%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN354+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 03:27:19 EDT 2023 % Result : Theorem 4.81s 1.43s % Output : Proof 5.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYN354+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n021.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 : Sat Aug 26 21:30:57 EDT 2023 % 0.20/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 1.92/1.01 Prover 1: Preprocessing ... % 1.92/1.01 Prover 4: Preprocessing ... % 1.92/1.06 Prover 5: Preprocessing ... % 1.92/1.06 Prover 6: Preprocessing ... % 1.92/1.06 Prover 0: Preprocessing ... % 1.92/1.06 Prover 3: Preprocessing ... % 1.92/1.06 Prover 2: Preprocessing ... % 2.90/1.14 Prover 5: Proving ... % 2.90/1.14 Prover 2: Proving ... % 2.90/1.14 Prover 3: Constructing countermodel ... % 2.90/1.14 Prover 4: Constructing countermodel ... % 2.90/1.14 Prover 6: Proving ... % 2.90/1.15 Prover 1: Constructing countermodel ... % 2.90/1.15 Prover 0: Proving ... % 3.50/1.22 Prover 1: gave up % 3.50/1.23 Prover 3: gave up % 3.50/1.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.50/1.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.50/1.24 Prover 7: Preprocessing ... % 3.50/1.26 Prover 8: Preprocessing ... % 3.50/1.27 Prover 7: Warning: ignoring some quantifiers % 3.50/1.27 Prover 7: Constructing countermodel ... % 4.04/1.30 Prover 8: Warning: ignoring some quantifiers % 4.04/1.30 Prover 8: Constructing countermodel ... % 4.04/1.32 Prover 7: gave up % 4.04/1.32 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 4.04/1.33 Prover 9: Preprocessing ... % 4.04/1.33 Prover 8: gave up % 4.04/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.04/1.35 Prover 10: Preprocessing ... % 4.63/1.38 Prover 10: Warning: ignoring some quantifiers % 4.63/1.38 Prover 10: Constructing countermodel ... % 4.63/1.38 Prover 9: Constructing countermodel ... % 4.63/1.39 Prover 10: gave up % 4.63/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.81/1.41 Prover 11: Preprocessing ... % 4.81/1.43 Prover 0: proved (775ms) % 4.81/1.43 % 4.81/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.81/1.43 % 4.81/1.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.81/1.44 Prover 9: stopped % 4.81/1.44 Prover 6: stopped % 4.81/1.44 Prover 5: stopped % 4.81/1.44 Prover 2: stopped % 4.81/1.45 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 4.81/1.45 Prover 11: Constructing countermodel ... % 4.81/1.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.81/1.46 Prover 19: Preprocessing ... % 4.81/1.46 Prover 13: Preprocessing ... % 4.81/1.47 Prover 16: Preprocessing ... % 4.81/1.48 Prover 13: Warning: ignoring some quantifiers % 4.81/1.48 Prover 13: Constructing countermodel ... % 4.81/1.49 Prover 16: Warning: ignoring some quantifiers % 4.81/1.49 Prover 16: Constructing countermodel ... % 4.81/1.49 Prover 13: gave up % 4.81/1.50 Prover 16: gave up % 4.81/1.50 Prover 19: