%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC474_1 : TPTP v8.3.0. Released v8.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 : Tue May 14 09:00:32 EDT 2024 % Result : Theorem 12.25s 2.56s % Output : Proof 13.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SWC474_1 : TPTP v8.3.0. Released v8.3.0. % 0.04/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Mon May 13 14:58:23 EDT 2024 % 0.13/0.35 % CPUTime : % 0.69/0.69 ________ _____ % 0.69/0.69 ___ __ \_________(_)________________________________ % 0.69/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.69/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.69/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.69/0.69 % 0.69/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.69/0.69 (2023-06-19) % 0.69/0.69 % 0.69/0.69 (c) Philipp Rümmer, 2009-2023 % 0.69/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.69/0.69 Amanda Stjerna. % 0.69/0.69 Free software under BSD-3-Clause. % 0.69/0.69 % 0.69/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.69/0.69 % 0.69/0.70 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.71 Running up to 7 provers in parallel. % 0.78/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.78/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.78/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.78/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.78/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.78/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.78/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.40/1.22 Prover 5: Preprocessing ... % 2.40/1.22 Prover 4: Preprocessing ... % 2.40/1.22 Prover 6: Preprocessing ... % 2.40/1.22 Prover 3: Preprocessing ... % 2.40/1.22 Prover 2: Preprocessing ... % 2.40/1.22 Prover 1: Preprocessing ... % 2.40/1.22 Prover 0: Preprocessing ... % 3.50/1.44 Prover 6: Constructing countermodel ... % 3.50/1.44 Prover 3: Constructing countermodel ... % 4.18/1.44 Prover 1: Constructing countermodel ... % 4.18/1.44 Prover 0: Proving ... % 4.18/1.45 Prover 4: Constructing countermodel ... % 4.18/1.48 Prover 5: Proving ... % 4.18/1.49 Prover 2: Proving ... % 4.58/1.54 Prover 1: gave up % 4.58/1.54 Prover 3: gave up % 4.58/1.54 Prover 6: gave up % 4.58/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.58/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.58/1.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.08/1.57 Prover 8: Preprocessing ... % 5.08/1.57 Prover 9: Preprocessing ... % 5.08/1.57 Prover 7: Preprocessing ... % 5.45/1.63 Prover 8: Warning: ignoring some quantifiers % 5.45/1.63 Prover 8: Constructing countermodel ... % 5.45/1.65 Prover 9: Constructing countermodel ... % 5.45/1.65 Prover 7: Constructing countermodel ... % 12.25/2.56 Prover 9: proved (1024ms) % 12.25/2.56 % 12.25/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.25/2.56 % 12.64/2.57 Prover 2: stopped % 12.64/2.57 Prover 5: proved (1836ms) % 12.64/2.57 % 12.64/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.64/2.57 % 12.64/2.57 Prover 0: proved (1847ms) % 12.64/2.57 % 12.64/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.64/2.58 % 12.64/2.