%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.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 : Fri Sep 1 00:50:54 EDT 2023 % Result : Theorem 16.29s 3.02s % Output : Proof 27.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n016.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sun Aug 27 22:18:29 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 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 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 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 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 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 % 4.53/1.52 Prover 2: Preprocessing ... % 4.53/1.52 Prover 1: Preprocessing ... % 4.53/1.52 Prover 3: Preprocessing ... % 4.53/1.52 Prover 5: Preprocessing ... % 4.53/1.53 Prover 4: Preprocessing ... % 4.53/1.53 Prover 0: Preprocessing ... % 4.53/1.55 Prover 6: Preprocessing ... % 12.41/2.53 Prover 1: Warning: ignoring some quantifiers % 12.96/2.60 Prover 4: Warning: ignoring some quantifiers % 12.96/2.60 Prover 5: Proving ... % 13.31/2.61 Prover 1: Constructing countermodel ... % 13.31/2.61 Prover 3: Warning: ignoring some quantifiers % 13.31/2.62 Prover 2: Proving ... % 13.31/2.62 Prover 6: Proving ... % 13.31/2.62 Prover 0: Proving ... % 13.31/2.63 Prover 3: Constructing countermodel ... % 13.59/2.66 Prover 4: Constructing countermodel ... % 16.18/3.02 Prover 0: proved (2372ms) % 16.18/3.02 % 16.29/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.29/3.02 % 16.29/3.02 Prover 2: stopped % 16.29/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.29/3.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.29/3.02 Prover 6: stopped % 16.29/3.03 Prover 3: stopped % 16.29/3.03 Prover 5: stopped % 16.29/3.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.29/3.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.29/3.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.30/3.28 Prover 8: Preprocessing ... % 18.30/3.30 Prover 13: Preprocessing ... % 18.30/3.30 Prover 7: Preprocessing ... % 18.50/3.31 Prover 10: Preprocessing ... % 18.50/3.32 Prover 11: Preprocessing ... % 18.63/3.56 Prover 10: Warning: ignoring some quantifiers % 18.63/3.59 Prover 7: Warning: ignoring some quantifiers % 18.63/3.61 Prover 10: Constructing countermodel ... % 20.49/3.62 Prover 7: Constructing countermodel ... % 20.49/3.63 Prover 8: Warning: ignoring some quantifiers % 20.49/3.63 Prover 13: Warning: ignoring some quantifiers % 20.49/3.65 Prover 13: Constructing countermodel ... % 20.49/3.68 Prover 8: Constructing countermodel ... % 21.32/3.74 Prover 11: Warning: ignoring some quantifiers % 21.97/3.77 Prover 11: Constructing countermodel ... % 27.00/4.45 Prover 4: Found proof (size 15) % 27.00/4.45 Prover 4: proved (3801ms) % 27.00/4.45 Prover 7: stopped % 27.00/4.45 Prover 13: stopped % 27.00/4.45 Prover 11: stopped % 27.00/4.45 Prover 10: stopped % 27.00/4.46 Prover 8: stopped % 27.00/4.46 Prover 1: stopped % 27.00/4.46 % 27.00/4.