%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO528+1 : TPTP v8.1.2. Released v7.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 : Wed Aug 30 23:23:36 EDT 2023 % Result : Theorem 82.48s 11.69s % Output : Proof 83.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : GEO528+1 : TPTP v8.1.2. Released v7.0.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n005.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 22:15:22 EDT 2023 % 0.14/0.36 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.45/1.76 Prover 4: Preprocessing ... % 7.45/1.76 Prover 1: Preprocessing ... % 7.65/1.79 Prover 3: Preprocessing ... % 7.65/1.79 Prover 5: Preprocessing ... % 7.65/1.79 Prover 2: Preprocessing ... % 7.65/1.79 Prover 0: Preprocessing ... % 7.65/1.79 Prover 6: Preprocessing ... % 19.26/3.32 Prover 5: Proving ... % 19.26/3.32 Prover 2: Proving ... % 19.64/3.45 Prover 1: Warning: ignoring some quantifiers % 20.95/3.58 Prover 3: Warning: ignoring some quantifiers % 20.95/3.59 Prover 6: Proving ... % 20.95/3.60 Prover 1: Constructing countermodel ... % 21.53/3.65 Prover 3: Constructing countermodel ... % 27.92/4.51 Prover 4: Constructing countermodel ... % 28.25/4.60 Prover 0: Proving ... % 66.08/9.48 Prover 3: gave up % 66.51/9.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 69.22/9.85 Prover 7: Preprocessing ... % 70.80/10.13 Prover 7: Warning: ignoring some quantifiers % 71.53/10.16 Prover 7: Constructing countermodel ... % 74.49/10.55 Prover 2: stopped % 74.49/10.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 77.99/10.97 Prover 8: Preprocessing ... % 81.10/11.41 Prover 8: Warning: ignoring some quantifiers % 81.77/11.50 Prover 8: Constructing countermodel ... % 82.48/11.67 Prover 7: Found proof (size 44) % 82.48/11.67 Prover 7: proved (2193ms) % 82.48/11.67 Prover 5: stopped % 82.48/11.67 Prover 8: stopped % 82.48/11.68 Prover 0: stopped % 82.48/11.69 Prover 1: stopped % 82.48/11.69 Prover 6: stopped % 82.48/11.69 Prover 4: stopped % 82.48/11.69 % 82.48/11.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 82.48/11.69 % 82.48/11.69 % SZS output start Proof for theBenchmark % 82.48/11.71 Assumptions after simplification: % 82.48/11.71 --------------------------------- % 82.48/11.71 % 82.48/11.71 (aSatz10_14) % 83.43/11.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) & % 83.43/11.74 reflect(v0, v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 83.43/11.74 opposite(v2, v0, v1, v3) & ~ s_col(v0, v1, v2)) % 83.43/11.74 % 83.43/11.74 (aSatz10_2a) % 83.43/11.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = v0 | % 83.43/11.74 ~ (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | perp(v0, % 83.43/11.74 v1, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 83.43/11.74 = v0 | ~ (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 83.43/11.74 ? [v4: $i] : (midpoint(v2, v3) = v4 & $i(v4) & s_col(v0, v1, v4))) % 83.43/11.74 % 83.43/11.74 (aSatz10_5) % 83.43/11.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 83.43/11.74 (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | reflect(v0, % 83.43/11.74 v1, v3) = v2) % 83.43/11.74 % 83.43/11.74 (aSatz10_8a) % 83.43/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (reflect(v0, v1, v2) = % 83.43/11.75 v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | s_col(v0, v1, v2)) % 83.43/11.75 % 83.43/11.75 (aSatz10_8b) % 83.43/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = v0 | % 83.43/11.75 ~ (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 83.43/11.75 s_col(v0, v1, v2)) % 83.43/11.75 % 83.43/11.75 (aSatz8_22) % 83.43/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (midpoint(v0, v1) = v2) | ~ % 83.43/11.75 $i(v1) | ~ $i(v0) | s_m(v0, v2, v1)) % 83.43/11.75 % 83.43/11.75 (d_Defn7_1) % 83.69/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 83.69/11.75 ~ s_m(v0, v1, v2) | s_t(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 83.69/11.75 $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ s_m(v0, v1, v2) | s_e(v1, v0, % 83.69/11.75 v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ % 83.69/11.75 $i(v1) | ~ $i(v0) | ~ s_t(v0, v1, v2) | ~ s_e(v1, v0, v1, v2) | s_m(v0, % 83.69/11.75 v1, v2)) % 83.69/11.75 % 83.69/11.75 (d_Defn9_1) % 83.69/11.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 83.69/11.76 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ s_col(v0, % 83.69/11.76 v1, v4) | ~ s_t(v2, v4, v3) | opposite(v2, v0, v1, v3) | s_col(v0, v1, % 83.69/11.76 v3) | s_col(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 83.69/11.76 [v3: $i] : ! [v4: $i] : ( ~ (il(v2, v3, v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 83.69/11.76 | ~ $i(v1) | ~ $i(v0) | ~ opposite(v2, v0, v1, v3) | s_col(v0, v1, v4)) & % 83.69/11.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 83.69/11.76 (il(v2, v3, v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 83.69/11.76 ~ opposite(v2, v0, v1, v3) | s_t(v2, v4, v3)) & ! [v0: $i] : ! [v1: $i] : % 83.69/11.76 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 83.69/11.76 opposite(v2, v0, v1, v3) | ~ s_col(v0, v1, v3)) & ! [v0: $i] : ! [v1: $i] % 83.69/11.76 : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 83.69/11.76 ~ opposite(v2, v0, v1, v3) | ~ s_col(v0, v1, v2)) % 83.69/11.76 % 83.69/11.76 Further assumptions not needed in the proof: % 83.69/11.76 -------------------------------------------- % 83.69/11.76 aA1, aA2, aA3, aA4, aA5, aA6, aA7, aA8, aExtCol2, aExtPerp, aExtPerp2, % 83.69/11.76 aExtPerp3, aExtPerp4, aExtPerp5, aExtPerp6, aExtSameSide1, aExtSameSide2, % 83.69/11.76 aLemma9_13a, aLemma9_13b, aLemma9_13c, aLemma9_13d, aLemma9_13e, aLemma9_13f, % 83.69/11.76 aLemma9_13f_case1, aLemma9_13f_case2, aLemma9_13g, aNarbouxLemma1, aSatz10_10, % 83.69/11.76 aSatz10_10a, aSatz10_12, aSatz10_12a, aSatz10_12b, aSatz10_12c, aSatz10_2b, % 83.69/11.76 aSatz10_4, aSatz10_6, aSatz10_7, aSatz2_1, aSatz2_11, aSatz2_12, aSatz2_13, % 83.69/11.76 aSatz2_14, aSatz2_15, aSatz2_2, aSatz2_3, aSatz2_4, aSatz2_5, aSatz2_8, % 83.69/11.76 aSatz3_1, aSatz3_13a, aSatz3_13b, aSatz3_13c, aSatz3_14a, aSatz3_14b, aSatz3_17, % 83.69/11.76 aSatz3_2, aSatz3_3, aSatz3_4, aSatz3_5a, aSatz3_5b, aSatz3_6a, aSatz3_6b, % 83.69/11.76 aSatz3_7a, aSatz3_7b, aSatz4_11a, aSatz4_11b, aSatz4_11c, aSatz4_11d, % 83.69/11.76 aSatz4_11e, aSatz4_12, aSatz4_12b, aSatz4_13, aSatz4_14, aSatz4_16, aSatz4_17, % 83.69/11.76 aSatz4_18, aSatz4_19, aSatz4_2, aSatz4_3, aSatz4_5, aSatz4_6, aSatz5_1, % 83.69/11.76 aSatz5_10, aSatz5_11, aSatz5_12a1, aSatz5_12a2, aSatz5_12b, aSatz5_2, aSatz5_3, % 83.69/11.76 aSatz5_5a, aSatz5_5b, aSatz5_6, aSatz5_7, aSatz5_8, aSatz5_9, aSatz6_11a, % 83.69/11.76 aSatz6_11b, aSatz6_13a, aSatz6_13b, aSatz6_15a, aSatz6_15b, aSatz6_15c, % 83.69/11.76 aSatz6_15d, aSatz6_16a, aSatz6_16b, aSatz6_17a, aSatz6_17b, aSatz6_18, % 83.69/11.76 aSatz6_21, aSatz6_25, aSatz6_28, aSatz6_2a, aSatz6_2b, aSatz6_3a, aSatz6_3b, % 83.69/11.76 aSatz6_4a, aSatz6_4b, aSatz6_5, aSatz6_6, aSatz6_7, aSatz7_10a, aSatz7_10b, % 