%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV191+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 : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:55:17 EDT 2023 % Result : Theorem 16.76s 3.02s % Output : Proof 20.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWV191+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 06:40:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.73/1.51 Prover 1: Preprocessing ... % 5.73/1.51 Prover 4: Preprocessing ... % 5.73/1.54 Prover 5: Preprocessing ... % 5.73/1.54 Prover 0: Preprocessing ... % 5.73/1.54 Prover 3: Preprocessing ... % 5.73/1.55 Prover 6: Preprocessing ... % 5.73/1.56 Prover 2: Preprocessing ... % 11.02/2.28 Prover 1: Warning: ignoring some quantifiers % 12.13/2.37 Prover 3: Warning: ignoring some quantifiers % 12.13/2.39 Prover 6: Proving ... % 12.13/2.41 Prover 1: Constructing countermodel ... % 12.13/2.41 Prover 3: Constructing countermodel ... % 12.13/2.42 Prover 4: Warning: ignoring some quantifiers % 13.28/2.56 Prover 4: Constructing countermodel ... % 13.28/2.60 Prover 5: Proving ... % 13.28/2.61 Prover 0: Proving ... % 13.28/2.68 Prover 2: Proving ... % 16.76/3.01 Prover 3: proved (2366ms) % 16.76/3.01 % 16.76/3.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.76/3.02 % 16.76/3.02 Prover 2: stopped % 16.76/3.03 Prover 6: stopped % 16.76/3.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.76/3.03 Prover 0: stopped % 16.76/3.04 Prover 5: stopped % 16.76/3.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.76/3.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.76/3.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.76/3.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.99/3.18 Prover 7: Preprocessing ... % 18.24/3.22 Prover 10: Preprocessing ... % 18.52/3.23 Prover 11: Preprocessing ... % 18.52/3.24 Prover 13: Preprocessing ... % 18.52/3.24 Prover 1: Found proof (size 21) % 18.52/3.24 Prover 1: proved (2598ms) % 18.52/3.24 Prover 4: stopped % 18.52/3.25 Prover 8: Preprocessing ... % 18.52/3.28 Prover 10: stopped % 18.52/3.28 Prover 7: stopped % 18.75/3.34 Prover 11: stopped % 18.75/3.37 Prover 13: stopped % 19.48/3.44 Prover 8: Warning: ignoring some quantifiers % 19.76/3.45 Prover 8: Constructing countermodel ... % 19.86/3.48 Prover 8: stopped % 19.86/3.48 % 19.86/3.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.86/3.48 % 19.86/3.48 % SZS output start Proof for theBenchmark % 19.86/3.49 Assumptions after simplification: % 19.86/3.49 --------------------------------- % 19.86/3.49 % 19.86/3.49 (finite_domain_0) % 19.86/3.51 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.86/3.51 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.86/3.51 % 19.86/3.51 (irreflexivity_gt) % 19.86/3.52 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 19.86/3.52 % 19.86/3.52 (leq_gt1) % 20.13/3.52 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 20.13/3.52 leq(v0, v1) = 0) % 20.13/3.52 % 20.13/3.52 (leq_gt_pred) % 20.13/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.13/3.52 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 20.13/3.52 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 20.13/3.52 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 20.13/3.52 | gt(v1, v0) = 0) % 20.13/3.52 % 20.13/3.52 (pred_succ) % 20.13/3.52 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 20.13/3.52 % 20.13/3.52 (quaternion_ds1_inuse_0002) % 20.13/3.53 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 20.13/3.53 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use & % 20.13/3.53 a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, n3) = % 20.13/3.53 use & a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, % 20.13/3.53 n1) = use & a_select2(xinit_noise_defuse, n0) = use & % 20.13/3.53 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 20.13/3.53 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 20.13/3.53 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 20.13/3.53 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 20.13/3.53 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 20.13/3.53 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 20.13/3.53 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 20.13/3.53 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 20.13/3.53 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 20.13/3.53 a_select2(rho_defuse, n0) = use & $i(z_defuse) & $i(xinit_noise_defuse) & % 20.13/3.53 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 20.13/3.53 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & % 20.13/3.53 $i(tptp_minus_1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 % 20.13/3.53 = use) & a_select3(z_defuse, v0, v1) = v2 & leq(v1, tptp_minus_1) = 0 & % 20.13/3.53 leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & % 20.13/3.53 $i(v0)) % 20.13/3.53 % 20.13/3.53 (succ_tptp_minus_1) % 20.13/3.53 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 20.13/3.53 % 20.13/3.53 (function-axioms) % 20.13/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.13/3.54 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 20.13/3.54 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.13/3.54 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 20.13/3.54 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.13/3.54 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 20.13/3.54 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.13/3.54 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 20.13/3.54 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.13/3.54 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 20.13/3.54 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.13/3.54 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 20.13/3.54 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 20.13/3.54 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 20.13/3.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 20.13/3.54 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.13/3.54 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 20.13/3.54 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.13/3.54 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 20.13/3.