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.64/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.64/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.64/2.59 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.64/2.62 Prover 10: Preprocessing ... % 12.64/2.62 Prover 11: Preprocessing ... % 12.64/2.63 Prover 13: Preprocessing ... % 12.64/2.63 Prover 16: Preprocessing ... % 13.26/2.66 Prover 7: Found proof (size 53) % 13.26/2.66 Prover 7: proved (1121ms) % 13.26/2.66 Prover 10: stopped % 13.26/2.66 Prover 4: Found proof (size 53) % 13.26/2.66 Prover 4: proved (1928ms) % 13.26/2.66 Prover 16: stopped % 13.26/2.66 Prover 8: stopped % 13.26/2.67 Prover 13: stopped % 13.45/2.68 Prover 11: Constructing countermodel ... % 13.45/2.69 Prover 11: stopped % 13.45/2.69 % 13.45/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.45/2.69 % 13.45/2.70 % SZS output start Proof for theBenchmark % 13.45/2.71 Assumptions after simplification: % 13.45/2.71 --------------------------------- % 13.45/2.71 % 13.45/2.71 (conjecture_1) % 13.45/2.72 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 13.45/2.72 fast(v0) = v2 & small(v0) = v1) % 13.45/2.72 % 13.45/2.72 (formula_1) % 13.45/2.72 ! [v0: int] : ! [v1: int] : ( ~ (f0(v0) = v1) | ? [v2: int] : ($product(v2, % 13.45/2.72 v0) = v1 & $product(v0, v0) = v2)) % 13.45/2.72 % 13.45/2.72 (formula_10) % 13.45/2.73 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 13.45/2.73 ~ (u1(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 13.45/2.73 ($lesseq(1, v0)) | ~ (u1($sum(v0, -1), v1) = v2) | ? [v3: int] : (u1(v0, % 13.45/2.73 v1) = v3 & f1(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 13.45/2.73 : ( ~ ($lesseq(1, v0)) | ~ (u1(v0, v1) = v2) | ? [v3: int] : (u1($sum(v0, % 13.45/2.73 -1), v1) = v3 & f1(v3) = v2)) % 13.45/2.73 % 13.45/2.73 (formula_11) % 13.45/2.73 ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) | ? [v2: int] : (u1(g1, v2) = % 13.45/2.73 v1 & h1(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h1(v0) = v1) | ? % 13.45/2.73 [v2: int] : (v1(v0) = v2 & u1(g1, v1) = v2)) % 13.45/2.73 % 13.45/2.73 (formula_12) % 13.45/2.73 ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | ? [v2: int] : (v1(v0) = % 13.45/2.73 v2 & $product(v2, v0) = $difference(v1, v0))) & ! [v0: int] : ! [v1: % 13.45/2.73 int] : ( ~ (v1(v0) = v1) | ? [v2: int] : (fast(v0) = v2 & $product(v1, v0) % 13.45/2.73 = $difference(v2, v0))) % 13.45/2.73 % 13.45/2.73 (formula_2) % 13.45/2.73 g0 = 2 % 13.45/2.73 % 13.45/2.73 (formula_3) % 13.45/2.73 ! [v0: int] : ! [v1: int] : (v1 = v0 | ~ (h0(v0) = v1)) % 13.45/2.73 % 13.45/2.73 (formula_4) % 13.45/2.74 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 13.45/2.74 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 13.45/2.74 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 13.45/2.74 