%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV160+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 : n031.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 22:55:09 EDT 2023 % Result : Theorem 16.65s 3.19s % Output : Proof 21.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n031.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 07:01:40 EDT 2023 % 0.12/0.35 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.80/1.45 Prover 1: Preprocessing ... % 4.80/1.45 Prover 4: Preprocessing ... % 4.80/1.46 Prover 2: Preprocessing ... % 4.80/1.46 Prover 5: Preprocessing ... % 4.80/1.46 Prover 0: Preprocessing ... % 4.80/1.46 Prover 6: Preprocessing ... % 4.80/1.46 Prover 3: Preprocessing ... % 11.43/2.33 Prover 1: Warning: ignoring some quantifiers % 12.19/2.43 Prover 1: Constructing countermodel ... % 12.19/2.44 Prover 3: Warning: ignoring some quantifiers % 12.19/2.46 Prover 6: Proving ... % 12.19/2.47 Prover 3: Constructing countermodel ... % 12.87/2.55 Prover 4: Warning: ignoring some quantifiers % 13.54/2.65 Prover 4: Constructing countermodel ... % 13.54/2.66 Prover 5: Proving ... % 13.76/2.68 Prover 0: Proving ... % 14.40/2.75 Prover 2: Proving ... % 16.65/3.19 Prover 3: proved (2554ms) % 16.65/3.19 % 16.65/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.65/3.19 % 16.65/3.19 Prover 5: stopped % 16.65/3.19 Prover 6: stopped % 17.78/3.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.78/3.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.78/3.21 Prover 0: stopped % 17.78/3.22 Prover 2: stopped % 17.78/3.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.78/3.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.78/3.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.73/3.32 Prover 1: Found proof (size 10) % 18.73/3.32 Prover 1: proved (2685ms) % 18.73/3.33 Prover 4: stopped % 19.57/3.41 Prover 10: Preprocessing ... % 19.57/3.41 Prover 7: Preprocessing ... % 19.57/3.42 Prover 8: Preprocessing ... % 19.57/3.44 Prover 13: Preprocessing ... % 19.57/3.45 Prover 11: Preprocessing ... % 19.57/3.49 Prover 10: stopped % 19.57/3.49 Prover 7: stopped % 20.33/3.56 Prover 11: stopped % 20.33/3.57 Prover 13: stopped % 20.87/3.62 Prover 8: Warning: ignoring some quantifiers % 20.87/3.64 Prover 8: Constructing countermodel ... % 20.87/3.64 Prover 8: stopped % 20.87/3.64 % 20.87/3.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.87/3.64 % 20.87/3.65 % SZS output start Proof for theBenchmark % 20.87/3.65 Assumptions after simplification: % 20.87/3.65 --------------------------------- % 20.87/3.65 % 20.87/3.65 (cl5_nebula_norm_0010) % 20.87/3.69 $i(q) & $i(n135299) & $i(pv47) & $i(pv84) & $i(tptp_pi) & $i(rho) & $i(sigma) % 20.87/3.69 & $i(tptp_minus_2) & $i(tptp_sum_index) & $i(mu) & $i(pv10) & $i(x) & $i(n4) & % 20.87/3.69 $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 20.87/3.69 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 20.87/3.69 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 20.87/3.69 [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 20.87/3.69 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 20.87/3.69 [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? % 20.87/3.69 [v29: $i] : ? [v30: $i] : (sqrt(v11) = v12 & tptp_term_equals(pv47, % 20.87/3.69 tptp_sum_index) = v17 & exp(v24) = v25 & exp(v7) = v8 & times(v25, v26) = % 20.87/3.69 v27 & times(v22, v22) = v23 & times(v19, v19) = v20 & times(v12, v22) = v28 % 20.87/3.69 & times(v12, v5) = v13 & times(v8, v9) = v10 & times(v5, v5) = v6 & % 20.87/3.69 