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.00/4.46 % 27.00/4.46 % SZS output start Proof for theBenchmark % 27.00/4.47 Assumptions after simplification: % 27.00/4.47 --------------------------------- % 27.00/4.47 % 27.00/4.47 (prime_coprime) % 27.20/4.48 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1, % 27.20/4.48 $difference(v0, v1))) | ~ ($lesseq(1, v1)) | ~ (coprime(v1, v0) = v2) % 27.20/4.48 | ~ (prime(v0) = 0)) & ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ % 27.20/4.48 ($lesseq(2, v0)) | ~ (prime(v0) = v1) | ? [v2: int] : ? [v3: int] : ( ~ % 27.20/4.48 (v3 = 0) & $lesseq(1, $difference(v0, v2)) & $lesseq(1, v2) & coprime(v2, % 27.20/4.48 v0) = v3)) & ! [v0: int] : ( ~ ($lesseq(v0, 1)) | ~ (prime(v0) = 0)) % 27.20/4.48 % 27.20/4.48 (wP_parameter_largest_prime_factor) % 27.20/4.50 ty(int) & ? [v0: uni] : ? [v1: int] : ? [v2: int] : ? [v3: uni] : ? [v4: % 27.20/4.50 uni] : ? [v5: list_int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 27.20/4.50 [v9: list_int] : ? [v10: uni] : ? [v11: int] : ? [v12: uni] : ? [v13: uni] % 27.20/4.50 : ? [v14: list_int] : ? [v15: int] : ? [v16: int] : ? [v17: int] : ( ~ % 27.20/4.50 (v17 = 0) & $lesseq(1, $difference(v16, v11)) & $lesseq(1, $difference(v16, % 27.20/4.50 v8)) & $lesseq(v11, v7) & $lesseq(v8, v11) & $lesseq(1, v11) & % 27.20/4.50 $lesseq(v8, v1) & $lesseq(2, v8) & $lesseq(v7, v1) & $lesseq(v2, v1) & % 27.20/4.50 $lesseq(2, v2) & t2tb1(v11) = v12 & t2tb1(v2) = v3 & tb2t(v13) = v14 & % 27.20/4.50 tb2t(v4) = v5 & t2tb(v9) = v10 & cons(int, v12, v10) = v13 & cons(int, v3, % 27.20/4.50 v0) = v4 & nil(int) = v0 & coprime(v11, v16) = v17 & prime(v16) = 0 & % 27.20/4.50 prime(v11) = 0 & prime(v8) = 0 & divides(v16, v7) = 0 & divides(v16, v1) = 0 % 27.20/4.50 & divides(v15, v7) = 0 & divides(v11, v7) = 0 & divides(v8, v1) = 0 & % 27.20/4.50 divides(v7, v7) = 0 & divides(v6, v1) = 0 & divides(v2, v1) = 0 & div(v7, % 27.20/4.50 v11) = v15 & div(v1, v2) = v6 & $product(v15, v11) = v7 & $product(v6, v2) % 27.20/4.50 = v1 & list_int(v14) & list_int(v9) & list_int(v5) & uni(v13) & uni(v12) & % 27.20/4.50 uni(v10) & uni(v4) & uni(v3) & uni(v0) & ! [v18: int] : ! [v19: int] : % 27.20/4.50 (v19 = 0 | ~ ($lesseq(1, $difference(v18, v8))) | ~ (divides(v18, v7) = % 27.20/4.50 v19) | ? [v20: any] : ? [v21: any] : (prime(v18) = v20 & divides(v18, % 27.20/4.50 v1) = v21 & ( ~ (v21 = 0) | ~ (v20 = 0)))) & ! [v18: int] : ! [v19: % 27.20/4.50 int] : (v19 = 0 | ~ ($lesseq(2, v18)) | ~ (divides(v18, v1) = v19) | ? % 27.20/4.50 [v20: int] : ( ~ (v20 = 0) & divides(v18, v7) = v20)) & ! [v18: int] : ! % 27.20/4.50 [v19: MultipleValueBool] : ( ~ ($lesseq(1, $difference(v8, v18))) | ~ % 27.20/4.50 ($lesseq(2, v18)) | ~ (divides(v18, v1) = v19) | ? [v20: int] : ( ~ (v20 % 27.20/4.50 = 0) & divides(v18, v7) = v20)) & ! [v18: int] : ! [v19: any] : ( ~ % 27.20/4.50 ($lesseq(1, $difference(v18, v2))) | ~ (coprime(v2, v18) = v19) | ? % 27.20/4.50 [v20: any] : ? [v21: any] : ? [v22: any] : (prime(v18) = v20 & % 27.20/4.50 divides(v18, v6) = v22 & divides(v18, v1) = v21 & ( ~ (v21 = 0) | ~ % 27.20/4.50 (v20 = 0) | (v22 = 0 & v19 = 0)))) & ! [v18: int] : ! [v19: any] : ( % 27.20/4.50 ~ ($lesseq(1, $difference(v18, v2))) | ~ (divides(v18, v6) = v19) | ? % 27.20/4.50 [v20: any] : ? [v21: any] : ? [v22: any] : (coprime(v2, v18) = v22 & % 27.20/4.50 prime(v18) = v20 & divides(v18, v1) = v21 & ( ~ (v21 = 0) | ~ (v20 = 0) % 27.20/4.50 | (v22 = 0 & v19 = 0)))) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.50 $difference(v11, v18))) | ~ ($lesseq(2, v18)) | ~ (divides(v18, v7) % 27.20/4.50 = 0)) & ! [v18: int] : ( ~ ($lesseq(1, $difference(v8, v18))) | ~ % 27.20/4.50 ($lesseq(2, v18)) | ~ (divides(v18, v7) = 0)) & ! [v18: int] : ( ~ % 27.20/4.50 ($lesseq(1, $difference(v2, v18))) | ~ ($lesseq(2, v18)) | ~ % 27.20/4.50 (divides(v18, v1) = 0)) & ! [v18: int] : ( ~ ($lesseq(1, $difference(v18, % 27.20/4.50 v8))) | ~ (prime(v18) = 0) | ? [v19: any] : ? [v20: any] : % 27.20/4.50 (divides(v18, v7) = v20 & divides(v18, v1) = v19 & ( ~ (v19 = 0) | v20 = % 27.20/4.50 0))) & ! [v18: int] : ( ~ ($lesseq(1, $difference(v18, v8))) | ~ % 27.20/4.50 (divides(v18, v1) = 0) | ? [v19: any] : ? [v20: any] : (prime(v18) = v19 % 27.20/4.50 & divides(v18, v7) = v20 & ( ~ (v19 = 0) | v20 = 0))) & ! [v18: int] : % 27.20/4.50 ( ~ ($lesseq(1, $difference(v18, v2))) | ~ (prime(v18) = 0) | ? [v19: any] % 27.20/4.50 : ? [v20: any] : ? [v21: any] : (coprime(v2, v18) = v20 & divides(v18, % 27.20/4.50 v6) = v21 & divides(v18, v1) = v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = % 27.20/4.50 0)))) & ! [v18: int] : ( ~ ($lesseq(1, $difference(v18, v2))) | ~ % 27.20/4.50 (divides(v18, v1) = 0) | ? [v19: any] : ? [v20: any] : ? [v21: any] : % 27.20/4.50 (coprime(v2, v18) = v20 & prime(v18) = v19 & divides(v18, v6) = v21 & ( ~ % 27.20/4.50 (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! [v18: int] : ( ~ ($lesseq(2, % 27.20/4.50 v18)) | ~ (divides(v18, v7) = 0) | divides(v18, v1) = 0)) % 27.20/4.50 % 27.20/4.50 Further assumptions not needed in the proof: % 27.20/4.50 -------------------------------------------- % 27.20/4.50 abs_def, abs_le, abs_pos, assoc, bool_inversion, bridgeL, bridgeL1, bridgeR, % 