%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV039+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 : n004.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 22:54:40 EDT 2023 % Result : Theorem 20.01s 3.28s % Output : Proof 20.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.07 % Problem : SWV039+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.04/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.26 % Computer : n004.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Tue Aug 29 03:58:37 EDT 2023 % 0.07/0.26 % CPUTime : % 0.12/0.53 ________ _____ % 0.12/0.53 ___ __ \_________(_)________________________________ % 0.12/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.12/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.12/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.12/0.53 % 0.12/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.12/0.53 (2023-06-19) % 0.12/0.53 % 0.12/0.53 (c) Philipp Rümmer, 2009-2023 % 0.12/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.12/0.53 Amanda Stjerna. % 0.12/0.53 Free software under BSD-3-Clause. % 0.12/0.53 % 0.12/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.12/0.53 % 0.12/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.12/0.54 Running up to 7 provers in parallel. % 0.12/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.12/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.12/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.12/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.12/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.12/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.12/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.04/1.29 Prover 1: Preprocessing ... % 4.04/1.29 Prover 4: Preprocessing ... % 4.97/1.33 Prover 0: Preprocessing ... % 4.97/1.33 Prover 6: Preprocessing ... % 4.97/1.33 Prover 5: Preprocessing ... % 4.97/1.33 Prover 3: Preprocessing ... % 4.97/1.33 Prover 2: Preprocessing ... % 10.53/2.04 Prover 1: Warning: ignoring some quantifiers % 11.16/2.13 Prover 3: Warning: ignoring some quantifiers % 11.16/2.15 Prover 3: Constructing countermodel ... % 11.16/2.15 Prover 1: Constructing countermodel ... % 11.74/2.18 Prover 6: Proving ... % 11.74/2.18 Prover 4: Warning: ignoring some quantifiers % 12.45/2.28 Prover 4: Constructing countermodel ... % 12.45/2.29 Prover 5: Proving ... % 12.82/2.35 Prover 0: Proving ... % 12.82/2.37 Prover 2: Proving ... % 20.01/3.27 Prover 1: Found proof (size 183) % 20.01/3.27 Prover 1: proved (2718ms) % 20.01/3.27 Prover 3: stopped % 20.01/3.27 Prover 4: stopped % 20.01/3.27 Prover 2: stopped % 20.01/3.27 Prover 5: stopped % 20.01/3.27 Prover 6: stopped % 20.01/3.27 Prover 0: stopped % 20.01/3.27 % 20.01/3.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.01/3.28 % 20.01/3.29 % SZS output start Proof for theBenchmark % 20.01/3.29 Assumptions after simplification: % 20.01/3.29 --------------------------------- % 20.01/3.29 % 20.01/3.29 (finite_domain_0) % 20.01/3.31 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.01/3.32 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 20.01/3.32 % 20.01/3.32 (gauss_init_0069) % 20.34/3.33 $i(s_try7_init) & $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & % 20.34/3.33 $i(loopcounter) & $i(s_center7_init) & $i(s_values7_init) & $i(simplex7_init) % 20.34/3.33 & $i(s_worst7) & $i(s_sworst7) & $i(s_best7) & $i(s_worst7_init) & % 20.34/3.33 $i(s_sworst7_init) & $i(s_best7_init) & $i(init) & $i(n3) & $i(n2) & $i(n1) & % 20.34/3.33 $i(n0) & ? [v0: any] : ? [v1: $i] : (s_worst7_init = init & s_sworst7_init = % 20.34/3.33 init & s_best7_init = init & minus(n0, n1) = v1 & leq(s_worst7, n3) = 0 & % 20.34/3.33 leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n0, s_worst7) = 0 & % 20.34/3.33 leq(n0, s_sworst7) = 0 & leq(n0, s_best7) = 0 & gt(loopcounter, n1) = v0 & % 20.34/3.33 $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 20.34/3.33 (a_select2(s_center7_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 20.34/3.33 any] : (leq(v2, n2) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 20.34/3.33 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 20.34/3.33 (a_select2(s_values7_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 20.34/3.33 any] : (leq(v2, n3) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 20.34/3.33 0)))) & ! [v2: $i] : ( ~ (leq(v2, n2) = 0) | ~ $i(v2) | ? [v3: % 20.34/3.33 int] : ( ~ (v3 = 0) & leq(n0, v2) = v3) | ! [v3: $i] : ! [v4: $i] : % 20.34/3.33 (v4 = init | ~ (a_select3(simplex7_init, v3, v2) = v4) | ~ $i(v3) | ? % 20.34/3.33 [v5: any] : ? [v6: any] : (leq(v3, n3) = v6 & leq(n0, v3) = v5 & ( ~ % 20.34/3.33 (v6 = 0) | ~ (v5 = 0))))) & ( ~ (v0 = 0) | (pvar1402_init = init & % 20.34/3.33 pvar1401_init = init & pvar1400_init = init)) & ( ? [v2: $i] : ? [v3: % 20.34/3.33 $i] : ( ~ (v3 = init) & a_select2(s_try7_init, v2) = v3 & leq(v2, v1) = % 20.34/3.33 0 & leq(n0, v2) = 0 & $i(v3) & $i(v2)) | ? [v2: $i] : ? [v3: $i] : ( ~ % 20.34/3.33 (v3 = init) & a_select2(s_center7_init, v2) = v3 & leq(v2, n2) = 0 & % 20.34/3.33 leq(n0, v2) = 0 & $i(v3) & $i(v2)) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 % 20.34/3.33 = init) & a_select2(s_values7_init, v2) = v3 & leq(v2, n3) = 0 & % 20.34/3.33 leq(n0, v2) = 0 & $i(v3) & $i(v2)) | ? [v2: $i] : (leq(v2, n2) = 0 & % 20.34/3.33 leq(n0, v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = init) & % 20.34/3.33 a_select3(simplex7_init, v3, v2) = v4 & leq(v3, n3) = 0 & leq(n0, v3) % 20.34/3.33 = 0 & $i(v4) & $i(v3))) | (v0 = 0 & ( ~ (pvar1402_init = init) | ~ % 20.34/3.33 (pvar1401_init = init) | ~ (pvar1400_init = init))))) % 20.34/3.33 % 20.34/3.33 (gt_3_tptp_minus_1) % 20.34/3.33 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1) % 20.34/3.33 % 20.34/3.33 (irreflexivity_gt) % 20.34/3.33 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 20.34/3.33 % 20.34/3.33 (leq_gt1) % 20.34/3.33 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 20.34/3.33 leq(v0, v1) = 0) % 20.34/3.33 % 20.34/3.33 (leq_gt_pred) % 20.34/3.