Warning: ignoring some quantifiers % 4.81/1.50 Prover 19: Constructing countermodel ... % 4.81/1.52 Prover 19: gave up % 4.81/1.55 Prover 4: Found proof (size 48) % 4.81/1.55 Prover 4: proved (902ms) % 4.81/1.55 Prover 11: stopped % 4.81/1.55 % 4.81/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.81/1.55 % 5.23/1.57 % SZS output start Proof for theBenchmark % 5.23/1.57 Assumptions after simplification: % 5.23/1.57 --------------------------------- % 5.23/1.57 % 5.23/1.57 (church_46_20_1) % 5.23/1.60 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (big_f(v0, v1) = v2 % 5.23/1.60 & big_g(v0, v1) = v3 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 5.23/1.60 any] : ( ~ (big_f(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : % 5.23/1.60 ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ? [v12: any] % 5.23/1.60 : ? [v13: any] : (v3 = 0 & v2 = 0 & big_f(v1, v5) = v7 & big_f(v1, v4) = % 5.23/1.60 v9 & big_f(v0, v4) = v8 & big_g(v5, v10) = v12 & big_g(v4, v10) = v13 & % 5.23/1.60 big_g(v1, v10) = v11 & $i(v10) & ( ~ (v13 = 0) | v11 = 0) & ( ~ (v11 = % 5.23/1.60 0) | v13 = 0) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v6 = 0)) & ( ~ (v6 % 5.23/1.60 = 0) | v7 = 0 | (( ~ (v12 = 0) | ~ (v11 = 0)) & (v12 = 0 | v11 = % 5.23/1.60 0)))))) % 5.23/1.60 % 5.23/1.60 (function-axioms) % 5.23/1.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.23/1.61 [v3: $i] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) & ! % 5.23/1.61 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 5.23/1.61 $i] : (v1 = v0 | ~ (big_g(v3, v2) = v1) | ~ (big_g(v3, v2) = v0)) % 5.23/1.61 % 5.23/1.61 Those formulas are unsatisfiable: % 5.23/1.61 --------------------------------- % 5.23/1.61 % 5.23/1.61 Begin of proof % 5.23/1.61 | % 5.23/1.61 | ALPHA: (function-axioms) implies: % 5.23/1.61 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.23/1.61 | ! [v3: $i] : (v1 = v0 | ~ (big_g(v3, v2) = v1) | ~ (big_g(v3, v2) = % 5.23/1.61 | v0)) % 5.23/1.61 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.23/1.61 | ! [v3: $i] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = % 5.23/1.61 | v0)) % 5.23/1.61 | % 5.23/1.61 | DELTA: instantiating (church_46_20_1) with fresh symbols all_3_0, all_3_1, % 5.23/1.61 | all_3_2, all_3_3 gives: % 5.23/1.62 | (3) big_f(all_3_3, all_3_2) = all_3_1 & big_g(all_3_3, all_3_2) = all_3_0 & % 5.23/1.62 | $i(all_3_2) & $i(all_3_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 5.23/1.62 | ( ~ (big_f(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 5.23/1.62 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] % 5.23/1.62 | : ? [v9: any] : (all_3_0 = 0 & all_3_1 = 0 & big_f(all_3_2, v1) = v3 % 5.23/1.62 | & big_f(all_3_2, v0) = v5 & big_f(all_3_3, v0) = v4 & big_g(v1, v6) % 5.23/1.62 | = v8 & big_g(v0, v6) = v9 & big_g(all_3_2, v6) = v7 & $i(v6) & ( ~ % 5.23/1.62 | (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | v9 = 0) & ( ~ (v5 = 0) | ~ % 5.23/1.62 | (v4 = 0) | ~ (v2 = 0)) & ( ~ (v2 = 0) | v3 = 0 | (( ~ (v8 = 0) | % 5.23/1.62 | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))))) % 5.23/1.62 | % 5.23/1.62 | ALPHA: (3) implies: % 5.23/1.62 | (4) $i(all_3_3) % 5.23/1.62 | (5) $i(all_3_2) % 5.23/1.62 | (6) big_f(all_3_3, all_3_2) = all_3_1 % 5.23/1.62 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (big_f(v0, v1) = v2) | % 5.23/1.62 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 5.23/1.62 | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (all_3_0 = % 5.23/1.62 | 0 & all_3_1 = 0 & big_f(all_3_2, v1) = v3 & big_f(all_3_2, v0) = v5 % 5.23/1.62 | & big_f(all_3_3, v0) = v4 & big_g(v1, v6) = v8 & big_g(v0, v6) = v9 % 5.23/1.62 | & big_g(all_3_2, v6) = v7 & $i(v6) & ( ~ (v9 = 0) | v7 = 0) & ( ~ % 5.23/1.62 | (v7 = 0) | v9 = 0) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v2 = 0)) & % 5.23/1.62 | ( ~ (v2 = 0) | v3 = 0 | (( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 % 5.23/1.62 | = 0))))) % 5.23/1.62 | % 5.23/1.62 | GROUND_INST: instantiating (7) with all_3_3, all_3_2, all_3_1, simplifying % 5.23/1.62 | with (4), (5), (6) gives: % 5.23/1.63 | (8) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 5.23/1.63 | : ? [v5: any] : ? [v6: any] : (all_3_0 = 0 & all_3_1 = 0 & % 5.23/1.63 | big_f(all_3_2, all_3_2) = v0 & big_f(all_3_2, all_3_3) = v2 & % 5.23/1.63 | big_f(all_3_3, all_3_3) = v1 & big_g(all_3_2, v3) = v5 & % 5.23/1.63 | big_g(all_3_2, v3) = v4 & big_g(all_3_3, v3) = v6 & $i(v3) & ( ~ (v6 % 5.23/1.63 | = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0) & ( ~ (v2 = 0) | ~ (v1 = % 5.23/1.63 | 0)) & (v0 = 0 | (( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = % 5.23/1.63 | 0)))) % 5.23/1.63 | % 5.23/1.63 | DELTA: instantiating (8) with fresh symbols all_11_0, all_11_1, all_11_2, % 5.23/1.63 | all_11_3, all_11_4, all_11_5, all_11_6 gives: % 5.23/1.63 | (9) all_3_0 = 0 & all_3_1 = 0 & big_f(all_3_2, all_3_2) = all_11_6 & % 5.23/1.63 | big_f(all_3_2, all_3_3) = all_11_4 & big_f(all_3_3, all_3_3) = all_11_5 % 5.23/1.63 | & big_g(all_3_2, all_11_3) = all_11_1 & big_g(all_3_2, all_11_3) = % 5.23/1.63 | all_11_2 & big_g(all_3_3, all_11_3) = all_11_0 & $i(all_11_3) & ( ~ % 5.23/1.63 | (all_11_0 = 0) | all_11_2 = 0) & ( ~ (all_11_2 = 0) | all_11_0 = 0) & % 5.23/1.63 | ( ~ (all_11_4 = 0) | ~ (all_11_5 = 0)) & (all_11_6 = 0 | (( ~ % 5.23/1.63 | (all_11_1 = 0) | ~ (all_11_2 = 0)) & (all_11_1 = 0 | all_11_2 = % 5.23/1.63 | 0))) % 5.23/1.63 | % 5.23/1.63 | ALPHA: (9) implies: % 5.23/1.63 | (10) all_3_1 = 0 % 5.23/1.63 | (11) big_g(all_3_2, all_11_3) = all_11_2 % 5.23/1.63 | (12) big_g(all_3_2, all_11_3) = all_11_1 % 5.23/1.63 | (13) big_f(all_3_2, all_3_3) = all_11_4 % 5.23/1.63 | (14) big_f(all_3_2, all_3_2) = all_11_6 % 5.23/1.63 | (15) all_11_6 = 0 | (( ~ (all_11_1 = 0) | ~ (all_11_2 = 0)) & (all_11_1 = % 5.23/1.63 | 0 | all_11_2 = 0)) % 5.23/1.63 | % 5.23/1.63 | REDUCE: (6), (10) imply: % 5.23/1.63 | (16) big_f(all_3_3, all_3_2) = 0 % 5.23/1.63 | % 5.23/1.63 | GROUND_INST: instantiating (1) with all_11_2, all_11_1, all_11_3, all_3_2, % 5.23/1.63 | simplifying with (11), (12) gives: % 5.23/1.63 | (17) all_11_1 = all_11_2 % 5.23/1.63 | % 5.23/1.63 | BETA: splitting (15) gives: % 5.23/1.63 | % 5.23/1.63 | Case 1: % 5.23/1.63 | | % 5.23/1.63 | | (18) all_11_6 = 0 % 5.23/1.63 | | % 5.23/1.63 | | REDUCE: (14), (18) imply: % 5.23/1.63 | | (19) big_f(all_3_2, all_3_2) = 0 % 5.23/1.63 | | % 5.23/1.63 | | GROUND_INST: instantiating (7) with all_3_2, all_3_3, all_11_4, simplifying % 5.23/1.63 | | with (4), (5), (13) gives: % 5.23/1.64 | | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 5.23/1.64 | | any] : ? [v5: any] : ? [v6: any] : (all_3_0 = 0 & all_3_1 = 0 & % 5.23/1.64 | | big_f(all_3_2, all_3_2) = v2 & big_f(all_3_2, all_3_3) = v0 & % 5.23/1.64 | | big_f(all_3_3, all_3_2) = v1 & big_g(all_3_2, v3) = v6 & % 5.23/1.64 | | big_g(all_3_2, v3) = v4 & big_g(all_3_3, v3) = v5 & $i(v3) & ( ~ % 5.23/1.64 | | (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0) & ( ~ (v2 = 0) | ~ % 5.23/1.64 | | (v1 = 0) | ~ (all_11_4 = 0)) & ( ~ (all_11_4 = 0) | v0 = 0 | (( % 5.23/1.64 | | ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))) % 5.23/1.64 | | % 5.23/1.64 | | GROUND_INST: instantiating (7) with all_3_2, all_3_2, 0, simplifying with % 5.23/1.64 | | (5), (19) gives: % 5.23/1.64 | | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 5.23/1.64 | | any] : ? [v5: any] : ? [v6: any] : (all_3_0 = 0 & all_3_1 = 0 & % 5.23/1.64 | | big_f(all_3_2, all_3_2) = v2 & big_f(all_3_2, all_3_2) = v0 & % 5.23/1.64 | | big_f(all_3_3, all_3_2) = v1 & big_g(all_3_2, v3) = v6 & % 5.23/1.64 | | big_g(all_3_2, v3) = v5 & big_g(all_3_2, v3) = v4 & $i(v3) & ( ~ % 5.23/1.64 | | (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0) & ( ~ (v2 = 0) | ~ % 5.23/1.64 | | (v1 = 0)) & (v0 = 0 | (( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | % 5.23/1.64 | | v4 = 0)))) % 5.23/1.64 | | % 5.23/1.64 | | DELTA: instantiating (21) with fresh symbols all_26_0, all_26_1, all_26_2, % 5.23/1.64 | | all_26_3, all_26_4, all_26_5, all_26_6 gives: % 5.23/1.64 | | (22) all_3_0 = 0 & all_3_1 = 0 & big_f(all_3_2, all_3_2) = all_26_4 & % 5.23/1.64 | | big_f(all_3_2, all_3_2) = all_26_6 & big_f(all_3_3, all_3_2) = % 5.23/1.64 | | all_26_5 & big_g(all_3_2, all_26_3) = all_26_0 & big_g(all_3_2, % 5.23/1.64 | | all_26_3) = all_26_1 & big_g(all_3_2, all_26_3) = all_26_2 & % 5.23/1.64 | | $i(all_26_3) & ( ~ (all_26_0 = 0) | all_26_2 = 0) & ( ~ (all_26_2 = % 5.23/1.64 | | 0) | all_26_0 = 0) & ( ~ (all_26_4 = 0) | ~ (all_26_5 = 0)) & % 5.23/1.64 | | (all_26_6 = 0 | (( ~ (all_26_1 = 0) | ~ (all_26_2 = 0)) & (all_26_1 % 5.23/1.64 | | = 0 | all_26_2 = 0))) % 5.23/1.64 | | % 5.23/1.64 | | ALPHA: (22) implies: % 5.23/1.64 | | (23) big_f(all_3_3, all_3_2) = all_26_5 % 5.23/1.64 | | (24) big_f(all_3_2, all_3_2) = all_26_4 % 5.23/1.64 | | (25) ~ (all_26_4 = 0) | ~ (all_26_5 = 0) % 5.23/1.64 | | % 5.23/1.64 | | DELTA: instantiating (8) with fresh symbols all_28_0, all_28_1, all_28_2, % 5.23/1.64 | | all_28_3, all_28_4, all_28_5, all_28_6 gives: % 5.23/1.64 | | (26) all_3_0 = 0 & all_3_1 = 0 & big_f(all_3_2, all_3_2) = all_28_6 & % 5.23/1.64 | | big_f(all_3_2, all_3_3) = all_28_4 & big_f(all_3_3, all_3_3) = % 5.23/1.64 | | all_28_5 & big_g(all_3_2, all_28_3) = all_28_1 & big_g(all_3_2, % 5.23/1.64 | | all_28_3) = all_28_2 & big_g(all_3_3, all_28_3) = all_28_0 & % 5.23/1.64 | | $i(all_28_3) & ( ~ (all_28_0 = 0) | all_28_2 = 0) & ( ~ (all_28_2 = % 5.23/1.64 | | 0) | all_28_0 = 0) & ( ~ (all_28_4 = 0) | ~ (all_28_5 = 0)) & % 5.23/1.64 | | (all_28_6 = 0 | (( ~ (all_28_1 = 0) | ~ (all_28_2 = 0)) & (all_28_1 % 5.23/1.64 | | = 0 | all_28_2 = 0))) % 5.23/1.64 | | % 5.23/1.64 | | ALPHA: (26) implies: % 5.23/1.64 | | (27) big_f(all_3_2, all_3_2) = all_28_6 % 5.23/1.64 | | % 5.23/1.64 | | DELTA: instantiating (20) with fresh symbols all_30_0, all_30_1, all_30_2, % 5.23/1.64 | | all_30_3, all_30_4, all_30_5, all_30_6 gives: % 5.23/1.64 | | (28) all_3_0 = 0 & all_3_1 = 0 & big_f(all_3_2, all_3_2) = all_30_4 & % 5.23/1.64 | | big_f(all_3_2, all_3_3) = all_30_6 & big_f(all_3_3, all_3_2) = % 5.23/1.64 | | all_30_5 & big_g(all_3_2, all_30_3) = all_30_0 & big_g(all_3_2, % 5.23/1.64 | | all_30_3) = all_30_2 & big_g(all_3_3, all_30_3) = all_30_1 & % 5.23/1.64 | | $i(all_30_3) & ( ~ (all_30_0 = 0) | all_30_2 = 0) & ( ~ (all_30_2 = % 5.23/1.64 | | 0) | all_30_0 = 0) & ( ~ (all_30_4 = 0) | ~ (all_30_5 = 0) | ~ % 5.23/1.64 | | (all_11_4 = 0)) & ( ~ (all_11_4 = 0) | all_30_6 = 0 | (( ~ % 5.23/1.64 | | (all_30_1 = 0) | ~ (all_30_2 = 0)) & (all_30_1 = 0 | all_30_2 % 5.23/1.64 | | = 0))) % 5.23/1.64 | | % 5.23/1.64 | | ALPHA: (28) implies: % 5.23/1.65 | | (29) big_f(all_3_3, all_3_2) = all_30_5 % 5.23/1.65 | | (30) big_f(all_3_2, all_3_2) = all_30_4 % 5.23/1.65 | | % 5.23/1.65 | | GROUND_INST: instantiating (2) with 0, all_30_5, all_3_2, all_3_3, % 5.23/1.65 | | simplifying with (16), (29) gives: % 5.23/1.65 | | (31) all_30_5 = 0 % 5.23/1.65 | | % 5.23/1.65 | | GROUND_INST: instantiating (2) with all_26_5, all_30_5, all_3_2, all_3_3, % 5.23/1.65 | | simplifying with (23), (29) gives: % 5.23/1.65 | | (32) all_30_5 = all_26_5 % 5.23/1.65 | | % 5.23/1.65 | | GROUND_INST: instantiating (2) with 0, all_28_6, all_3_2, all_3_2, % 5.23/1.65 | | simplifying with (19), (27) gives: % 5.23/1.65 | | (33) all_28_6 = 0 % 5.23/1.65 | | % 5.23/1.65 | | GROUND_INST: instantiating (2) with all_28_6, all_30_4, all_3_2, all_3_2, % 5.23/1.65 | | simplifying with (27), (30) gives: % 5.23/1.65 | | (34) all_30_4 = all_28_6 % 5.23/1.65 | | % 5.23/1.65 | | GROUND_INST: instantiating (2) with all_26_4, all_30_4, all_3_2, all_3_2, % 5.23/1.65 | | simplifying with (24), (30) gives: % 5.23/1.65 | | (35) all_30_4 = all_26_4 % 5.23/1.65 | | % 5.23/1.65 | | COMBINE_EQS: (34), (35) imply: % 5.23/1.65 | | (36) all_28_6 = all_26_4 % 5.23/1.65 | | % 5.23/1.65 | | SIMP: (36) implies: % 5.23/1.65 | | (37) all_28_6 = all_26_4 % 5.23/1.65 | | % 5.23/1.65 | | COMBINE_EQS: (31), (32) imply: % 5.23/1.65 | | (38) all_26_5 = 0 % 5.23/1.65 | | % 5.23/1.65 | | SIMP: (38) implies: % 5.23/1.65 | | (39) all_26_5 = 0 % 5.23/1.65 | | % 5.23/1.65 | | COMBINE_EQS: (33), (37) imply: % 5.23/1.65 | | (40) all_26_4 = 0 % 5.23/1.65 | | % 5.23/1.65 | | BETA: splitting (25) gives: % 5.23/1.65 | | % 5.23/1.65 | | Case 1: % 5.23/1.65 | | | % 5.23/1.65 | | | (41) ~ (all_26_4 = 0) % 5.23/1.65 | | | % 5.23/1.65 | | | REDUCE: (40), (41) imply: % 5.23/1.65 | | | (42) $false % 5.23/1.65 | | | % 5.23/1.65 | | | CLOSE: (42) is inconsistent. % 5.23/1.65 | | | % 5.23/1.65 | | Case 2: % 5.23/1.65 | | | % 5.23/1.65 | | | (43) ~ (all_26_5 = 0) % 5.23/1.65 | | | % 5.23/1.65 | | | REDUCE: (39), (43) imply: % 5.23/1.65 | | | (44) $false % 5.23/1.65 | | | % 5.23/1.65 | | | CLOSE: (44) is inconsistent. % 5.23/1.65 | | | % 5.23/1.65 | | End of split % 5.23/1.65 | | % 5.23/1.65 | Case 2: % 5.23/1.65 | | % 5.23/1.65 | | (45) ( ~ (all_11_1 = 0) | ~ (all_11_2 = 0)) & (all_11_1 = 0 | all_11_2 = % 5.23/1.65 | | 0) % 5.23/1.65 | | % 5.23/1.65 | | ALPHA: (45) implies: % 5.23/1.65 | | (46) all_11_1 = 0 | all_11_2 = 0 % 5.23/1.65 | | (47) ~ (all_11_1 = 0) | ~ (all_11_2 = 0) % 5.23/1.65 | | % 5.23/1.65 | | BETA: splitting (46) gives: % 5.23/1.65 | | % 5.23/1.65 | | Case 1: % 5.23/1.65 | | | % 5.23/1.65 | | | (48) all_11_1 = 0 % 5.23/1.65 | | | % 5.23/1.65 | | | COMBINE_EQS: (17), (48) imply: % 5.23/1.65 | | | (49) all_11_2 = 0 % 5.23/1.65 | | | % 5.23/1.65 | | | BETA: splitting (47) gives: % 5.23/1.65 | | | % 5.23/1.65 | | | Case 1: % 5.23/1.65 | | | | % 5.23/1.65 | | | | (50) ~ (all_11_1 = 0) % 5.23/1.65 | | | | % 5.23/1.65 | | | | REDUCE: (48), (50) imply: % 5.23/1.65 | | | | (51) $false % 5.23/1.65 | | | | % 5.23/1.65 | | | | CLOSE: (51) is inconsistent. % 5.23/1.65 | | | | % 5.23/1.65 | | | Case 2: % 5.23/1.65 | | | | % 5.23/1.65 | | | | (52) ~ (all_11_2 = 0) % 5.23/1.65 | | | | % 5.23/1.65 | | | | REDUCE: (49), (52) imply: % 5.23/1.65 | | | | (53) $false % 5.23/1.65 | | | | % 5.23/1.65 | | | | CLOSE: (53) is inconsistent. % 5.23/1.65 | | | | % 5.23/1.66 | | | End of split % 5.23/1.66 | | | % 5.23/1.66 | | Case 2: % 5.23/1.66 | | | % 5.23/1.66 | | | (54) all_11_2 = 0 % 5.23/1.66 | | | (55) ~ (all_11_1 = 0) % 5.23/1.66 | | | % 5.23/1.66 | | | COMBINE_EQS: (17), (54) imply: % 5.23/1.66 | | | (56) all_11_1 = 0 % 5.23/1.66 | | | % 5.23/1.66 | | | REDUCE: (55), (56) imply: % 5.23/1.66 | | | (57) $false % 5.23/1.66 | | | % 5.23/1.66 | | | CLOSE: (57) is inconsistent. % 5.23/1.66 | | | % 5.23/1.66 | | End of split % 5.23/1.66 | | % 5.23/1.66 | End of split % 5.23/1.66 | % 5.23/1.66 End of proof % 5.23/1.66 % SZS output end Proof for theBenchmark % 5.23/1.66 % 5.23/1.66 1032ms %------------------------------------------------------------------------------