%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV048+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 : n011.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 22:54:42 EDT 2023 % Result : Theorem 15.39s 2.83s % Output : Proof 19.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWV048+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n011.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 09:45:41 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.78/1.40 Prover 4: Preprocessing ... % 5.30/1.43 Prover 1: Preprocessing ... % 5.40/1.45 Prover 0: Preprocessing ... % 5.40/1.45 Prover 2: Preprocessing ... % 5.40/1.45 Prover 3: Preprocessing ... % 5.40/1.45 Prover 6: Preprocessing ... % 5.40/1.45 Prover 5: Preprocessing ... % 11.57/2.28 Prover 1: Warning: ignoring some quantifiers % 11.57/2.32 Prover 3: Warning: ignoring some quantifiers % 12.14/2.35 Prover 4: Warning: ignoring some quantifiers % 12.14/2.36 Prover 3: Constructing countermodel ... % 12.43/2.38 Prover 1: Constructing countermodel ... % 12.43/2.38 Prover 6: Proving ... % 12.90/2.44 Prover 4: Constructing countermodel ... % 13.09/2.48 Prover 5: Proving ... % 13.09/2.48 Prover 0: Proving ... % 13.09/2.55 Prover 2: Proving ... % 15.39/2.83 Prover 3: proved (2170ms) % 15.39/2.83 % 15.39/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.39/2.83 % 15.39/2.84 Prover 5: stopped % 15.39/2.84 Prover 2: stopped % 15.39/2.84 Prover 0: stopped % 15.39/2.86 Prover 6: stopped % 16.09/2.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.09/2.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.09/2.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.09/2.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.09/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.63/2.99 Prover 1: Found proof (size 21) % 16.63/2.99 Prover 1: proved (2346ms) % 16.63/2.99 Prover 4: stopped % 17.22/3.04 Prover 10: Preprocessing ... % 17.70/3.07 Prover 13: Preprocessing ... % 17.70/3.09 Prover 7: Preprocessing ... % 17.70/3.09 Prover 8: Preprocessing ... % 17.70/3.09 Prover 11: Preprocessing ... % 17.70/3.13 Prover 10: stopped % 17.70/3.15 Prover 7: stopped % 18.40/3.17 Prover 11: stopped % 18.40/3.22 Prover 13: stopped % 18.88/3.27 Prover 8: Warning: ignoring some quantifiers % 19.06/3.28 Prover 8: Constructing countermodel ... % 19.11/3.30 Prover 8: stopped % 19.11/3.30 % 19.11/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.11/3.30 % 19.17/3.31 % SZS output start Proof for theBenchmark % 19.19/3.31 Assumptions after simplification: % 19.19/3.31 --------------------------------- % 19.19/3.31 % 19.19/3.31 (cl5_nebula_norm_0016) % 19.19/3.34 $i(x) & $i(pv81) & $i(pv78) & $i(pv35) & $i(pv79) & $i(q) & $i(n135300) & % 19.19/3.34 $i(n5) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 19.19/3.34 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (times(v4, v5) % 19.19/3.34 = v6 & minus(n135300, n1) = v0 & minus(n5, n1) = v2 & minus(n0, n1) = v3 & % 19.19/3.34 sum(n0, v3, v6) = v7 & sum(n0, v0, v1) = pv78 & a_select3(q, pv81, pv35) = % 19.19/3.34 v4 & a_select3(q, pv79, pv35) = v1 & a_select2(x, pv81) = v5 & leq(pv35, v2) % 19.19/3.34 = 0 & leq(n0, pv35) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 19.19/3.34 $i(v2) & $i(v1) & $i(v0) & ((pv78 = n0 & ~ true) | ( ~ (v7 = n0) & ~ (pv78 % 19.19/3.34 = n0)))) % 19.19/3.34 % 19.19/3.34 (gt_3_tptp_minus_1) % 19.19/3.34 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1) % 19.19/3.34 % 19.19/3.34 (pred_minus_1) % 19.19/3.34 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 19.19/3.34 (pred(v0) = v1 & $i(v1))) % 19.19/3.34 % 19.19/3.34 (pred_succ) % 19.19/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 19.19/3.34 % 19.19/3.34 (succ_tptp_minus_1) % 19.19/3.34 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 19.19/3.34 % 19.19/3.34 (sum_plus_base) % 19.19/3.34 $i(tptp_minus_1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, % 19.19/3.34 tptp_minus_1, v0) = v1) | ~ $i(v0)) % 19.19/3.34 % 19.19/3.34 (ttrue) % 19.19/3.34 true % 19.19/3.34 % 19.19/3.34 (function-axioms) % 19.19/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.19/3.35 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.19/3.35 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.19/3.35 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.19/3.35 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.19/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.19/3.35 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.19/3.35 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.19/3.35 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.19/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.19/3.35 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.19/3.