83.69/11.76 aSatz7_13, aSatz7_15a, aSatz7_15b, aSatz7_16a, aSatz7_16b, aSatz7_17, aSatz7_18, % 83.69/11.76 aSatz7_19, aSatz7_2, aSatz7_20, aSatz7_21, aSatz7_22, aSatz7_22a, aSatz7_22b, % 83.69/11.76 aSatz7_25, aSatz7_3a, aSatz7_3b, aSatz7_4a, aSatz7_4b, aSatz7_6, aSatz7_7, % 83.69/11.76 aSatz7_8, aSatz7_9, aSatz8_10, aSatz8_12a, aSatz8_12b, aSatz8_13a, aSatz8_13b, % 83.69/11.76 aSatz8_14a, aSatz8_14b, aSatz8_14c, aSatz8_15, aSatz8_16a, aSatz8_16b, % 83.69/11.76 aSatz8_18, aSatz8_18a, aSatz8_2, aSatz8_20a, aSatz8_20b, aSatz8_21, aSatz8_21a, % 83.69/11.76 aSatz8_22b, aSatz8_24, aSatz8_24a, aSatz8_24b, aSatz8_3, aSatz8_4, aSatz8_5, % 83.69/11.76 aSatz8_6, aSatz8_7, aSatz8_8, aSatz8_9, aSatz9_13, aSatz9_16, aSatz9_19b, % 83.69/11.76 aSatz9_2, aSatz9_3, aSatz9_3a, aSatz9_4, aSatz9_4a, aSatz9_4a2, aSatz9_4b, % 83.69/11.76 aSatz9_4c, aSatz9_5, aSatz9_6, aSatz9_8, aSatz9_9, aSideReflect, aext1, aperp1, % 83.69/11.76 d_Defn2_10, d_Defn4_1, d_Defn4_10, d_Defn4_15, d_Defn4_4, d_Defn5_4, d_Defn6_1, % 83.69/11.76 d_Defn7_23, d_Defn8_1, d_Defn8_11a, d_Defn8_11b, d_Defn9_7, d_insert % 83.69/11.76 % 83.69/11.76 Those formulas are unsatisfiable: % 83.69/11.76 --------------------------------- % 83.69/11.76 % 83.69/11.76 Begin of proof % 83.69/11.77 | % 83.69/11.77 | ALPHA: (aSatz10_2a) implies: % 83.69/11.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 83.69/11.77 | (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 83.69/11.77 | [v4: $i] : (midpoint(v2, v3) = v4 & $i(v4) & s_col(v0, v1, v4))) % 83.69/11.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = % 83.69/11.77 | v0 | ~ (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 83.69/11.77 | $i(v0) | perp(v0, v1, v2, v3)) % 83.69/11.77 | % 83.69/11.77 | ALPHA: (d_Defn7_1) implies: % 83.69/11.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 83.69/11.77 | $i(v0) | ~ s_m(v0, v1, v2) | s_t(v0, v1, v2)) % 83.69/11.77 | % 83.69/11.77 | ALPHA: (d_Defn9_1) implies: % 83.69/11.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 83.69/11.77 | (v1 = v0 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 83.69/11.77 | ~ s_col(v0, v1, v4) | ~ s_t(v2, v4, v3) | opposite(v2, v0, v1, v3) | % 83.69/11.77 | s_col(v0, v1, v3) | s_col(v0, v1, v2)) % 83.69/11.77 | % 83.69/11.78 | DELTA: instantiating (aSatz10_14) with fresh symbols all_208_0, all_208_1, % 83.69/11.78 | all_208_2, all_208_3 gives: % 83.69/11.78 | (5) ~ (all_208_2 = all_208_3) & reflect(all_208_3, all_208_2, all_208_1) = % 83.69/11.78 | all_208_0 & $i(all_208_0) & $i(all_208_1) & $i(all_208_2) & % 83.69/11.78 | $i(all_208_3) & ~ opposite(all_208_1, all_208_3, all_208_2, all_208_0) % 83.69/11.78 | & ~ s_col(all_208_3, all_208_2, all_208_1) % 83.69/11.78 | % 83.69/11.78 | ALPHA: (5) implies: % 83.69/11.78 | (6) ~ (all_208_2 = all_208_3) % 83.69/11.78 | (7) ~ s_col(all_208_3, all_208_2, all_208_1) % 83.69/11.78 | (8) ~ opposite(all_208_1, all_208_3, all_208_2, all_208_0) % 83.69/11.78 | (9) $i(all_208_3) % 83.69/11.78 | (10) $i(all_208_2) % 83.69/11.78 | (11) $i(all_208_1) % 83.69/11.78 | (12) $i(all_208_0) % 83.69/11.78 | (13) reflect(all_208_3, all_208_2, all_208_1) = all_208_0 % 83.69/11.78 | % 83.69/11.78 | GROUND_INST: instantiating (aSatz10_8a) with all_208_3, all_208_2, all_208_1, % 83.69/11.78 | simplifying with (7), (9), (10), (11) gives: % 83.69/11.78 | (14) all_208_2 = all_208_3 | ~ (reflect(all_208_3, all_208_2, all_208_1) = % 83.69/11.78 | all_208_1) % 83.69/11.78 | % 83.69/11.78 | GROUND_INST: instantiating (2) with all_208_3, all_208_2, all_208_1, % 83.69/11.78 | all_208_0, simplifying with (9), (10), (11), (13) gives: % 83.69/11.78 | (15) all_208_0 = all_208_1 | all_208_2 = all_208_3 | perp(all_208_3, % 83.69/11.78 | all_208_2, all_208_1, all_208_0) % 83.69/11.78 | % 83.69/11.78 | GROUND_INST: instantiating (aSatz10_5) with all_208_3, all_208_2, all_208_1, % 83.69/11.78 | all_208_0, simplifying with (9), (10), (11), (13) gives: % 83.69/11.78 | (16) all_208_2 = all_208_3 | reflect(all_208_3, all_208_2, all_208_0) = % 83.69/11.78 | all_208_1 % 83.69/11.78 | % 83.69/11.78 | GROUND_INST: instantiating (1) with all_208_3, all_208_2, all_208_1, % 83.69/11.78 | all_208_0, simplifying with (9), (10), (11), (13) gives: % 83.69/11.78 | (17) all_208_2 = all_208_3 | ? [v0: $i] : (midpoint(all_208_1, all_208_0) % 83.69/11.78 | = v0 & $i(v0) & s_col(all_208_3, all_208_2, v0)) % 83.69/11.78 | % 83.69/11.78 | BETA: splitting (16) gives: % 83.69/11.78 | % 83.69/11.78 | Case 1: % 83.69/11.78 | | % 83.69/11.79 | | (18) reflect(all_208_3, all_208_2, all_208_0) = all_208_1 % 83.69/11.79 | | % 83.69/11.79 | | BETA: splitting (17) gives: % 83.69/11.79 | | % 83.69/11.79 | | Case 1: % 83.69/11.79 | | | % 83.69/11.79 | | | (19) all_208_2 = all_208_3 % 83.69/11.79 | | | % 83.69/11.79 | | | REDUCE: (6), (19) imply: % 83.69/11.79 | | | (20) $false % 83.69/11.79 | | | % 83.69/11.79 | | | CLOSE: (20) is inconsistent. % 83.69/11.79 | | | % 83.69/11.79 | | Case 2: % 83.69/11.79 | | | % 83.69/11.79 | | | (21) ? [v0: $i] : (midpoint(all_208_1, all_208_0) = v0 & $i(v0) & % 83.69/11.79 | | | s_col(all_208_3, all_208_2, v0)) % 83.69/11.79 | | | % 83.69/11.79 | | | DELTA: instantiating (21) with fresh symbol all_229_0 gives: % 83.69/11.79 | | | (22) midpoint(all_208_1, all_208_0) = all_229_0 & $i(all_229_0) & % 83.69/11.79 | | | s_col(all_208_3, all_208_2, all_229_0) % 83.69/11.79 | | | % 83.69/11.79 | | | ALPHA: (22) implies: % 83.69/11.79 | | | (23) s_col(all_208_3, all_208_2, all_229_0) % 83.69/11.79 | | | (24) $i(all_229_0) % 83.69/11.79 | | | (25) midpoint(all_208_1, all_208_0) = all_229_0 % 83.69/11.79 | | | % 83.69/11.79 | | | BETA: splitting (14) gives: % 83.69/11.79 | | | % 83.69/11.79 | | | Case 1: % 83.69/11.79 | | | | % 83.69/11.79 | | | | (26) ~ (reflect(all_208_3, all_208_2, all_208_1) = all_208_1) % 83.69/11.79 | | | | % 83.69/11.79 | | | | PRED_UNIFY: (13), (26) imply: % 83.69/11.79 | | | | (27) ~ (all_208_0 = all_208_1) % 83.69/11.79 | | | | % 83.69/11.79 | | | | BETA: splitting (15) gives: % 83.69/11.79 | | | | % 83.69/11.79 | | | | Case 1: % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | GROUND_INST: instantiating (aSatz8_22) with all_208_1, all_208_0, % 83.69/11.79 | | | | | all_229_0, simplifying with (11), (12), (25) gives: % 83.69/11.79 | | | | | (28) s_m(all_208_1, all_229_0, all_208_0) % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | GROUND_INST: instantiating (aSatz10_8b) with all_208_3, all_208_2, % 83.69/11.79 | | | | | all_208_0, all_208_1, simplifying with (9), (10), (12), % 83.69/11.79 | | | | | (18) gives: % 83.69/11.79 | | | | | (29) all_208_0 = all_208_1 | all_208_2 = all_208_3 | ~ % 83.69/11.79 | | | | | s_col(all_208_3, all_208_2, all_208_0) % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | BETA: splitting (29) gives: % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | Case 1: % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | (30) ~ s_col(all_208_3, all_208_2, all_208_0) % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | GROUND_INST: instantiating (3) with all_208_1, all_229_0, all_208_0, % 83.69/11.79 | | | | | | simplifying with (11), (12), (24), (28) gives: % 83.69/11.79 | | | | | | (31) s_t(all_208_1, all_229_0, all_208_0) % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | GROUND_INST: instantiating (4) with all_208_3, all_208_2, all_208_1, % 83.69/11.79 | | | | | | all_208_0, all_229_0, simplifying with (7), (8), (9), % 83.69/11.79 | | | | | | (10), (11), (12), (23), (24), (30), (31) gives: % 83.69/11.79 | | | | | | (32) all_208_2 = all_208_3 % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | REDUCE: (6), (32) imply: % 83.69/11.79 | | | | | | (33) $false % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | CLOSE: (33) is inconsistent. % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | Case 2: % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | (34) all_208_0 = all_208_1 | all_208_2 = all_208_3 % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | | REF_CLOSE: (6), (27), (34) are inconsistent by sub-proof #1. % 83.69/11.79 | | | | | | % 83.69/11.79 | | | | | End of split % 83.69/11.79 | | | | | % 83.69/11.79 | | | | Case 2: % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | (35) all_208_0 = all_208_1 | all_208_2 = all_208_3 % 83.69/11.79 | | | | | % 83.69/11.79 | | | | | REF_CLOSE: (6), (27), (35) are inconsistent by sub-proof #1. % 83.69/11.79 | | | | | % 83.69/11.79 | | | | End of split % 83.69/11.79 | | | | % 83.69/11.79 | | | Case 2: % 83.69/11.79 | | | | % 83.69/11.79 | | | | (36) all_208_2 = all_208_3 % 83.69/11.79 | | | | % 83.69/11.79 | | | | REDUCE: (6), (36) imply: % 83.69/11.79 | | | | (37) $false % 83.69/11.79 | | | | % 83.69/11.79 | | | | CLOSE: (37) is inconsistent. % 83.69/11.79 | | | | % 83.69/11.79 | | | End of split % 83.69/11.79 | | | % 83.69/11.79 | | End of split % 83.69/11.79 | | % 83.69/11.79 | Case 2: % 83.69/11.79 | | % 83.69/11.79 | | (38) all_208_2 = all_208_3 % 83.69/11.79 | | % 83.69/11.79 | | REDUCE: (6), (38) imply: % 83.69/11.79 | | (39) $false % 83.69/11.79 | | % 83.69/11.79 | | CLOSE: (39) is inconsistent. % 83.69/11.79 | | % 83.69/11.79 | End of split % 83.69/11.80 | % 83.69/11.80 End of proof % 83.69/11.80 % 83.69/11.80 Sub-proof #1 shows that the following formulas are inconsistent: % 83.69/11.80 ---------------------------------------------------------------- % 83.69/11.80 (1) all_208_0 = all_208_1 | all_208_2 = all_208_3 % 83.69/11.80 (2) ~ (all_208_0 = all_208_1) % 83.69/11.80 (3) ~ (all_208_2 = all_208_3) % 83.69/11.80 % 83.69/11.80 Begin of proof % 83.69/11.80 | % 83.69/11.80 | BETA: splitting (1) gives: % 83.69/11.80 | % 83.69/11.80 | Case 1: % 83.69/11.80 | | % 83.69/11.80 | | (4) all_208_0 = all_208_1 % 83.69/11.80 | | % 83.69/11.80 | | REDUCE: (2), (4) imply: % 83.69/11.80 | | (5) $false % 83.69/11.80 | | % 83.69/11.80 | | CLOSE: (5) is inconsistent. % 83.69/11.80 | | % 83.69/11.80 | Case 2: % 83.69/11.80 | | % 83.69/11.80 | | (6) all_208_2 = all_208_3 % 83.69/11.80 | | % 83.69/11.80 | | REDUCE: (3), (6) imply: % 83.69/11.80 | | (7) $false % 83.69/11.80 | | % 83.69/11.80 | | CLOSE: (7) is inconsistent. % 83.69/11.80 | | % 83.69/11.80 | End of split % 83.69/11.80 | % 83.69/11.80 End of proof % 83.69/11.80 % SZS output end Proof for theBenchmark % 83.69/11.80 % 83.69/11.80 11166ms %------------------------------------------------------------------------------