TSTP Solution File: SWV142+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV142+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 : n010.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 22:55:05 EDT 2023
% Result : Theorem 15.04s 2.91s
% Output : Proof 19.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWV142+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.37 % Computer : n010.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Aug 29 02:36:19 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.64 ________ _____
% 0.23/0.64 ___ __ \_________(_)________________________________
% 0.23/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.64
% 0.23/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.64 (2023-06-19)
% 0.23/0.64
% 0.23/0.64 (c) Philipp Rümmer, 2009-2023
% 0.23/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.64 Amanda Stjerna.
% 0.23/0.64 Free software under BSD-3-Clause.
% 0.23/0.64
% 0.23/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.64
% 0.23/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.23/0.66 Running up to 7 provers in parallel.
% 0.23/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.23/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.23/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.23/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.23/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.23/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.23/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.17/1.53 Prover 4: Preprocessing ...
% 5.17/1.53 Prover 1: Preprocessing ...
% 5.17/1.57 Prover 6: Preprocessing ...
% 5.17/1.57 Prover 0: Preprocessing ...
% 5.17/1.57 Prover 2: Preprocessing ...
% 5.17/1.57 Prover 5: Preprocessing ...
% 5.17/1.57 Prover 3: Preprocessing ...
% 12.55/2.44 Prover 1: Warning: ignoring some quantifiers
% 12.80/2.47 Prover 3: Warning: ignoring some quantifiers
% 12.80/2.49 Prover 3: Constructing countermodel ...
% 13.27/2.54 Prover 4: Warning: ignoring some quantifiers
% 13.27/2.55 Prover 1: Constructing countermodel ...
% 13.27/2.55 Prover 6: Proving ...
% 14.31/2.69 Prover 4: Constructing countermodel ...
% 14.31/2.73 Prover 5: Proving ...
% 14.81/2.75 Prover 0: Proving ...
% 15.04/2.86 Prover 2: Proving ...
% 15.04/2.91 Prover 3: proved (2240ms)
% 15.04/2.91
% 15.04/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.04/2.91
% 15.04/2.91 Prover 5: stopped
% 15.04/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.04/2.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.04/2.92 Prover 2: stopped
% 15.04/2.93 Prover 0: stopped
% 15.04/2.93 Prover 6: stopped
% 15.04/2.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.04/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.04/2.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.23/3.10 Prover 1: Found proof (size 32)
% 17.23/3.10 Prover 1: proved (2436ms)
% 17.53/3.11 Prover 4: stopped
% 17.53/3.12 Prover 10: Preprocessing ...
% 17.53/3.12 Prover 11: Preprocessing ...
% 17.53/3.13 Prover 8: Preprocessing ...
% 17.53/3.13 Prover 13: Preprocessing ...
% 17.53/3.14 Prover 7: Preprocessing ...
% 17.75/3.21 Prover 10: stopped
% 17.75/3.22 Prover 7: stopped
% 18.38/3.23 Prover 13: stopped
% 18.38/3.25 Prover 11: stopped
% 18.71/3.35 Prover 8: Warning: ignoring some quantifiers
% 19.05/3.37 Prover 8: Constructing countermodel ...
% 19.05/3.39 Prover 8: stopped
% 19.05/3.39
% 19.05/3.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.05/3.39
% 19.05/3.40 % SZS output start Proof for theBenchmark
% 19.23/3.41 Assumptions after simplification:
% 19.23/3.41 ---------------------------------
% 19.23/3.41
% 19.23/3.41 (gauss_array_0012)
% 19.23/3.45 $i(s_worst7) & $i(s_sworst7) & $i(s_best7) & $i(loopcounter) & $i(pv1341) &
% 19.23/3.45 $i(tptp_float_0_001) & $i(n3) & $i(n1) & $i(n0) & ? [v0: MultipleValueBool] :
% 19.23/3.45 ? [v1: MultipleValueBool] : ? [v2: MultipleValueBool] : ? [v3: int] : ?