27.20/4.50 bridgeR1, comm, compatOrderMult, cons_proj_1_def, cons_proj_1_sort, % 27.20/4.50 cons_proj_2_def, cons_proj_2_sort, cons_sort, contents_def, contents_sort, % 27.20/4.50 coprime_def, div_1, div_bound, div_inf, div_mod, div_mult, div_mult1, % 27.20/4.50 div_sign_neg, div_sign_pos, divides_0, divides_1_n, divides_antisym, % 27.20/4.50 divides_bounds, divides_def, divides_factorl, divides_factorr, divides_left, % 27.20/4.50 divides_minusr, divides_mod_computer, divides_mod_euclidean, divides_multl, % 27.20/4.50 divides_multr, divides_n_1, divides_oppl, divides_oppl_rev, divides_oppr, % 27.20/4.50 divides_oppr_rev, divides_plusr, divides_refl, divides_right, divides_trans, % 27.20/4.50 euclid, even_2k, even_def, even_divides, even_even, even_not_odd, even_odd, % 27.20/4.50 even_or_odd, even_prime, gauss, gcd_0_neg, gcd_0_pos, gcd_computer_mod, % 27.20/4.50 gcd_coprime, gcd_def1, gcd_def2, gcd_def3, gcd_euclid, gcd_euclidean_mod, % 27.20/4.50 gcd_mult, gcd_nonneg, gcd_opp, gcd_unique, list_inversion, match_bool_False, % 27.20/4.50 match_bool_True, match_bool_sort, match_list_Cons, match_list_Nil, % 27.20/4.50 match_list_sort, mk_ref_sort, mod_1, mod_bound, mod_divides_computer, % 27.20/4.50 mod_divides_euclidean, mod_inf, mod_mult, mod_mult1, mod_sign_neg, mod_sign_pos, % 27.20/4.50 nil_Cons, nil_sort, not_prime_1, odd_2k1, odd_def, odd_divides, odd_even, % 27.20/4.50 odd_not_even, odd_odd, odd_prime, prime_2, prime_3, prime_def, prime_divisors, % 27.20/4.50 ref_inversion, rounds_toward_zero, small_divisors, t2tb_sort, t2tb_sort1, % 27.20/4.50 true_False, tuple0_inversion, witness_sort % 27.20/4.50 % 27.20/4.50 Those formulas are unsatisfiable: % 27.20/4.50 --------------------------------- % 27.20/4.50 % 27.20/4.50 Begin of proof % 27.20/4.50 | % 27.20/4.51 | ALPHA: (prime_coprime) implies: % 27.20/4.51 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1, % 27.20/4.51 | $difference(v0, v1))) | ~ ($lesseq(1, v1)) | ~ (coprime(v1, v0) % 27.20/4.51 | = v2) | ~ (prime(v0) = 0)) % 27.20/4.51 | % 27.20/4.51 | ALPHA: (wP_parameter_largest_prime_factor) implies: % 27.20/4.52 | (2) ? [v0: uni] : ? [v1: int] : ? [v2: int] : ? [v3: uni] : ? [v4: % 27.20/4.52 | uni] : ? [v5: list_int] : ? [v6: int] : ? [v7: int] : ? [v8: int] % 27.20/4.52 | : ? [v9: list_int] : ? [v10: uni] : ? [v11: int] : ? [v12: uni] : % 27.20/4.52 | ? [v13: uni] : ? [v14: list_int] : ? [v15: int] : ? [v16: int] : ? % 27.20/4.52 | [v17: int] : ( ~ (v17 = 0) & $lesseq(1, $difference(v16, v11)) & % 27.20/4.52 | $lesseq(1, $difference(v16, v8)) & $lesseq(v11, v7) & $lesseq(v8, % 27.20/4.52 | v11) & $lesseq(1, v11) & $lesseq(v8, v1) & $lesseq(2, v8) & % 27.20/4.52 | $lesseq(v7, v1) & $lesseq(v2, v1) & $lesseq(2, v2) & t2tb1(v11) = v12 % 27.20/4.52 | & t2tb1(v2) = v3 & tb2t(v13) = v14 & tb2t(v4) = v5 & t2tb(v9) = v10 & % 27.20/4.52 | cons(int, v12, v10) = v13 & cons(int, v3, v0) = v4 & nil(int) = v0 & % 27.20/4.52 | coprime(v11, v16) = v17 & prime(v16) = 0 & prime(v11) = 0 & prime(v8) % 27.20/4.52 | = 0 & divides(v16, v7) = 0 & divides(v16, v1) = 0 & divides(v15, v7) % 27.20/4.52 | = 0 & divides(v11, v7) = 0 & divides(v8, v1) = 0 & divides(v7, v7) = % 27.20/4.52 | 0 & divides(v6, v1) = 0 & divides(v2, v1) = 0 & div(v7, v11) = v15 & % 27.20/4.52 | div(v1, v2) = v6 & $product(v15, v11) = v7 & $product(v6, v2) = v1 & % 27.20/4.52 | list_int(v14) & list_int(v9) & list_int(v5) & uni(v13) & uni(v12) & % 27.20/4.52 | uni(v10) & uni(v4) & uni(v3) & uni(v0) & ! [v18: int] : ! [v19: % 27.20/4.52 | int] : (v19 = 0 | ~ ($lesseq(1, $difference(v18, v8))) | ~ % 27.20/4.52 | (divides(v18, v7) = v19) | ? [v20: any] : ? [v21: any] : % 27.20/4.52 | (prime(v18) = v20 & divides(v18, v1) = v21 & ( ~ (v21 = 0) | ~ % 27.20/4.52 | (v20 = 0)))) & ! [v18: int] : ! [v19: int] : (v19 = 0 | ~ % 27.20/4.52 | ($lesseq(2, v18)) | ~ (divides(v18, v1) = v19) | ? [v20: int] : ( % 27.20/4.52 | ~ (v20 = 0) & divides(v18, v7) = v20)) & ! [v18: int] : ! [v19: % 27.20/4.52 | MultipleValueBool] : ( ~ ($lesseq(1, $difference(v8, v18))) | ~ % 27.20/4.52 | ($lesseq(2, v18)) | ~ (divides(v18, v1) = v19) | ? [v20: int] : ( % 27.20/4.52 | ~ (v20 = 0) & divides(v18, v7) = v20)) & ! [v18: int] : ! [v19: % 27.20/4.52 | any] : ( ~ ($lesseq(1, $difference(v18, v2))) | ~ (coprime(v2, % 27.20/4.52 | v18) = v19) | ? [v20: any] : ? [v21: any] : ? [v22: any] : % 27.20/4.52 | (prime(v18) = v20 & divides(v18, v6) = v22 & divides(v18, v1) = v21 % 27.20/4.52 | & ( ~ (v21 = 0) | ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & ! % 27.20/4.52 | [v18: int] : ! [v19: any] : ( ~ ($lesseq(1, $difference(v18, v2))) | % 27.20/4.52 | ~ (divides(v18, v6) = v19) | ? [v20: any] : ? [v21: any] : ? % 27.20/4.52 | [v22: any] : (coprime(v2, v18) = v22 & prime(v18) = v20 & % 27.20/4.52 | divides(v18, v1) = v21 & ( ~ (v21 = 0) | ~ (v20 = 0) | (v22 = 0 % 27.20/4.52 | & v19 = 0)))) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v11, v18))) | ~ ($lesseq(2, v18)) | ~ % 27.20/4.52 | (divides(v18, v7) = 0)) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v8, v18))) | ~ ($lesseq(2, v18)) | ~ % 27.20/4.52 | (divides(v18, v7) = 0)) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v2, v18))) | ~ ($lesseq(2, v18)) | ~ % 27.20/4.52 | (divides(v18, v1) = 0)) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v18, v8))) | ~ (prime(v18) = 0) | ? [v19: any] : % 27.20/4.52 | ? [v20: any] : (divides(v18, v7) = v20 & divides(v18, v1) = v19 & ( % 27.20/4.52 | ~ (v19 = 0) | v20 = 0))) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v18, v8))) | ~ (divides(v18, v1) = 0) | ? [v19: % 27.20/4.52 | any] : ? [v20: any] : (prime(v18) = v19 & divides(v18, v7) = v20 % 27.20/4.52 | & ( ~ (v19 = 0) | v20 = 0))) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v18, v2))) | ~ (prime(v18) = 0) | ? [v19: any] : % 27.20/4.52 | ? [v20: any] : ? [v21: any] : (coprime(v2, v18) = v20 & % 27.20/4.52 | divides(v18, v6) = v21 & divides(v18, v1) = v19 & ( ~ (v19 = 0) | % 27.20/4.52 | (v21 = 0 & v20 = 0)))) & ! [v18: int] : ( ~ ($lesseq(1, % 27.20/4.52 | $difference(v18, v2))) | ~ (divides(v18, v1) = 0) | ? [v19: % 27.20/4.52 | any] : ? [v20: any] : ? [v21: any] : (coprime(v2, v18) = v20 & % 27.20/4.52 | prime(v18) = v19 & divides(v18, v6) = v21 & ( ~ (v19 = 0) | (v21 % 27.20/4.52 | = 0 & v20 = 0)))) & ! [v18: int] : ( ~ ($lesseq(2, v18)) | % 27.20/4.52 | ~ (divides(v18, v7) = 0) | divides(v18, v1) = 0)) % 27.20/4.52 | % 27.20/4.52 | DELTA: instantiating (2) with fresh symbols all_146_0, all_146_1, all_146_2, % 27.20/4.52 | all_146_3, all_146_4, all_146_5, all_146_6, all_146_7, all_146_8, % 27.20/4.52 | all_146_9, all_146_10, all_146_11, all_146_12, all_146_13, all_146_14, % 27.20/4.52 | all_146_15, all_146_16, all_146_17 gives: % 27.20/4.53 | (3) ~ (all_146_0 = 0) & $lesseq(1, $difference(all_146_1, all_146_6)) & % 27.20/4.53 | $lesseq(1, $difference(all_146_1, all_146_9)) & $lesseq(all_146_6, % 27.20/4.53 | all_146_10) & $lesseq(all_146_9, all_146_6) & $lesseq(1, all_146_6) & % 27.20/4.53 | $lesseq(all_146_9, all_146_16) & $lesseq(2, all_146_9) & % 27.20/4.53 | $lesseq(all_146_10, all_146_16) & $lesseq(all_146_15, all_146_16) & % 27.20/4.53 | $lesseq(2, all_146_15) & t2tb1(all_146_6) = all_146_5 & % 27.20/4.53 | t2tb1(all_146_15) = all_146_14 & tb2t(all_146_4) = all_146_3 & % 27.20/4.53 | tb2t(all_146_13) = all_146_12 & t2tb(all_146_8) = all_146_7 & cons(int, % 27.20/4.53 | all_146_5, all_146_7) = all_146_4 & cons(int, all_146_14, all_146_17) % 27.20/4.53 | = all_146_13 & nil(int) = all_146_17 & coprime(all_146_6, all_146_1) = % 27.20/4.53 | all_146_0 & prime(all_146_1) = 0 & prime(all_146_6) = 0 & % 27.20/4.53 | prime(all_146_9) = 0 & divides(all_146_1, all_146_10) = 0 & % 27.20/4.53 | divides(all_146_1, all_146_16) = 0 & divides(all_146_2, all_146_10) = 0 % 27.20/4.53 | & divides(all_146_6, all_146_10) = 0 & divides(all_146_9, all_146_16) = % 27.20/4.53 | 0 & divides(all_146_10, all_146_10) = 0 & divides(all_146_11, % 27.20/4.53 | all_146_16) = 0 & divides(all_146_15, all_146_16) = 0 & % 27.20/4.53 | div(all_146_10, all_146_6) = all_146_2 & div(all_146_16, all_146_15) = % 27.20/4.53 | all_146_11 & $product(all_146_2, all_146_6) = all_146_10 & % 27.20/4.53 | $product(all_146_11, all_146_15) = all_146_16 & list_int(all_146_3) & % 27.20/4.53 | list_int(all_146_8) & list_int(all_146_12) & uni(all_146_4) & % 27.20/4.53 | uni(all_146_5) & uni(all_146_7) & uni(all_146_13) & uni(all_146_14) & % 27.20/4.53 | uni(all_146_17) & ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ % 27.20/4.53 | ($lesseq(1, $difference(v0, all_146_9))) | ~ (divides(v0, % 27.20/4.53 | all_146_10) = v1) | ? [v2: any] : ? [v3: any] : (prime(v0) = v2 % 27.20/4.53 | & divides(v0, all_146_16) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! % 27.20/4.53 | [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(2, v0)) | ~ % 27.20/4.53 | (divides(v0, all_146_16) = v1) | ? [v2: int] : ( ~ (v2 = 0) & % 27.20/4.53 | divides(v0, all_146_10) = v2)) & ! [v0: int] : ! [v1: % 27.20/4.53 | MultipleValueBool] : ( ~ ($lesseq(1, $difference(all_146_9, v0))) | % 27.20/4.53 | ~ ($lesseq(2, v0)) | ~ (divides(v0, all_146_16) = v1) | ? [v2: int] % 27.20/4.53 | : ( ~ (v2 = 0) & divides(v0, all_146_10) = v2)) & ! [v0: int] : ! % 27.20/4.53 | [v1: any] : ( ~ ($lesseq(1, $difference(v0, all_146_15))) | ~ % 27.20/4.53 | (coprime(all_146_15, v0) = v1) | ? [v2: any] : ? [v3: any] : ? % 27.20/4.53 | [v4: any] : (prime(v0) = v2 & divides(v0, all_146_11) = v4 & % 27.20/4.53 | divides(v0, all_146_16) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v4 = 0 % 27.20/4.53 | & v1 = 0)))) & ! [v0: int] : ! [v1: any] : ( ~ ($lesseq(1, % 27.20/4.53 | $difference(v0, all_146_15))) | ~ (divides(v0, all_146_11) = v1) % 27.20/4.53 | | ? [v2: any] : ? [v3: any] : ? [v4: any] : (coprime(all_146_15, % 27.20/4.53 | v0) = v4 & prime(v0) = v2 & divides(v0, all_146_16) = v3 & ( ~ % 27.20/4.53 | (v3 = 0) | ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: int] : ( % 27.20/4.53 | ~ ($lesseq(1, $difference(all_146_6, v0))) | ~ ($lesseq(2, v0)) | ~ % 27.20/4.53 | (divides(v0, all_146_10) = 0)) & ! [v0: int] : ( ~ ($lesseq(1, % 27.20/4.53 | $difference(all_146_9, v0))) | ~ ($lesseq(2, v0)) | ~ % 27.20/4.53 | (divides(v0, all_146_10) = 0)) & ! [v0: int] : ( ~ ($lesseq(1, % 27.20/4.53 | $difference(all_146_15, v0))) | ~ ($lesseq(2, v0)) | ~ % 27.20/4.53 | (divides(v0, all_146_16) = 0)) & ! [v0: int] : ( ~ ($lesseq(1, % 27.20/4.53 | $difference(v0, all_146_9))) | ~ (prime(v0) = 0) | ? [v1: any] % 27.20/4.53 | : ? [v2: any] : (divides(v0, all_146_10) = v2 & divides(v0, % 27.20/4.53 | all_146_16) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: int] : ( ~ % 27.20/4.53 | ($lesseq(1, $difference(v0, all_146_9))) | ~ (divides(v0, % 27.20/4.53 | all_146_16) = 0) | ? [v1: any] : ? [v2: any] : (prime(v0) = v1 % 27.20/4.53 | & divides(v0, all_146_10) = v2 