%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU406+1 : TPTP v8.1.2. Released v3.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 17:44:32 EDT 2023 % Result : Theorem 16.79s 3.03s % Output : Proof 17.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU406+1 : TPTP v8.1.2. Released v3.4.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Aug 23 17:51:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.44/1.00 Prover 1: Preprocessing ... % 2.44/1.00 Prover 4: Preprocessing ... % 2.44/1.04 Prover 2: Preprocessing ... % 2.44/1.04 Prover 5: Preprocessing ... % 2.44/1.04 Prover 0: Preprocessing ... % 2.44/1.04 Prover 3: Preprocessing ... % 2.44/1.04 Prover 6: Preprocessing ... % 5.06/1.39 Prover 1: Warning: ignoring some quantifiers % 5.06/1.40 Prover 3: Warning: ignoring some quantifiers % 5.06/1.40 Prover 4: Warning: ignoring some quantifiers % 5.06/1.41 Prover 3: Constructing countermodel ... % 5.06/1.41 Prover 2: Proving ... % 5.06/1.41 Prover 5: Proving ... % 5.06/1.41 Prover 4: Constructing countermodel ... % 5.06/1.43 Prover 6: Proving ... % 5.06/1.43 Prover 1: Constructing countermodel ... % 5.06/1.46 Prover 0: Proving ... % 8.76/1.95 Prover 3: gave up % 8.76/1.96 Prover 1: gave up % 8.76/1.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.76/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.76/1.99 Prover 7: Preprocessing ... % 9.44/2.02 Prover 8: Preprocessing ... % 9.44/2.06 Prover 7: Warning: ignoring some quantifiers % 9.44/2.07 Prover 7: Constructing countermodel ... % 10.12/2.10 Prover 8: Warning: ignoring some quantifiers % 10.12/2.11 Prover 8: Constructing countermodel ... % 11.69/2.41 Prover 8: gave up % 11.69/2.43 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 11.69/2.46 Prover 9: Preprocessing ... % 13.07/2.54 Prover 9: Warning: ignoring some quantifiers % 13.07/2.55 Prover 9: Constructing countermodel ... % 16.79/3.02 Prover 4: Found proof (size 95) % 16.79/3.02 Prover 4: proved (2402ms) % 16.79/3.02 Prover 9: stopped % 16.79/3.02 Prover 7: stopped % 16.79/3.02 Prover 2: stopped % 16.79/3.02 Prover 0: stopped % 16.79/3.03 Prover 6: stopped % 16.79/3.03 Prover 5: stopped % 16.79/3.03 % 16.79/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.79/3.03 % 16.79/3.05 % SZS output start Proof for theBenchmark % 16.79/3.05 Assumptions after simplification: % 16.79/3.05 --------------------------------- % 16.79/3.05 % 16.79/3.05 (commutativity_k2_xboole_0) % 16.79/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k2_xboole_0(v1, v0) = v2) | ~ % 16.79/3.08 $i(v1) | ~ $i(v0) | (k2_xboole_0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 16.79/3.08 [v1: $i] : ! [v2: $i] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ $i(v1) | ~ % 16.79/3.08 $i(v0) | (k2_xboole_0(v1, v0) = v2 & $i(v2))) % 16.79/3.08 % 16.79/3.08 (d2_xboole_0) % 17.36/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 17.36/3.10 | ~ (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = v4) | ~ $i(v3) | % 17.36/3.10 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = % 17.36/3.10 0) & ~ (v5 = 0) & r2_hidden(v3, v1) = v6 & r2_hidden(v3, v0) = v5)) & % 17.36/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 17.36/3.10 | ~ (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = v4) | ~ $i(v3) | % 17.36/3.10 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 17.36/3.10 (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 17.36/3.10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = % 17.36/3.10 0 | ~ (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = v4) | ~ $i(v3) % 17.36/3.10 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 17.36/3.10 (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 17.36/3.10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 17.36/3.10 (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = v4) | ~ $i(v3) | ~ % 17.36/3.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 17.36/3.10 (r2_hidden(v3, v2) = v6 & r2_hidden(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & % 17.36/3.10 ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.36/3.10 : ! [v4: any] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = v4) % 17.36/3.10 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 17.36/3.10 any] : (r2_hidden(v3, v2) = v6 & r2_hidden(v3, v1) = v5 & (v6 = 0 | ( ~ % 17.36/3.10 (v5 = 0) & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.36/3.10 ! [v3: $i] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = 0) | ~ % 17.36/3.10 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 17.36/3.10 (r2_hidden(v3, v1) = v5 & r2_hidden(v3, v0) = v4 & (v5 = 0 | v4 = 0))) & ? % 17.36/3.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 17.36/3.10 (k2_xboole_0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] % 17.36/3.10 : ? [v5: any] : ? [v6: any] : ? [v7: any] : (r2_hidden(v4, v2) = v7 & % 17.36/3.10 r2_hidden(v4, v1) = v6 & r2_hidden(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | % 17.36/3.10 ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 17.36/3.10 % 17.36/3.10 (t1_latsum_1) % 17.36/3.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 17.36/3.10 $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 17.36/3.10 (k4_xboole_0(v2, v3) = v5 & k2_xboole_0(v2, v3) = v4 & r2_hidden(v1, v5) = v7 % 17.36/3.10 & r2_hidden(v1, v4) = 0 & r2_hidden(v1, v3) = v9 & r2_hidden(v0, v5) = v6 & % 17.36/3.10 r2_hidden(v0, v4) = 0 & r2_hidden(v0, v3) = v8 & $i(v5) & $i(v4) & $i(v3) & % 17.36/3.10 $i(v2) & $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0)) & ( ~ (v9 = 0) | ~ % 17.36/3.10 (v6 = 0)) & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v7 = 0) | ~ (v6 = 0))) % 17.36/3.10 % 17.36/3.10 (t39_xboole_1) % 17.36/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k4_xboole_0(v1, v0) = v2) | ~ % 17.36/3.10 $i(v1) | ~ $i(v0) | ? [v3: $i] : (k2_xboole_0(v0, v2) = v3 & % 17.36/3.10 k2_xboole_0(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.36/3.10 $i] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 17.36/3.10 (k4_xboole_0(v1, v0) = v3 & k2_xboole_0(v0, v3) = v2 & $i(v3) & $i(v2))) % 17.36/3.10 % 17.36/3.10 (function-axioms) % 17.36/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.36/3.11 (k4_xboole_0(v3, v2) = v1) | ~ (k4_xboole_0(v3, v2) = v0)) & ! [v0: % 17.36/3.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.36/3.11 : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) = v0)) & % 17.36/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.36/3.11 (k2_xboole_0(v3, v2) = v1) | ~ (k2_xboole_0(v3, v2) = v0)) & ! [v0: % 17.36/3.