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 13.45/2.74 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 13.45/2.74 -1), v1) = v3 & f0(v3) = v2)) % 13.45/2.74 % 13.45/2.74 (formula_5) % 13.45/2.74 ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : (u0(g0, v2) = % 13.45/2.74 v1 & h0(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h0(v0) = v1) | ? % 13.45/2.74 [v2: int] : (v0(v0) = v2 & u0(g0, v1) = v2)) % 13.45/2.74 % 13.45/2.74 (formula_6) % 13.74/2.74 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : (v0(v0) = % 13.74/2.74 v2 & $product(v2, v0) = $difference(v1, v0))) & ! [v0: int] : ! [v1: % 13.74/2.74 int] : ( ~ (v0(v0) = v1) | ? [v2: int] : (small(v0) = v2 & $product(v1, v0) % 13.74/2.74 = $difference(v2, v0))) % 13.74/2.74 % 13.74/2.74 (formula_7) % 13.74/2.74 ! [v0: int] : ! [v1: int] : ( ~ (f1(v0) = v1) | ? [v2: int] : ($product(v2, % 13.74/2.74 v0) = v1 & $product(v0, v0) = v2)) % 13.74/2.74 % 13.74/2.74 (formula_8) % 13.74/2.74 g1 = 1 % 13.74/2.74 % 13.74/2.74 (formula_9) % 13.74/2.74 ! [v0: int] : ! [v1: int] : ( ~ (h1(v0) = v1) | ? [v2: int] : ($product(v2, % 13.74/2.74 v0) = v1 & $product(v0, v0) = v2)) % 13.74/2.74 % 13.74/2.74 Those formulas are unsatisfiable: % 13.74/2.74 --------------------------------- % 13.74/2.74 % 13.74/2.74 Begin of proof % 13.74/2.74 | % 13.74/2.74 | ALPHA: (formula_4) implies: % 13.74/2.74 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 13.74/2.74 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 13.74/2.74 | f0(v3) = v2)) % 13.74/2.75 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 13.74/2.75 | 0) | ~ (u0(v0, v1) = v2)) % 13.74/2.75 | % 13.74/2.75 | ALPHA: (formula_5) implies: % 13.74/2.75 | (3) ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : % 13.74/2.75 | (u0(g0, v2) = v1 & h0(v0) = v2)) % 13.74/2.75 | % 13.74/2.75 | ALPHA: (formula_6) implies: % 13.74/2.75 | (4) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : % 13.74/2.75 | (v0(v0) = v2 & $product(v2, v0) = $difference(v1, v0))) % 13.74/2.75 | % 13.74/2.75 | ALPHA: (formula_10) implies: % 13.74/2.75 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 13.74/2.75 | (u1(v0, v1) = v2) | ? [v3: int] : (u1($sum(v0, -1), v1) = v3 & % 13.74/2.75 | f1(v3) = v2)) % 13.74/2.75 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 13.74/2.75 | 0) | ~ (u1(v0, v1) = v2)) % 13.74/2.75 | % 13.74/2.75 | ALPHA: (formula_11) implies: % 13.74/2.75 | (7) ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) | ? [v2: int] : % 13.74/2.75 | (u1(g1, v2) = v1 & h1(v0) = v2)) % 13.74/2.75 | % 13.74/2.75 | ALPHA: (formula_12) implies: % 13.74/2.75 | (8) ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | ? [v2: int] : % 13.74/2.75 | (v1(v0) = v2 & $product(v2, v0) = $difference(v1, v0))) % 13.74/2.75 | % 13.74/2.75 | DELTA: instantiating (conjecture_1) with fresh symbols all_14_0, all_14_1, % 13.74/2.75 | all_14_2 gives: % 13.74/2.75 | (9) ~ (all_14_0 = all_14_1) & $lesseq(0, all_14_2) & fast(all_14_2) = % 13.74/2.75 | all_14_0 & small(all_14_2) = all_14_1 % 13.74/2.75 | % 13.74/2.75 | ALPHA: (9) implies: % 13.74/2.75 | (10) ~ (all_14_0 = all_14_1) % 13.74/2.75 | (11) small(all_14_2) = all_14_1 % 13.74/2.75 | (12) fast(all_14_2) = all_14_0 % 13.74/2.75 | % 13.74/2.75 | GROUND_INST: instantiating (4) with all_14_2, all_14_1, simplifying with (11) % 13.74/2.75 | gives: % 13.74/2.75 | (13) ? [v0: int] : (v0(all_14_2) = v0 & $product(v0, all_14_2) = % 13.74/2.75 | $difference(all_14_1, all_14_2)) % 13.74/2.75 | % 13.74/2.75 | GROUND_INST: instantiating (8) with all_14_2, all_14_0, simplifying with (12) % 13.74/2.75 | gives: % 13.74/2.75 | (14) ? [v0: int] : (v1(all_14_2) = v0 & $product(v0, all_14_2) = % 13.74/2.75 | $difference(all_14_0, all_14_2)) % 13.74/2.75 | % 13.74/2.75 | DELTA: instantiating (14) with fresh symbol all_24_0 gives: % 13.74/2.75 | (15) v1(all_14_2) = all_24_0 & $product(all_24_0, all_14_2) = % 13.74/2.75 | $difference(all_14_0, all_14_2) % 13.74/2.75 | % 13.74/2.75 | ALPHA: (15) implies: % 13.74/2.75 | (16) $product(all_24_0, all_14_2) = $difference(all_14_0, all_14_2) % 13.74/2.75 | (17) v1(all_14_2) = all_24_0 % 13.74/2.75 | % 13.74/2.75 | DELTA: instantiating (13) with fresh symbol all_26_0 gives: % 13.74/2.76 | (18) v0(all_14_2) = all_26_0 & $product(all_26_0, all_14_2) = % 13.74/2.76 | $difference(all_14_1, all_14_2) % 13.74/2.76 | % 13.74/2.76 | ALPHA: (18) implies: % 13.74/2.76 | (19) $product(all_26_0, all_14_2) = $difference(all_14_1, all_14_2) % 13.74/2.76 | (20) v0(all_14_2) = all_26_0 % 13.74/2.76 | % 13.74/2.76 | GROUND_INST: instantiating (3) with all_14_2, all_26_0, simplifying with (20) % 13.74/2.76 | gives: % 13.83/2.76 | (21) ? [v0: int] : (u0(g0, v0) = all_26_0 & h0(all_14_2) = v0) % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (7) with all_14_2, all_24_0, simplifying with (17) % 13.83/2.76 | gives: % 13.83/2.76 | (22) ? [v0: int] : (u1(g1, v0) = all_24_0 & h1(all_14_2) = v0) % 13.83/2.76 | % 13.83/2.76 | DELTA: instantiating (22) with fresh symbol all_35_0 gives: % 13.83/2.76 | (23) u1(g1, all_35_0) = all_24_0 & h1(all_14_2) = all_35_0 % 13.83/2.76 | % 13.83/2.76 | ALPHA: (23) implies: % 13.83/2.76 | (24) h1(all_14_2) = all_35_0 % 13.83/2.76 | (25) u1(g1, all_35_0) = all_24_0 % 13.83/2.76 | % 13.83/2.76 | DELTA: instantiating (21) with fresh symbol all_37_0 gives: % 13.83/2.76 | (26) u0(g0, all_37_0) = all_26_0 & h0(all_14_2) = all_37_0 % 13.83/2.76 | % 13.83/2.76 | ALPHA: (26) implies: % 13.83/2.76 | (27) h0(all_14_2) = all_37_0 % 13.83/2.76 | (28) u0(g0, all_37_0) = all_26_0 % 13.83/2.76 | % 13.83/2.76 | REDUCE: (25), (formula_8) imply: % 13.83/2.76 | (29) u1(1, all_35_0) = all_24_0 % 13.83/2.76 | % 13.83/2.76 | REDUCE: (28), (formula_2) imply: % 13.83/2.76 | (30) u0(2, all_37_0) = all_26_0 % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (formula_3) with all_14_2, all_37_0, simplifying % 13.83/2.76 | with (27) gives: % 13.83/2.76 | (31) all_37_0 = all_14_2 % 13.83/2.76 | % 13.83/2.76 | REDUCE: (30), (31) imply: % 13.83/2.76 | (32) u0(2, all_14_2) = all_26_0 % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (1) with 2, all_14_2, all_26_0, simplifying with % 13.83/2.76 | (32) gives: % 13.83/2.76 | (33) ? [v0: int] : (u0(1, all_14_2) = v0 & f0(v0) = all_26_0) % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (formula_9) with all_14_2, all_35_0, simplifying % 13.83/2.76 | with (24) gives: % 13.83/2.76 | (34) ? [v0: int] : ($product(v0, all_14_2) = all_35_0 & $product(all_14_2, % 13.83/2.76 | all_14_2) = v0) % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (5) with 1, all_35_0, all_24_0, simplifying with % 13.83/2.76 | (29) gives: % 13.83/2.76 | (35) ? [v0: int] : (u1(0, all_35_0) = v0 & f1(v0) = all_24_0) % 13.83/2.76 | % 13.83/2.76 | DELTA: instantiating (35) with fresh symbol all_51_0 gives: % 13.83/2.76 | (36) u1(0, all_35_0) = all_51_0 & f1(all_51_0) = all_24_0 % 13.83/2.76 | % 13.83/2.76 | ALPHA: (36) implies: % 13.83/2.76 | (37) f1(all_51_0) = all_24_0 % 13.83/2.76 | (38) u1(0, all_35_0) = all_51_0 % 13.83/2.76 | % 13.83/2.76 | DELTA: instantiating (33) with fresh symbol all_55_0 gives: % 13.83/2.76 | (39) u0(1, all_14_2) = all_55_0 & f0(all_55_0) = all_26_0 % 13.83/2.76 | % 13.83/2.76 | ALPHA: (39) implies: % 13.83/2.76 | (40) f0(all_55_0) = all_26_0 % 13.83/2.76 | (41) u0(1, all_14_2) = all_55_0 % 13.83/2.76 | % 13.83/2.76 | DELTA: instantiating (34) with fresh symbol all_59_0 gives: % 13.83/2.76 | (42) $product(all_59_0, all_14_2) = all_35_0 & $product(all_14_2, all_14_2) % 13.83/2.76 | = all_59_0 % 13.83/2.76 | % 13.83/2.76 | ALPHA: (42) implies: % 13.83/2.76 | (43) $product(all_14_2, all_14_2) = all_59_0 % 13.83/2.76 | (44) $product(all_59_0, all_14_2) = all_35_0 % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (6) with 0, all_35_0, all_51_0, simplifying with % 13.83/2.76 | (38) gives: % 13.83/2.76 | (45) all_51_0 = all_35_0 % 13.83/2.76 | % 13.83/2.76 | REDUCE: (37), (45) imply: % 13.83/2.76 | (46) f1(all_35_0) = all_24_0 % 13.83/2.76 | % 13.83/2.76 | GROUND_INST: instantiating (formula_1) with all_55_0, all_26_0, simplifying % 13.83/2.76 | with (40) gives: % 13.83/2.77 | (47) ? [v0: int] : ($product(v0, all_55_0) = all_26_0 & $product(all_55_0, % 13.83/2.77 | all_55_0) = v0) % 13.83/2.77 | % 13.83/2.77 | GROUND_INST: instantiating (1) with 1, all_14_2, all_55_0, simplifying with % 13.83/2.77 | (41) gives: % 13.83/2.77 | (48) ? [v0: int] : (u0(0, all_14_2) = v0 & f0(v0) = all_55_0) % 13.83/2.77 | % 13.83/2.77 | GROUND_INST: instantiating (formula_7) with all_35_0, all_24_0, simplifying % 13.83/2.77 | with (46) gives: % 13.83/2.77 | (49) ? [v0: int] : ($product(v0, all_35_0) = all_24_0 & $product(all_35_0, % 13.83/2.77 | all_35_0) = v0) % 13.83/2.77 | % 13.83/2.77 | DELTA: instantiating (49) with fresh symbol all_79_0 gives: % 13.83/2.77 | (50) $product(all_79_0, all_35_0) = all_24_0 & $product(all_35_0, all_35_0) % 13.83/2.77 | = all_79_0 % 13.83/2.77 | % 13.83/2.77 | ALPHA: (50) implies: % 13.83/2.77 | (51) $product(all_35_0, all_35_0) = all_79_0 % 13.83/2.77 | (52) $product(all_79_0, all_35_0) = all_24_0 % 13.83/2.77 | % 13.83/2.77 | DELTA: instantiating (48) with fresh symbol all_85_0 gives: % 13.83/2.77 | (53) u0(0, all_14_2) = all_85_0 & f0(all_85_0) = all_55_0 % 13.83/2.77 | % 13.83/2.77 | ALPHA: (53) implies: % 13.83/2.77 | (54) f0(all_85_0) = all_55_0 % 13.83/2.77 | (55) u0(0, all_14_2) = all_85_0 % 13.83/2.77 | % 13.83/2.77 | DELTA: instantiating (47) with fresh symbol all_87_0 gives: % 13.83/2.77 | (56) $product(all_87_0, all_55_0) = all_26_0 & $product(all_55_0, all_55_0) % 13.83/2.77 | = all_87_0 % 13.83/2.77 | % 13.83/2.77 | ALPHA: (56) implies: % 13.83/2.77 | (57) $product(all_55_0, all_55_0) = all_87_0 % 13.83/2.77 | (58) $product(all_87_0, all_55_0) = all_26_0 % 13.83/2.77 | % 13.83/2.77 | GROUND_INST: instantiating (2) with 0, all_14_2, all_85_0, simplifying with % 13.83/2.77 | (55) gives: % 13.83/2.77 | (59) all_85_0 = all_14_2 % 13.83/2.77 | % 13.83/2.77 | REDUCE: (54), (59) imply: % 13.83/2.77 | (60) f0(all_14_2) = all_55_0 % 13.83/2.77 | % 13.83/2.77 | GROUND_INST: instantiating (formula_1) with all_14_2, all_55_0, simplifying % 13.83/2.77 | with (60) gives: % 13.83/2.77 | (61) ? [v0: int] : ($product(v0, all_14_2) = all_55_0 & $product(all_14_2, % 13.83/2.77 | all_14_2) = v0) % 13.83/2.77 | % 13.83/2.77 | DELTA: instantiating (61) with fresh symbol all_116_0 gives: % 13.83/2.77 | (62) $product(all_116_0, all_14_2) = all_55_0 & $product(all_14_2, % 13.83/2.77 | all_14_2) = all_116_0 % 13.83/2.77 | % 13.83/2.77 | ALPHA: (62) implies: % 13.83/2.77 | (63) $product(all_14_2, all_14_2) = all_116_0 % 13.83/2.77 | (64) $product(all_116_0, all_14_2) = all_55_0 % 13.83/2.77 | % 13.83/2.77 | THEORY_AXIOM GroebnerMultiplication: % 13.83/2.77 | (65) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 13.83/2.77 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : % 13.83/2.77 | ! [v9: int] : ! [v10: int] : (v2 = v1 | ~ ($product(v10, v0) = v6) | % 13.83/2.77 | ~ ($product(v9, v6) = v4) | ~ ($product(v8, v5) = v3) | ~ % 13.83/2.77 | ($product(v7, v0) = v5) | ~ ($product(v6, v6) = v9) | ~ % 13.83/2.77 | ($product(v5, v5) = v8) | ~ ($product(v4, v0) = $difference(v1, % 13.83/2.77 | v0)) | ~ ($product(v3, v0) = $difference(v2, v0)) | ~ % 13.83/2.77 | ($product(v0, v0) = v10) | ~ ($product(v0, v0) = v7)) % 13.83/2.77 | % 13.83/2.77 | GROUND_INST: instantiating (65) with all_14_2, all_14_1, all_14_0, all_24_0, % 13.83/2.77 | all_26_0, all_35_0, all_55_0, all_59_0, all_79_0, all_87_0, % 13.83/2.77 | all_116_0, simplifying with (16), (19), (43), (44), (51), (52), % 13.83/2.77 | (57), (58), (63), (64) gives: % 13.83/2.77 | (66) all_14_0 = all_14_1 % 13.83/2.77 | % 13.83/2.77 | REDUCE: (10), (66) imply: % 13.83/2.77 | (67) $false % 13.83/2.77 | % 13.83/2.77 | CLOSE: (67) is inconsistent. % 13.83/2.77 | % 13.83/2.77 End of proof % 13.83/2.78 % SZS output end Proof for theBenchmark % 13.83/2.78 % 13.83/2.78 2079ms %------------------------------------------------------------------------------