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3, % 19.19/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.19/3.35 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.19/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ % 19.19/3.35 (plus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.19/3.35 : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! % 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.19/3.35 (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! % 19.19/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) % 19.19/3.35 | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.19/3.35 ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! % 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.19/3.35 (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, v2) = v0)) & ! % 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.19/3.35 (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: $i] : ! % 19.19/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (uniform_int_rnd(v3, v2) % 19.19/3.35 = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 19.19/3.35 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (geq(v3, % 19.19/3.35 v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 19.19/3.35 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (lt(v3, % 19.19/3.35 v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.19/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) % 19.19/3.35 = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.19/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = % 19.19/3.35 v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.19/3.35 (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 19.19/3.35 : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! % 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ % 19.19/3.35 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.19/3.35 (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.19/3.35 % 19.19/3.35 Further assumptions not needed in the proof: % 19.19/3.35 -------------------------------------------- % 19.19/3.35 const_array1_select, const_array2_select, defuse, finite_domain_0, % 19.19/3.35 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 19.19/3.35 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2, % 19.19/3.35 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0, % 19.19/3.35 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, % 19.19/3.35 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, % 19.19/3.35 gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, % 19.19/3.35 leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 19.19/3.35 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 19.19/3.35 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.19/3.35 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 19.19/3.35 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 19.19/3.35 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 19.19/3.35 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 19.19/3.35 successor_1, successor_2, successor_3, successor_4, successor_5, % 19.19/3.35 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 19.19/3.35 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.19/3.35 % 19.19/3.35 Those formulas are unsatisfiable: % 19.19/3.35 --------------------------------- % 19.19/3.35 % 19.19/3.35 Begin of proof % 19.19/3.36 | % 19.19/3.36 | ALPHA: (sum_plus_base) implies: % 19.19/3.36 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) = % 19.19/3.36 | v1) | ~ $i(v0)) % 19.19/3.36 | % 19.19/3.36 | ALPHA: (succ_tptp_minus_1) implies: % 19.19/3.36 | (2) succ(tptp_minus_1) = n0 % 19.19/3.36 | % 19.19/3.36 | ALPHA: (pred_minus_1) implies: % 19.19/3.36 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 19.19/3.36 | (pred(v0) = v1 & $i(v1))) % 19.19/3.36 | % 19.19/3.36 | ALPHA: (gt_3_tptp_minus_1) implies: % 19.19/3.36 | (4) $i(tptp_minus_1) % 19.19/3.36 | % 19.19/3.36 | ALPHA: (cl5_nebula_norm_0016) implies: % 19.19/3.36 | (5) $i(n0) % 19.19/3.36 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.19/3.36 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (times(v4, v5) = v6 & % 19.19/3.36 | minus(n135300, n1) = v0 & minus(n5, n1) = v2 & minus(n0, n1) = v3 & % 19.19/3.36 | sum(n0, v3, v6) = v7 & sum(n0, v0, v1) = pv78 & a_select3(q, pv81, % 19.19/3.36 | pv35) = v4 & a_select3(q, pv79, pv35) = v1 & a_select2(x, pv81) = % 19.19/3.36 | v5 & leq(pv35, v2) = 0 & leq(n0, pv35) = 0 & $i(v7) & $i(v6) & $i(v5) % 19.19/3.36 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((pv78 = n0 & ~ true) % 19.19/3.36 | | ( ~ (v7 = n0) & ~ (pv78 = n0)))) % 19.19/3.36 | % 19.19/3.36 | ALPHA: (function-axioms) implies: % 19.19/3.36 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) % 19.19/3.36 | | ~ (pred(v2) = v0)) % 19.19/3.36 | % 19.19/3.36 | DELTA: instantiating (6) with fresh symbols all_61_0, all_61_1, all_61_2, % 19.19/3.36 | all_61_3, all_61_4, all_61_5, all_61_6, all_61_7 gives: % 19.19/3.36 | (8) times(all_61_3, all_61_2) = all_61_1 & minus(n135300, n1) = all_61_7 & % 19.19/3.36 | minus(n5, n1) = all_61_5 & minus(n0, n1) = all_61_4 & sum(n0, all_61_4, % 19.19/3.36 | all_61_1) = all_61_0 & sum(n0, all_61_7, all_61_6) = pv78 & % 19.19/3.36 | a_select3(q, pv81, pv35) = all_61_3 & a_select3(q, pv79, pv35) = % 19.19/3.36 | all_61_6 & a_select2(x, pv81) = all_61_2 & leq(pv35, all_61_5) = 0 & % 19.19/3.36 | leq(n0, pv35) = 0 & $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & % 19.19/3.36 | $i(all_61_3) & $i(all_61_4) & $i(all_61_5) & $i(all_61_6) & % 19.19/3.36 | $i(all_61_7) & ((pv78 = n0 & ~ true) | ( ~ (all_61_0 = n0) & ~ (pv78 % 19.19/3.36 | = n0))) % 19.19/3.36 | % 19.19/3.36 | ALPHA: (8) implies: % 19.19/3.36 | (9) $i(all_61_1) % 19.19/3.36 | (10) sum(n0, all_61_4, all_61_1) = all_61_0 % 19.19/3.36 | (11) minus(n0, n1) = all_61_4 % 19.19/3.36 | (12) (pv78 = n0 & ~ true) | ( ~ (all_61_0 = n0) & ~ (pv78 = n0)) % 19.19/3.36 | % 19.19/3.36 | BETA: splitting (12) gives: % 19.19/3.36 | % 19.19/3.36 | Case 1: % 19.19/3.36 | | % 19.19/3.36 | | (13) pv78 = n0 & ~ true % 19.19/3.36 | | % 19.19/3.36 | | ALPHA: (13) implies: % 19.19/3.36 | | (14) ~ true % 19.19/3.36 | | % 19.19/3.37 | | PRED_UNIFY: (14), (ttrue) imply: % 19.19/3.37 | | (15) $false % 19.19/3.37 | | % 19.19/3.37 | | CLOSE: (15) is inconsistent. % 19.19/3.37 | | % 19.19/3.37 | Case 2: % 19.19/3.37 | | % 19.19/3.37 | | (16) ~ (all_61_0 = n0) & ~ (pv78 = n0) % 19.19/3.37 | | % 19.19/3.37 | | ALPHA: (16) implies: % 19.19/3.37 | | (17) ~ (all_61_0 = n0) % 19.19/3.37 | | % 19.19/3.37 | | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying % 19.19/3.37 | | with (2), (4) gives: % 19.19/3.37 | | (18) pred(n0) = tptp_minus_1 % 19.19/3.37 | | % 19.19/3.37 | | GROUND_INST: instantiating (3) with n0, all_61_4, simplifying with (5), (11) % 19.19/3.37 | | gives: % 19.19/3.37 | | (19) pred(n0) = all_61_4 & $i(all_61_4) % 19.19/3.37 | | % 19.19/3.37 | | ALPHA: (19) implies: % 19.19/3.37 | | (20) pred(n0) = all_61_4 % 19.19/3.37 | | % 19.19/3.37 | | GROUND_INST: instantiating (7) with tptp_minus_1, all_61_4, n0, simplifying % 19.19/3.37 | | with (18), (20) gives: % 19.19/3.37 | | (21) all_61_4 = tptp_minus_1 % 19.19/3.37 | | % 19.19/3.37 | | REDUCE: (10), (21) imply: % 19.19/3.37 | | (22) sum(n0, tptp_minus_1, all_61_1) = all_61_0 % 19.19/3.37 | | % 19.19/3.37 | | GROUND_INST: instantiating (1) with all_61_1, all_61_0, simplifying with % 19.19/3.37 | | (9), (22) gives: % 19.19/3.37 | | (23) all_61_0 = n0 % 19.19/3.37 | | % 19.19/3.37 | | REDUCE: (17), (23) imply: % 19.19/3.37 | | (24) $false % 19.19/3.37 | | % 19.19/3.37 | | CLOSE: (24) is inconsistent. % 19.19/3.37 | | % 19.19/3.37 | End of split % 19.19/3.37 | % 19.19/3.37 End of proof % 19.19/3.37 % SZS output end Proof for theBenchmark % 19.19/3.37 % 19.19/3.37 2745ms %------------------------------------------------------------------------------