%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN551+1 : TPTP v8.1.2. Bugfixed v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 03:28:15 EDT 2023 % Result : Theorem 4.28s 1.30s % Output : Proof 6.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN551+1 : TPTP v8.1.2. Bugfixed v3.1.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 19:27:50 EDT 2023 % 0.12/0.33 % CPUTime : % 0.54/0.60 ________ _____ % 0.54/0.60 ___ __ \_________(_)________________________________ % 0.54/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.60 % 0.54/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.60 (2023-06-19) % 0.54/0.60 % 0.54/0.60 (c) Philipp Rümmer, 2009-2023 % 0.54/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.60 Amanda Stjerna. % 0.54/0.60 Free software under BSD-3-Clause. % 0.54/0.60 % 0.54/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.60 % 0.54/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.54/0.62 Running up to 7 provers in parallel. % 0.54/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.54/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.54/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.54/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.54/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.54/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.54/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.03/0.94 Prover 1: Preprocessing ... % 2.03/0.94 Prover 4: Preprocessing ... % 2.21/0.99 Prover 2: Preprocessing ... % 2.21/0.99 Prover 0: Preprocessing ... % 2.21/0.99 Prover 5: Preprocessing ... % 2.21/0.99 Prover 6: Preprocessing ... % 2.21/0.99 Prover 3: Preprocessing ... % 2.96/1.12 Prover 3: Constructing countermodel ... % 2.96/1.12 Prover 5: Constructing countermodel ... % 2.96/1.12 Prover 1: Constructing countermodel ... % 2.96/1.12 Prover 6: Proving ... % 2.96/1.13 Prover 4: Constructing countermodel ... % 2.96/1.13 Prover 0: Proving ... % 3.49/1.15 Prover 2: Proving ... % 4.28/1.30 Prover 3: proved (675ms) % 4.28/1.30 Prover 5: proved (674ms) % 4.28/1.30 % 4.28/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.28/1.30 % 4.28/1.30 % 4.28/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.28/1.30 % 4.28/1.30 Prover 6: stopped % 4.28/1.30 Prover 2: stopped % 4.73/1.32 Prover 0: stopped % 4.73/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.73/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.73/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.73/1.32 Prover 7: Preprocessing ... % 4.73/1.32 Prover 8: Preprocessing ... % 4.73/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.73/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.73/1.33 Prover 11: Preprocessing ... % 4.73/1.33 Prover 13: Preprocessing ... % 4.73/1.34 Prover 10: Preprocessing ... % 5.05/1.37 Prover 8: Warning: ignoring some quantifiers % 5.05/1.38 Prover 8: Constructing countermodel ... % 5.05/1.38 Prover 7: Constructing countermodel ... % 5.05/1.39 Prover 13: Constructing countermodel ... % 5.05/1.41 Prover 11: Constructing countermodel ... % 5.05/1.42 Prover 10: Constructing countermodel ... % 5.05/1.44 Prover 4: Found proof (size 44) % 5.05/1.44 Prover 