $i(n0)
% 19.21/3.26 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.21/3.26 | ? [v5: $i] : (minus(n410, n1) = v1 & minus(n330, n1) = v0 & minus(n0,
% 19.21/3.26 | n1) = v2 & tptp_const_array2(v3, v4, uninit) = v5 & dim(n0, n3) =
% 19.21/3.26 | v3 & dim(n0, n2) = v4 & geq(v1, n0) = 0 & geq(v0, n0) = 0 & $i(v5) &
% 19.21/3.26 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : (leq(v6,
% 19.21/3.26 | n2) = 0 & leq(n0, v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] :
% 19.21/3.26 | ( ~ (v8 = init) & a_select3(v5, v7, v6) = v8 & leq(v7, v2) = 0 &
% 19.21/3.26 | leq(n0, v7) = 0 & $i(v8) & $i(v7))))
% 19.21/3.26 |
% 19.21/3.26 | ALPHA: (function-axioms) implies:
% 19.21/3.26 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1)
% 19.21/3.26 | | ~ (pred(v2) = v0))
% 19.21/3.26 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.21/3.26 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 19.21/3.26 |
% 19.21/3.26 | DELTA: instantiating (7) with fresh symbols all_61_0, all_61_1, all_61_2,
% 19.21/3.26 | all_61_3, all_61_4, all_61_5 gives:
% 19.21/3.26 | (10) minus(n410, n1) = all_61_4 & minus(n330, n1) = all_61_5 & minus(n0,
% 19.21/3.26 | n1) = all_61_3 & tptp_const_array2(all_61_2, all_61_1, uninit) =
% 19.21/3.26 | all_61_0 & dim(n0, n3) = all_61_2 & dim(n0, n2) = all_61_1 &
% 19.21/3.26 | geq(all_61_4, n0) = 0 & geq(all_61_5, n0) = 0 & $i(all_61_0) &
% 19.21/3.26 | $i(all_61_1) & $i(all_61_2) & $i(all_61_3) & $i(all_61_4) &
% 19.21/3.26 | $i(all_61_5) & ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 &
% 19.21/3.26 | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) &
% 19.21/3.26 | a_select3(all_61_0, v1, v0) = v2 & leq(v1, all_61_3) = 0 & leq(n0,
% 19.21/3.26 | v1) = 0 & $i(v2) & $i(v1)))
% 19.21/3.26 |
% 19.21/3.26 | ALPHA: (10) implies:
% 19.21/3.26 | (11) minus(n0, n1) = all_61_3
% 19.21/3.26 | (12) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1:
% 19.21/3.26 | $i] : ? [v2: $i] : ( ~ (v2 = init) & a_select3(all_61_0, v1, v0)
% 19.21/3.26 | = v2 & leq(v1, all_61_3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1)))
% 19.21/3.26 |
% 19.21/3.26 | DELTA: instantiating (12) with fresh symbol all_78_0 gives:
% 19.21/3.26 | (13) leq(all_78_0, n2) = 0 & leq(n0, all_78_0) = 0 & $i(all_78_0) & ? [v0:
% 19.21/3.26 | $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select3(all_61_0, v0,
% 19.21/3.26 | all_78_0) = v1 & leq(v0, all_61_3) = 0 & leq(n0, v0) = 0 & $i(v1)
% 19.21/3.26 | & $i(v0))
% 19.21/3.26 |
% 19.21/3.26 | ALPHA: (13) implies:
% 19.21/3.26 | (14) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select3(all_61_0, v0,
% 19.21/3.26 | all_78_0) = v1 & leq(v0, all_61_3) = 0 & leq(n0, v0) = 0 & $i(v1)
% 19.21/3.26 | & $i(v0))
% 19.21/3.26 |
% 19.21/3.26 | DELTA: instantiating (14) with fresh symbols all_80_0, all_80_1 gives:
% 19.21/3.27 | (15) ~ (all_80_0 = init) & a_select3(all_61_0, all_80_1, all_78_0) =
% 19.21/3.27 | all_80_0 & leq(all_80_1, all_61_3) = 0 & leq(n0, all_80_1) = 0 &
% 19.21/3.27 | $i(all_80_0) & $i(all_80_1)