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.34/3.34 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 20.34/3.34 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 20.34/3.34 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 20.34/3.34 | gt(v1, v0) = 0) % 20.34/3.34 % 20.34/3.34 (pred_minus_1) % 20.34/3.34 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 20.34/3.34 (pred(v0) = v1 & $i(v1))) % 20.34/3.34 % 20.34/3.34 (pred_succ) % 20.34/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 20.34/3.34 % 20.34/3.34 (succ_tptp_minus_1) % 20.34/3.34 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 20.34/3.34 % 20.34/3.34 (function-axioms) % 20.34/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.34/3.35 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 20.34/3.35 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.34/3.35 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 20.34/3.35 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.34/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 20.34/3.35 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.34/3.35 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 20.34/3.35 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.34/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 20.34/3.35 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.34/3.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 20.34/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 20.34/3.35 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 20.34/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 20.34/3.35 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.34/3.35 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 20.34/3.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.34/3.35 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 20.34/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 20.34/3.35 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 20.34/3.35 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 20.34/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 20.34/3.35 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 20.34/3.35 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.34/3.35 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 20.34/3.35 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.34/3.35 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 20.34/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.34/3.35 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 20.34/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.34/3.35 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 20.34/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.34/3.35 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 20.34/3.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 20.34/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 20.34/3.35 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.34/3.35 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.34/3.35 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 20.34/3.35 % 20.34/3.35 Further assumptions not needed in the proof: % 20.34/3.35 -------------------------------------------- % 20.34/3.35 const_array1_select, const_array2_select, defuse, finite_domain_1, % 20.34/3.35 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 20.34/3.35 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 20.34/3.35 gt_3_0, gt_3_1, gt_3_2, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, % 20.34/3.35 gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, leq_geq, % 20.34/3.35 leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 20.34/3.35 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 20.34/3.35 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 20.34/3.35 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 20.34/3.35 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 20.34/3.35 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 20.34/3.35 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 20.34/3.35 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 20.34/3.35 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 20.34/3.35 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 20.34/3.35 % 20.34/3.35 Those formulas are unsatisfiable: % 20.34/3.35 --------------------------------- % 20.34/3.35 % 20.34/3.35 Begin of proof % 20.34/3.35 | % 20.34/3.35 | ALPHA: (leq_gt_pred) implies: % 20.34/3.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 20.34/3.35 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 20.34/3.35 | % 20.34/3.35 | ALPHA: (succ_tptp_minus_1) implies: % 20.34/3.35 | (2) succ(tptp_minus_1) = n0 % 20.34/3.35 | % 20.34/3.35 | ALPHA: (pred_minus_1) implies: % 20.34/3.35 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 20.34/3.35 | (pred(v0) = v1 & $i(v1))) % 20.34/3.35 | % 20.34/3.35 | ALPHA: (gt_3_tptp_minus_1) implies: % 20.34/3.35 | (4) $i(tptp_minus_1) % 20.34/3.35 | % 20.34/3.35 | ALPHA: (finite_domain_0) implies: % 20.34/3.35 | (5) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.34/3.35 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 20.34/3.35 | % 20.34/3.35 | ALPHA: (gauss_init_0069) implies: % 20.54/3.36 | (6) $i(n0) % 20.54/3.36 | (7) ? [v0: any] : ? [v1: $i] : (s_worst7_init = init & s_sworst7_init = % 20.54/3.36 | init & s_best7_init = init & minus(n0, n1) = v1 & leq(s_worst7, n3) = % 20.54/3.36 | 0 & leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n0, s_worst7) % 20.54/3.36 | = 0 & leq(n0, s_sworst7) = 0 & leq(n0, s_best7) = 0 & gt(loopcounter, % 20.54/3.36 | n1) = v0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 20.54/3.36 | (a_select2(s_center7_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : % 20.54/3.36 | ? [v5: any] : (leq(v2, n2) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | % 20.54/3.36 | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 