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.36/3.11 : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0)) & ! % 17.36/3.11 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 17.36/3.11 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0)) % 17.36/3.11 % 17.36/3.11 Further assumptions not needed in the proof: % 17.36/3.11 -------------------------------------------- % 17.36/3.11 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k2_xboole_0, dt_k4_xboole_0, % 17.36/3.11 dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, % 17.36/3.11 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0, t1_boole, t1_subset, % 17.36/3.11 t2_subset, t3_boole, t4_boole, t6_boole, t7_boole, t8_boole % 17.36/3.11 % 17.36/3.11 Those formulas are unsatisfiable: % 17.36/3.11 --------------------------------- % 17.36/3.11 % 17.36/3.11 Begin of proof % 17.36/3.11 | % 17.36/3.11 | ALPHA: (commutativity_k2_xboole_0) implies: % 17.36/3.11 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k2_xboole_0(v1, v0) = % 17.36/3.11 | v2) | ~ $i(v1) | ~ $i(v0) | (k2_xboole_0(v0, v1) = v2 & $i(v2))) % 17.36/3.11 | % 17.36/3.11 | ALPHA: (d2_xboole_0) implies: % 17.36/3.11 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 17.36/3.11 | (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = 0) | ~ $i(v3) | % 17.36/3.11 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 17.36/3.11 | (r2_hidden(v3, v1) = v5 & r2_hidden(v3, v0) = v4 & (v5 = 0 | v4 = % 17.36/3.11 | 0))) % 17.36/3.11 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 17.36/3.11 | ( ~ (k2_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = v4) | ~ % 17.36/3.11 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 17.36/3.11 | any] : (r2_hidden(v3, v2) = v6 & r2_hidden(v3, v0) = v5 & (v6 = 0 | % 17.36/3.11 | ( ~ (v5 = 0) & ~ (v4 = 0))))) % 17.36/3.11 | % 17.36/3.11 | ALPHA: (t39_xboole_1) implies: % 17.36/3.11 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k2_xboole_0(v0, v1) = % 17.36/3.11 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (k4_xboole_0(v1, v0) = % 17.36/3.11 | v3 & k2_xboole_0(v0, v3) = v2 & $i(v3) & $i(v2))) % 17.36/3.11 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k4_xboole_0(v1, v0) = % 17.36/3.11 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (k2_xboole_0(v0, v2) = % 17.36/3.11 | v3 & k2_xboole_0(v0, v1) = v3 & $i(v3))) % 17.36/3.11 | % 17.36/3.11 | ALPHA: (function-axioms) implies: % 17.36/3.12 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.36/3.12 | ! [v3: $i] : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ % 17.36/3.12 | (r2_hidden(v3, v2) = v0)) % 17.36/3.12 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.36/3.12 | (k2_xboole_0(v3, v2) = v1) | ~ (k2_xboole_0(v3, v2) = v0)) % 17.36/3.12 | % 17.36/3.12 | DELTA: instantiating (t1_latsum_1) with fresh symbols all_26_0, all_26_1, % 17.36/3.12 | all_26_2, all_26_3, all_26_4, all_26_5, all_26_6, all_26_7, all_26_8, % 17.36/3.12 | all_26_9 gives: % 17.36/3.12 | (8) k4_xboole_0(all_26_7, all_26_6) = all_26_4 & k2_xboole_0(all_26_7, % 17.36/3.12 | all_26_6) = all_26_5 & r2_hidden(all_26_8, all_26_4) = all_26_2 & % 17.36/3.12 | r2_hidden(all_26_8, all_26_5) = 0 & r2_hidden(all_26_8, all_26_6) = % 17.36/3.12 | all_26_0 & r2_hidden(all_26_9, all_26_4) = all_26_3 & % 17.36/3.12 | r2_hidden(all_26_9, all_26_5) = 0 & r2_hidden(all_26_9, all_26_6) = % 17.36/3.12 | all_26_1 & $i(all_26_4) & $i(all_26_5) & $i(all_26_6) & $i(all_26_7) & % 17.36/3.12 | $i(all_26_8) & $i(all_26_9) & ( ~ (all_26_0 = 0) | ~ (all_26_1 = 0)) & % 17.36/3.12 | ( ~ (all_26_0 = 0) | ~ (all_26_3 = 0)) & ( ~ (all_26_1 = 0) | ~ % 17.36/3.12 | (all_26_2 = 0)) & ( ~ (all_26_2 = 0) | ~ (all_26_3 = 0)) % 17.36/3.12 | % 17.36/3.12 | ALPHA: (8) implies: % 17.36/3.12 | (9) $i(all_26_9) % 17.36/3.12 | (10) $i(all_26_8) % 17.36/3.12 | (11) $i(all_26_7) % 17.36/3.12 | (12) $i(all_26_6) % 17.36/3.12 | (13) $i(all_26_5) % 17.36/3.12 | (14) $i(all_26_4) % 17.36/3.12 | (15) r2_hidden(all_26_9, all_26_6) = all_26_1 % 17.36/3.12 | (16) r2_hidden(all_26_9, all_26_5) = 0 % 17.36/3.12 | (17) r2_hidden(all_26_9, all_26_4) = all_26_3 % 17.36/3.12 | (18) r2_hidden(all_26_8, all_26_6) = all_26_0 % 17.36/3.12 | (19) r2_hidden(all_26_8, all_26_5) = 0 % 17.36/3.12 | (20) r2_hidden(all_26_8, all_26_4) = all_26_2 % 17.36/3.12 | (21) k2_xboole_0(all_26_7, all_26_6) = all_26_5 % 17.36/3.12 | (22) k4_xboole_0(all_26_7, all_26_6) = all_26_4 % 17.36/3.12 | (23) ~ (all_26_2 = 0) | ~ (all_26_3 = 0) % 17.36/3.12 | (24) ~ (all_26_1 = 0) | ~ (all_26_2 = 0) % 17.36/3.12 | (25) ~ (all_26_0 = 0) | ~ (all_26_3 = 0) % 17.36/3.12 | (26) ~ (all_26_0 = 0) | ~ (all_26_1 = 0) % 17.36/3.12 | % 17.36/3.12 | GROUND_INST: instantiating (2) with all_26_7, all_26_6, all_26_5, all_26_8, % 17.36/3.12 | simplifying with (10), (11), (12), (13), (19), (21) gives: % 17.36/3.12 | (27) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_8, all_26_6) = v1 & % 17.36/3.12 | r2_hidden(all_26_8, all_26_7) = v0 & (v1 = 0 | v0 = 0)) % 17.36/3.12 | % 17.36/3.12 | GROUND_INST: instantiating (3) with all_26_7, all_26_6, all_26_5, all_26_8, % 17.36/3.12 | all_26_0, simplifying with (10), (11), (12), (13), (18), (21) % 17.36/3.12 | gives: % 17.36/3.12 | (28) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_8, all_26_5) = v1 & % 17.36/3.12 | r2_hidden(all_26_8, all_26_7) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ % 17.36/3.12 | (all_26_0 = 0)))) % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (2) with all_26_7, all_26_6, all_26_5, all_26_9, % 17.36/3.13 | simplifying with (9), (11), (12), (13), (16), (21) gives: % 17.36/3.13 | (29) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_9, all_26_6) = v1 & % 17.36/3.13 | r2_hidden(all_26_9, all_26_7) = v0 & (v1 = 0 | v0 = 0)) % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (3) with all_26_7, all_26_6, all_26_5, all_26_9, % 17.36/3.13 | all_26_1, simplifying with (9), (11), (12), (13), (15), (21) % 17.36/3.13 | gives: % 17.36/3.13 | (30) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_9, all_26_5) = v1 & % 17.36/3.13 | r2_hidden(all_26_9, all_26_7) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ % 17.36/3.13 | (all_26_1 = 0)))) % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (1) with all_26_6, all_26_7, all_26_5, simplifying % 17.36/3.13 | with (11), (12), (21) gives: % 17.36/3.13 | (31) k2_xboole_0(all_26_6, all_26_7) = all_26_5 & $i(all_26_5) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (31) implies: % 17.36/3.13 | (32) k2_xboole_0(all_26_6, all_26_7) = all_26_5 % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (4) with all_26_7, all_26_6, all_26_5, simplifying % 17.36/3.13 | with (11), (12), (21) gives: % 17.36/3.13 | (33) ? [v0: $i] : (k4_xboole_0(all_26_6, all_26_7) = v0 & % 17.36/3.13 | k2_xboole_0(all_26_7, v0) = all_26_5 & $i(v0) & $i(all_26_5)) % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (5) with all_26_6, all_26_7, all_26_4, simplifying % 17.36/3.13 | with (11), (12), (22) gives: % 17.36/3.13 | (34) ? [v0: $i] : (k2_xboole_0(all_26_6, all_26_4) = v0 & % 17.36/3.13 | k2_xboole_0(all_26_6, all_26_7) = v0 & $i(v0)) % 17.36/3.13 | % 17.36/3.13 | DELTA: instantiating (34) with fresh symbol all_40_0 gives: % 17.36/3.13 | (35) k2_xboole_0(all_26_6, all_26_4) = all_40_0 & k2_xboole_0(all_26_6, % 17.36/3.13 | all_26_7) = all_40_0 & $i(all_40_0) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (35) implies: % 17.36/3.13 | (36) k2_xboole_0(all_26_6, all_26_7) = all_40_0 % 17.36/3.13 | (37) k2_xboole_0(all_26_6, all_26_4) = all_40_0 % 17.36/3.13 | % 17.36/3.13 | DELTA: instantiating (29) with fresh symbols all_44_0, all_44_1 gives: % 17.36/3.13 | (38) r2_hidden(all_26_9, all_26_6) = all_44_0 & r2_hidden(all_26_9, % 17.36/3.13 | all_26_7) = all_44_1 & (all_44_0 = 0 | all_44_1 = 0) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (38) implies: % 17.36/3.13 | (39) r2_hidden(all_26_9, all_26_6) = all_44_0 % 17.36/3.13 | % 17.36/3.13 | DELTA: instantiating (27) with fresh symbols all_46_0, all_46_1 gives: % 17.36/3.13 | (40) r2_hidden(all_26_8, all_26_6) = all_46_0 & r2_hidden(all_26_8, % 17.36/3.13 | all_26_7) = all_46_1 & (all_46_0 = 0 | all_46_1 = 0) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (40) implies: % 17.36/3.13 | (41) r2_hidden(all_26_8, all_26_6) = all_46_0 % 17.36/3.13 | % 17.36/3.13 | DELTA: instantiating (33) with fresh symbol all_48_0 gives: % 17.36/3.13 | (42) k4_xboole_0(all_26_6, all_26_7) = all_48_0 & k2_xboole_0(all_26_7, % 17.36/3.13 | all_48_0) = all_26_5 & $i(all_48_0) & $i(all_26_5) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (42) implies: % 17.36/3.13 | (43) $i(all_48_0) % 17.36/3.13 | (44) k2_xboole_0(all_26_7, all_48_0) = all_26_5 % 17.36/3.13 | % 17.36/3.13 | DELTA: instantiating (30) with fresh symbols all_52_0, all_52_1 gives: % 17.36/3.13 | (45) r2_hidden(all_26_9, all_26_5) = all_52_0 & r2_hidden(all_26_9, % 17.36/3.13 | all_26_7) = all_52_1 & (all_52_0 = 0 | ( ~ (all_52_1 = 0) & ~ % 17.36/3.13 | (all_26_1 = 0))) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (45) implies: % 17.36/3.13 | (46) r2_hidden(all_26_9, all_26_5) = all_52_0 % 17.36/3.13 | % 17.36/3.13 | DELTA: instantiating (28) with fresh symbols all_54_0, all_54_1 gives: % 17.36/3.13 | (47) r2_hidden(all_26_8, all_26_5) = all_54_0 & r2_hidden(all_26_8, % 17.36/3.13 | all_26_7) = all_54_1 & (all_54_0 = 0 | ( ~ (all_54_1 = 0) & ~ % 17.36/3.13 | (all_26_0 = 0))) % 17.36/3.13 | % 17.36/3.13 | ALPHA: (47) implies: % 17.36/3.13 | (48) r2_hidden(all_26_8, all_26_5) = all_54_0 % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (6) with all_26_1, all_44_0, all_26_6, all_26_9, % 17.36/3.13 | simplifying with (15), (39) gives: % 17.36/3.13 | (49) all_44_0 = all_26_1 % 17.36/3.13 | % 17.36/3.13 | GROUND_INST: instantiating (6) with 0, all_52_0, all_26_5, all_26_9, % 