%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV152+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 : n023.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 22:55:07 EDT 2023 % Result : Theorem 14.91s 2.77s % Output : Proof 15.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV152+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 11:00:10 EDT 2023 % 0.12/0.34 % CPUTime : % 0.66/0.63 ________ _____ % 0.66/0.63 ___ __ \_________(_)________________________________ % 0.66/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.64 (2023-06-19) % 0.66/0.64 % 0.66/0.64 (c) Philipp Rümmer, 2009-2023 % 0.66/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.64 Amanda Stjerna. % 0.66/0.64 Free software under BSD-3-Clause. % 0.66/0.64 % 0.66/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.64 % 0.66/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.65 Running up to 7 provers in parallel. % 0.66/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.25/1.35 Prover 1: Preprocessing ... % 4.25/1.36 Prover 4: Preprocessing ... % 4.52/1.41 Prover 5: Preprocessing ... % 4.52/1.41 Prover 0: Preprocessing ... % 4.52/1.41 Prover 6: Preprocessing ... % 4.52/1.41 Prover 3: Preprocessing ... % 4.52/1.43 Prover 2: Preprocessing ... % 10.16/2.12 Prover 1: Warning: ignoring some quantifiers % 10.43/2.20 Prover 4: Warning: ignoring some quantifiers % 10.43/2.21 Prover 3: Warning: ignoring some quantifiers % 10.43/2.23 Prover 6: Proving ... % 10.43/2.23 Prover 1: Constructing countermodel ... % 11.05/2.24 Prover 3: Constructing countermodel ... % 11.05/2.28 Prover 4: Constructing countermodel ... % 11.44/2.29 Prover 5: Proving ... % 11.44/2.30 Prover 0: Proving ... % 11.93/2.36 Prover 2: Proving ... % 14.91/2.77 Prover 1: Found proof (size 21) % 14.91/2.77 Prover 1: proved (2110ms) % 14.91/2.77 Prover 3: stopped % 14.91/2.77 Prover 4: stopped % 14.91/2.77 Prover 2: stopped % 14.91/2.77 Prover 6: stopped % 14.91/2.77 Prover 0: stopped % 14.91/2.77 Prover 5: stopped % 14.91/2.77 % 14.91/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.91/2.77 % 14.91/2.78 % SZS output start Proof for theBenchmark % 14.91/2.78 Assumptions after simplification: % 14.91/2.78 --------------------------------- % 14.91/2.78 % 14.91/2.78 (cl5_nebula_norm_0002) % 14.91/2.81 $i(tptp_sum_index) & $i(q) & $i(n4) & $i(n1) & $i(tptp_minus_1) & $i(n0) & ? % 14.91/2.81 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = n1) & sum(n0, n4, v1) = v2 & % 14.91/2.81 a_select3(q, v0, tptp_sum_index) = v1 & leq(v0, tptp_minus_1) = 0 & leq(n0, % 14.91/2.81 v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 14.91/2.81 % 14.91/2.81 (finite_domain_0) % 14.91/2.81 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 14.91/2.81 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 14.91/2.81 % 14.91/2.81 (irreflexivity_gt) % 14.91/2.81 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 14.91/2.81 % 14.91/2.81 (leq_gt1) % 14.91/2.81 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.91/2.81 leq(v0, v1) = 0) % 14.91/2.81 % 14.91/2.81 (leq_gt_pred) % 14.91/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.91/2.81 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 14.91/2.81 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 14.91/2.81 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 14.91/2.81 | gt(v1, v0) = 0) % 14.91/2.81 % 14.91/2.82 (pred_succ) % 14.91/2.82 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 14.91/2.82 % 14.91/2.82 (succ_tptp_minus_1) % 14.91/2.82 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 14.91/2.82 % 14.91/2.82 (function-axioms) % 14.91/2.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.91/2.83 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 14.91/2.83 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.91/2.83 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 14.91/2.83 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.91/2.83 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 14.91/2.83 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.91/2.83 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 14.91/2.83 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.91/2.83 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 14.91/2.83 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.91/2.83 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 14.91/2.83 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 14.91/2.83 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 14.91/2.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 14.91/2.83 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.91/2.83 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 14.91/2.83 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.91/2.83 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 14.91/2.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 14.91/2.83 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 14.91/2.83 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 14.91/2.83 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 14.91/2.83 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 14.91/2.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.91/2.83 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 14.91/2.83 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.91/2.83 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 14.91/2.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.91/2.83 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 14.91/2.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.91/2.83 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 14.91/2.