times(v2, v2) = v3 & times(n2, tptp_pi) = v11 & divide(v29, pv84) = v30 & % 21.32/3.69 divide(v27, v28) = v29 & divide(v21, v23) = v24 & divide(v20, tptp_minus_2) % 21.32/3.69 = v21 & divide(v10, v13) = v14 & divide(v4, v6) = v7 & divide(v3, % 21.32/3.69 tptp_minus_2) = v4 & minus(v0, v18) = v19 & minus(v0, v1) = v2 & sum(n0, % 21.32/3.69 n4, v14) = pv84 & a_select2(rho, pv47) = v26 & a_select2(rho, % 21.32/3.69 tptp_sum_index) = v9 & a_select2(sigma, pv47) = v22 & a_select2(sigma, % 21.32/3.69 tptp_sum_index) = v5 & a_select2(mu, pv47) = v18 & a_select2(mu, % 21.32/3.69 tptp_sum_index) = v1 & a_select2(x, pv10) = v0 & pred(pv47) = v15 & % 21.32/3.69 pred(pv10) = v16 & leq(pv47, n4) = 0 & leq(pv10, n135299) = 0 & leq(n0, % 21.32/3.69 pv47) = 0 & leq(n0, pv10) = 0 & $i(v30) & $i(v29) & $i(v28) & $i(v27) & % 21.32/3.69 $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 21.32/3.69 $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 21.32/3.69 $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 21.32/3.69 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v31: $i] : ! [v32: $i] : % 21.32/3.69 ! [v33: $i] : ! [v34: $i] : ! [v35: $i] : ! [v36: $i] : ! [v37: $i] : ! % 21.32/3.69 [v38: $i] : ! [v39: $i] : ! [v40: $i] : ! [v41: $i] : ! [v42: $i] : ! % 21.32/3.69 [v43: $i] : ( ~ (exp(v38) = v39) | ~ (times(v39, v40) = v41) | ~ % 21.32/3.69 (times(v36, v36) = v37) | ~ (times(v33, v33) = v34) | ~ (times(v12, v36) % 21.32/3.69 = v42) | ~ (divide(v41, v42) = v43) | ~ (divide(v35, v37) = v38) | ~ % 21.32/3.69 (divide(v34, tptp_minus_2) = v35) | ~ (minus(v0, v32) = v33) | ~ % 21.32/3.69 (a_select2(rho, v31) = v40) | ~ (a_select2(sigma, v31) = v36) | ~ % 21.32/3.69 (a_select2(mu, v31) = v32) | ~ $i(v31) | ? [v44: any] : ? [v45: any] : % 21.32/3.69 ? [v46: $i] : ? [v47: $i] : (divide(v43, pv84) = v47 & a_select3(q, pv10, % 21.32/3.69 v31) = v46 & leq(v31, v15) = v45 & leq(n0, v31) = v44 & $i(v47) & % 21.32/3.69 $i(v46) & ( ~ (v45 = 0) | ~ (v44 = 0) | v47 = v46))) & ! [v31: $i] : % 21.32/3.69 ! [v32: $i] : ( ~ (a_select3(q, v31, tptp_sum_index) = v32) | ~ $i(v31) | % 21.32/3.69 ? [v33: any] : ? [v34: any] : ? [v35: $i] : (sum(n0, n4, v32) = v35 & % 21.32/3.69 leq(v31, v16) = v34 & leq(n0, v31) = v33 & $i(v35) & ( ~ (v34 = 0) | ~ % 21.32/3.69 (v33 = 0) | v35 = n1))) & ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : % 21.32/3.69 ( ~ (v33 = n1) & cond(v17, v30, v31) = v32 & sum(n0, n4, v32) = v33 & % 21.32/3.69 a_select3(q, pv10, tptp_sum_index) = v31 & leq(pv10, v16) = 0 & $i(v33) & % 21.32/3.69 $i(v32) & $i(v31))) % 21.32/3.69 % 21.32/3.69 (irreflexivity_gt) % 21.32/3.69 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 21.32/3.69 % 21.32/3.69 (leq_gt_pred) % 21.32/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.32/3.69 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.32/3.69 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 21.32/3.69 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 21.32/3.69 | gt(v1, v0) = 0) % 21.32/3.69 % 21.32/3.69 Further assumptions not needed in the proof: % 21.32/3.69 -------------------------------------------- % 21.32/3.69 const_array1_select, const_array2_select, defuse, finite_domain_0, % 21.32/3.69 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 21.32/3.69 finite_domain_5, gt_0_tptp_minus_1, gt_0_tptp_minus_2, gt_135299_0, gt_135299_1, % 21.32/3.69 gt_135299_2, gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, % 21.32/3.69 gt_135299_tptp_minus_2, gt_1_0, gt_1_tptp_minus_1, gt_1_tptp_minus_2, gt_2_0, % 21.32/3.69 