% 19.23/3.45 [v4: MultipleValueBool] : ? [v5: MultipleValueBool] : ? [v6: int] : ( ~ (v6
% 19.23/3.45 = 0) & ~ (v3 = 0) & leq(s_worst7, n3) = v5 & leq(s_sworst7, n3) = v4 &
% 19.23/3.45 leq(s_best7, n3) = v3 & leq(tptp_float_0_001, pv1341) = 0 & leq(n1,
% 19.23/3.45 loopcounter) = 0 & leq(n0, s_worst7) = v2 & leq(n0, s_sworst7) = v1 &
% 19.23/3.45 leq(n0, s_best7) = v0 & gt(loopcounter, n0) = v6)
% 19.23/3.45
% 19.23/3.45 (leq_succ_gt)
% 19.23/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2,
% 19.23/3.45 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0)
% 19.23/3.45
% 19.23/3.45 (successor_1)
% 19.23/3.46 succ(n0) = n1 & $i(n1) & $i(n0)
% 19.23/3.46
% 19.23/3.46 (successor_2)
% 19.23/3.46 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 19.23/3.46
% 19.23/3.46 (successor_3)
% 19.23/3.46 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 19.23/3.46 succ(n0) = v0 & $i(v1) & $i(v0))
% 19.23/3.46
% 19.23/3.46 (successor_4)
% 19.23/3.46 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 19.23/3.46 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 19.23/3.46
% 19.23/3.46 (successor_5)
% 19.23/3.46 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 19.23/3.46 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 19.23/3.46 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 19.23/3.46
% 19.23/3.46 (function-axioms)
% 19.23/3.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.23/3.47 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 19.23/3.47 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.23/3.47 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 19.23/3.47 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.23/3.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 19.23/3.47 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.23/3.47 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 19.23/3.47 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.23/3.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 19.23/3.47 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.23/3.47 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 19.23/3.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.23/3.47 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 19.23/3.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 19.23/3.47 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.23/3.47 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 19.23/3.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 19.23/3.47 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 19.23/3.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 19.23/3.47 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 19.23/3.47 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 19.23/3.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.23/3.47 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 19.23/3.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.23/3.47 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 19.23/3.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 19.23/3.47 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 19.23/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.23/3.47 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 19.23/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.23/3.47 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 19.23/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.23/3.47 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 19.23/3.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 19.23/3.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 19.23/3.47 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.23/3.47 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.23/3.47 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 19.23/3.47
% 19.23/3.47 Further assumptions not needed in the proof:
% 19.23/3.47 --------------------------------------------
% 19.23/3.48 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 19.23/3.48 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 19.23/3.48 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1,
% 19.23/3.48 gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1,
% 19.23/3.48 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,
% 19.23/3.48 gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2,
% 19.23/3.48 leq_gt_pred, leq_minus, leq_succ, leq_succ_gt_equiv, leq_succ_succ, lt_gt,
% 19.23/3.48 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 19.23/3.48 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 19.23/3.48 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 19.23/3.48 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 19.23/3.48 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 19.23/3.48 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 19.23/3.48 succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float,
% 19.23/3.48 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 19.23/3.48 uniform_int_rand_ranges_lo
% 19.23/3.48
% 19.23/3.48 Those formulas are unsatisfiable:
% 19.23/3.48 ---------------------------------
% 19.23/3.48
% 19.23/3.48 Begin of proof
% 19.23/3.48 |
% 19.23/3.48 | ALPHA: (successor_4) implies:
% 19.23/3.48 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 19.23/3.48 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 19.23/3.48 |
% 19.23/3.48 | ALPHA: (successor_5) implies:
% 19.23/3.48 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 19.23/3.48 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 19.23/3.48 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 19.23/3.48 |