20.54/3.36 | (a_select2(s_values7_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : % 20.54/3.36 | ? [v5: any] : (leq(v2, n3) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | % 20.54/3.36 | ~ (v4 = 0)))) & ! [v2: $i] : ( ~ (leq(v2, n2) = 0) | ~ % 20.54/3.36 | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & leq(n0, v2) = v3) | ! [v3: % 20.54/3.36 | $i] : ! [v4: $i] : (v4 = init | ~ (a_select3(simplex7_init, v3, % 20.54/3.36 | v2) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 20.54/3.36 | (leq(v3, n3) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 20.54/3.36 | 0))))) & ( ~ (v0 = 0) | (pvar1402_init = init & % 20.54/3.36 | pvar1401_init = init & pvar1400_init = init)) & ( ? [v2: $i] : ? % 20.54/3.36 | [v3: $i] : ( ~ (v3 = init) & a_select2(s_try7_init, v2) = v3 & % 20.54/3.36 | leq(v2, v1) = 0 & leq(n0, v2) = 0 & $i(v3) & $i(v2)) | ? [v2: % 20.54/3.36 | $i] : ? [v3: $i] : ( ~ (v3 = init) & a_select2(s_center7_init, % 20.54/3.36 | v2) = v3 & leq(v2, n2) = 0 & leq(n0, v2) = 0 & $i(v3) & $i(v2)) % 20.54/3.36 | | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = init) & % 20.54/3.36 | a_select2(s_values7_init, v2) = v3 & leq(v2, n3) = 0 & leq(n0, % 20.54/3.36 | v2) = 0 & $i(v3) & $i(v2)) | ? [v2: $i] : (leq(v2, n2) = 0 & % 20.54/3.36 | leq(n0, v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = % 20.54/3.36 | init) & a_select3(simplex7_init, v3, v2) = v4 & leq(v3, n3) = % 20.54/3.36 | 0 & leq(n0, v3) = 0 & $i(v4) & $i(v3))) | (v0 = 0 & ( ~ % 20.54/3.36 | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.36 | (pvar1400_init = init))))) % 20.54/3.36 | % 20.54/3.36 | ALPHA: (function-axioms) implies: % 20.54/3.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) % 20.54/3.36 | | ~ (pred(v2) = v0)) % 20.54/3.36 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.54/3.36 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.54/3.36 | % 20.54/3.36 | DELTA: instantiating (7) with fresh symbols all_76_0, all_76_1 gives: % 20.54/3.37 | (10) s_worst7_init = init & s_sworst7_init = init & s_best7_init = init & % 20.54/3.37 | minus(n0, n1) = all_76_0 & leq(s_worst7, n3) = 0 & leq(s_sworst7, n3) % 20.54/3.37 | = 0 & leq(s_best7, n3) = 0 & leq(n0, s_worst7) = 0 & leq(n0, % 20.54/3.37 | s_sworst7) = 0 & leq(n0, s_best7) = 0 & gt(loopcounter, n1) = % 20.54/3.37 | all_76_1 & $i(all_76_0) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 20.54/3.37 | (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 20.54/3.37 | [v3: any] : (leq(v0, n2) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 20.54/3.37 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 20.54/3.37 | (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 20.54/3.37 | [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 20.54/3.37 | (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | % 20.54/3.37 | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! % 20.54/3.37 | [v2: $i] : (v2 = init | ~ (a_select3(simplex7_init, v1, v0) = v2) | % 20.54/3.37 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & % 20.54/3.37 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ % 20.54/3.37 | (all_76_1 = 0) | (pvar1402_init = init & pvar1401_init = init & % 20.54/3.37 | pvar1400_init = init)) & ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 20.54/3.37 | init) & a_select2(s_try7_init, v0) = v1 & leq(v0, all_76_0) = 0 % 20.54/3.37 | & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 20.54/3.37 | ( ~ (v1 = init) & a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = % 20.54/3.37 | 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] % 20.54/3.37 | : ( ~ (v1 = init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 20.54/3.37 | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 20.54/3.37 | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : % 20.54/3.37 | ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, % 20.54/3.37 | n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_1 = 0 % 20.54/3.37 | & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.37 | (pvar1400_init = init)))) % 20.54/3.37 | % 20.54/3.37 | ALPHA: (10) implies: % 20.54/3.37 | (11) minus(n0, n1) = all_76_0 % 20.54/3.37 | (12) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(s_try7_init, % 20.54/3.37 | v0) = v1 & leq(v0, all_76_0) = 0 & leq(n0, v0) = 0 & $i(v1) & % 20.54/3.37 | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.37 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 20.54/3.37 | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.37 | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = % 20.54/3.37 | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) % 20.54/3.37 | = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 20.54/3.37 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 20.54/3.37 | v1) = 0 & $i(v2) & $i(v1))) | (all_76_1 = 0 & ( ~ (pvar1402_init % 20.54/3.37 | = init) | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 20.54/3.37 | init))) % 20.54/3.37 | (13) ~ (all_76_1 = 0) | (pvar1402_init = init & pvar1401_init = init & % 20.54/3.37 | pvar1400_init = init) % 20.54/3.37 | (14) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 20.54/3.37 | (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = % 20.54/3.37 | init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? % 20.54/3.37 | [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & % 20.54/3.37 | ( ~ (v4 = 0) | ~ (v3 = 0))))) % 20.54/3.37 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 20.54/3.37 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 20.54/3.37 | n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 20.54/3.38 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 20.54/3.38 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 20.54/3.38 | n2) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 20.54/3.38 | % 20.54/3.38 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 20.54/3.38 | (2), (4) gives: % 20.54/3.38 | (17) pred(n0) = tptp_minus_1 % 20.54/3.38 | % 