17.36/3.13 | simplifying with (16), (46) gives: % 17.36/3.14 | (50) all_52_0 = 0 % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (6) with all_26_0, all_46_0, all_26_6, all_26_8, % 17.36/3.14 | simplifying with (18), (41) gives: % 17.36/3.14 | (51) all_46_0 = all_26_0 % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (6) with 0, all_54_0, all_26_5, all_26_8, % 17.36/3.14 | simplifying with (19), (48) gives: % 17.36/3.14 | (52) all_54_0 = 0 % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (7) with all_26_5, all_40_0, all_26_7, all_26_6, % 17.36/3.14 | simplifying with (32), (36) gives: % 17.36/3.14 | (53) all_40_0 = all_26_5 % 17.36/3.14 | % 17.36/3.14 | REDUCE: (37), (53) imply: % 17.36/3.14 | (54) k2_xboole_0(all_26_6, all_26_4) = all_26_5 % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (1) with all_48_0, all_26_7, all_26_5, simplifying % 17.36/3.14 | with (11), (43), (44) gives: % 17.36/3.14 | (55) k2_xboole_0(all_48_0, all_26_7) = all_26_5 & $i(all_26_5) % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (2) with all_26_6, all_26_7, all_26_5, all_26_8, % 17.36/3.14 | simplifying with (10), (11), (12), (13), (19), (32) gives: % 17.36/3.14 | (56) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_8, all_26_6) = v0 & % 17.36/3.14 | r2_hidden(all_26_8, all_26_7) = v1 & (v1 = 0 | v0 = 0)) % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (2) with all_26_6, all_26_7, all_26_5, all_26_9, % 17.36/3.14 | simplifying with (9), (11), (12), (13), (16), (32) gives: % 17.36/3.14 | (57) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_9, all_26_6) = v0 & % 17.36/3.14 | r2_hidden(all_26_9, all_26_7) = v1 & (v1 = 0 | v0 = 0)) % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (2) with all_26_6, all_26_4, all_26_5, all_26_8, % 17.36/3.14 | simplifying with (10), (12), (13), (14), (19), (54) gives: % 17.36/3.14 | (58) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_8, all_26_4) = v1 & % 17.36/3.14 | r2_hidden(all_26_8, all_26_6) = v0 & (v1 = 0 | v0 = 0)) % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (2) with all_26_6, all_26_4, all_26_5, all_26_9, % 17.36/3.14 | simplifying with (9), (12), (13), (14), (16), (54) gives: % 17.36/3.14 | (59) ? [v0: any] : ? [v1: any] : (r2_hidden(all_26_9, all_26_4) = v1 & % 17.36/3.14 | r2_hidden(all_26_9, all_26_6) = v0 & (v1 = 0 | v0 = 0)) % 17.36/3.14 | % 17.36/3.14 | DELTA: instantiating (57) with fresh symbols all_76_0, all_76_1 gives: % 17.36/3.14 | (60) r2_hidden(all_26_9, all_26_6) = all_76_1 & r2_hidden(all_26_9, % 17.36/3.14 | all_26_7) = all_76_0 & (all_76_0 = 0 | all_76_1 = 0) % 17.36/3.14 | % 17.36/3.14 | ALPHA: (60) implies: % 17.36/3.14 | (61) r2_hidden(all_26_9, all_26_6) = all_76_1 % 17.36/3.14 | % 17.36/3.14 | DELTA: instantiating (59) with fresh symbols all_82_0, all_82_1 gives: % 17.36/3.14 | (62) r2_hidden(all_26_9, all_26_4) = all_82_0 & r2_hidden(all_26_9, % 17.36/3.14 | all_26_6) = all_82_1 & (all_82_0 = 0 | all_82_1 = 0) % 17.36/3.14 | % 17.36/3.14 | ALPHA: (62) implies: % 17.36/3.14 | (63) r2_hidden(all_26_9, all_26_6) = all_82_1 % 17.36/3.14 | (64) r2_hidden(all_26_9, all_26_4) = all_82_0 % 17.36/3.14 | (65) all_82_0 = 0 | all_82_1 = 0 % 17.36/3.14 | % 17.36/3.14 | DELTA: instantiating (58) with fresh symbols