4: proved (815ms) % 5.05/1.44 Prover 13: stopped % 5.05/1.44 Prover 8: stopped % 5.05/1.44 Prover 1: stopped % 5.05/1.44 Prover 11: stopped % 5.05/1.44 Prover 7: stopped % 5.66/1.44 Prover 10: stopped % 5.66/1.44 % 5.66/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.66/1.44 % 5.66/1.45 % SZS output start Proof for theBenchmark % 5.66/1.46 Assumptions after simplification: % 5.66/1.46 --------------------------------- % 5.66/1.46 % 5.66/1.46 (prove_this_cute_thing) % 5.83/1.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 5.83/1.50 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 5.83/1.50 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? % 5.83/1.50 [v16: $i] : ? [v17: $i] : ($i(v15) & $i(v10) & $i(v9) & $i(v6) & $i(v1) & % 5.83/1.50 $i(v0) & ((v17 = v15 & g(v15) = v16 & f(v16) = v15 & $i(v16) & ! [v18: $i] % 5.83/1.50 : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : (v19 = v18 | ~ (g(v19) = % 5.83/1.50 v21) | ~ (g(v18) = v20) | ~ (f(v21) = v19) | ~ (f(v20) = v18) | % 5.83/1.50 ~ $i(v19) | ~ $i(v18)) & ( ! [v18: $i] : ! [v19: $i] : ( ~ (f(v18) = % 5.83/1.50 v19) | ~ $i(v18) | ? [v20: $i] : ( ~ (v20 = v18) & g(v19) = v20 % 5.83/1.50 & $i(v20))) | (v14 = v10 & v12 = v9 & ~ (v10 = v9) & g(v13) = v10 % 5.83/1.50 & g(v11) = v9 & f(v10) = v13 & f(v9) = v11 & $i(v13) & $i(v11)))) | % 5.83/1.50 (v8 = v6 & g(v7) = v6 & f(v6) = v7 & $i(v7) & ! [v18: $i] : ! [v19: $i] % 5.83/1.50 : ! [v20: $i] : ! [v21: $i] : (v19 = v18 | ~ (g(v21) = v19) | ~ % 5.83/1.50 (g(v20) = v18) | ~ (f(v19) = v21) | ~ (f(v18) = v20) | ~ $i(v19) | % 5.83/1.50 ~ $i(v18)) & ( ! [v18: $i] : ! [v19: $i] : ( ~ (g(v18) = v19) | ~ % 5.83/1.50 $i(v18) | ? [v20: $i] : ( ~ (v20 = v18) & f(v19) = v20 & $i(v20))) % 5.83/1.50 | (v5 = v1 & v3 = v0 & ~ (v1 = v0) & g(v1) = v4 & g(v0) = v2 & f(v4) % 5.83/1.50 = v1 & f(v2) = v0 & $i(v4) & $i(v2)))))) % 5.83/1.50 % 5.83/1.50 (function-axioms) % 5.83/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) | ~ % 5.83/1.50 (g(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 5.83/1.50 (f(v2) = v1) | ~ (f(v2) = v0)) % 5.83/1.50 % 5.83/1.50 Those formulas are unsatisfiable: % 5.83/1.50 --------------------------------- % 5.83/1.50 % 5.83/1.50 Begin of proof % 5.83/1.50 | % 5.83/1.50 | ALPHA: (function-axioms) implies: % 5.83/1.50 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | % 5.83/1.50 | ~ (f(v2) = v0)) % 5.83/1.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) | % 5.83/1.50 | ~ (g(v2) = v0)) % 5.83/1.50 | % 5.83/1.51 | DELTA: instantiating (prove_this_cute_thing) with fresh symbols all_3_0, % 5.83/1.51 | all_3_1, all_3_2, all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8, % 5.83/1.51 | all_3_9, all_3_10, all_3_11, all_3_12, all_3_13, all_3_14, all_3_15, % 5.83/1.51 | all_3_16, all_3_17 gives: % 5.83/1.51 | (3) $i(all_3_2) & $i(all_3_7) & $i(all_3_8) & $i(all_3_11) & $i(all_3_16) & % 5.83/1.51 | $i(all_3_17) & ((all_3_0 = all_3_2 & g(all_3_2) = all_3_1 & f(all_3_1) % 5.83/1.51 | = all_3_2 & $i(all_3_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 5.83/1.51 | ! [v3: $i] : (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ % 5.83/1.51 | (f(v3) = v1) | ~ (f(v2) = v0) | ~ $i(v1) | ~ $i(v0)) & ( ! % 5.83/1.51 | [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: % 5.83/1.51 | $i] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2))) | (all_3_3 = % 5.83/1.51 | all_3_7 & all_3_5 = all_3_8 & ~ (all_3_7 = all_3_8) & % 5.83/1.52 | g(all_3_4) = all_3_7 & g(all_3_6) = all_3_8 & f(all_3_7) = % 5.83/1.52 | all_3_4 & f(all_3_8) = all_3_6 & $i(all_3_4) & $i(all_3_6)))) | % 5.83/1.52 | (all_3_9 = all_3_11 & g(all_3_10) = all_3_11 & f(all_3_11) = all_3_10 % 5.83/1.52 | & $i(all_3_10) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 5.83/1.52 | $i] : (v1 = v0 | ~ (g(v3) = v1) | ~ (g(v2) = v0) | ~ (f(v1) = % 5.83/1.52 | v3) | ~ (f(v0) = v2) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] : % 5.83/1.52 | ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ % 5.83/1.52 | (v2 = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 = all_3_16 & % 5.83/1.52 | all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) & g(all_3_16) = % 5.83/1.52 | all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) = all_3_16 & % 5.83/1.52 | f(all_3_15) = all_3_17 & $i(all_3_13) & $i(all_3_15))))) % 5.83/1.52 | % 5.83/1.52 | ALPHA: (3) implies: % 5.83/1.52 | (4) $i(all_3_11) % 5.83/1.52 | (5) $i(all_3_2) % 5.83/1.52 | (6) (all_3_0 = all_3_2 & g(all_3_2) = all_3_1 & f(all_3_1) = all_3_2 & % 5.83/1.52 | $i(all_3_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 5.83/1.52 | (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ (f(v3) = v1) | ~ % 5.83/1.52 | (f(v2) = v0) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] : ! [v1: $i] % 5.83/1.52 | : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 = v0) & % 5.83/1.52 | g(v1) = v2 & $i(v2))) | (all_3_3 = all_3_7 & all_3_5 = all_3_8 % 5.83/1.52 | & ~ (all_3_7 = all_3_8) & g(all_3_4) = all_3_7 & g(all_3_6) = % 5.83/1.52 | all_3_8 & f(all_3_7) = all_3_4 & f(all_3_8) = all_3_6 & % 5.83/1.52 | $i(all_3_4) & $i(all_3_6)))) | (all_3_9 = all_3_11 & g(all_3_10) % 5.83/1.52 | = all_3_11 & f(all_3_11) = all_3_10 & $i(all_3_10) & ! [v0: $i] : ! % 5.83/1.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (g(v3) = v1) | % 5.83/1.52 | ~ (g(v2) = v0) | ~ (f(v1) = v3) | ~ (f(v0) = v2) | ~ $i(v1) | ~ % 5.83/1.52 | $i(v0)) & ( ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) % 5.83/1.52 | | ? [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 % 5.83/1.52 | = all_3_16 & all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) & % 5.83/1.52 | g(all_3_16) = all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) = % 5.83/1.52 | all_3_16 & f(all_3_15) = all_3_17 & $i(all_3_13) & % 5.83/1.52 | $i(all_3_15)))) % 5.83/1.52 | % 5.83/1.52 | BETA: splitting (6) gives: % 5.83/1.52 | % 5.83/1.52 | Case 1: % 5.83/1.52 | | % 5.83/1.53 | | (7) all_3_0 = all_3_2 & g(all_3_2) = all_3_1 & f(all_3_1) = all_3_2 & % 5.83/1.53 | | $i(all_3_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 5.83/1.53 | | (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ (f(v3) = v1) | ~ % 5.83/1.53 | | (f(v2) = v0) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] : ! [v1: $i] % 5.83/1.53 | | : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 = v0) & % 5.83/1.53 | | g(v1) = v2 & $i(v2))) | (all_3_3 = all_3_7 & all_3_5 = all_3_8 % 5.83/1.53 | | & ~ (all_3_7 = all_3_8) & g(all_3_4) = all_3_7 & g(all_3_6) = % 5.83/1.53 | | all_3_8 & f(all_3_7) = all_3_4 & f(all_3_8) = all_3_6 & % 5.83/1.53 | | $i(all_3_4) & $i(all_3_6))) % 5.83/1.53 | | % 5.83/1.53 | | ALPHA: (7) implies: % 5.83/1.53 | | (8) $i(all_3_1) % 5.83/1.53 | | (9) f(all_3_1) = all_3_2 % 5.83/1.53 | | (10) g(all_3_2) = all_3_1 % 5.83/1.53 | | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: % 5.83/1.53 | | $i] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2))) | (all_3_3 = all_3_7 % 5.83/1.53 | | & all_3_5 = all_3_8 & ~ (all_3_7 = all_3_8) & g(all_3_4) = % 5.83/1.53 | | all_3_7 & g(all_3_6) = all_3_8 & f(all_3_7) = all_3_4 & f(all_3_8) % 5.83/1.53 | | = all_3_6 & $i(all_3_4) & $i(all_3_6)) % 6.10/1.53 | | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 6.10/1.53 | | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ (f(v3) = v1) | ~ (f(v2) = % 6.10/1.53 | | v0) | ~ $i(v1) | ~ $i(v0)) % 6.10/1.53 | | % 6.10/1.53 | | BETA: splitting (11) gives: % 6.10/1.53 | | % 6.10/1.53 | | Case 1: % 6.10/1.53 | | | % 6.10/1.53 | | | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: % 6.10/1.53 | | | $i] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2))) % 6.10/1.53 | | | % 6.10/1.53 | | | GROUND_INST: instantiating (13) with all_3_1, all_3_2, simplifying with % 6.10/1.53 | | | (8), (9) gives: % 6.10/1.53 | | | (14) ? [v0: any] : ( ~ (v0 = all_3_1) & g(all_3_2) = v0 & $i(v0)) % 6.10/1.53 | | | % 6.10/1.53 | | | DELTA: instantiating (14) with fresh symbol all_20_0 gives: % 6.10/1.53 | | | (15) ~ (all_20_0 = all_3_1) & g(all_3_2) = all_20_0 & $i(all_20_0) % 6.10/1.53 | | | % 6.10/1.53 | | | ALPHA: (15) implies: % 6.10/1.54 | | | (16) ~ (all_20_0 = all_3_1) % 6.10/1.54 | | | (17) g(all_3_2) = all_20_0 % 6.10/1.54 | | | % 6.10/1.54 | | | GROUND_INST: instantiating (2) with all_3_1, all_20_0, all_3_2, % 6.10/1.54 | | | simplifying with (10), (17) gives: % 6.10/1.54 | | | (18) all_20_0 = all_3_1 % 6.10/1.54 | | | % 6.10/1.54 | | | REDUCE: (16), (18) imply: % 6.10/1.54 | | | (19) $false % 6.10/1.54 | | | % 6.10/1.54 | | | CLOSE: (19) is inconsistent. % 6.10/1.54 | | | % 6.10/1.54 | | Case 2: % 6.10/1.54 | | | % 6.10/1.54 | | | (20) all_3_3 = all_3_7 & all_3_5 = all_3_8 & ~ (all_3_7 = all_3_8) & % 6.10/1.54 | | | g(all_3_4) = all_3_7 & g(all_3_6) = all_3_8 & f(all_3_7) = all_3_4 % 6.10/1.54 | | | & f(all_3_8) = all_3_6 & $i(all_3_4) & $i(all_3_6) % 6.10/1.54 | | | % 6.10/1.54 | | | ALPHA: (20) implies: % 6.10/1.54 | | | (21) ~ (all_3_7 = all_3_8) % 6.10/1.54 | | | (22) $i(all_3_6) % 6.10/1.54 | | | (23) $i(all_3_4) % 6.10/1.54 | | | (24) f(all_3_8) = all_3_6 % 6.10/1.54 | | | (25) f(all_3_7) = all_3_4 % 6.10/1.54 | | | (26) g(all_3_6) = all_3_8 % 6.10/1.54 | | | (27) g(all_3_4) = all_3_7 % 6.10/1.54 | | | % 6.10/1.54 | | | GROUND_INST: instantiating (12) with all_3_6, all_3_2, all_3_8, all_3_1, % 6.10/1.54 | | | simplifying with (5), (9), (10), (22), (24), (26) gives: % 6.10/1.54 | | | (28) all_3_2 = all_3_6 % 6.10/1.54 | | | % 6.10/1.54 | | | GROUND_INST: instantiating (12) with all_3_4, all_3_2, all_3_7, all_3_1, % 6.10/1.54 | | | simplifying with (5), (9), (10), (23), (25), (27) gives: % 6.10/1.54 | | | (29) all_3_2 = all_3_4 % 6.10/1.54 | | | % 6.10/1.54 | | | COMBINE_EQS: (28), (29) imply: % 6.10/1.54 | | | (30) all_3_4 = all_3_6 % 6.10/1.54 | | | % 6.10/1.54 | | | REDUCE: (10), (28) imply: % 6.10/1.54 | | | (31) g(all_3_6) = all_3_1 % 6.10/1.54 | | | % 6.10/1.54 | | | REDUCE: (27), (30) imply: % 6.10/1.54 | | | (32) g(all_3_6) = all_3_7 % 6.10/1.54 | | | % 6.10/1.54 | | | GROUND_INST: instantiating (2) with all_3_8, all_3_1, all_3_6, simplifying % 6.10/1.54 | | | with (26), (31) gives: % 6.10/1.54 | | | (33) all_3_1 = all_3_8 % 6.10/1.54 | | | % 6.10/1.54 | | | GROUND_INST: instantiating (2) with all_3_7, all_3_1, all_3_6, simplifying % 6.10/1.54 | | | with (31), (32) gives: % 6.10/1.54 | | | (34) all_3_1 = all_3_7 % 6.10/1.54 | | | % 6.10/1.54 | | | COMBINE_EQS: (33), (34) imply: % 6.10/1.54 | | | (35) all_3_7 = all_3_8 % 6.10/1.54 | | | % 6.10/1.55 | | | REDUCE: (21), (35) imply: % 6.10/1.55 | | | (36) $false % 6.10/1.55 | | | % 6.10/1.55 | | | CLOSE: (36) is inconsistent. % 6.10/1.55 | | | % 6.10/1.55 | | End of split % 6.10/1.55 | | % 6.10/1.55 | Case 2: % 6.10/1.55 | | % 6.10/1.55 | | (37) all_3_9 = all_3_11 & g(all_3_10) = all_3_11 & f(all_3_11) = all_3_10 % 6.10/1.55 | | & $i(all_3_10) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 6.10/1.55 | | $i] : (v1 = v0 | ~ (g(v3) = v1) | ~ (g(v2) = v0) | ~ (f(v1) = % 6.10/1.55 | | v3) | ~ (f(v0) = v2) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] : % 6.10/1.55 | | ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 % 6.10/1.55 | | = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 = all_3_16 & % 6.10/1.55 | | all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) & g(all_3_16) = % 6.10/1.55 | | all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) = all_3_16 & % 6.10/1.55 | | f(all_3_15) = all_3_17 & $i(all_3_13) & $i(all_3_15))) % 6.10/1.55 | | % 6.10/1.55 | | ALPHA: (37) implies: % 6.10/1.55 | | (38) $i(all_3_10) % 6.10/1.55 | | (39) f(all_3_11) = all_3_10 % 6.10/1.55 | | (40) g(all_3_10) = all_3_11 % 6.18/1.55 | | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: % 6.18/1.55 | | $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 = % 6.18/1.55 | | all_3_16 & all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) & % 6.18/1.55 | | g(all_3_16) = all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) = % 6.18/1.55 | | all_3_16 & f(all_3_15) = all_3_17 & $i(all_3_13) & $i(all_3_15)) % 6.18/1.55 | | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 6.18/1.55 | | ~ (g(v3) = v1) | ~ (g(v2) = v0) | ~ (f(v1) = v3) | ~ (f(v0) = % 6.18/1.55 | | v2) | ~ $i(v1) | ~ $i(v0)) % 6.18/1.55 | | % 6.18/1.55 | | BETA: splitting (41) gives: % 6.18/1.55 | | % 6.18/1.55 | | Case 1: % 6.18/1.55 | | | % 6.18/1.55 | | | (43) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: % 6.18/1.55 | | | $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) % 6.18/1.55 | | | % 6.18/1.55 | | | GROUND_INST: instantiating (43) with all_3_10, all_3_11, simplifying with % 6.18/1.55 | | | (38), (40) gives: % 6.18/1.55 | | | (44) ? [v0: any] : ( ~ (v0 = all_3_10) & f(all_3_11) = v0 & $i(v0)) % 6.18/1.55 | | | % 6.18/1.55 | | | DELTA: instantiating (44) with fresh symbol all_20_0 gives: % 6.18/1.55 | | | (45) ~ (all_20_0 = all_3_10) & f(all_3_11) = all_20_0 & $i(all_20_0) % 6.18/1.55 | | | % 6.18/1.55 | | | ALPHA: (45) implies: % 6.18/1.55 | | | (46) ~ (all_20_0 = all_3_10) % 6.18/1.55 | | | (47) f(all_3_11) = all_20_0 % 6.18/1.55 | | | % 6.18/1.55 | | | GROUND_INST: instantiating (1) with all_3_10, all_20_0, all_3_11, % 6.18/1.55 | | | simplifying with (39), (47) gives: % 6.18/1.55 | | | (48) all_20_0 = all_3_10 % 6.18/1.55 | | | % 6.18/1.55 | | | REDUCE: (46), (48) imply: % 6.18/1.55 | | | (49) $false % 6.18/1.55 | | | % 6.18/1.55 | | | CLOSE: (49) is inconsistent. % 6.18/1.55 | | | % 6.18/1.55 | | Case 2: % 6.18/1.55 | | | % 6.18/1.56 | | | (50) all_3_12 = all_3_16 & all_3_14 = all_3_17 & ~ (all_3_16 = % 6.18/1.56 | | | all_3_17) & g(all_3_16) = all_3_13 & g(all_3_17) = all_3_15 & % 6.18/1.56 | | | f(all_3_13) = all_3_16 & f(all_3_15) = all_3_17 & $i(all_3_13) & % 6.18/1.56 | | | $i(all_3_15) % 6.18/1.56 | | | % 6.18/1.56 | | | ALPHA: (50) implies: % 6.18/1.56 | | | (51) ~ (all_3_16 = all_3_17) % 6.18/1.56 | | | (52) $i(all_3_15) % 6.18/1.56 | | | (53) $i(all_3_13) % 6.18/1.56 | | | (54) f(all_3_15) = all_3_17 % 6.18/1.56 | | | (55) f(all_3_13) = all_3_16 % 6.18/1.56 | | | (56) g(all_3_17) = all_3_15 % 6.18/1.56 | | | (57) g(all_3_16) = all_3_13 % 6.18/1.56 | | | % 6.18/1.56 | | | GROUND_INST: instantiating (42) with all_3_15, all_3_11, all_3_17, % 6.18/1.56 | | | all_3_10, simplifying with (4), (39), (40), (52), (54), (56) % 6.18/1.56 | | | gives: % 6.18/1.56 | | | (58) all_3_11 = all_3_15 % 6.18/1.56 | | | % 6.18/1.56 | | | GROUND_INST: instantiating (42) with all_3_13, all_3_11, all_3_16, % 6.18/1.56 | | | all_3_10, simplifying with (4), (39), (40), (53), (55), (57) % 6.18/1.56 | | | gives: % 6.18/1.56 | | | (59) all_3_11 = all_3_13 % 6.18/1.56 | | | % 6.18/1.56 | | | COMBINE_EQS: (58), (59) imply: % 6.18/1.56 | | | (60) all_3_13 = all_3_15 % 6.18/1.56 | | | % 6.18/1.56 | | | REDUCE: (39), (58) imply: % 6.18/1.56 | | | (61) f(all_3_15) = all_3_10 % 6.18/1.56 | | | % 6.18/1.56 | | | REDUCE: (55), (60) imply: % 6.18/1.56 | | | (62) f(all_3_15) = all_3_16 % 6.18/1.56 | | | % 6.18/1.56 | | | GROUND_INST: instantiating (1) with all_3_17, all_3_10, all_3_15, % 6.18/1.56 | | | simplifying with (54), (61) gives: % 6.18/1.56 | | | (63) all_3_10 = all_3_17 % 6.18/1.56 | | | % 6.18/1.56 | | | GROUND_INST: instantiating (1) with all_3_16, all_3_10, all_3_15, % 6.18/1.56 | | | simplifying with (61), (62) gives: % 6.18/1.56 | | | (64) all_3_10 = all_3_16 % 6.18/1.56 | | | % 6.18/1.56 | | | COMBINE_EQS: (63), (64) imply: % 6.18/1.56 | | | (65) all_3_16 = all_3_17 % 6.18/1.56 | | | % 6.18/1.56 | | | REDUCE: (51), (65) imply: % 6.18/1.56 | | | (66) $false % 6.18/1.56 | | | % 6.18/1.56 | | | CLOSE: (66) is inconsistent. % 6.18/1.56 | | | % 6.18/1.56 | | End of split % 6.18/1.56 | | % 6.18/1.56 | End of split % 6.18/1.56 | % 6.18/1.56 End of proof % 6.18/1.56 % SZS output end Proof for theBenchmark % 6.18/1.56 % 6.18/1.56 958ms %------------------------------------------------------------------------------