gt_2_1, gt_2_tptp_minus_1, gt_2_tptp_minus_2, gt_3_0, gt_3_1, gt_3_2, % 21.32/3.69 gt_3_tptp_minus_1, gt_3_tptp_minus_2, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 21.32/3.69 gt_4_tptp_minus_1, gt_4_tptp_minus_2, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, % 21.32/3.69 gt_5_tptp_minus_1, gt_5_tptp_minus_2, gt_succ, gt_tptp_minus_1_tptp_minus_2, % 21.32/3.69 leq_geq, leq_gt1, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 21.32/3.69 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 21.32/3.69 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 21.32/3.69 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 21.32/3.69 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 21.32/3.69 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 21.32/3.69 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 21.32/3.69 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2, % 21.32/3.69 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float, % 21.32/3.69 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 21.32/3.69 uniform_int_rand_ranges_lo % 21.32/3.69 % 21.32/3.69 Those formulas are unsatisfiable: % 21.32/3.69 --------------------------------- % 21.32/3.69 % 21.32/3.69 Begin of proof % 21.32/3.69 | % 21.32/3.69 | ALPHA: (leq_gt_pred) implies: % 21.32/3.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 21.32/3.69 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 21.32/3.69 | % 21.32/3.69 | ALPHA: (cl5_nebula_norm_0010) implies: % 21.32/3.70 | (2) $i(pv10) % 21.36/3.70 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.36/3.70 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 21.36/3.70 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 21.36/3.70 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 21.36/3.70 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 21.36/3.70 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : % 21.36/3.70 | ? [v29: $i] : ? [v30: $i] : (sqrt(v11) = v12 & tptp_term_equals(pv47, % 21.36/3.70 | tptp_sum_index) = v17 & exp(v24) = v25 & exp(v7) = v8 & times(v25, % 21.36/3.70 | v26) = v27 & times(v22, v22) = v23 & times(v19, v19) = v20 & % 21.36/3.70 | times(v12, v22) = v28 & times(v12, v5) = v13 & times(v8, v9) = v10 & % 21.36/3.70 | times(v5, v5) = v6 & times(v2, v2) = v3 & times(n2, tptp_pi) = v11 & % 21.36/3.70 | divide(v29, pv84) = v30 & divide(v27, v28) = v29 & divide(v21, v23) = % 21.36/3.70 | v24 & divide(v20, tptp_minus_2) = v21 & divide(v10, v13) = v14 & % 21.36/3.70 | divide(v4, v6) = v7 & divide(v3, tptp_minus_2) = v4 & minus(v0, v18) % 21.36/3.70 | = v19 & minus(v0, v1) = v2 & sum(n0, n4, v14) = pv84 & a_select2(rho, % 21.36/3.70 | pv47) = v26 & a_select2(rho, tptp_sum_index) = v9 & % 21.36/3.70 | a_select2(sigma, pv47) = v22 & a_select2(sigma, tptp_sum_index) = v5 % 21.36/3.70 | & a_select2(mu, pv47) = v18 & a_select2(mu, tptp_sum_index) = v1 & % 21.36/3.70 | a_select2(x, pv10) = v0 & pred(pv47) = v15 & pred(pv10) = v16 & % 21.36/3.70 | leq(pv47, n4) = 0 & leq(pv10, n135299) = 0 & leq(n0, pv47) = 0 & % 21.36/3.70 | leq(n0, pv10) = 0 & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & % 21.36/3.70 | $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & % 21.36/3.70 | $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 21.36/3.70 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 21.36/3.70 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v31: $i] : ! [v32: % 21.36/3.70 | $i] : ! [v33: $i] : ! [v34: $i] : ! [v35: $i] : ! [v36: $i] : % 21.36/3.70 | ! [v37: $i] : ! [v38: $i] : ! [v39: $i] : ! [v40: $i] : ! [v41: % 21.36/3.70 | $i] : ! [v42: $i] : ! [v43: $i] : ( ~ (exp(v38) = v39) | ~ % 21.36/3.70 | (times(v39, v40) = v41) | ~ (times(v36, v36) = v37) | ~ % 21.36/3.70 | (times(v33, v33) = v34) | ~ (times(v12, v36) = v42) | ~ % 21.36/3.70 | (divide(v41, v42) = v43) | ~ (divide(v35, v37) = v38) | ~ % 21.36/3.70 | (divide(v34, tptp_minus_2) = v35) | ~ (minus(v0, v32) = v33) | ~ % 21.36/3.70 | (a_select2(rho, v31) = v40) | ~ (a_select2(sigma, v31) = v36) | ~ % 21.36/3.70 | (a_select2(mu, v31) = v32) | ~ $i(v31) | ? [v44: any] : ? [v45: % 21.36/3.70 | any] : ? [v46: $i] : ? [v47: $i] : (divide(v43, pv84) = v47 & % 21.36/3.70 | a_select3(q, pv10, v31) = v46 & leq(v31, v15) = v45 & leq(n0, % 21.36/3.70 | v31) = v44 & $i(v47) & $i(v46) & ( ~ (v45 = 0) | ~ (v44 = 0) | % 21.36/3.70 | v47 = v46))) & ! [v31: $i] : ! [v32: $i] : ( ~ (a_select3(q, % 21.36/3.70 | v31, tptp_sum_index) = v32) | ~ $i(v31) | ? [v33: any] : ? % 21.36/3.70 | [v34: any] : ? [v35: $i] : (sum(n0, n4, v32) = v35 & leq(v31, v16) % 21.36/3.70 | = v34 & leq(n0, v31) = v33 & $i(v35) & ( ~ (v34 = 0) | ~ (v33 = % 21.36/3.70 | 0) | v35 = n1))) & ? [v31: $i] : ? [v32: $i] : ? [v33: $i] % 21.36/3.70 | : ( ~ (v33 = n1) & cond(v17, v30, v31) = v32 & sum(n0, n4, v32) = v33 % 21.36/3.70 | & a_select3(q, pv10, tptp_sum_index) = v31 & leq(pv10, v16) = 0 & % 21.36/3.70 | $i(v33) & $i(v32) & $i(v31))) % 21.36/3.70 | % 21.36/3.70 | DELTA: instantiating (3) with fresh symbols all_76_0, all_76_1, all_76_2, % 21.36/3.70 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7, all_76_8, all_76_9, % 21.36/3.70 | all_76_10, all_76_11, all_76_12, all_76_13, all_76_14, all_76_15, % 21.36/3.70 | all_76_16, all_76_17, all_76_18, all_76_19, all_76_20, all_76_21, % 21.36/3.70 | all_76_22, all_76_23, all_76_24, all_76_25, all_76_26, all_76_27, % 21.36/3.70 | all_76_28, all_76_29, all_76_30 gives: % 21.36/3.71 | (4) sqrt(all_76_19) = all_76_18 & tptp_term_equals(pv47, tptp_sum_index) = % 21.36/3.71 | all_76_13 & exp(all_76_6) = all_76_5 & exp(all_76_23) = all_76_22 & % 21.36/3.71 | times(all_76_5, all_76_4) = all_76_3 & times(all_76_8, all_76_8) = % 21.36/3.71 | all_76_7 & times(all_76_11, all_76_11) = all_76_10 & times(all_76_18, % 21.36/3.71 | all_76_8) = all_76_2 & times(all_76_18, all_76_25) = all_76_17 & % 21.36/3.71 | times(all_76_22, all_76_21) = all_76_20 & times(all_76_25, all_76_25) = % 21.36/3.71 | all_76_24 & times(all_76_28, all_76_28) = all_76_27 & times(n2, % 21.36/3.71 | tptp_pi) = all_76_19 & divide(all_76_1, pv84) = all_76_0 & % 21.36/3.71 | divide(all_76_3, all_76_2) = all_76_1 & divide(all_76_9, all_76_7) = % 21.36/3.71 | all_76_6 & divide(all_76_10, tptp_minus_2) = all_76_9 & % 21.36/3.71 | divide(all_76_20, all_76_17) = all_76_16 & divide(all_76_26, all_76_24) % 21.36/3.71 | = all_76_23 & divide(all_76_27, tptp_minus_2) = all_76_26 & % 21.36/3.71 | minus(all_76_30, all_76_12) = all_76_11 & minus(all_76_30, all_76_29) = % 21.36/3.71 | all_76_28 & sum(n0, n4, all_76_16) = pv84 & a_select2(rho, pv47) = % 21.36/3.71 | all_76_4 & a_select2(rho, tptp_sum_index) = all_76_21 & % 21.36/3.71 | a_select2(sigma, pv47) = all_76_8 & a_select2(sigma, tptp_sum_index) = % 21.36/3.71 | all_76_25 & a_select2(mu, pv47) = all_76_12 & a_select2(mu, % 21.36/3.71 | tptp_sum_index) = all_76_29 & a_select2(x, pv10) = all_76_30 & % 21.36/3.71 | pred(pv47) = all_76_15 & pred(pv10) = all_76_14 & leq(pv47, n4) = 0 & % 21.36/3.71 | leq(pv10, n135299) = 0 & leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & % 21.36/3.71 | $i(all_76_0) & $i(all_76_1) & $i(all_76_2) & $i(all_76_3) & % 21.36/3.71 | $i(all_76_4) & $i(all_76_5) & $i(all_76_6) & $i(all_76_7) & % 21.36/3.71 | $i(all_76_8) & $i(all_76_9) & $i(all_76_10) & $i(all_76_11) & % 21.36/3.71 | $i(all_76_12) & $i(all_76_13) & $i(all_76_14) & $i(all_76_15) & % 21.36/3.71 | $i(all_76_16) & $i(all_76_17) & $i(all_76_18) & $i(all_76_19) & % 21.36/3.71 | $i(all_76_20) & $i(all_76_21) & $i(all_76_22) & $i(all_76_23) & % 21.36/3.71 | $i(all_76_24) & $i(all_76_25) & $i(all_76_26) & $i(all_76_27) & % 21.36/3.71 | $i(all_76_28) & $i(all_76_29) & $i(all_76_30) & ! [v0: $i] : ! [v1: % 21.36/3.71 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 21.36/3.71 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 21.36/3.71 | [v11: $i] : ! [v12: $i] : ( ~ (exp(v7) = v8) | ~ (times(v8, v9) = % 21.36/3.71 | v10) | ~ (times(v5, v5) = v6) | ~ (times(v2, v2) = v3) | ~ % 21.36/3.71 | (times(all_76_18, v5) = v11) | ~ (divide(v10, v11) = v12) | ~ % 21.36/3.71 | (divide(v4, v6) = v7) | ~ (divide(v3, tptp_minus_2) = v4) | ~ % 21.36/3.71 | (minus(all_76_30, v1) = v2) | ~ (a_select2(rho, v0) = v9) | ~ % 21.36/3.71 | (a_select2(sigma, v0) = v5) | ~ (a_select2(mu, v0) = v1) | ~ $i(v0) % 21.36/3.71 | | ? [v13: any] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : % 21.36/3.71 | (divide(v12, pv84) = v16 & a_select3(q, pv10, v0) = v15 & leq(v0, % 21.36/3.71 | all_76_15) = v14 & leq(n0, v0) = v13 & $i(v16) & $i(v15) & ( ~ % 21.36/3.71 | (v14 = 0) | ~ (v13 = 0) | v16 = v15))) & ! [v0: $i] : ! [v1: % 21.36/3.71 | $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~ $i(v0) | ? % 21.36/3.71 | [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1) = v4 & % 21.36/3.71 | leq(v0, all_76_14) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) % 21.36/3.71 | | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 21.36/3.71 | $i] : ( ~ (v2 = n1) & cond(all_76_13, all_76_0, v0) = v1 & sum(n0, % 21.36/3.71 | n4, v1) = v2 & a_select3(q, pv10, tptp_sum_index) = v0 & leq(pv10, % 21.36/3.71 | all_76_14) = 0 & $i(v2) & $i(v1) & $i(v0)) % 21.36/3.71 | % 21.36/3.71 | ALPHA: (4) implies: % 21.36/3.71 | (5) pred(pv10) = all_76_14 % 21.36/3.71 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = n1) & % 21.36/3.71 | cond(all_76_13, all_76_0, v0) = v1 & sum(n0, n4, v1) = v2 & % 21.36/3.71 | a_select3(q, pv10, tptp_sum_index) = v0 & leq(pv10, all_76_14) = 0 & % 21.36/3.71 | $i(v2) & $i(v1) & $i(v0)) % 21.36/3.71 | % 21.36/3.71 | DELTA: instantiating (6) with fresh symbols all_79_0, all_79_1, all_79_2 % 21.36/3.71 | gives: % 21.36/3.71 | (7) ~ (all_79_0 = n1) & cond(all_76_13, all_76_0, all_79_2) = all_79_1 & % 21.36/3.71 | sum(n0, n4, all_79_1) = all_79_0 & a_select3(q, pv10, tptp_sum_index) = % 21.36/3.71 | all_79_2 & leq(pv10, all_76_14) = 0 & $i(all_79_0) & $i(all_79_1) & % 21.36/3.71 | $i(all_79_2) % 21.36/3.71 | % 21.36/3.71 | ALPHA: (7) implies: % 21.36/3.71 | (8) leq(pv10, all_76_14) = 0 % 21.36/3.71 | % 21.36/3.71 | GROUND_INST: instantiating (1) with pv10, pv10, all_76_14, simplifying with % 21.36/3.71 | (2), (5), (8) gives: % 21.36/3.71 | (9) gt(pv10, pv10) = 0 % 21.36/3.71 | % 21.36/3.71 | GROUND_INST: instantiating (irreflexivity_gt) with pv10, simplifying with (2), % 21.36/3.71 | (9) gives: % 21.36/3.71 | (10) $false % 21.36/3.71 | % 21.36/3.71 | CLOSE: (10) is inconsistent. % 21.36/3.71 | % 21.36/3.71 End of proof % 21.36/3.72 % SZS output end Proof for theBenchmark % 21.36/3.72 % 21.36/3.72 3102ms %------------------------------------------------------------------------------