20.54/3.38 | GROUND_INST: instantiating (3) with n0, all_76_0, simplifying with (6), (11) % 20.54/3.38 | gives: % 20.54/3.38 | (18) pred(n0) = all_76_0 & $i(all_76_0) % 20.54/3.38 | % 20.54/3.38 | ALPHA: (18) implies: % 20.54/3.38 | (19) pred(n0) = all_76_0 % 20.54/3.38 | % 20.54/3.38 | GROUND_INST: instantiating (8) with tptp_minus_1, all_76_0, n0, simplifying % 20.54/3.38 | with (17), (19) gives: % 20.54/3.38 | (20) all_76_0 = tptp_minus_1 % 20.54/3.38 | % 20.54/3.38 | BETA: splitting (13) gives: % 20.54/3.38 | % 20.54/3.38 | Case 1: % 20.54/3.38 | | % 20.54/3.38 | | (21) ~ (all_76_1 = 0) % 20.54/3.38 | | % 20.54/3.38 | | BETA: splitting (12) gives: % 20.54/3.38 | | % 20.54/3.38 | | Case 1: % 20.54/3.38 | | | % 20.54/3.38 | | | (22) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.38 | | | a_select2(s_try7_init, v0) = v1 & leq(v0, all_76_0) = 0 & % 20.54/3.38 | | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 20.54/3.38 | | | ( ~ (v1 = init) & a_select2(s_center7_init, v0) = v1 & leq(v0, n2) % 20.54/3.38 | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.38 | | | % 20.54/3.38 | | | BETA: splitting (22) gives: % 20.54/3.38 | | | % 20.54/3.38 | | | Case 1: % 20.54/3.38 | | | | % 20.54/3.38 | | | | (23) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.38 | | | | a_select2(s_try7_init, v0) = v1 & leq(v0, all_76_0) = 0 & % 20.54/3.38 | | | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.38 | | | | % 20.54/3.38 | | | | DELTA: instantiating (23) with fresh symbols all_186_0, all_186_1 gives: % 20.54/3.38 | | | | (24) ~ (all_186_0 = init) & a_select2(s_try7_init, all_186_1) = % 20.54/3.38 | | | | all_186_0 & leq(all_186_1, all_76_0) = 0 & leq(n0, all_186_1) = % 20.54/3.38 | | | | 0 & $i(all_186_0) & $i(all_186_1) % 20.54/3.38 | | | | % 20.54/3.38 | | | | REF_CLOSE: (1), (5), (6), (9), (17), (20), (24), (irreflexivity_gt), % 20.54/3.38 | | | | (leq_gt1) are inconsistent by sub-proof #4. % 20.54/3.38 | | | | % 20.54/3.38 | | | Case 2: % 20.54/3.38 | | | | % 20.54/3.38 | | | | (25) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.38 | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 20.54/3.38 | | | | v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.38 | | | | % 20.54/3.38 | | | | DELTA: instantiating (25) with fresh symbols all_186_0, all_186_1 gives: % 20.54/3.38 | | | | (26) ~ (all_186_0 = init) & a_select2(s_center7_init, all_186_1) = % 20.54/3.38 | | | | all_186_0 & leq(all_186_1, n2) = 0 & leq(n0, all_186_1) = 0 & % 20.54/3.38 | | | | $i(all_186_0) & $i(all_186_1) % 20.54/3.38 | | | | % 20.54/3.38 | | | | REF_CLOSE: (9), (16), (26) are inconsistent by sub-proof #3. % 20.54/3.38 | | | | % 20.54/3.38 | | | End of split % 20.54/3.38 | | | % 20.54/3.38 | | Case 2: % 20.54/3.38 | | | % 20.54/3.38 | | | (27) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.38 | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 20.54/3.38 | | | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 20.54/3.38 | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 20.54/3.38 | | | init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) % 20.54/3.38 | | | = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_1 = 0 & ( % 20.54/3.38 | | | ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.38 | | | (pvar1400_init = init))) % 20.54/3.38 | | | % 20.54/3.38 | | | BETA: splitting (27) gives: % 20.54/3.38 | | | % 20.54/3.38 | | | Case 1: % 20.54/3.38 | | | | % 20.54/3.39 | | | | (28) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.39 | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 20.54/3.39 | | | | v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.39 | | | | % 20.54/3.39 | | | | DELTA: instantiating (28) with fresh symbols all_186_0, all_186_1 gives: % 20.54/3.39 | | | | (29) ~ (all_186_0 = init) & a_select2(s_values7_init, all_186_1) = % 20.54/3.39 | | | | all_186_0 & leq(all_186_1, n3) = 0 & leq(n0, all_186_1) = 0 & % 20.54/3.39 | | | | $i(all_186_0) & $i(all_186_1) % 20.54/3.39 | | | | % 20.54/3.39 | | | | REF_CLOSE: (9), (15), (29) are inconsistent by sub-proof #2. % 20.54/3.39 | | | | % 20.54/3.39 | | | Case 2: % 20.54/3.39 | | | | % 20.54/3.39 | | | | (30) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 20.54/3.39 | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 20.54/3.39 | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 20.54/3.39 | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_1 = 0 & ( ~ % 20.54/3.39 | | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.39 | | | | (pvar1400_init = init))) % 20.54/3.39 | | | | % 20.54/3.39 | | | | BETA: splitting (30) gives: % 20.54/3.39 | | | | % 20.54/3.39 | | | | Case 1: % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | (31) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 20.54/3.39 | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 20.54/3.39 | | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 20.54/3.39 | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | DELTA: instantiating (31) with fresh symbol all_186_0 gives: % 20.54/3.39 | | | | | (32) leq(all_186_0, n2) = 0 & leq(n0, all_186_0) = 0 & % 20.54/3.39 | | | | | $i(all_186_0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.39 | | | | | a_select3(simplex7_init, v0, all_186_0) = v1 & leq(v0, n3) = % 20.54/3.39 | | | | | 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | REF_CLOSE: (9), (14), (32) are inconsistent by sub-proof #1. % 20.54/3.39 | | | | | % 20.54/3.39 | | | | Case 2: % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | (33) all_76_1 = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init % 20.54/3.39 | | | | | = init) | ~ (pvar1400_init = init)) % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | ALPHA: (33) implies: % 20.54/3.39 | | | | | (34) all_76_1 = 0 % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | REDUCE: (21), (34) imply: % 20.54/3.39 | | | | | (35) $false % 20.54/3.39 | | | | | % 20.54/3.39 | | | | | CLOSE: (35) is inconsistent. % 20.54/3.39 | | | | | % 