%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN551+3 : TPTP v8.1.2. Bugfixed v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 3.69s 1.28s % Output : Proof 5.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYN551+3 : TPTP v8.1.2. Bugfixed v3.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n004.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 : Sat Aug 26 21:28:08 EDT 2023 % 0.20/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.79/0.96 Prover 4: Preprocessing ... % 1.79/0.96 Prover 1: Preprocessing ... % 1.79/1.01 Prover 2: Preprocessing ... % 1.79/1.01 Prover 3: Preprocessing ... % 1.79/1.01 Prover 0: Preprocessing ... % 1.79/1.01 Prover 5: Preprocessing ... % 1.79/1.01 Prover 6: Preprocessing ... % 2.73/1.12 Prover 1: Constructing countermodel ... % 2.73/1.12 Prover 3: Constructing countermodel ... % 2.73/1.12 Prover 6: Proving ... % 2.73/1.12 Prover 4: Constructing countermodel ... % 2.73/1.13 Prover 5: Constructing countermodel ... % 2.73/1.15 Prover 0: Proving ... % 3.34/1.18 Prover 2: Proving ... % 3.69/1.27 Prover 5: proved (618ms) % 3.69/1.28 % 3.69/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.69/1.28 % 3.69/1.28 Prover 3: stopped % 3.69/1.28 Prover 6: stopped % 3.69/1.29 Prover 2: stopped % 3.69/1.29 Prover 0: stopped % 3.69/1.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.69/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.69/1.29 Prover 7: Preprocessing ... % 3.69/1.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.69/1.29 Prover 8: Preprocessing ... % 3.69/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.69/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.69/1.31 Prover 13: Preprocessing ... % 4.26/1.32 Prover 10: Preprocessing ... % 4.26/1.32 Prover 11: Preprocessing ... % 4.26/1.35 Prover 7: Constructing countermodel ... % 4.26/1.35 Prover 8: Warning: ignoring some quantifiers % 4.26/1.36 Prover 8: Constructing countermodel ... % 4.26/1.36 Prover 13: Constructing countermodel ... % 4.26/1.36 Prover 10: Constructing countermodel ... % 4.26/1.39 Prover 11: Constructing countermodel ... % 4.96/1.41 Prover 1: Found proof (size 51) % 4.96/1.41 Prover 1: proved (759ms) % 4.96/1.41 Prover 11: stopped % 4.96/1.41 Prover 8: stopped % 4.96/1.41 Prover 10: stopped % 4.96/1.41 Prover 4: stopped % 4.96/1.41 Prover 7: stopped % 4.96/1.41 Prover 13: stopped % 4.96/1.41 % 4.96/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.96/1.41 % 4.96/1.42 % SZS output start Proof for theBenchmark % 4.96/1.42 Assumptions after simplification: % 4.96/1.42 --------------------------------- % 4.96/1.42 % 4.96/1.42 (prove_this_cute_thing) % 4.96/1.46 ( ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 4.96/1.46 [v3: $i] : ( ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2 & $i(v3) & $i(v2)) | ? % 4.96/1.46 [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) & ? [v0: $i] : ? [v1: % 4.96/1.46 $i] : (g(v1) = v0 & f(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 4.96/1.46 $i] : (v2 = v0 | ~ (f(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = % 4.96/1.46 v2) & g(v3) = v4 & $i(v4))))) | ( ! [v0: $i] : ! [v1: $i] : ( ~ % 4.96/1.46 (f(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v2 = v0) & % 4.96/1.46 g(v3) = v2 & f(v2) = v3 & $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) % 4.96/1.46 & g(v1) = v2 & $i(v2))) & ? [v0: $i] : ? [v1: $i] : (g(v0) = v1 & % 4.96/1.46 f(v1) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ % 4.96/1.46 (g(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & f(v3) = v4 & % 4.96/1.46 $i(v4))))) % 4.96/1.46 % 4.96/1.46 (function-axioms) % 4.96/1.