%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV164+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 : n003.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 22:55:10 EDT 2023 % Result : Theorem 16.12s 2.91s % Output : Proof 20.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.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 09:49:26 EDT 2023 % 0.13/0.35 % 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 % 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.57/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.47/1.36 Prover 1: Preprocessing ... % 4.47/1.37 Prover 4: Preprocessing ... % 4.47/1.40 Prover 2: Preprocessing ... % 4.47/1.40 Prover 6: Preprocessing ... % 4.47/1.40 Prover 3: Preprocessing ... % 4.47/1.40 Prover 5: Preprocessing ... % 4.47/1.40 Prover 0: Preprocessing ... % 10.19/2.14 Prover 1: Warning: ignoring some quantifiers % 11.17/2.21 Prover 1: Constructing countermodel ... % 11.17/2.22 Prover 3: Warning: ignoring some quantifiers % 11.17/2.24 Prover 4: Warning: ignoring some quantifiers % 11.44/2.27 Prover 3: Constructing countermodel ... % 11.44/2.27 Prover 6: Proving ... % 12.11/2.36 Prover 4: Constructing countermodel ... % 12.46/2.39 Prover 5: Proving ... % 12.46/2.48 Prover 0: Proving ... % 13.03/2.51 Prover 2: Proving ... % 16.12/2.91 Prover 3: proved (2274ms) % 16.12/2.91 % 16.12/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.12/2.91 % 16.12/2.92 Prover 6: stopped % 16.12/2.92 Prover 5: stopped % 16.12/2.92 Prover 2: stopped % 16.12/2.92 Prover 0: stopped % 16.12/2.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.12/2.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.12/2.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.12/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.12/2.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.96/2.99 Prover 1: Found proof (size 23) % 16.96/2.99 Prover 1: proved (2352ms) % 16.96/3.00 Prover 4: stopped % 18.36/3.17 Prover 8: Preprocessing ... % 18.36/3.18 Prover 11: Preprocessing ... % 18.36/3.19 Prover 7: Preprocessing ... % 18.36/3.19 Prover 10: Preprocessing ... % 18.64/3.20 Prover 13: Preprocessing ... % 18.89/3.24 Prover 7: stopped % 18.89/3.26 Prover 10: stopped % 18.89/3.26 Prover 11: stopped % 18.89/3.28 Prover 13: stopped % 19.44/3.35 Prover 8: Warning: ignoring some quantifiers % 19.44/3.37 Prover 8: Constructing countermodel ... % 19.44/3.37 Prover 8: stopped % 19.44/3.37 % 19.44/3.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.44/3.37 % 19.44/3.38 % SZS output start Proof for theBenchmark % 19.44/3.38 Assumptions after simplification: % 19.44/3.38 --------------------------------- % 19.44/3.38 % 19.44/3.38 (cl5_nebula_norm_0014) % 19.75/3.42 $i(tptp_pi) & $i(rho) & $i(sigma) & $i(tptp_minus_2) & $i(mu) & $i(x) & % 19.75/3.42 $i(tptp_sum_index) & $i(q) & $i(n135299) & $i(pv10) & $i(n4) & $i(n2) & $i(n1) % 19.75/3.42 & $i(tptp_minus_1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 19.75/3.42 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 19.75/3.42 : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 19.75/3.42 [v14: $i] : ? [v15: $i] : ? [v16: $i] : (sqrt(v2) = v3 & exp(v10) = v11 & % 19.75/3.42 times(v11, v12) = v13 & times(v8, v8) = v9 & times(v5, v5) = v6 & times(v3, % 19.75/3.42 v8) = v14 & times(n2, tptp_pi) = v2 & divide(v13, v14) = v15 & divide(v7, % 19.75/3.42 v9) = v10 & divide(v6, tptp_minus_2) = v7 & minus(v1, v4) = v5 & sum(n0, % 19.75/3.42 n4, v15) = v16 & a_select2(rho, tptp_sum_index) = v12 & a_select2(sigma, % 19.75/3.42 tptp_sum_index) = v8 & a_select2(mu, tptp_sum_index) = v4 & a_select2(x, % 19.75/3.42 pv10) = v1 & pred(pv10) = v0 & leq(pv10, n135299) = 0 & leq(n0, pv10) = 0 % 19.75/3.42 & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 19.75/3.42 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 19.75/3.42 $i(v1) & $i(v0) & ! [v17: $i] : ! [v18: $i] : ( ~ (a_select3(q, v17, % 19.75/3.42 tptp_sum_index) = v18) | ~ $i(v17) | ? [v19: any] : ? [v20: any] : % 19.75/3.42 ? [v21: $i] : (sum(n0, n4, v18) = v21 & leq(v17, v0) = v20 & leq(n0, v17) % 19.75/3.42 = v19 & $i(v21) & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = n1))) & ? [v17: % 19.75/3.42 $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: % 19.75/3.42 $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: % 19.75/3.42 $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ( ~ (v31 % 19.75/3.42 = v18) & exp(v25) = v26 & times(v26, v27) = v28 & times(v23, v23) = v24 % 19.75/3.42 & times(v20, v20) = v21 & times(v3, v23) = v29 & divide(v30, v16) = v31 & % 19.75/3.42 divide(v28, v29) = v30 & divide(v22, v24) = v25 & divide(v21, % 19.75/3.42 tptp_minus_2) = v22 & minus(v1, v19) = v20 & a_select3(q, pv10, v17) = % 19.75/3.42 v18 & a_select2(rho, v17) = v27 & a_select2(sigma, v17) = v23 & % 19.75/3.42 a_select2(mu, v17) = v19 & leq(v17, tptp_minus_1) = 0 & leq(n0, v17) = 0 & % 19.75/3.42 $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & % 19.75/3.42 $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 19.75/3.42 $i(v17))) % 19.75/3.42 % 19.75/3.42 (finite_domain_0) % 19.75/3.42 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.75/3.42 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.75/3.42 % 19.75/3.42 (irreflexivity_gt) % 19.75/3.42 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 19.75/3.42 % 19.75/3.42 (leq_gt1) % 19.75/3.42 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.75/3.42 leq(v0, v1) = 0) % 19.75/3.42 % 19.75/3.42 (leq_gt_pred) % 19.75/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.75/3.42 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.75/3.42 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 19.75/3.42 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 19.75/3.42 | gt(v1, v0) = 0) % 19.75/3.42 % 19.75/3.42 (pred_succ) % 19.75/3.42 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 19.75/3.42 % 19.75/3.42 (succ_tptp_minus_1) % 19.75/3.42 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 19.75/3.42 % 19.75/3.42 (function-axioms) % 19.75/3.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.75/3.43 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.75/3.43 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.75/3.43 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.75/3.43 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.75/3.43 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.75/3.43 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.75/3.43 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.75/3.43 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.75/3.43 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.75/3.43 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.75/3.43 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3, % 19.75/3.43 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.75/3.43 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] : % 19.75/3.43 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | % 19.75/3.43 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 19.75/3.43 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: % 19.75/3.43 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, % 19.75/3.43 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.75/3.43 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ % 19.75/3.43 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.75/3.43 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = % 19.75/3.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.75/3.43 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.75/3.43 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ % 19.75/3.43 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 19.75/3.43 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) % 19.75/3.43 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 19.75/3.43 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & % 19.75/3.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.75/3.43 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.75/3.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.75/3.43 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.75/3.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.75/3.43 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.75/3.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.75/3.43 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.75/3.