% 19.21/3.27 |
% 19.21/3.27 | ALPHA: (15) implies:
% 19.21/3.27 | (16) $i(all_80_1)
% 19.21/3.27 | (17) leq(n0, all_80_1) = 0
% 19.21/3.27 | (18) leq(all_80_1, all_61_3) = 0
% 19.21/3.27 |
% 19.21/3.27 | GROUND_INST: instantiating (5) with all_80_1, simplifying with (16), (17)
% 19.21/3.27 | gives:
% 19.21/3.27 | (19) all_80_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_80_1, n0) = v0)
% 19.21/3.27 |
% 19.21/3.27 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with
% 19.21/3.27 | (2), (4) gives:
% 19.21/3.27 | (20) pred(n0) = tptp_minus_1
% 19.21/3.27 |
% 19.21/3.27 | GROUND_INST: instantiating (3) with n0, all_61_3, simplifying with (6), (11)
% 19.21/3.27 | gives:
% 19.21/3.27 | (21) pred(n0) = all_61_3 & $i(all_61_3)
% 19.21/3.27 |
% 19.21/3.27 | ALPHA: (21) implies:
% 19.21/3.27 | (22) pred(n0) = all_61_3
% 19.21/3.27 |
% 19.21/3.27 | GROUND_INST: instantiating (8) with tptp_minus_1, all_61_3, n0, simplifying
% 19.21/3.27 | with (20), (22) gives:
% 19.21/3.27 | (23) all_61_3 = tptp_minus_1
% 19.21/3.27 |
% 19.21/3.27 | REDUCE: (18), (23) imply:
% 19.21/3.27 | (24) leq(all_80_1, tptp_minus_1) = 0
% 19.21/3.27 |
% 19.21/3.27 | GROUND_INST: instantiating (1) with all_80_1, n0, tptp_minus_1, simplifying
% 19.21/3.27 | with (6), (16), (20), (24) gives:
% 19.21/3.27 | (25) gt(n0, all_80_1) = 0
% 19.21/3.27 |
% 19.21/3.27 | GROUND_INST: instantiating (leq_gt1) with all_80_1, n0, simplifying with (6),
% 19.21/3.27 | (16), (25) gives:
% 19.21/3.27 | (26) leq(all_80_1, n0) = 0
% 19.21/3.27 |
% 19.21/3.27 | BETA: splitting (19) gives:
% 19.21/3.27 |
% 19.21/3.27 | Case 1:
% 19.21/3.27 | |
% 19.21/3.27 | | (27) all_80_1 = n0
% 19.21/3.27 | |
% 19.21/3.27 | | REDUCE: (25), (27) imply:
% 19.21/3.27 | | (28) gt(n0, n0) = 0
% 19.21/3.27 | |
% 19.21/3.27 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (6),
% 19.21/3.27 | | (28) gives:
% 19.21/3.27 | | (29) $false
% 19.21/3.27 | |
% 19.21/3.27 | | CLOSE: (29) is inconsistent.
% 19.21/3.27 | |
% 19.21/3.27 | Case 2:
% 19.21/3.27 | |
% 19.21/3.27 | | (30) ? [v0: int] : ( ~ (v0 = 0) & leq(all_80_1, n0) = v0)
% 19.21/3.27 | |
% 19.21/3.27 | | DELTA: instantiating (30) with fresh symbol all_124_0 gives:
% 19.21/3.27 | | (31) ~ (all_124_0 = 0) & leq(all_80_1, n0) = all_124_0
% 19.21/3.27 | |
% 19.21/3.27 | | ALPHA: (31) implies:
% 19.21/3.27 | | (32) ~ (all_124_0 = 0)
% 19.21/3.27 | | (33) leq(all_80_1, n0) = all_124_0
% 19.21/3.27 | |
% 19.21/3.27 | | GROUND_INST: instantiating (9) with 0, all_124_0, n0, all_80_1, simplifying
% 19.21/3.27 | | with (26), (33) gives:
% 19.21/3.27 | | (34) all_124_0 = 0
% 19.21/3.27 | |
% 19.21/3.27 | | REDUCE: (32), (34) imply:
% 19.21/3.27 | | (35) $false
% 19.21/3.27 | |
% 19.21/3.27 | | CLOSE: (35) is inconsistent.
% 19.21/3.27 | |
% 19.21/3.27 | End of split
% 19.21/3.27 |
% 19.21/3.27 End of proof
% 19.21/3.27 % SZS output end Proof for theBenchmark
% 19.21/3.28
% 19.21/3.28 2664ms
%------------------------------------------------------------------------------