all_84_0, all_84_1 gives: % 17.36/3.14 | (66) r2_hidden(all_26_8, all_26_4) = all_84_0 & r2_hidden(all_26_8, % 17.36/3.14 | all_26_6) = all_84_1 & (all_84_0 = 0 | all_84_1 = 0) % 17.36/3.14 | % 17.36/3.14 | ALPHA: (66) implies: % 17.36/3.14 | (67) r2_hidden(all_26_8, all_26_6) = all_84_1 % 17.36/3.14 | (68) r2_hidden(all_26_8, all_26_4) = all_84_0 % 17.36/3.14 | (69) all_84_0 = 0 | all_84_1 = 0 % 17.36/3.14 | % 17.36/3.14 | DELTA: instantiating (56) with fresh symbols all_86_0, all_86_1 gives: % 17.36/3.14 | (70) r2_hidden(all_26_8, all_26_6) = all_86_1 & r2_hidden(all_26_8, % 17.36/3.14 | all_26_7) = all_86_0 & (all_86_0 = 0 | all_86_1 = 0) % 17.36/3.14 | % 17.36/3.14 | ALPHA: (70) implies: % 17.36/3.14 | (71) r2_hidden(all_26_8, all_26_6) = all_86_1 % 17.36/3.14 | % 17.36/3.14 | GROUND_INST: instantiating (6) with all_26_1, all_82_1, all_26_6, all_26_9, % 17.36/3.14 | simplifying with (15), (63) gives: % 17.36/3.14 | (72) all_82_1 = all_26_1 % 17.36/3.14 | % 17.36/3.15 | GROUND_INST: instantiating (6) with all_76_1, all_82_1, all_26_6, all_26_9, % 17.36/3.15 | simplifying with (61), (63) gives: % 17.36/3.15 | (73) all_82_1 = all_76_1 % 17.36/3.15 | % 17.36/3.15 | GROUND_INST: instantiating (6) with all_26_3, all_82_0, all_26_4, all_26_9, % 17.36/3.15 | simplifying with (17), (64) gives: % 17.36/3.15 | (74) all_82_0 = all_26_3 % 17.36/3.15 | % 17.36/3.15 | GROUND_INST: instantiating (6) with all_26_0, all_86_1, all_26_6, all_26_8, % 17.36/3.15 | simplifying with (18), (71) gives: % 17.36/3.15 | (75) all_86_1 = all_26_0 % 17.36/3.15 | % 17.36/3.15 | GROUND_INST: instantiating (6) with all_84_1, all_86_1, all_26_6, all_26_8, % 17.36/3.15 | simplifying with (67), (71) gives: % 17.36/3.15 | (76) all_86_1 = all_84_1 % 17.36/3.15 | % 17.36/3.15 | GROUND_INST: instantiating (6) with all_26_2, all_84_0, all_26_4, all_26_8, % 17.36/3.15 | simplifying with (20), (68) gives: % 17.36/3.15 | (77) all_84_0 = all_26_2 % 17.36/3.15 | % 17.36/3.15 | COMBINE_EQS: (75), (76) imply: % 17.36/3.15 | (78) all_84_1 = all_26_0 % 17.36/3.15 | % 17.36/3.15 | SIMP: (78) implies: % 17.36/3.15 | (79) all_84_1 = all_26_0 % 17.36/3.15 | % 17.36/3.15 | COMBINE_EQS: (72), (73) imply: % 17.36/3.15 | (80) all_76_1 = all_26_1 % 17.36/3.15 | % 17.36/3.15 | BETA: splitting (23) gives: % 17.36/3.15 | % 17.36/3.15 | Case 1: % 17.36/3.15 | | % 17.36/3.15 | | (81) ~ (all_26_2 = 0) % 17.36/3.15 | | % 17.36/3.15 | | BETA: splitting (69) gives: % 17.36/3.15 | | % 17.36/3.15 | | Case 1: % 17.36/3.15 | | | % 17.36/3.15 | | | (82) all_84_0 = 0 % 17.36/3.15 | | | % 17.36/3.15 | | | COMBINE_EQS: (77), (82) imply: % 17.36/3.15 | | | (83) all_26_2 = 0 % 17.36/3.15 | | | % 17.36/3.15 | | | SIMP: (83) implies: % 17.36/3.15 | | | (84) all_26_2 = 0 % 17.36/3.15 | | | % 17.36/3.15 | | | REDUCE: (81), (84) imply: % 17.36/3.15 | | | (85) $false % 17.36/3.15 | | | % 17.36/3.15 | | | CLOSE: (85) is inconsistent. % 17.36/3.15 | | | % 17.36/3.15 | | Case 2: % 17.36/3.15 | | | % 17.36/3.15 | | | (86) all_84_1 = 0 % 17.36/3.15 | | | % 17.36/3.15 | | | COMBINE_EQS: (79), (86) imply: % 17.36/3.15 | | | (87) all_26_0 = 0 % 17.36/3.15 | | | % 17.36/3.15 | | | BETA: splitting (25) gives: % 17.36/3.15 | | | % 17.36/3.15 | | | Case 1: % 17.36/3.15 | | | | % 17.36/3.15 | | | | (88) ~ (all_26_0 = 0) % 17.36/3.15 | | | | % 17.36/3.15 | | | | REDUCE: (87), (88) imply: % 17.36/3.15 | | | | (89) $false % 17.36/3.15 | | | | % 17.36/3.15 | | | | CLOSE: (89) is inconsistent. % 17.36/3.15 | | | | % 17.36/3.15 | | | Case 2: % 17.36/3.15 | | | | % 17.36/3.15 | | | | (90) ~ (all_26_3 = 0) % 17.36/3.15 | | | | % 17.36/3.15 | | | | BETA: splitting (26) gives: % 17.36/3.15 | | | | % 17.36/3.15 | | | | Case 1: % 17.36/3.15 | | | | | % 17.36/3.15 | | | | | (91) ~ (all_26_0 = 0) % 17.36/3.15 | | | | | % 17.36/3.15 | | | | | REDUCE: (87), (91) imply: % 17.36/3.15 | | | | | (92) $false % 17.36/3.15 | | | | | % 17.36/3.15 | | | | | CLOSE: (92) is inconsistent. % 17.36/3.15 | | | | | % 17.36/3.15 | | | | Case 2: % 17.36/3.15 | | | | | % 17.36/3.15 | | | | | (93) ~ (all_26_1 = 0) % 17.36/3.15 | | | | | % 17.36/3.15 | | | | | REF_CLOSE: (65), (72), (74), (90), (93) are inconsistent by sub-proof % 17.36/3.15 | | | | | #1. % 17.36/3.15 | | | | | % 17.36/3.15 | | | | End of split % 17.36/3.15 | | | | % 17.36/3.15 | | | End of split % 17.36/3.15 | | | % 17.36/3.15 | | End of split % 17.36/3.15 | | % 17.36/3.15 | Case 2: % 17.36/3.15 | | % 17.36/3.15 | | (94) all_26_2 = 0 % 17.36/3.15 | | (95) ~ (all_26_3 = 0) % 17.36/3.15 | | % 17.36/3.15 | | BETA: splitting (24) gives: % 17.36/3.15 | | % 17.36/3.15 | | Case 1: % 17.36/3.15 | | | % 17.36/3.15 | | | (96) ~ (all_26_1 = 0) % 17.36/3.15 | | | % 17.36/3.15 | | | REF_CLOSE: (65), (72), (74), (95), (96) are inconsistent by sub-proof #1. % 17.36/3.15 | | | % 17.36/3.15 | | Case 2: % 17.36/3.15 | | | % 17.36/3.15 | | | (97) ~ (all_26_2 = 0) % 17.36/3.15 | | | % 17.36/3.15 | | | REDUCE: (94), (97) imply: % 17.36/3.15 | | | (98) $false % 17.36/3.15 | | | % 17.36/3.15 | | | CLOSE: (98) is inconsistent. % 17.36/3.15 | | | % 17.36/3.15 | | End of split % 17.36/3.15 | | % 17.36/3.15 | End of split % 17.36/3.15 | % 17.36/3.15 End of proof % 17.36/3.15 % 17.36/3.15 Sub-proof #1 shows that the following formulas are inconsistent: % 17.36/3.15 ---------------------------------------------------------------- % 17.36/3.15 (1) ~ (all_26_1 = 0) % 17.36/3.15 (2) ~ (all_26_3 = 0) % 17.36/3.15 (3) all_82_1 = all_26_1 % 17.36/3.15 (4) all_82_0 = 0 | all_82_1 = 0 % 17.36/3.15 (5) all_82_0 = all_26_3 % 17.36/3.15 % 17.36/3.15 Begin of proof % 17.36/3.15 | % 17.36/3.15 | BETA: splitting (4) gives: % 17.36/3.15 | % 17.36/3.15 | Case 1: % 17.36/3.15 | | % 17.36/3.15 | | (6) all_82_0 = 0 % 17.36/3.15 | | % 17.36/3.15 | | COMBINE_EQS: (5), (6) imply: % 17.36/3.16 | | (7) all_26_3 = 0 % 17.36/3.16 | | % 17.36/3.16 | | REDUCE: (2), (7) imply: % 17.36/3.16 | | (8) $false % 17.36/3.16 | | % 17.36/3.16 | | CLOSE: (8) is inconsistent. % 17.36/3.16 | | % 17.36/3.16 | Case 2: % 17.36/3.16 | | % 17.36/3.16 | | (9) all_82_1 = 0 % 17.36/3.16 | | % 17.36/3.16 | | COMBINE_EQS: (3), (9) imply: % 17.36/3.16 | | (10) all_26_1 = 0 % 17.36/3.16 | | % 17.36/3.16 | | REDUCE: (1), (10) imply: % 17.36/3.16 | | (11) $false % 17.36/3.16 | | % 17.36/3.16 | | CLOSE: (11) is inconsistent. % 17.36/3.16 | | % 17.36/3.16 | End of split % 17.36/3.16 | % 17.36/3.16 End of proof % 17.36/3.16 % SZS output end Proof for theBenchmark % 17.36/3.16 % 17.36/3.16 2558ms %------------------------------------------------------------------------------