20.54/3.39 | | | | End of split % 20.54/3.39 | | | | % 20.54/3.39 | | | End of split % 20.54/3.39 | | | % 20.54/3.39 | | End of split % 20.54/3.39 | | % 20.54/3.39 | Case 2: % 20.54/3.39 | | % 20.54/3.39 | | (36) pvar1402_init = init & pvar1401_init = init & pvar1400_init = init % 20.54/3.39 | | % 20.54/3.39 | | ALPHA: (36) implies: % 20.54/3.39 | | (37) pvar1400_init = init % 20.54/3.39 | | (38) pvar1401_init = init % 20.54/3.39 | | (39) pvar1402_init = init % 20.54/3.39 | | % 20.54/3.39 | | BETA: splitting (12) gives: % 20.54/3.39 | | % 20.54/3.39 | | Case 1: % 20.54/3.39 | | | % 20.54/3.39 | | | (40) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.39 | | | a_select2(s_try7_init, v0) = v1 & leq(v0, all_76_0) = 0 & % 20.54/3.39 | | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 20.54/3.39 | | | ( ~ (v1 = init) & a_select2(s_center7_init, v0) = v1 & leq(v0, n2) % 20.54/3.39 | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.39 | | | % 20.54/3.39 | | | BETA: splitting (40) gives: % 20.54/3.39 | | | % 20.54/3.39 | | | Case 1: % 20.54/3.39 | | | | % 20.54/3.39 | | | | (41) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.39 | | | | a_select2(s_try7_init, v0) = v1 & leq(v0, all_76_0) = 0 & % 20.54/3.39 | | | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.39 | | | | % 20.54/3.39 | | | | DELTA: instantiating (41) with fresh symbols all_186_0, all_186_1 gives: % 20.54/3.39 | | | | (42) ~ (all_186_0 = init) & a_select2(s_try7_init, all_186_1) = % 20.54/3.39 | | | | all_186_0 & leq(all_186_1, all_76_0) = 0 & leq(n0, all_186_1) = % 20.54/3.39 | | | | 0 & $i(all_186_0) & $i(all_186_1) % 20.54/3.39 | | | | % 20.54/3.39 | | | | REF_CLOSE: (1), (5), (6), (9), (17), (20), (42), (irreflexivity_gt), % 20.54/3.39 | | | | (leq_gt1) are inconsistent by sub-proof #4. % 20.54/3.39 | | | | % 20.54/3.39 | | | Case 2: % 20.54/3.39 | | | | % 20.54/3.39 | | | | (43) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.39 | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 20.54/3.39 | | | | v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.39 | | | | % 20.54/3.39 | | | | DELTA: instantiating (43) with fresh symbols all_186_0, all_186_1 gives: % 20.54/3.39 | | | | (44) ~ (all_186_0 = init) & a_select2(s_center7_init, all_186_1) = % 20.54/3.39 | | | | all_186_0 & leq(all_186_1, n2) = 0 & leq(n0, all_186_1) = 0 & % 20.54/3.39 | | | | $i(all_186_0) & $i(all_186_1) % 20.54/3.39 | | | | % 20.54/3.39 | | | | REF_CLOSE: (9), (16), (44) are inconsistent by sub-proof #3. % 20.54/3.39 | | | | % 20.54/3.39 | | | End of split % 20.54/3.39 | | | % 20.54/3.39 | | Case 2: % 20.54/3.39 | | | % 20.54/3.40 | | | (45) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.40 | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 20.54/3.40 | | | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 20.54/3.40 | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 20.54/3.40 | | | init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) % 20.54/3.40 | | | = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_1 = 0 & ( % 20.54/3.40 | | | ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.40 | | | (pvar1400_init = init))) % 20.54/3.40 | | | % 20.54/3.40 | | | BETA: splitting (45) gives: % 20.54/3.40 | | | % 20.54/3.40 | | | Case 1: % 20.54/3.40 | | | | % 20.54/3.40 | | | | (46) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.40 | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 20.54/3.40 | | | | v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.40 | | | | % 20.54/3.40 | | | | DELTA: instantiating (46) with fresh symbols all_186_0, all_186_1 gives: % 20.54/3.40 | | | | (47) ~ (all_186_0 = init) & a_select2(s_values7_init, all_186_1) = % 20.54/3.40 | | | | all_186_0 & leq(all_186_1, n3) = 0 & leq(n0, all_186_1) = 0 & % 20.54/3.40 | | | | $i(all_186_0) & $i(all_186_1) % 20.54/3.40 | | | | % 20.54/3.40 | | | | REF_CLOSE: (9), (15), (47) are inconsistent by sub-proof #2. % 20.54/3.40 | | | | % 20.54/3.40 | | | Case 2: % 20.54/3.40 | | | | % 20.54/3.40 | | | | (48) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 20.54/3.40 | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 20.54/3.40 | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 20.54/3.40 | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_1 = 0 & ( ~ % 20.54/3.40 | | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.40 | | | | (pvar1400_init = init))) % 20.54/3.40 | | | | % 20.54/3.40 | | | | BETA: splitting (48) gives: % 20.54/3.40 | | | | % 20.54/3.40 | | | | Case 1: % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | (49) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 20.54/3.40 | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 20.54/3.40 | | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 20.54/3.40 | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | DELTA: instantiating (49) with fresh symbol all_186_0 gives: % 20.54/3.40 | | | | | (50) leq(all_186_0, n2) = 0 & leq(n0, all_186_0) = 0 & % 20.54/3.40 | | | | | $i(all_186_0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.54/3.40 | | | | | a_select3(simplex7_init, v0, all_186_0) = v1 & leq(v0, n3) = % 20.54/3.40 | | | | | 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | REF_CLOSE: (9), (14), (50) are inconsistent by sub-proof #1. % 20.54/3.40 | | | | | % 20.54/3.40 | | | | Case 2: % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | (51) all_76_1 = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init % 20.54/3.40 | | | | | = init) | ~ (pvar1400_init = init)) % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | ALPHA: (51) implies: % 20.54/3.40 | | | | | (52) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 20.54/3.40 | | | | | (pvar1400_init = init) % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | BETA: splitting (52) gives: % 20.54/3.40 | | | | | % 20.54/3.40 | | | | | Case 1: % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | | (53) ~ (pvar1402_init = init) % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | | REDUCE: (39), (53) imply: % 20.54/3.40 | | | | | | (54) $false % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | | CLOSE: (54) is inconsistent. % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | Case 2: % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | | (55) ~ (pvar1401_init = init) | ~ (pvar1400_init = init) % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | | BETA: splitting (55) gives: % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | | Case 1: % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | | (56) ~ (pvar1401_init = init) % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | | REDUCE: (38), (56) imply: % 20.54/3.40 | | | | | | | (57) $false % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | | CLOSE: (57) is inconsistent. % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | Case 2: % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | | (58) ~ (pvar1400_init = init) % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | | REDUCE: (37), (58) imply: % 20.54/3.40 | | | | | | | (59) $false % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | | CLOSE: (59) is inconsistent. % 20.54/3.40 | | | | | | | % 20.54/3.40 | | | | | | End of split % 20.54/3.40 | | | | | | % 20.54/3.40 | | | | | End of split % 20.54/3.40 | | | | | % 20.54/3.40 | | | | End of split % 20.54/3.40 | | | | % 20.54/3.40 | | | End of split % 20.54/3.40 | | | % 20.54/3.40 | | End of split % 20.54/3.40 | | % 20.54/3.40 | End of split % 20.54/3.40 | % 20.54/3.40 End of proof % 20.54/3.40 % 20.54/3.40 Sub-proof #1 shows that the following formulas are inconsistent: % 20.54/3.40 ---------------------------------------------------------------- % 20.54/3.40 (1) leq(all_186_0, n2) = 0 & leq(n0, all_186_0) = 0 & $i(all_186_0) & ? [v0: % 20.54/3.40 $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select3(simplex7_init, v0, % 20.54/3.40 all_186_0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 20.54/3.40 $i(v0)) % 20.54/3.41 (2) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 20.54/3.41 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 20.54/3.41 ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? [v3: any] % 20.54/3.41 : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) % 20.54/3.41 | ~ (v3 = 0))))) % 20.54/3.41 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.54/3.41 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.54/3.41 % 20.54/3.41 Begin of proof % 20.54/3.41 | % 20.54/3.41 | ALPHA: (1) implies: % 20.54/3.41 | (4) $i(all_186_0) % 20.54/3.41 | (5) leq(n0, all_186_0) = 0 % 20.54/3.41 | (6) leq(all_186_0, n2) = 0 % 20.54/3.41 | (7) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select3(simplex7_init, % 20.54/3.41 | v0, all_186_0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 20.54/3.41 | $i(v0)) % 20.54/3.41 | % 20.54/3.41 | DELTA: instantiating (7) with fresh symbols all_188_0, all_188_1 gives: % 20.54/3.41 | (8) ~ (all_188_0 = init) & a_select3(simplex7_init, all_188_1, all_186_0) % 20.54/3.41 | = all_188_0 & leq(all_188_1, n3) = 0 & leq(n0, all_188_1) = 0 & % 20.54/3.41 | $i(all_188_0) & $i(all_188_1) % 20.54/3.41 | % 20.54/3.41 | ALPHA: (8) implies: % 20.54/3.41 | (9) ~ (all_188_0 = init) % 20.54/3.41 | (10) $i(all_188_1) % 20.54/3.41 | (11) leq(n0, all_188_1) = 0 % 20.54/3.41 | (12) leq(all_188_1, n3) = 0 % 20.54/3.41 | (13) a_select3(simplex7_init, all_188_1, all_186_0) = all_188_0 % 20.54/3.41 | % 20.54/3.41 | GROUND_INST: instantiating (2) with all_186_0, simplifying with (4), (6) % 20.54/3.41 | gives: % 20.54/3.41 | (14) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_186_0) = v0) | ! [v0: $i] : % 20.54/3.41 | ! [v1: $i] : (v1 = init | ~ (a_select3(simplex7_init, v0, all_186_0) % 20.54/3.41 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n3) = % 20.54/3.41 | v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 20.54/3.41 | % 20.54/3.41 | BETA: splitting (14) gives: % 20.54/3.41 | % 20.54/3.41 | Case 1: % 20.54/3.41 | | % 20.54/3.41 | | (15) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_186_0) = v0) % 20.54/3.41 | | % 20.54/3.41 | | DELTA: instantiating (15) with fresh symbol all_199_0 gives: % 20.54/3.41 | | (16) ~ (all_199_0 = 0) & leq(n0, all_186_0) = all_199_0 % 20.54/3.41 | | % 20.54/3.41 | | ALPHA: (16) implies: % 20.54/3.41 | | (17) ~ (all_199_0 = 0) % 20.54/3.41 | | (18) leq(n0, all_186_0) = all_199_0 % 20.54/3.41 | | % 20.54/3.41 | | GROUND_INST: instantiating (3) with 0, all_199_0, all_186_0, n0, simplifying % 20.54/3.41 | | with (5), (18) gives: % 20.54/3.41 | | (19) all_199_0 = 0 % 20.54/3.41 | | % 20.54/3.41 | | REDUCE: (17), (19) imply: % 20.54/3.41 | | (20) $false % 20.54/3.41 | | % 20.54/3.41 | | CLOSE: (20) is inconsistent. % 20.54/3.41 | | % 20.54/3.41 | Case 2: % 20.54/3.41 | | % 20.54/3.41 | | (21) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 20.54/3.41 | | (a_select3(simplex7_init, v0, all_186_0) = v1) | ~ $i(v0) | ? % 20.54/3.41 | | [v2: any] : ? [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & % 20.54/3.41 | | ( ~ (v3 = 0) | ~ (v2 = 0)))) % 20.54/3.41 | | % 20.54/3.41 | | GROUND_INST: instantiating (21) with all_188_1, all_188_0, simplifying with % 20.54/3.41 | | (10), (13) gives: % 20.54/3.41 | | (22) all_188_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_188_1, n3) % 20.54/3.41 | | = v1 & leq(n0, all_188_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.54/3.41 | | % 20.54/3.41 | | BETA: splitting (22) gives: % 20.54/3.41 | | % 20.54/3.41 | | Case 1: % 20.54/3.41 | | | % 20.54/3.41 | | | (23) all_188_0 = init % 20.54/3.41 | | | % 20.54/3.41 | | | REDUCE: (9), (23) imply: % 20.54/3.41 | | | (24) $false % 20.54/3.41 | | | % 20.54/3.41 | | | CLOSE: (24) is inconsistent. % 20.54/3.41 | | | % 20.54/3.41 | | Case 2: % 20.54/3.41 | | | % 20.54/3.41 | | | (25) ? [v0: any] : ? [v1: any] : (leq(all_188_1, n3) = v1 & leq(n0, % 20.54/3.41 | | | all_188_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.54/3.41 | | | % 20.54/3.41 | | | DELTA: instantiating (25) with fresh symbols all_203_0, all_203_1 gives: % 20.54/3.41 | | | (26) leq(all_188_1, n3) = all_203_0 & leq(n0, all_188_1) = all_203_1 & % 20.54/3.41 | | | ( ~ (all_203_0 = 0) | ~ (all_203_1 = 0)) % 20.54/3.41 | | | % 20.54/3.41 | | | ALPHA: (26) implies: % 20.54/3.41 | | | (27) leq(n0, all_188_1) = all_203_1 % 20.54/3.41 | | | (28) leq(all_188_1, n3) = all_203_0 % 20.54/3.41 | | | (29) ~ (all_203_0 = 0) | ~ (all_203_1 = 0) % 20.54/3.41 | | | % 20.54/3.41 | | | GROUND_INST: instantiating (3) with 0, all_203_1, all_188_1, n0, % 20.54/3.41 | | | simplifying with (11), (27) gives: % 20.54/3.41 | | | (30) all_203_1 = 0 % 20.54/3.41 | | | % 20.54/3.41 | | | GROUND_INST: instantiating (3) with 0, all_203_0, n3, all_188_1, % 20.54/3.41 | | | simplifying with (12), (28) gives: % 20.54/3.41 | | | (31) all_203_0 = 0 % 20.54/3.41 | | | % 20.54/3.41 | | | BETA: splitting (29) gives: % 20.54/3.41 | | | % 20.54/3.41 | | | Case 1: % 20.54/3.41 | | | | % 20.54/3.41 | | | | (32) ~ (all_203_0 = 0) % 20.54/3.41 | | | | % 20.54/3.41 | | | | REDUCE: (31), (32) imply: % 20.54/3.41 | | | | (33) $false % 20.54/3.41 | | | | % 20.54/3.41 | | | | CLOSE: (33) is inconsistent. % 20.54/3.41 | | | | % 20.54/3.41 | | | Case 2: % 20.54/3.41 | | | | % 20.54/3.41 | | | | (34) ~ (all_203_1 = 0) % 20.54/3.41 | | | | % 20.54/3.41 | | | | REDUCE: (30), (34) imply: % 20.54/3.41 | | | | (35) $false % 20.54/3.41 | | | | % 20.54/3.41 | | | | CLOSE: (35) is inconsistent. % 20.54/3.41 | | | | % 20.54/3.41 | | | End of split % 20.54/3.41 | | | % 20.54/3.41 | | End of split % 20.54/3.41 | | % 20.54/3.41 | End of split % 20.54/3.41 | % 20.54/3.41 End of proof % 20.54/3.41 % 20.54/3.41 Sub-proof #2 shows that the following formulas are inconsistent: % 20.54/3.41 ---------------------------------------------------------------- % 20.54/3.41 (1) ~ (all_186_0 = init) & a_select2(s_values7_init, all_186_1) = all_186_0 % 20.54/3.41 & leq(all_186_1, n3) = 0 & leq(n0, all_186_1) = 0 & $i(all_186_0) & % 20.54/3.41 $i(all_186_1) % 20.54/3.42 (2) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 20.54/3.42 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n3) % 20.54/3.42 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 20.54/3.42 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.54/3.42 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.54/3.42 % 20.54/3.42 Begin of proof % 20.54/3.42 | % 20.54/3.42 | ALPHA: (1) implies: % 20.54/3.42 | (4) ~ (all_186_0 = init) % 20.54/3.42 | (5) $i(all_186_1) % 20.54/3.42 | (6) leq(n0, all_186_1) = 0 % 20.54/3.42 | (7) leq(all_186_1, n3) = 0 % 20.54/3.42 | (8) a_select2(s_values7_init, all_186_1) = all_186_0 % 20.54/3.42 | % 20.54/3.42 | GROUND_INST: instantiating (2) with all_186_1, all_186_0, simplifying with % 20.54/3.42 | (5), (8) gives: % 20.54/3.42 | (9) all_186_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_186_1, n3) = % 20.54/3.42 | v1 & leq(n0, all_186_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.54/3.42 | % 20.54/3.42 | BETA: splitting (9) gives: % 20.54/3.42 | % 20.54/3.42 | Case 1: % 20.54/3.42 | | % 20.54/3.42 | | (10) all_186_0 = init % 20.54/3.42 | | % 20.54/3.42 | | REDUCE: (4), (10) imply: % 20.54/3.42 | | (11) $false % 20.54/3.42 | | % 20.54/3.42 | | CLOSE: (11) is inconsistent. % 20.54/3.42 | | % 20.54/3.42 | Case 2: % 20.54/3.42 | | % 20.54/3.42 | | (12) ? [v0: any] : ? [v1: any] : (leq(all_186_1, n3) = v1 & leq(n0, % 20.54/3.42 | | all_186_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.54/3.42 | | % 20.54/3.42 | | DELTA: instantiating (12) with fresh symbols all_198_0, all_198_1 gives: % 20.54/3.42 | | (13) leq(all_186_1, n3) = all_198_0 & leq(n0, all_186_1) = all_198_1 & ( % 20.54/3.42 | | ~ (all_198_0 = 0) | ~ (all_198_1 = 0)) % 20.54/3.42 | | % 20.54/3.42 | | ALPHA: (13) implies: % 20.54/3.42 | | (14) leq(n0, all_186_1) = all_198_1 % 20.54/3.42 | | (15) leq(all_186_1, n3) = all_198_0 % 20.54/3.42 | | (16) ~ (all_198_0 = 0) | ~ (all_198_1 = 0) % 20.54/3.42 | | % 20.54/3.42 | | GROUND_INST: instantiating (3) with 0, all_198_1, all_186_1, n0, simplifying % 20.54/3.42 | | with (6), (14) gives: % 20.54/3.42 | | (17) all_198_1 = 0 % 20.54/3.42 | | % 20.54/3.42 | | GROUND_INST: instantiating (3) with 0, all_198_0, n3, all_186_1, simplifying % 20.54/3.42 | | with (7), (15) gives: % 20.54/3.42 | | (18) all_198_0 = 0 % 20.54/3.42 | | % 20.54/3.42 | | BETA: splitting (16) gives: % 20.54/3.42 | | % 20.54/3.42 | | Case 1: % 20.54/3.42 | | | % 20.54/3.42 | | | (19) ~ (all_198_0 = 0) % 20.54/3.42 | | | % 20.54/3.42 | | | REDUCE: (18), (19) imply: % 20.54/3.42 | | | (20) $false % 20.54/3.42 | | | % 20.54/3.42 | | | CLOSE: (20) is inconsistent. % 20.54/3.42 | | | % 20.54/3.42 | | Case 2: % 20.54/3.42 | | | % 20.54/3.42 | | | (21) ~ (all_198_1 = 0) % 20.54/3.42 | | | % 20.54/3.42 | | | REDUCE: (17), (21) imply: % 20.54/3.42 | | | (22) $false % 20.54/3.42 | | | % 20.54/3.42 | | | CLOSE: (22) is inconsistent. % 20.54/3.42 | | | % 20.54/3.42 | | End of split % 20.54/3.42 | | % 20.54/3.42 | End of split % 20.54/3.42 | % 20.54/3.42 End of proof % 20.54/3.42 % 20.54/3.42 Sub-proof #3 shows that the following formulas are inconsistent: % 20.54/3.42 ---------------------------------------------------------------- % 20.54/3.42 (1) ~ (all_186_0 = init) & a_select2(s_center7_init, all_186_1) = all_186_0 % 20.54/3.42 & leq(all_186_1, n2) = 0 & leq(n0, all_186_1) = 0 & $i(all_186_0) & % 20.54/3.42 $i(all_186_1) % 20.54/3.42 (2) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 20.54/3.42 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n2) % 20.54/3.42 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 20.54/3.42 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.54/3.42 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.54/3.42 % 20.54/3.42 Begin of proof % 20.54/3.42 | % 20.54/3.42 | ALPHA: (1) implies: % 20.54/3.42 | (4) ~ (all_186_0 = init) % 20.54/3.42 | (5) $i(all_186_1) % 20.54/3.42 | (6) leq(n0, all_186_1) = 0 % 