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) | ~ % 4.96/1.46 (g(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 4.96/1.46 (f(v2) = v1) | ~ (f(v2) = v0)) % 4.96/1.46 % 4.96/1.46 Those formulas are unsatisfiable: % 4.96/1.46 --------------------------------- % 4.96/1.46 % 4.96/1.46 Begin of proof % 4.96/1.46 | % 4.96/1.46 | ALPHA: (function-axioms) implies: % 4.96/1.46 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | % 4.96/1.46 | ~ (f(v2) = v0)) % 4.96/1.46 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) | % 4.96/1.46 | ~ (g(v2) = v0)) % 4.96/1.46 | % 4.96/1.46 | BETA: splitting (prove_this_cute_thing) gives: % 4.96/1.46 | % 5.34/1.46 | Case 1: % 5.34/1.46 | | % 5.34/1.47 | | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: % 5.34/1.47 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2 & % 5.34/1.47 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 & % 5.34/1.47 | | $i(v2))) & ? [v0: $i] : ? [v1: $i] : (g(v1) = v0 & f(v0) = v1 & % 5.34/1.47 | | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (f(v2) % 5.34/1.47 | | = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & g(v3) = v4 & % 5.34/1.47 | | $i(v4)))) % 5.34/1.47 | | % 5.34/1.47 | | ALPHA: (3) implies: % 5.34/1.47 | | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: % 5.34/1.47 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2 & % 5.34/1.47 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 & % 5.34/1.47 | | $i(v2))) % 5.34/1.47 | | (5) ? [v0: $i] : ? [v1: $i] : (g(v1) = v0 & f(v0) = v1 & $i(v1) & % 5.34/1.47 | | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (f(v2) = v3) | % 5.34/1.47 | | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & g(v3) = v4 & $i(v4)))) % 5.34/1.47 | | % 5.34/1.47 | | DELTA: instantiating (5) with fresh symbols all_10_0, all_10_1 gives: % 5.34/1.48 | | (6) g(all_10_0) = all_10_1 & f(all_10_1) = all_10_0 & $i(all_10_0) & % 5.34/1.48 | | $i(all_10_1) & ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~ % 5.34/1.48 | | (f(v0) = v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & g(v1) = % 5.34/1.48 | | v2 & $i(v2))) % 5.34/1.48 | | % 5.34/1.48 | | ALPHA: (6) implies: % 5.34/1.48 | | (7) $i(all_10_0) % 5.34/1.48 | | (8) f(all_10_1) = all_10_0 % 5.34/1.48 | | (9) g(all_10_0) = all_10_1 % 5.34/1.48 | | (10) ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~ (f(v0) = v1) | ~ % 5.34/1.48 | | $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2))) % 5.34/1.48 | | % 5.34/1.48 | | GROUND_INST: instantiating (4) with all_10_0, all_10_1, simplifying with % 5.34/1.48 | | (7), (9) gives: % 5.34/1.48 | | (11) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v0) = v1 & % 5.34/1.48 | | f(v1) = v0 & $i(v1) & $i(v0)) | ? [v0: any] : ( ~ (v0 = all_10_0) % 5.34/1.48 | | & f(all_10_1) = v0 & $i(v0)) % 5.34/1.48 | | % 5.34/1.48 | | BETA: splitting (11) gives: % 5.34/1.48 | | % 5.34/1.48 | | Case 1: % 5.34/1.48 | | | % 5.34/1.48 | | | (12) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v0) = v1 & % 5.34/1.48 | | | f(v1) = v0 & $i(v1) & $i(v0)) % 5.34/1.48 | | | % 5.34/1.48 | | | DELTA: instantiating (12) with fresh symbols all_19_0, all_19_1 gives: % 5.34/1.48 | | | (13) ~ (all_19_1 = all_10_0) & g(all_19_1) = all_19_0 & f(all_19_0) = % 5.34/1.48 | | | all_19_1 & $i(all_19_0) & $i(all_19_1) % 5.34/1.48 | | | % 5.34/1.48 | | | ALPHA: (13) implies: % 5.34/1.48 | | | (14) ~ (all_19_1 = all_10_0) % 5.34/1.48 | | | (15) $i(all_19_0) % 5.34/1.48 | | | (16) f(all_19_0) = all_19_1 % 5.34/1.48 | | | (17) g(all_19_1) = all_19_0 % 5.34/1.48 | | | % 5.34/1.48 | | | GROUND_INST: instantiating (10) with all_19_0, all_19_1, simplifying with % 5.34/1.48 | | | (15), (16) gives: % 5.34/1.48 | | | (18) all_19_0 = all_10_1 | ? [v0: any] : ( ~ (v0 = all_19_0) & % 5.34/1.48 | | | g(all_19_1) = v0 & $i(v0)) % 5.34/1.48 | | | % 5.34/1.48 | | | BETA: splitting (18) gives: % 5.34/1.48 | | | % 5.34/1.48 | | | Case 1: % 5.34/1.48 | | | | % 5.34/1.48 | | | | (19) all_19_0 = all_10_1 % 5.34/1.48 | | | | % 5.34/1.48 | | | | REDUCE: (16), (19) imply: % 5.34/1.48 | | | | (20) f(all_10_1) = all_19_1 % 5.34/1.48 | | | | % 5.34/1.48 | | | | GROUND_INST: instantiating (1) with all_10_0, all_19_1, all_10_1, % 5.34/1.48 | | | | simplifying with (8), (20) gives: % 5.34/1.49 | | | | (21) all_19_1 = all_10_0 % 5.34/1.49 | | | | % 5.34/1.49 | | | | REDUCE: (14), (21) imply: % 5.34/1.49 | | | | (22) $false % 5.34/1.49 | | | | % 5.34/1.49 | | | | CLOSE: (22) is inconsistent. % 5.34/1.49 | | | | % 5.34/1.49 | | | Case 2: % 5.34/1.49 | | | | % 5.34/1.49 | | | | (23) ? [v0: any] : ( ~ (v0 = all_19_0) & g(all_19_1) = v0 & $i(v0)) % 5.34/1.49 | | | | % 5.34/1.49 | | | | DELTA: instantiating (23) with fresh symbol all_33_0 gives: % 5.34/1.49 | | | | (24) ~ (all_33_0 = all_19_0) & g(all_19_1) = all_33_0 & $i(all_33_0) % 5.34/1.49 | | | | % 5.34/1.49 | | | | ALPHA: (24) implies: % 5.34/1.49 | | | | (25) ~ (all_33_0 = all_19_0) % 5.34/1.49 | | | | (26) g(all_19_1) = all_33_0 % 5.34/1.49 | | | | % 5.34/1.49 | | | | GROUND_INST: instantiating (2) with all_19_0, all_33_0, all_19_1, % 5.34/1.49 | | | | simplifying with (17), (26) gives: % 5.34/1.49 | | | | (27) all_33_0 = all_19_0 % 5.34/1.49 | | | | % 5.34/1.49 | | | | REDUCE: (25), (27) imply: % 5.34/1.49 | | | | (28) $false % 5.34/1.49 | | | | % 5.34/1.49 | | | | CLOSE: (28) is inconsistent. % 5.34/1.49 | | | | % 5.34/1.49 | | | End of split % 5.34/1.49 | | | % 5.34/1.49 | | Case 2: % 5.34/1.49 | | | % 5.34/1.49 | | | (29) ? [v0: any] : ( ~ (v0 = all_10_0) & f(all_10_1) = v0 & $i(v0)) % 5.34/1.49 | | | % 5.34/1.49 | | | DELTA: instantiating (29) with fresh symbol all_19_0 gives: % 5.34/1.49 | | | (30) ~ (all_19_0 = all_10_0) & f(all_10_1) = all_19_0 & $i(all_19_0) % 5.34/1.49 | | | % 5.34/1.49 | | | ALPHA: (30) implies: % 5.34/1.49 | | | (31) ~ (all_19_0 = all_10_0) % 5.34/1.49 | | | (32) f(all_10_1) = all_19_0 % 5.34/1.49 | | | % 5.34/1.49 | | | GROUND_INST: instantiating (1) with all_10_0, all_19_0, all_10_1, % 5.34/1.49 | | | simplifying with (8), (32) gives: % 5.34/1.49 | | | (33) all_19_0 = all_10_0 % 5.34/1.49 | | | % 5.34/1.49 | | | REDUCE: (31), (33) imply: % 5.34/1.49 | | | (34) $false % 5.34/1.49 | | | % 5.34/1.49 | | | CLOSE: (34) is inconsistent. % 5.34/1.49 | | | % 5.34/1.49 | | End of split % 5.34/1.49 | | % 5.34/1.49 | Case 2: % 5.34/1.49 | | % 5.34/1.49 | | (35) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: % 5.34/1.49 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3 & % 5.34/1.49 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & g(v1) = v2 & % 5.34/1.49 | | $i(v2))) & ? [v0: $i] : ? [v1: $i] : (g(v0) = v1 & f(v1) = v0 % 5.34/1.49 | | & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ % 5.34/1.49 | | (g(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & f(v3) = % 5.34/1.49 | | v4 & $i(v4)))) % 5.34/1.49 | | % 5.34/1.49 | | ALPHA: (35) implies: % 5.34/1.49 | | (36) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: % 5.34/1.49 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3 & % 5.34/1.49 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & g(v1) = v2 & % 5.34/1.50 | | $i(v2))) % 5.34/1.50 | | (37) ? [v0: $i] : ? [v1: $i] : (g(v0) = v1 & f(v1) = v0 & $i(v1) & % 5.34/1.50 | | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (g(v2) = v3) | % 5.34/1.50 | | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & f(v3) = v4 & $i(v4)))) % 5.49/1.50 | | % 5.49/1.50 | | DELTA: instantiating (37) with fresh symbols all_10_0, all_10_1 gives: % 5.49/1.50 | | (38) g(all_10_1) = all_10_0 & f(all_10_0) = all_10_1 & $i(all_10_0) & % 5.49/1.50 | | $i(all_10_1) & ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~ % 5.49/1.50 | | (g(v0) = v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & f(v1) = % 5.49/1.50 | | v2 & $i(v2))) % 5.49/1.50 | | % 5.49/1.50 | | ALPHA: (38) implies: % 5.49/1.50 | | (39) $i(all_10_0) % 5.49/1.50 | | (40) f(all_10_0) = all_10_1 % 5.49/1.50 | | (41) g(all_10_1) = all_10_0 % 5.49/1.50 | | (42) ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~ (g(v0) = v1) | ~ % 5.49/1.50 | | $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) % 5.49/1.50 | | % 5.49/1.50 | | GROUND_INST: instantiating (36) with all_10_0, all_10_1, simplifying with % 5.49/1.50 | | (39), (40) gives: % 5.49/1.50 | | (43) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v1) = v0 & % 5.49/1.50 | | f(v0) = v1 & $i(v1) & $i(v0)) | ? [v0: any] : ( ~ (v0 = all_10_0) % 5.49/1.50 | | & g(all_10_1) = v0 & $i(v0)) % 5.49/1.50 | | % 5.49/1.50 | | BETA: splitting (43) gives: % 5.49/1.50 | | % 5.49/1.50 | | Case 1: % 5.49/1.50 | | | % 5.49/1.50 | | | (44) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v1) = v0 & % 5.49/1.50 | | | f(v0) = v1 & $i(v1) & $i(v0)) % 5.49/1.50 | | | % 5.49/1.50 | | | DELTA: instantiating (44) with fresh symbols all_19_0, all_19_1 gives: % 5.49/1.50 | | | (45) ~ (all_19_1 = all_10_0) & g(all_19_0) = all_19_1 & f(all_19_1) = % 5.49/1.50 | | | all_19_0 & $i(all_19_0) & $i(all_19_1) % 5.49/1.50 | | | % 5.49/1.50 | | | ALPHA: (45) implies: % 5.49/1.50 | | | (46) ~ (all_19_1 = all_10_0) % 5.49/1.50 | | | (47) $i(all_19_0) % 5.49/1.50 | | | (48) f(all_19_1) = all_19_0 % 5.49/1.51 | | | (49) g(all_19_0) = all_19_1 % 5.49/1.51 | | | % 5.49/1.51 | | | GROUND_INST: instantiating (42) with all_19_0, all_19_1, simplifying with % 5.49/1.51 | | | (47), (49) gives: % 5.49/1.51 | | | (50) all_19_0 = all_10_1 | ? [v0: any] : ( ~ (v0 = all_19_0) & % 5.49/1.51 | | | f(all_19_1) = v0 & $i(v0)) % 5.49/1.51 | | | % 5.49/1.51 | | | BETA: splitting (50) gives: % 5.49/1.51 | | | % 5.49/1.51 | | | Case 1: % 5.49/1.51 | | | | % 5.49/1.51 | | | | (51) all_19_0 = all_10_1 % 5.49/1.51 | | | | % 5.49/1.51 | | | | REDUCE: (49), (51) imply: % 5.49/1.51 | | | | (52) g(all_10_1) = all_19_1 % 5.49/1.51 | | | | % 5.49/1.51 | | | | GROUND_INST: instantiating (2) with all_10_0, all_19_1, all_10_1, % 5.49/1.51 | | | | simplifying with (41), (52) gives: % 5.49/1.51 | | | | (53) all_19_1 = all_10_0 % 5.49/1.51 | | | | % 5.49/1.51 | | | | REDUCE: (46), (53) imply: % 5.49/1.51 | | | | (54) $false % 5.49/1.51 | | | | % 5.49/1.51 | | | | CLOSE: (54) is inconsistent. % 5.49/1.51 | | | | % 5.49/1.51 | | | Case 2: % 5.49/1.51 | | | | % 5.49/1.51 | | | | (55) ? [v0: any] : ( ~ (v0 = all_19_0) & f(all_19_1) = v0 & $i(v0)) % 5.49/1.51 | | | | % 5.49/1.51 | | | | DELTA: instantiating (55) with fresh symbol all_28_0 gives: % 5.49/1.51 | | | | (56) ~ (all_28_0 = all_19_0) & f(all_19_1) = all_28_0 & $i(all_28_0) % 5.49/1.51 | | | | % 5.49/1.51 | | | | ALPHA: (56) implies: % 5.49/1.51 | | | | (57) ~ (all_28_0 = all_19_0) % 5.49/1.51 | | | | (58) f(all_19_1) = all_28_0 % 5.49/1.51 | | | | % 5.49/1.51 | | | | GROUND_INST: instantiating (1) with all_19_0, all_28_0, all_19_1, % 5.49/1.51 | | | | simplifying with (48), (58) gives: % 5.49/1.51 | | | | (59) all_28_0 = all_19_0 % 5.49/1.51 | | | | % 5.49/1.51 | | | | REDUCE: (57), (59) imply: % 5.49/1.51 | | | | (60) $false % 5.49/1.51 | | | | % 5.49/1.51 | | | | CLOSE: (60) is inconsistent. % 5.49/1.51 | | | | % 5.49/1.51 | | | End of split % 5.49/1.51 | | | % 5.49/1.51 | | Case 2: % 5.49/1.51 | | | % 5.49/1.51 | | | (61) ? [v0: any] : ( ~ (v0 = all_10_0) & g(all_10_1) = v0 & $i(v0)) % 5.49/1.51 | | | % 5.49/1.51 | | | DELTA: instantiating (61) with fresh symbol all_19_0 gives: % 5.49/1.51 | | | (62) ~ (all_19_0 = all_10_0) & g(all_10_1) = all_19_0 & $i(all_19_0) % 5.49/1.51 | | | % 5.49/1.51 | | | ALPHA: (62) implies: % 5.49/1.51 | | | (63) ~ (all_19_0 = all_10_0) % 5.49/1.51 | | | (64) g(all_10_1) = all_19_0 % 5.49/1.51 | | | % 5.49/1.51 | | | GROUND_INST: instantiating (2) with all_10_0, all_19_0, all_10_1, % 5.49/1.51 | | | simplifying with (41), (64) gives: % 5.49/1.51 | | | (65) all_19_0 = all_10_0 % 5.49/1.51 | | | % 5.49/1.51 | | | REDUCE: (63), (65) imply: % 5.49/1.51 | | | (66) $false % 5.49/1.51 | | | % 5.49/1.51 | | | CLOSE: (66) is inconsistent. % 5.49/1.51 | | | % 5.49/1.51 | | End of split % 5.49/1.51 | | % 5.49/1.51 | End of split % 5.49/1.51 | % 5.49/1.51 End of proof % 5.49/1.51 % SZS output end Proof for theBenchmark % 5.49/1.51 % 5.49/1.51 881ms %------------------------------------------------------------------------------