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) & % 19.75/3.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (exp(v2) = v1) | ~ % 19.75/3.43 (exp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.75/3.43 (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.75/3.43 $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : % 19.75/3.43 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 19.75/3.43 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ % 19.75/3.43 (pred(v2) = v0)) % 19.75/3.43 % 19.75/3.43 Further assumptions not needed in the proof: % 19.75/3.43 -------------------------------------------- % 19.75/3.43 const_array1_select, const_array2_select, defuse, finite_domain_1, % 19.75/3.43 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 19.75/3.43 gt_0_tptp_minus_1, gt_0_tptp_minus_2, gt_135299_0, gt_135299_1, gt_135299_2, % 19.75/3.43 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, % 19.75/3.43 gt_135299_tptp_minus_2, gt_1_0, gt_1_tptp_minus_1, gt_1_tptp_minus_2, gt_2_0, % 19.75/3.43 gt_2_1, gt_2_tptp_minus_1, gt_2_tptp_minus_2, gt_3_0, gt_3_1, gt_3_2, % 19.75/3.43 gt_3_tptp_minus_1, gt_3_tptp_minus_2, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 19.75/3.43 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, % 19.75/3.43 gt_5_tptp_minus_1, gt_5_tptp_minus_2, gt_succ, gt_tptp_minus_1_tptp_minus_2, % 19.75/3.43 leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 19.75/3.43 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 19.75/3.43 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.75/3.43 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1, % 19.75/3.43 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 19.75/3.43 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 19.75/3.43 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 19.75/3.43 succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5, % 19.75/3.43 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 19.75/3.43 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.75/3.43 % 19.75/3.43 Those formulas are unsatisfiable: % 19.75/3.43 --------------------------------- % 19.75/3.43 % 19.75/3.43 Begin of proof % 19.75/3.43 | % 19.75/3.44 | ALPHA: (leq_gt_pred) implies: % 19.75/3.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 19.75/3.44 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 19.75/3.44 | % 19.75/3.44 | ALPHA: (succ_tptp_minus_1) implies: % 19.75/3.44 | (2) succ(tptp_minus_1) = n0 % 19.75/3.44 | % 19.75/3.44 | ALPHA: (finite_domain_0) implies: % 19.75/3.44 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.75/3.44 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.75/3.44 | % 19.75/3.44 | ALPHA: (cl5_nebula_norm_0014) implies: % 19.75/3.44 | (4) $i(n0) % 19.75/3.44 | (5) $i(tptp_minus_1) % 19.75/3.44 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.75/3.44 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 19.75/3.44 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 19.75/3.44 | ? [v15: $i] : ? [v16: $i] : (sqrt(v2) = v3 & exp(v10) = v11 & % 19.75/3.44 | times(v11, v12) = v13 & times(v8, v8) = v9 & times(v5, v5) = v6 & % 19.75/3.44 | times(v3, v8) = v14 & times(n2, tptp_pi) = v2 & divide(v13, v14) = % 19.75/3.44 | v15 & divide(v7, v9) = v10 & divide(v6, tptp_minus_2) = v7 & % 19.75/3.44 | minus(v1, v4) = v5 & sum(n0, n4, v15) = v16 & a_select2(rho, % 19.75/3.44 | tptp_sum_index) = v12 & a_select2(sigma, tptp_sum_index) = v8 & % 19.75/3.44 | a_select2(mu, tptp_sum_index) = v4 & a_select2(x, pv10) = v1 & % 19.75/3.44 | pred(pv10) = v0 & leq(pv10, n135299) = 0 & leq(n0, pv10) = 0 & % 19.75/3.44 | $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 19.75/3.44 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 19.75/3.44 | & $i(v1) & $i(v0) & ! [v17: $i] : ! [v18: $i] : ( ~ (a_select3(q, % 19.75/3.44 | v17, tptp_sum_index) = v18) | ~ $i(v17) | ? [v19: any] : ? % 19.75/3.44 | [v20: any] : ? [v21: $i] : (sum(n0, n4, v18) = v21 & leq(v17, v0) % 19.75/3.44 | = v20 & leq(n0, v17) = v19 & $i(v21) & ( ~ (v20 = 0) | ~ (v19 = % 19.75/3.44 | 0) | v21 = n1))) & ? [v17: $i] : ? [v18: $i] : ? [v19: $i] % 19.75/3.44 | : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 19.75/3.44 