% 19.23/3.48 | ALPHA: (successor_1) implies:
% 19.23/3.48 | (3) succ(n0) = n1
% 19.23/3.48 |
% 19.23/3.48 | ALPHA: (successor_2) implies:
% 19.23/3.48 | (4) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 19.23/3.48 |
% 19.23/3.48 | ALPHA: (successor_3) implies:
% 19.23/3.48 | (5) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) =
% 19.23/3.48 | v0 & $i(v1) & $i(v0))
% 19.23/3.48 |
% 19.23/3.48 | ALPHA: (gauss_array_0012) implies:
% 19.23/3.49 | (6) $i(n0)
% 19.23/3.49 | (7) $i(loopcounter)
% 19.23/3.49 | (8) ? [v0: MultipleValueBool] : ? [v1: MultipleValueBool] : ? [v2:
% 19.23/3.49 | MultipleValueBool] : ? [v3: int] : ? [v4: MultipleValueBool] : ?
% 19.23/3.49 | [v5: MultipleValueBool] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v3 = 0) &
% 19.23/3.49 | leq(s_worst7, n3) = v5 & leq(s_sworst7, n3) = v4 & leq(s_best7, n3) =
% 19.23/3.49 | v3 & leq(tptp_float_0_001, pv1341) = 0 & leq(n1, loopcounter) = 0 &
% 19.23/3.49 | leq(n0, s_worst7) = v2 & leq(n0, s_sworst7) = v1 & leq(n0, s_best7) =
% 19.23/3.49 | v0 & gt(loopcounter, n0) = v6)
% 19.23/3.49 |
% 19.23/3.49 | ALPHA: (function-axioms) implies:
% 19.23/3.49 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1)
% 19.23/3.49 | | ~ (succ(v2) = v0))
% 19.23/3.49 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 19.23/3.49 | : ! [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) =
% 19.23/3.49 | v0))
% 19.23/3.49 |
% 19.23/3.49 | DELTA: instantiating (4) with fresh symbol all_49_0 gives:
% 19.23/3.49 | (11) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0)
% 19.23/3.49 |
% 19.23/3.49 | ALPHA: (11) implies:
% 19.23/3.49 | (12) succ(n0) = all_49_0
% 19.23/3.49 |
% 19.23/3.49 | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1 gives:
% 19.23/3.49 | (13) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1
% 19.23/3.49 | & $i(all_51_0) & $i(all_51_1)
% 19.23/3.49 |
% 19.23/3.49 | ALPHA: (13) implies:
% 19.23/3.49 | (14) succ(n0) = all_51_1
% 19.23/3.49 |
% 19.23/3.49 | DELTA: instantiating (1) with fresh symbols all_53_0, all_53_1, all_53_2
% 19.23/3.49 | gives:
% 19.23/3.49 | (15) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) =
% 19.23/3.49 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) &
% 19.23/3.49 | $i(all_53_2)
% 19.23/3.49 |
% 19.23/3.49 | ALPHA: (15) implies:
% 19.23/3.49 | (16) succ(n0) = all_53_2
% 19.23/3.49 |
% 19.23/3.49 | DELTA: instantiating (2) with fresh symbols all_55_0, all_55_1, all_55_2,
% 19.23/3.49 | all_55_3 gives:
% 19.23/3.49 | (17) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) =
% 19.23/3.49 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 &
% 19.23/3.49 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3)
% 19.23/3.49 |
% 19.23/3.49 | ALPHA: (17) implies:
% 19.23/3.49 | (18) succ(n0) = all_55_3
% 19.23/3.49 |
% 19.23/3.49 | DELTA: instantiating (8) with fresh symbols all_57_0, all_57_1, all_57_2,
% 19.23/3.49 | all_57_3, all_57_4, all_57_5, all_57_6 gives:
% 19.23/3.49 | (19) ~ (all_57_0 = 0) & ~ (all_57_3 = 0) & leq(s_worst7, n3) = all_57_1 &
% 19.23/3.49 | leq(s_sworst7, n3) = all_57_2 & leq(s_best7, n3) = all_57_3 &
% 19.23/3.49 | leq(tptp_float_0_001, pv1341) = 0 & leq(n1, loopcounter) = 0 & leq(n0,
% 19.23/3.49 | s_worst7) = all_57_4 & leq(n0, s_sworst7) = all_57_5 & leq(n0,
% 19.23/3.49 | s_best7) = all_57_6 & gt(loopcounter, n0) = all_57_0
% 19.23/3.49 |
% 19.23/3.49 | ALPHA: (19) implies:
% 19.23/3.49 | (20) ~ (all_57_0 = 0)
% 19.23/3.49 | (21) gt(loopcounter, n0) = all_57_0
% 19.23/3.49 | (22) leq(n1, loopcounter) = 0
% 19.23/3.49 |
% 19.23/3.50 | GROUND_INST: instantiating (9) with all_51_1, all_53_2, n0, simplifying with
% 19.23/3.50 | (14), (16) gives:
% 19.23/3.50 | (23) all_53_2 = all_51_1
% 19.23/3.50 |
% 19.23/3.50 | GROUND_INST: instantiating (9) with all_49_0, all_53_2, n0, simplifying with
% 19.23/3.50 | (12), (16) gives:
% 19.23/3.50 | (24) all_53_2 = all_49_0
% 19.23/3.50 |
% 19.23/3.50 | GROUND_INST: instantiating (9) with all_51_1, all_55_3, n0, simplifying with
% 19.23/3.50 | (14), (18) gives:
% 19.23/3.50 | (25) all_55_3 = all_51_1
% 19.23/3.50 |
% 19.23/3.50 | GROUND_INST: instantiating (9) with n1, all_55_3, n0, simplifying with (3),
% 19.23/3.50 | (18) gives:
% 19.23/3.50 | (26) all_55_3 = n1
% 19.23/3.50 |
% 19.23/3.50 | COMBINE_EQS: (25), (26) imply:
% 19.23/3.50 | (27) all_51_1 = n1
% 19.23/3.50 |
% 19.23/3.50 | SIMP: (27) implies:
% 19.23/3.50 | (28) all_51_1 = n1
% 19.23/3.50 |
% 19.23/3.50 | COMBINE_EQS: (23), (24) imply:
% 19.23/3.50 | (29) all_51_1 = all_49_0
% 19.23/3.50 |
% 19.23/3.50 | SIMP: (29) implies:
% 19.23/3.50 | (30) all_51_1 = all_49_0
% 19.23/3.50 |
% 19.23/3.50 | COMBINE_EQS: (28), (30) imply:
% 19.23/3.50 | (31) all_49_0 = n1
% 19.23/3.50 |
% 19.23/3.50 | GROUND_INST: instantiating (leq_succ_gt) with n0, loopcounter, n1, simplifying
% 19.23/3.50 | with (3), (6), (7), (22) gives:
% 19.23/3.50 | (32) gt(loopcounter, n0) = 0
% 19.23/3.50 |
% 19.23/3.50 | GROUND_INST: instantiating (10) with all_57_0, 0, n0, loopcounter, simplifying
% 19.23/3.50 | with (21), (32) gives:
% 19.23/3.50 | (33) all_57_0 = 0
% 19.23/3.50 |
% 19.23/3.50 | REDUCE: (20), (33) imply:
% 19.23/3.50 | (34) $false
% 19.23/3.50 |
% 19.23/3.50 | CLOSE: (34) is inconsistent.
% 19.23/3.50 |
% 19.23/3.50 End of proof
% 19.23/3.50 % SZS output end Proof for theBenchmark
% 19.23/3.50
% 19.23/3.50 2855ms
%------------------------------------------------------------------------------