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: % 27.20/4.53 | int] : ( ~ ($lesseq(1, $difference(v0, all_146_15))) | ~ (prime(v0) % 27.20/4.53 | = 0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 27.20/4.53 | (coprime(all_146_15, v0) = v2 & divides(v0, all_146_11) = v3 & % 27.20/4.53 | divides(v0, all_146_16) = v1 & ( ~ (v1 = 0) | (v3 = 0 & v2 = 0)))) % 27.20/4.53 | & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_146_15))) | ~ % 27.20/4.53 | (divides(v0, all_146_16) = 0) | ? [v1: any] : ? [v2: any] : ? [v3: % 27.20/4.53 | any] : (coprime(all_146_15, v0) = v2 & prime(v0) = v1 & divides(v0, % 27.20/4.53 | all_146_11) = v3 & ( ~ (v1 = 0) | (v3 = 0 & v2 = 0)))) & ! [v0: % 27.20/4.53 | int] : ( ~ ($lesseq(2, v0)) | ~ (divides(v0, all_146_10) = 0) | % 27.20/4.53 | divides(v0, all_146_16) = 0) % 27.20/4.53 | % 27.20/4.53 | ALPHA: (3) implies: % 27.20/4.53 | (4) ~ (all_146_0 = 0) % 27.20/4.53 | (5) $lesseq(1, all_146_6) % 27.20/4.53 | (6) $lesseq(1, $difference(all_146_1, all_146_6)) % 27.20/4.53 | (7) prime(all_146_1) = 0 % 27.20/4.53 | (8) coprime(all_146_6, all_146_1) = all_146_0 % 27.20/4.53 | % 27.20/4.53 | GROUND_INST: instantiating (1) with all_146_1, all_146_6, all_146_0, % 27.20/4.53 | simplifying with (7), (8) gives: % 27.20/4.53 | (9) all_146_0 = 0 | ~ ($lesseq(1, $difference(all_146_1, all_146_6))) | ~ % 27.20/4.53 | ($lesseq(1, all_146_6)) % 27.20/4.53 | % 27.20/4.53 | BETA: splitting (9) gives: % 27.20/4.53 | % 27.20/4.53 | Case 1: % 27.20/4.53 | | % 27.47/4.53 | | (10) $lesseq(all_146_6, 0) % 27.47/4.53 | | % 27.47/4.53 | | COMBINE_INEQS: (5), (10) imply: % 27.47/4.53 | | (11) $false % 27.47/4.54 | | % 27.47/4.54 | | CLOSE: (11) is inconsistent. % 27.47/4.54 | | % 27.47/4.54 | Case 2: % 27.47/4.54 | | % 27.47/4.54 | | (12) all_146_0 = 0 | ~ ($lesseq(1, $difference(all_146_1, all_146_6))) % 27.47/4.54 | | % 27.47/4.54 | | BETA: splitting (12) gives: % 27.47/4.54 | | % 27.47/4.54 | | Case 1: % 27.47/4.54 | | | % 27.47/4.54 | | | (13) $lesseq(all_146_1, all_146_6) % 27.47/4.54 | | | % 27.47/4.54 | | | COMBINE_INEQS: (6), (13) imply: % 27.47/4.54 | | | (14) $false % 27.47/4.54 | | | % 27.47/4.54 | | | CLOSE: (14) is inconsistent. % 27.47/4.54 | | | % 27.47/4.54 | | Case 2: % 27.47/4.54 | | | % 27.47/4.54 | | | (15) all_146_0 = 0 % 27.47/4.54 | | | % 27.47/4.54 | | | REDUCE: (4), (15) imply: % 27.47/4.54 | | | (16) $false % 27.47/4.54 | | | % 27.47/4.54 | | | CLOSE: (16) is inconsistent. % 27.47/4.54 | | | % 27.47/4.54 | | End of split % 27.47/4.54 | | % 27.47/4.54 | End of split % 27.47/4.54 | % 27.47/4.54 End of proof % 27.47/4.54 % SZS output end Proof for theBenchmark % 27.47/4.54 % 27.47/4.54 3907ms %------------------------------------------------------------------------------