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.91/2.84 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 14.91/2.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 14.91/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 14.91/2.84 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.91/2.84 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.91/2.84 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 14.91/2.84 % 14.91/2.84 Further assumptions not needed in the proof: % 14.91/2.84 -------------------------------------------- % 14.91/2.84 const_array1_select, const_array2_select, defuse, finite_domain_1, % 14.91/2.84 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 14.91/2.84 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 14.91/2.84 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, % 14.91/2.84 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, % 14.91/2.84 gt_succ, leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 14.91/2.84 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 14.91/2.84 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 14.91/2.84 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1, % 14.91/2.84 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 14.91/2.84 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 14.91/2.84 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 14.91/2.84 succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5, % 14.91/2.84 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 14.91/2.84 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 14.91/2.84 % 14.91/2.84 Those formulas are unsatisfiable: % 14.91/2.84 --------------------------------- % 14.91/2.84 % 14.91/2.84 Begin of proof % 14.91/2.84 | % 14.91/2.84 | ALPHA: (leq_gt_pred) implies: % 14.91/2.84 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 14.91/2.84 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 14.91/2.84 | % 14.91/2.84 | ALPHA: (succ_tptp_minus_1) implies: % 14.91/2.84 | (2) succ(tptp_minus_1) = n0 % 14.91/2.84 | % 14.91/2.84 | ALPHA: (finite_domain_0) implies: % 14.91/2.84 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 14.91/2.84 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 14.91/2.84 | % 14.91/2.84 | ALPHA: (cl5_nebula_norm_0002) implies: % 14.91/2.84 | (4) $i(n0) % 14.91/2.84 | (5) $i(tptp_minus_1) % 14.91/2.84 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = n1) & sum(n0, n4, % 14.91/2.84 | v1) = v2 & a_select3(q, v0, tptp_sum_index) = v1 & leq(v0, % 14.91/2.84 | tptp_minus_1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 14.91/2.84 | % 14.91/2.84 | ALPHA: (function-axioms) implies: % 14.91/2.84 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.91/2.84 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 14.91/2.84 | % 14.91/2.85 | DELTA: instantiating (6) with fresh symbols all_55_0, all_55_1, all_55_2 % 14.91/2.85 | gives: % 14.91/2.85 | (8) ~ (all_55_0 = n1) & sum(n0, n4, all_55_1) = all_55_0 & a_select3(q, % 14.91/2.85 | all_55_2, tptp_sum_index) = all_55_1 & leq(all_55_2, tptp_minus_1) = % 14.91/2.85 | 0 & leq(n0, all_55_2) = 0 & $i(all_55_0) & $i(all_55_1) & $i(all_55_2) % 14.91/2.85 | % 14.91/2.85 | ALPHA: (8) implies: % 14.91/2.85 | (9) $i(all_55_2) % 14.91/2.85 | (10) leq(n0, all_55_2) = 0 % 14.91/2.85 | (11) leq(all_55_2, tptp_minus_1) = 0 % 14.91/2.85 | % 15.41/2.85 | GROUND_INST: instantiating (3) with all_55_2, simplifying with (9), (10) % 15.41/2.85 | gives: % 15.41/2.85 | (12) all_55_2 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_55_2, n0) = v0) % 15.41/2.85 | % 15.41/2.85 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 15.41/2.85 | (2), (5) gives: % 15.41/2.85 | (13) pred(n0) = tptp_minus_1 % 15.41/2.85 | % 15.41/2.85 | GROUND_INST: instantiating (1) with all_55_2, n0, tptp_minus_1, simplifying % 15.41/2.85 | with (4), (9), (11), (13) gives: % 15.41/2.85 | (14) gt(n0, all_55_2) = 0 % 15.41/2.85 | % 15.41/2.85 | GROUND_INST: instantiating (leq_gt1) with all_55_2, n0, simplifying with (4), % 15.41/2.85 | (9), (14) gives: % 15.41/2.85 | (15) leq(all_55_2, n0) = 0 % 15.41/2.85 | % 15.41/2.85 | BETA: splitting (12) gives: % 15.41/2.85 | % 15.41/2.85 | Case 1: % 15.41/2.85 | | % 15.41/2.85 | | (16) all_55_2 = n0 % 15.41/2.85 | | % 15.41/2.85 | | REDUCE: (14), (16) imply: % 15.41/2.85 | | (17) gt(n0, n0) = 0 % 15.41/2.85 | | % 15.41/2.85 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4), % 15.41/2.85 | | (17) gives: % 15.41/2.85 | | (18) $false % 15.41/2.85 | | % 15.41/2.85 | | CLOSE: (18) is inconsistent. % 15.41/2.85 | | % 15.41/2.85 | Case 2: % 15.41/2.85 | | % 15.41/2.85 | | (19) ? [v0: int] : ( ~ (v0 = 0) & leq(all_55_2, n0) = v0) % 15.41/2.85 | | % 15.41/2.85 | | DELTA: instantiating (19) with fresh symbol all_116_0 gives: % 15.41/2.85 | | (20) ~ (all_116_0 = 0) & leq(all_55_2, n0) = all_116_0 % 15.41/2.85 | | % 15.41/2.85 | | ALPHA: (20) implies: % 15.41/2.85 | | (21) ~ (all_116_0 = 0) % 15.41/2.85 | | (22) leq(all_55_2, n0) = all_116_0 % 15.41/2.85 | | % 15.41/2.85 | | GROUND_INST: instantiating (7) with 0, all_116_0, n0, all_55_2, simplifying % 15.41/2.85 | | with (15), (22) gives: % 15.41/2.85 | | (23) all_116_0 = 0 % 15.41/2.85 | | % 15.41/2.85 | | REDUCE: (21), (23) imply: % 15.41/2.85 | | (24) $false % 15.41/2.85 | | % 15.41/2.85 | | CLOSE: (24) is inconsistent. % 15.41/2.85 | | % 15.41/2.85 | End of split % 15.41/2.85 | % 15.41/2.85 End of proof % 15.41/2.85 % SZS output end Proof for theBenchmark % 15.41/2.85 % 15.41/2.85 2218ms %------------------------------------------------------------------------------