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] % 19.75/3.44 | : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ( ~ (v31 = v18) & % 19.75/3.44 | exp(v25) = v26 & times(v26, v27) = v28 & times(v23, v23) = v24 & % 19.75/3.44 | times(v20, v20) = v21 & times(v3, v23) = v29 & divide(v30, v16) = % 19.75/3.44 | v31 & divide(v28, v29) = v30 & divide(v22, v24) = v25 & divide(v21, % 19.75/3.44 | tptp_minus_2) = v22 & minus(v1, v19) = v20 & a_select3(q, pv10, % 19.75/3.44 | v17) = v18 & a_select2(rho, v17) = v27 & a_select2(sigma, v17) = % 19.75/3.44 | v23 & a_select2(mu, v17) = v19 & leq(v17, tptp_minus_1) = 0 & % 19.75/3.44 | leq(n0, v17) = 0 & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) % 19.75/3.44 | & $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 19.75/3.44 | $i(v20) & $i(v19) & $i(v18) & $i(v17))) % 19.75/3.45 | % 19.75/3.45 | ALPHA: (function-axioms) implies: % 19.75/3.45 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.75/3.45 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.75/3.45 | % 19.75/3.45 | DELTA: instantiating (6) with fresh symbols all_76_0, all_76_1, all_76_2, % 19.75/3.45 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7, all_76_8, all_76_9, % 19.75/3.45 | all_76_10, all_76_11, all_76_12, all_76_13, all_76_14, all_76_15, % 19.75/3.45 | all_76_16 gives: % 19.75/3.45 | (8) sqrt(all_76_14) = all_76_13 & exp(all_76_6) = all_76_5 & % 19.75/3.45 | times(all_76_5, all_76_4) = all_76_3 & times(all_76_8, all_76_8) = % 19.75/3.45 | all_76_7 & times(all_76_11, all_76_11) = all_76_10 & times(all_76_13, % 19.75/3.45 | all_76_8) = all_76_2 & times(n2, tptp_pi) = all_76_14 & % 19.75/3.45 | divide(all_76_3, all_76_2) = all_76_1 & divide(all_76_9, all_76_7) = % 19.75/3.45 | all_76_6 & divide(all_76_10, tptp_minus_2) = all_76_9 & % 19.75/3.45 | minus(all_76_15, all_76_12) = all_76_11 & sum(n0, n4, all_76_1) = % 19.75/3.45 | all_76_0 & a_select2(rho, tptp_sum_index) = all_76_4 & a_select2(sigma, % 19.75/3.45 | tptp_sum_index) = all_76_8 & a_select2(mu, tptp_sum_index) = % 19.75/3.45 | all_76_12 & a_select2(x, pv10) = all_76_15 & pred(pv10) = all_76_16 & % 19.75/3.45 | leq(pv10, n135299) = 0 & leq(n0, pv10) = 0 & $i(all_76_0) & % 19.75/3.45 | $i(all_76_1) & $i(all_76_2) & $i(all_76_3) & $i(all_76_4) & % 19.75/3.45 | $i(all_76_5) & $i(all_76_6) & $i(all_76_7) & $i(all_76_8) & % 19.75/3.45 | $i(all_76_9) & $i(all_76_10) & $i(all_76_11) & $i(all_76_12) & % 19.75/3.45 | $i(all_76_13) & $i(all_76_14) & $i(all_76_15) & $i(all_76_16) & ! [v0: % 19.75/3.45 | $i] : ! [v1: $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~ % 19.75/3.45 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1) % 19.75/3.45 | = v4 & leq(v0, all_76_16) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ % 19.75/3.45 | (v3 = 0) | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] : % 19.75/3.45 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 19.75/3.45 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 19.75/3.45 | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = v1) & exp(v8) = % 19.75/3.45 | v9 & times(v9, v10) = v11 & times(v6, v6) = v7 & times(v3, v3) = v4 & % 19.75/3.45 | times(all_76_13, v6) = v12 & divide(v13, all_76_0) = v14 & % 19.75/3.45 | divide(v11, v12) = v13 & divide(v5, v7) = v8 & divide(v4, % 19.75/3.45 | tptp_minus_2) = v5 & minus(all_76_15, v2) = v3 & a_select3(q, pv10, % 19.75/3.45 | v0) = v1 & a_select2(rho, v0) = v10 & a_select2(sigma, v0) = v6 & % 19.75/3.45 | a_select2(mu, v0) = v2 & leq(v0, tptp_minus_1) = 0 & leq(n0, v0) = 0 % 19.75/3.45 | & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 19.75/3.45 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 19.75/3.45 | $i(v0)) % 19.75/3.45 | % 19.75/3.45 | ALPHA: (8) implies: % 19.75/3.45 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.75/3.45 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 19.75/3.45 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 19.75/3.45 | ( ~ (v14 = v1) & exp(v8) = v9 & times(v9, v10) = v11 & times(v6, v6) = % 19.75/3.45 | v7 & times(v3, v3) = v4 & times(all_76_13, v6) = v12 & divide(v13, % 19.75/3.45 | all_76_0) = v14 & divide(v11, v12) = v13 & divide(v5, v7) = v8 & % 19.75/3.45 | divide(v4, tptp_minus_2) = v5 & minus(all_76_15, v2) = v3 & % 19.75/3.45 | a_select3(q, pv10, v0) = v1 & a_select2(rho, v0) = v10 & % 19.75/3.45 | a_select2(sigma, v0) = v6 & a_select2(mu, v0) = v2 & leq(v0, % 19.75/3.45 | tptp_minus_1) = 0 & leq(n0, v0) = 0 & $i(v14) & $i(v13) & $i(v12) & % 19.75/3.45 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 19.75/3.45 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.75/3.45 | % 19.75/3.45 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2, % 19.75/3.45 | all_79_3, all_79_4, all_79_5, all_79_6, all_79_7, all_79_8, all_79_9, % 19.75/3.45 | all_79_10, all_79_11, all_79_12, all_79_13, all_79_14 gives: % 19.75/3.46 | (10) ~ (all_79_0 = all_79_13) & exp(all_79_6) = all_79_5 & times(all_79_5, % 19.75/3.46 | all_79_4) = all_79_3 & times(all_79_8, all_79_8) = all_79_7 & % 19.75/3.46 | times(all_79_11, all_79_11) = all_79_10 & times(all_76_13, all_79_8) = % 19.75/3.46 | all_79_2 & divide(all_79_1, all_76_0) = all_79_0 & divide(all_79_3, % 19.75/3.46 | all_79_2) = all_79_1 & divide(all_79_9, all_79_7) = all_79_6 & % 19.75/3.46 | divide(all_79_10, tptp_minus_2) = all_79_9 & minus(all_76_15, % 19.75/3.46 | all_79_12) = all_79_11 & a_select3(q, pv10, all_79_14) = all_79_13 & % 19.75/3.46 | a_select2(rho, all_79_14) = all_79_4 & a_select2(sigma, all_79_14) = % 19.75/3.46 | all_79_8 & a_select2(mu, all_79_14) = all_79_12 & leq(all_79_14, % 19.75/3.46 | tptp_minus_1) = 0 & leq(n0, all_79_14) = 0 & $i(all_79_0) & % 19.75/3.46 | $i(all_79_1) & $i(all_79_2) & $i(all_79_3) & $i(all_79_4) & % 19.75/3.46 | $i(all_79_5) & $i(all_79_6) & $i(all_79_7) & $i(all_79_8) & % 19.75/3.46 | $i(all_79_9) & $i(all_79_10) & $i(all_79_11) & $i(all_79_12) & % 19.75/3.46 | $i(all_79_13) & $i(all_79_14) % 19.75/3.46 | % 19.75/3.46 | ALPHA: (10) implies: % 19.75/3.46 | (11) $i(all_79_14) % 19.75/3.46 | (12) leq(n0, all_79_14) = 0 % 19.75/3.46 | (13) leq(all_79_14, tptp_minus_1) = 0 % 19.75/3.46 | % 19.75/3.46 | GROUND_INST: instantiating (3) with all_79_14, simplifying with (11), (12) % 19.75/3.46 | gives: % 19.75/3.46 | (14) all_79_14 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_14, n0) = % 19.75/3.46 | v0) % 19.75/3.46 | % 19.75/3.46 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 19.75/3.46 | (2), (5) gives: % 19.75/3.46 | (15) pred(n0) = tptp_minus_1 % 19.75/3.46 | % 19.75/3.46 | GROUND_INST: instantiating (1) with all_79_14, n0, tptp_minus_1, simplifying % 19.75/3.46 | with (4), (11), (13), (15) gives: % 19.75/3.46 | (16) gt(n0, all_79_14) = 0 % 19.75/3.46 | % 19.75/3.46 | GROUND_INST: instantiating (leq_gt1) with all_79_14, n0, simplifying with (4), % 19.75/3.46 | (11), (16) gives: % 19.75/3.46 | (17) leq(all_79_14, n0) = 0 % 19.75/3.46 | % 19.75/3.46 | BETA: splitting (14) gives: % 19.75/3.46 | % 19.75/3.46 | Case 1: % 19.75/3.46 | | % 19.75/3.46 | | (18) all_79_14 = n0 % 19.75/3.46 | | % 20.08/3.46 | | REDUCE: (16), (18) imply: % 20.08/3.46 | | (19) gt(n0, n0) = 0 % 20.08/3.46 | | % 20.08/3.46 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4), % 20.08/3.46 | | (19) gives: % 20.08/3.46 | | (20) $false % 20.08/3.46 | | % 20.08/3.46 | | CLOSE: (20) is inconsistent. % 20.08/3.46 | | % 20.08/3.46 | Case 2: % 20.08/3.46 | | % 20.10/3.46 | | (21) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_14, n0) = v0) % 20.10/3.46 | | % 20.10/3.46 | | DELTA: instantiating (21) with fresh symbol all_119_0 gives: % 20.10/3.46 | | (22) ~ (all_119_0 = 0) & leq(all_79_14, n0) = all_119_0 % 20.10/3.46 | | % 20.10/3.46 | | ALPHA: (22) implies: % 20.10/3.46 | | (23) ~ (all_119_0 = 0) % 20.10/3.46 | | (24) leq(all_79_14, n0) = all_119_0 % 20.10/3.46 | | % 20.10/3.46 | | GROUND_INST: instantiating (7) with 0, all_119_0, n0, all_79_14, simplifying % 20.10/3.46 | | with (17), (24) gives: % 20.10/3.46 | | (25) all_119_0 = 0 % 20.10/3.47 | | % 20.10/3.47 | | REDUCE: (23), (25) imply: % 20.10/3.47 | | (26) $false % 20.10/3.47 | | % 20.10/3.47 | | CLOSE: (26) is inconsistent. % 20.10/3.47 | | % 20.10/3.47 | End of split % 20.10/3.47 | % 20.10/3.47 End of proof % 20.10/3.47 % SZS output end Proof for theBenchmark % 20.10/3.47 % 20.10/3.47 2848ms %------------------------------------------------------------------------------