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 20.13/3.54 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 20.13/3.54 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 20.13/3.54 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 20.13/3.54 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 20.13/3.54 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.13/3.54 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 20.13/3.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.13/3.54 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 20.13/3.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.54 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 20.13/3.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.54 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 20.13/3.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.54 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 20.13/3.54 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 20.13/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 20.13/3.54 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.13/3.54 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.13/3.54 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 20.13/3.54 % 20.13/3.54 Further assumptions not needed in the proof: % 20.13/3.54 -------------------------------------------- % 20.13/3.54 const_array1_select, const_array2_select, defuse, finite_domain_1, % 20.13/3.54 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 20.13/3.54 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 20.13/3.54 gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 20.13/3.54 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, % 20.13/3.54 gt_succ, leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 20.13/3.54 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 20.13/3.54 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 20.13/3.54 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1, % 20.13/3.54 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 20.13/3.54 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 20.13/3.54 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 20.13/3.54 succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5, % 20.13/3.54 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 20.13/3.54 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 20.13/3.54 % 20.13/3.54 Those formulas are unsatisfiable: % 20.13/3.54 --------------------------------- % 20.13/3.54 % 20.13/3.54 Begin of proof % 20.13/3.54 | % 20.13/3.54 | ALPHA: (leq_gt_pred) implies: % 20.13/3.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 20.13/3.54 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 20.13/3.54 | % 20.13/3.54 | ALPHA: (succ_tptp_minus_1) implies: % 20.13/3.54 | (2) succ(tptp_minus_1) = n0 % 20.13/3.54 | % 20.13/3.54 | ALPHA: (finite_domain_0) implies: % 20.13/3.54 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.13/3.54 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 20.13/3.54 | % 20.13/3.54 | ALPHA: (quaternion_ds1_inuse_0002) implies: % 20.13/3.55 | (4) $i(n0) % 20.13/3.55 | (5) $i(tptp_minus_1) % 20.13/3.55 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) & % 20.13/3.55 | a_select3(z_defuse, v0, v1) = v2 & leq(v1, tptp_minus_1) = 0 & % 20.13/3.55 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) % 20.13/3.55 | & $i(v0)) % 20.13/3.55 | % 20.13/3.55 | ALPHA: (function-axioms) implies: % 20.13/3.55 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.13/3.55 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.13/3.55 | % 20.13/3.55 | DELTA: instantiating (6) with fresh symbols all_55_0, all_55_1, all_55_2 % 20.13/3.55 | gives: % 20.13/3.55 | (8) ~ (all_55_0 = use) & a_select3(z_defuse, all_55_2, all_55_1) = % 20.13/3.55 | all_55_0 & leq(all_55_1, tptp_minus_1) = 0 & leq(all_55_2, n2) = 0 & % 20.13/3.55 | leq(n0, all_55_1) = 0 & leq(n0, all_55_2) = 0 & $i(all_55_0) & % 20.13/3.55 | $i(all_55_1) & $i(all_55_2) % 20.13/3.55 | % 20.13/3.55 | ALPHA: (8) implies: % 20.13/3.55 | (9) $i(all_55_1) % 20.13/3.55 | (10) leq(n0, all_55_1) = 0 % 20.13/3.55 | (11) leq(all_55_1, tptp_minus_1) = 0 % 20.13/3.55 | % 20.13/3.55 | GROUND_INST: instantiating (3) with all_55_1, simplifying with (9), (10) % 20.13/3.55 | gives: % 20.13/3.55 | (12) all_55_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_55_1, n0) = v0) % 20.13/3.55 | % 20.13/3.55 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 20.13/3.55 | (2), (5) gives: % 20.13/3.55 | (13) pred(n0) = tptp_minus_1 % 20.13/3.55 | % 20.13/3.55 | GROUND_INST: instantiating (1) with all_55_1, n0, tptp_minus_1, simplifying % 20.13/3.55 | with (4), (9), (11), (13) gives: % 20.13/3.55 | (14) gt(n0, all_55_1) = 0 % 20.13/3.55 | % 20.13/3.55 | GROUND_INST: instantiating (leq_gt1) with all_55_1, n0, simplifying with (4), % 20.13/3.55 | (9), (14) gives: % 20.13/3.55 | (15) leq(all_55_1, n0) = 0 % 20.13/3.55 | % 20.13/3.55 | BETA: splitting (12) gives: % 20.13/3.55 | % 20.13/3.55 | Case 1: % 20.13/3.55 | | % 20.13/3.55 | | (16) all_55_1 = n0 % 20.13/3.55 | | % 20.13/3.55 | | REDUCE: (14), (16) imply: % 20.13/3.55 | | (17) gt(n0, n0) = 0 % 20.13/3.55 | | % 20.13/3.55 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4), % 20.13/3.55 | | (17) gives: % 20.13/3.55 | | (18) $false % 20.31/3.55 | | % 20.31/3.55 | | CLOSE: (18) is inconsistent. % 20.31/3.55 | | % 20.31/3.55 | Case 2: % 20.31/3.55 | | % 20.31/3.55 | | (19) ? [v0: int] : ( ~ (v0 = 0) & leq(all_55_1, n0) = v0) % 20.31/3.55 | | % 20.31/3.55 | | DELTA: instantiating (19) with fresh symbol all_116_0 gives: % 20.31/3.55 | | (20) ~ (all_116_0 = 0) & leq(all_55_1, n0) = all_116_0 % 20.31/3.55 | | % 20.31/3.55 | | ALPHA: (20) implies: % 20.31/3.56 | | (21) ~ (all_116_0 = 0) % 20.31/3.56 | | (22) leq(all_55_1, n0) = all_116_0 % 20.31/3.56 | | % 20.31/3.56 | | GROUND_INST: instantiating (7) with 0, all_116_0, n0, all_55_1, simplifying % 20.31/3.56 | | with (15), (22) gives: % 20.31/3.56 | | (23) all_116_0 = 0 % 20.31/3.56 | | % 20.31/3.56 | | REDUCE: (21), (23) imply: % 20.31/3.56 | | (24) $false % 20.31/3.56 | | % 20.31/3.56 | | CLOSE: (24) is inconsistent. % 20.31/3.56 | | % 20.31/3.56 | End of split % 20.31/3.56 | % 20.31/3.56 End of proof % 20.31/3.56 % SZS output end Proof for theBenchmark % 20.31/3.56 % 20.31/3.56 2930ms %------------------------------------------------------------------------------