20.54/3.42 | (7) leq(all_186_1, n2) = 0 % 20.54/3.42 | (8) a_select2(s_center7_init, all_186_1) = all_186_0 % 20.54/3.42 | % 20.54/3.42 | GROUND_INST: instantiating (2) with all_186_1, all_186_0, simplifying with % 20.54/3.42 | (5), (8) gives: % 20.54/3.42 | (9) all_186_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_186_1, n2) = % 20.54/3.42 | v1 & leq(n0, all_186_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.54/3.42 | % 20.54/3.42 | BETA: splitting (9) gives: % 20.54/3.42 | % 20.54/3.42 | Case 1: % 20.54/3.42 | | % 20.54/3.42 | | (10) all_186_0 = init % 20.54/3.42 | | % 20.54/3.42 | | REDUCE: (4), (10) imply: % 20.54/3.42 | | (11) $false % 20.54/3.42 | | % 20.54/3.42 | | CLOSE: (11) is inconsistent. % 20.54/3.42 | | % 20.54/3.42 | Case 2: % 20.54/3.42 | | % 20.54/3.42 | | (12) ? [v0: any] : ? [v1: any] : (leq(all_186_1, n2) = v1 & leq(n0, % 20.54/3.42 | | all_186_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.54/3.42 | | % 20.54/3.42 | | DELTA: instantiating (12) with fresh symbols all_198_0, all_198_1 gives: % 20.54/3.42 | | (13) leq(all_186_1, n2) = all_198_0 & leq(n0, all_186_1) = all_198_1 & ( % 20.54/3.42 | | ~ (all_198_0 = 0) | ~ (all_198_1 = 0)) % 20.54/3.42 | | % 20.54/3.42 | | ALPHA: (13) implies: % 20.54/3.42 | | (14) leq(n0, all_186_1) = all_198_1 % 20.54/3.42 | | (15) leq(all_186_1, n2) = all_198_0 % 20.54/3.42 | | (16) ~ (all_198_0 = 0) | ~ (all_198_1 = 0) % 20.54/3.42 | | % 20.54/3.42 | | GROUND_INST: instantiating (3) with 0, all_198_1, all_186_1, n0, simplifying % 20.54/3.42 | | with (6), (14) gives: % 20.54/3.42 | | (17) all_198_1 = 0 % 20.54/3.42 | | % 20.54/3.42 | | GROUND_INST: instantiating (3) with 0, all_198_0, n2, all_186_1, simplifying % 20.54/3.42 | | with (7), (15) gives: % 20.54/3.42 | | (18) all_198_0 = 0 % 20.54/3.42 | | % 20.54/3.42 | | BETA: splitting (16) gives: % 20.54/3.42 | | % 20.54/3.42 | | Case 1: % 20.54/3.42 | | | % 20.54/3.42 | | | (19) ~ (all_198_0 = 0) % 20.54/3.42 | | | % 20.54/3.42 | | | REDUCE: (18), (19) imply: % 20.54/3.42 | | | (20) $false % 20.54/3.42 | | | % 20.54/3.42 | | | CLOSE: (20) is inconsistent. % 20.54/3.42 | | | % 20.54/3.42 | | Case 2: % 20.54/3.42 | | | % 20.54/3.42 | | | (21) ~ (all_198_1 = 0) % 20.54/3.42 | | | % 20.54/3.42 | | | REDUCE: (17), (21) imply: % 20.54/3.42 | | | (22) $false % 20.54/3.42 | | | % 20.54/3.42 | | | CLOSE: (22) is inconsistent. % 20.54/3.42 | | | % 20.54/3.42 | | End of split % 20.54/3.42 | | % 20.54/3.42 | End of split % 20.54/3.42 | % 20.54/3.42 End of proof % 20.54/3.42 % 20.54/3.42 Sub-proof #4 shows that the following formulas are inconsistent: % 20.54/3.42 ---------------------------------------------------------------- % 20.54/3.42 (1) all_76_0 = tptp_minus_1 % 20.54/3.42 (2) ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) % 20.54/3.42 | leq(v0, v1) = 0) % 20.54/3.43 (3) ~ (all_186_0 = init) & a_select2(s_try7_init, all_186_1) = all_186_0 & % 20.54/3.43 leq(all_186_1, all_76_0) = 0 & leq(n0, all_186_1) = 0 & $i(all_186_0) & % 20.54/3.43 $i(all_186_1) % 20.54/3.43 (4) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: int] % 20.54/3.43 : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 20.54/3.43 (5) ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 20.54/3.43 (6) $i(n0) % 20.54/3.43 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 20.54/3.43 (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 20.54/3.43 (8) pred(n0) = tptp_minus_1 % 20.54/3.43 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.54/3.43 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.54/3.43 % 20.54/3.43 Begin of proof % 20.54/3.43 | % 20.54/3.43 | ALPHA: (3) implies: % 20.54/3.43 | (10) $i(all_186_1) % 20.54/3.43 | (11) leq(n0, all_186_1) = 0 % 20.54/3.43 | (12) leq(all_186_1, all_76_0) = 0 % 20.54/3.43 | % 20.54/3.43 | REDUCE: (1), (12) imply: % 20.54/3.43 | (13) leq(all_186_1, tptp_minus_1) = 0 % 20.54/3.43 | % 20.54/3.43 | GROUND_INST: instantiating (4) with all_186_1, simplifying with (10), (11) % 20.54/3.43 | gives: % 20.54/3.43 | (14) all_186_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_186_1, n0) = % 20.54/3.43 | v0) % 20.54/3.43 | % 20.54/3.43 | GROUND_INST: instantiating (7) with all_186_1, n0, tptp_minus_1, simplifying % 20.54/3.43 | with (6), (8), (10), (13) gives: % 20.54/3.43 | (15) gt(n0, all_186_1) = 0 % 20.54/3.43 | % 20.54/3.43 | GROUND_INST: instantiating (2) with all_186_1, n0, simplifying with (6), (10), % 20.54/3.43 | (15) gives: % 20.54/3.43 | (16) leq(all_186_1, n0) = 0 % 20.54/3.43 | % 20.54/3.43 | BETA: splitting (14) gives: % 20.54/3.43 | % 20.54/3.43 | Case 1: % 20.54/3.43 | | % 20.54/3.43 | | (17) all_186_1 = n0 % 20.54/3.43 | | % 20.54/3.43 | | REDUCE: (15), (17) imply: % 20.54/3.43 | | (18) gt(n0, n0) = 0 % 20.54/3.43 | | % 20.54/3.43 | | GROUND_INST: instantiating (5) with n0, simplifying with (6), (18) gives: % 20.54/3.43 | | (19) $false % 20.54/3.43 | | % 20.54/3.43 | | CLOSE: (19) is inconsistent. % 20.54/3.43 | | % 20.54/3.43 | Case 2: % 20.54/3.43 | | % 20.54/3.43 | | (20) ? [v0: int] : ( ~ (v0 = 0) & leq(all_186_1, n0) = v0) % 20.54/3.43 | | % 20.54/3.43 | | DELTA: instantiating (20) with fresh symbol all_204_0 gives: % 20.54/3.43 | | (21) ~ (all_204_0 = 0) & leq(all_186_1, n0) = all_204_0 % 20.54/3.43 | | % 20.54/3.43 | | ALPHA: (21) implies: % 20.54/3.43 | | (22) ~ (all_204_0 = 0) % 20.54/3.43 | | (23) leq(all_186_1, n0) = all_204_0 % 20.54/3.43 | | % 20.54/3.43 | | GROUND_INST: instantiating (9) with 0, all_204_0, n0, all_186_1, simplifying % 20.54/3.43 | | with (16), (23) gives: % 20.54/3.43 | | (24) all_204_0 = 0 % 20.54/3.43 | | % 20.54/3.43 | | REDUCE: (22), (24) imply: % 20.54/3.43 | | (25) $false % 20.54/3.43 | | % 20.54/3.43 | | CLOSE: (25) is inconsistent. % 20.54/3.43 | | % 20.54/3.43 | End of split % 20.54/3.43 | % 20.54/3.43 End of proof % 20.54/3.43 % SZS output end Proof for theBenchmark % 20.54/3.43 % 20.54/3.43 2897ms %------------------------------------------------------------------------------