%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN069+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 : n027.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 03:26:27 EDT 2023 % Result : Theorem 3.80s 1.35s % Output : Proof 6.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN069+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n027.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 18:45:50 EDT 2023 % 0.12/0.34 % 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. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.82/0.97 Prover 1: Preprocessing ... % 1.82/0.97 Prover 4: Preprocessing ... % 2.42/1.03 Prover 3: Preprocessing ... % 2.42/1.03 Prover 2: Preprocessing ... % 2.42/1.03 Prover 0: Preprocessing ... % 2.42/1.03 Prover 5: Preprocessing ... % 2.42/1.03 Prover 6: Preprocessing ... % 2.86/1.14 Prover 5: Proving ... % 2.86/1.14 Prover 2: Proving ... % 2.86/1.16 Prover 1: Constructing countermodel ... % 2.86/1.16 Prover 6: Proving ... % 3.39/1.17 Prover 3: Constructing countermodel ... % 3.63/1.21 Prover 4: Constructing countermodel ... % 3.63/1.21 Prover 0: Proving ... % 3.80/1.26 Prover 3: gave up % 3.80/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.80/1.27 Prover 1: gave up % 3.80/1.29 Prover 7: Preprocessing ... % 3.80/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.80/1.31 Prover 7: Warning: ignoring some quantifiers % 3.80/1.31 Prover 8: Preprocessing ... % 3.80/1.32 Prover 7: Constructing countermodel ... % 3.80/1.34 Prover 0: proved (720ms) % 3.80/1.35 % 3.80/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.80/1.35 % 3.80/1.35 Prover 5: stopped % 3.80/1.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.80/1.36 Prover 2: stopped % 3.80/1.36 Prover 10: Preprocessing ... % 3.80/1.36 Prover 6: stopped % 3.80/1.37 Prover 8: Warning: ignoring some quantifiers % 3.80/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.80/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.80/1.37 Prover 8: Constructing countermodel ... % 3.80/1.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 3.80/1.39 Prover 10: Warning: ignoring some quantifiers % 3.80/1.39 Prover 10: Constructing countermodel ... % 3.80/1.40 Prover 11: Preprocessing ... % 3.80/1.41 Prover 13: Preprocessing ... % 3.80/1.41 Prover 16: Preprocessing ... % 3.80/1.42 Prover 16: Warning: ignoring some quantifiers % 3.80/1.42 Prover 16: Constructing countermodel ... % 3.80/1.43 Prover 13: Warning: ignoring some quantifiers % 3.80/1.44 Prover 13: Constructing countermodel ... % 3.80/1.45 Prover 10: gave up % 5.16/1.46 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 5.16/1.46 Prover 4: Found proof (size 37) % 5.16/1.46 Prover 4: proved (838ms) % 5.16/1.46 Prover 8: stopped % 5.16/1.47 Prover 16: stopped % 5.16/1.47 Prover 13: stopped % 5.16/1.47 Prover 7: stopped % 5.16/1.47 Prover 19: Preprocessing ... % 5.16/1.49 Prover 11: Constructing countermodel ... % 5.16/1.49 Prover 11: stopped % 5.79/1.53 Prover 19: Warning: ignoring some quantifiers % 5.79/1.53 Prover 19: Constructing countermodel ... % 5.79/1.54 Prover 19: stopped % 5.79/1.54 % 5.79/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.79/1.54 % 5.79/1.55 % SZS output start Proof for theBenchmark % 5.79/1.55 Assumptions after simplification: % 5.79/1.55 --------------------------------- % 5.79/1.55 % 5.79/1.55 (pel45) % 5.79/1.57 ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (big_g(v1) = 0 & % 5.79/1.58 big_h(v0, v1) = 0 & $i(v1))) % 5.79/1.58 % 5.79/1.58 (pel45_1) % 5.79/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ % 5.79/1.58 (big_k(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 5.79/1.58 (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4 & % 5.79/1.58 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 5.79/1.58 (big_f(v0) = 0) | ~ (big_g(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 5.79/1.58 : ? [v4: int] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & % 5.79/1.58 big_j(v0, v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 5.79/1.58 (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_h(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 5.79/1.58 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) % 5.79/1.58 = 0 & big_j(v0, v3) = v4 & $i(v3))) % 5.79/1.58 % 5.79/1.58 (pel45_2) % 5.79/1.58 ! [v0: $i] : ( ~ (big_l(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 5.79/1.58 big_k(v0) = v1)) & ! [v0: $i] : ( ~ (big_k(v0) = 0) | ~ $i(v0) | ? [v1: % 5.79/1.58 int] : ( ~ (v1 = 0) & big_l(v0) = v1)) % 5.79/1.58 % 5.79/1.58 (pel45_3) % 5.79/1.59 ? [v0: $i] : (big_f(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 5.79/1.59 ~ (big_l(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & big_h(v0, % 5.79/1.59 v1) = v3)) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (big_j(v0, v1) % 5.79/1.59 = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (big_g(v1) = v3 & % 5.79/1.59 big_h(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ % 5.79/1.59 (big_g(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (big_h(v0, v1) % 5.79/1.59 = v2 & big_j(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v1: $i] : ( ~ % 5.79/1.59 (big_h(v0, v1) = 0) | ~ $i(v1) | big_l(v1) = 0) & ! [v1: $i] : ( ~ % 5.79/1.59 (big_h(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (big_g(v1) % 5.79/1.59 = v2 & big_j(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))) % 5.79/1.59 % 5.79/1.59 (function-axioms) % 5.79/1.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.79/1.60 [v3: $i] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0)) & ! % 5.79/1.60 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 5.79/1.60 $i] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = v0)) & ! % 5.79/1.60 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 5.79/1.60 | ~ (big_l(v2) = v1) | ~ (big_l(v2) = v0)) & ! [v0: MultipleValueBool] : % 5.79/1.60 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ % 5.79/1.60 (big_f(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 5.79/1.60 : ! [v2: $i] : (v1 = v0 | ~ (big_k(v2) = v1) | ~ (big_k(v2) = v0)) & ! % 5.79/1.60 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 5.79/1.60 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) % 5.79/1.60 % 5.79/1.60 Those formulas are unsatisfiable: % 5.79/1.60 --------------------------------- % 5.79/1.60 % 5.79/1.60 Begin of proof % 5.79/1.60 | % 5.79/1.60 | ALPHA: (pel45_1) implies: % 5.79/1.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (big_f(v0) = 0) % 5.79/1.60 | | ~ (big_k(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 5.79/1.60 | int] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, % 5.79/1.60 | v3) = v4 & $i(v3))) % 5.79/1.60 | % 5.79/1.60 | ALPHA: (pel45_2) implies: % 5.79/1.60 | (2) ! [v0: $i] : ( ~ (big_l(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 5.79/1.60 | = 0) & big_k(v0) = v1)) % 5.79/1.60 | % 5.79/1.60 | ALPHA: (function-axioms) implies: % 6.17/1.60 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.17/1.60 | ! [v3: $i] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = % 6.17/1.60 | v0)) % 6.17/1.60 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.17/1.60 | ! [v3: $i] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = % 6.17/1.60 | v0)) % 6.17/1.60 | % 6.17/1.60 | DELTA: instantiating (pel45_3) with fresh symbol all_6_0 gives: % 6.17/1.61 | (5) big_f(all_6_0) = 0 & $i(all_6_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 6.17/1.61 | | ~ (big_l(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 6.17/1.61 | big_h(all_6_0, v0) = v2)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 6.17/1.61 | ~ (big_j(all_6_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 6.17/1.61 | : (big_g(v0) = v2 & big_h(all_6_0, v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = % 6.17/1.61 | 0)))) & ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0) | ? [v1: % 6.17/1.61 | any] : ? [v2: any] : (big_h(all_6_0, v0) = v1 & big_j(all_6_0, v0) % 6.17/1.61 | = v2 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: $i] : ( ~ (big_h(all_6_0, % 6.17/1.61 | v0) = 0) | ~ $i(v0) | big_l(v0) = 0) & ! [v0: $i] : ( ~ % 6.17/1.61 | (big_h(all_6_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 6.17/1.61 | (big_g(v0) = v1 & big_j(all_6_0, v0) = v2 & ( ~ (v1 = 0) | v2 = 0))) % 6.17/1.61 | % 6.17/1.61 | ALPHA: (5) implies: % 6.17/1.61 | (6) $i(all_6_0) % 6.17/1.61 | (7) big_f(all_6_0) = 0 % 6.17/1.61 | (8) ! [v0: $i] : ( ~ (big_h(all_6_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : % 6.17/1.61 | ? [v2: any] : (big_g(v0) = v1 & big_j(all_6_0, v0) = v2 & ( ~ (v1 = % 6.17/1.61 | 0) | v2 = 0))) % 6.17/1.61 | (9) ! [v0: $i] : ( ~ (big_h(all_6_0, v0) = 0) | ~ $i(v0) | big_l(v0) = 0) % 6.17/1.61 | (10) ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 6.17/1.61 | any] : (big_h(all_6_0, v0) = v1 & big_j(all_6_0, v0) = v2 & ( ~ % 6.17/1.61 | (v1 = 0) | v2 = 0))) % 6.17/1.61 | % 6.17/1.61 | GROUND_INST: instantiating (pel45) with all_6_0, simplifying with (6), (7) % 6.17/1.61 | gives: % 6.17/1.61 | (11) ? [v0: $i] : (big_g(v0) = 0 & big_h(all_6_0, v0) = 0 & $i(v0)) % 6.17/1.61 | % 6.17/1.61 | DELTA: instantiating (11) with fresh symbol all_14_0 gives: % 6.17/1.61 | (12) big_g(all_14_0) = 0 & big_h(all_6_0, all_14_0) = 0 & $i(all_14_0) % 6.17/1.61 | % 6.17/1.61 | ALPHA: (12) implies: % 6.17/1.61 | (13) $i(all_14_0) % 6.17/1.61 | (14) big_h(all_6_0, all_14_0) = 0 % 6.17/1.61 | % 6.17/1.61 | GROUND_INST: instantiating (9) with all_14_0, simplifying with (13), (14) % 6.17/1.61 | gives: % 6.17/1.61 | (15) big_l(all_14_0) = 0 % 6.17/1.61 | % 6.17/1.61 | GROUND_INST: instantiating (2) with all_14_0, simplifying with (13), (15) % 6.17/1.61 | gives: % 6.17/1.61 | (16) ? [v0: int] : ( ~ (v0 = 0) & big_k(all_14_0) = v0) % 6.17/1.61 | % 6.17/1.61 | DELTA: instantiating (16) with fresh symbol all_39_0 gives: % 6.17/1.61 | (17) ~ (all_39_0 = 0) & big_k(all_14_0) = all_39_0 % 6.17/1.61 | % 6.17/1.61 | ALPHA: (17) implies: % 6.17/1.62 | (18) ~ (all_39_0 = 0) % 6.17/1.62 | (19) big_k(all_14_0) = all_39_0 % 6.17/1.62 | % 6.17/1.62 | GROUND_INST: instantiating (1) with all_6_0, all_14_0, all_39_0, simplifying % 6.17/1.62 | with (6), (7), (13), (19) gives: % 6.17/1.62 | (20) all_39_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_g(v0) = % 6.17/1.62 | 0 & big_h(all_6_0, v0) = 0 & big_j(all_6_0, v0) = v1 & $i(v0)) % 6.17/1.62 | % 6.17/1.62 | BETA: splitting (20) gives: % 6.17/1.62 | % 6.17/1.62 | Case 1: % 6.17/1.62 | | % 6.17/1.62 | | (21) all_39_0 = 0 % 6.17/1.62 | | % 6.17/1.62 | | REDUCE: (18), (21) imply: % 6.17/1.62 | | (22) $false % 6.17/1.62 | | % 6.17/1.62 | | CLOSE: (22) is inconsistent. % 6.17/1.62 | | % 6.17/1.62 | Case 2: % 6.17/1.62 | | % 6.17/1.62 | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_g(v0) = 0 & % 6.17/1.62 | | big_h(all_6_0, v0) = 0 & big_j(all_6_0, v0) = v1 & $i(v0)) % 6.17/1.62 | | % 6.17/1.62 | | DELTA: instantiating (23) with fresh symbols all_48_0, all_48_1 gives: % 6.17/1.62 | | (24) ~ (all_48_0 = 0) & big_g(all_48_1) = 0 & big_h(all_6_0, all_48_1) = % 6.17/1.62 | | 0 & big_j(all_6_0, all_48_1) = all_48_0 & $i(all_48_1) % 6.17/1.62 | | % 6.17/1.62 | | ALPHA: (24) implies: % 6.17/1.62 | | (25) ~ (all_48_0 = 0) % 6.17/1.62 | | (26) $i(all_48_1) % 6.17/1.62 | | (27) big_j(all_6_0, all_48_1) = all_48_0 % 6.17/1.62 | | (28) big_h(all_6_0, all_48_1) = 0 % 6.17/1.62 | | (29) big_g(all_48_1) = 0 % 6.17/1.62 | | % 6.17/1.62 | | GROUND_INST: instantiating (8) with all_48_1, simplifying with (26), (28) % 6.17/1.62 | | gives: % 6.17/1.62 | | (30) ? [v0: any] : ? [v1: any] : (big_g(all_48_1) = v0 & big_j(all_6_0, % 6.17/1.62 | | all_48_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 6.17/1.62 | | % 6.17/1.62 | | GROUND_INST: instantiating (10) with all_48_1, simplifying with (26), (29) % 6.17/1.62 | | gives: % 6.17/1.62 | | (31) ? [v0: any] : ? [v1: any] : (big_h(all_6_0, all_48_1) = v0 & % 6.17/1.62 | | big_j(all_6_0, all_48_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 6.17/1.62 | | % 6.17/1.62 | | DELTA: instantiating (31) with fresh symbols all_56_0, all_56_1 gives: % 6.17/1.62 | | (32) big_h(all_6_0, all_48_1) = all_56_1 & big_j(all_6_0, all_48_1) = % 6.17/1.62 | | all_56_0 & ( ~ (all_56_1 = 0) | all_56_0 = 0) % 6.17/1.62 | | % 6.17/1.62 | | ALPHA: (32) implies: % 6.17/1.62 | | (33) big_j(all_6_0, all_48_1) = all_56_0 % 6.17/1.63 | | (34) big_h(all_6_0, all_48_1) = all_56_1 % 6.17/1.63 | | (35) ~ (all_56_1 = 0) | all_56_0 = 0 % 6.17/1.63 | | % 6.17/1.63 | | DELTA: instantiating (30) with fresh symbols all_58_0, all_58_1 gives: % 6.17/1.63 | | (36) big_g(all_48_1) = all_58_1 & big_j(all_6_0, all_48_1) = all_58_0 & ( % 6.17/1.63 | | ~ (all_58_1 = 0) | all_58_0 = 0) % 6.17/1.63 | | % 6.17/1.63 | | ALPHA: (36) implies: % 6.17/1.63 | | (37) big_j(all_6_0, all_48_1) = all_58_0 % 6.17/1.63 | | % 6.17/1.63 | | GROUND_INST: instantiating (3) with all_48_0, all_58_0, all_48_1, all_6_0, % 6.17/1.63 | | simplifying with (27), (37) gives: % 6.17/1.63 | | (38) all_58_0 = all_48_0 % 6.17/1.63 | | % 6.17/1.63 | | GROUND_INST: instantiating (3) with all_56_0, all_58_0, all_48_1, all_6_0, % 6.17/1.63 | | simplifying with (33), (37) gives: % 6.17/1.63 | | (39) all_58_0 = all_56_0 % 6.17/1.63 | | % 6.17/1.63 | | GROUND_INST: instantiating (4) with 0, all_56_1, all_48_1, all_6_0, % 6.17/1.63 | | simplifying with (28), (34) gives: % 6.17/1.63 | | (40) all_56_1 = 0 % 6.17/1.63 | | % 6.17/1.63 | | COMBINE_EQS: (38), (39) imply: % 6.17/1.63 | | (41) all_56_0 = all_48_0 % 6.17/1.63 | | % 6.17/1.63 | | BETA: splitting (35) gives: % 6.17/1.63 | | % 6.17/1.63 | | Case 1: % 6.17/1.63 | | | % 6.17/1.63 | | | (42) ~ (all_56_1 = 0) % 6.17/1.63 | | | % 6.17/1.63 | | | REDUCE: (40), (42) imply: % 6.17/1.63 | | | (43) $false % 6.17/1.63 | | | % 6.17/1.63 | | | CLOSE: (43) is inconsistent. % 6.17/1.63 | | | % 6.17/1.63 | | Case 2: % 6.17/1.63 | | | % 6.17/1.63 | | | (44) all_56_0 = 0 % 6.17/1.63 | | | % 6.17/1.63 | | | COMBINE_EQS: (41), (44) imply: % 6.17/1.63 | | | (45) all_48_0 = 0 % 6.17/1.63 | | | % 6.17/1.63 | | | SIMP: (45) implies: % 6.17/1.63 | | | (46) all_48_0 = 0 % 6.17/1.63 | | | % 6.17/1.63 | | | REDUCE: (25), (46) imply: % 6.17/1.63 | | | (47) $false % 6.17/1.63 | | | % 6.17/1.63 | | | CLOSE: (47) is inconsistent. % 6.17/1.63 | | | % 6.17/1.63 | | End of split % 6.17/1.63 | | % 6.17/1.63 | End of split % 6.17/1.63 | % 6.17/1.63 End of proof % 6.17/1.63 % SZS output end Proof for theBenchmark % 6.17/1.63 % 6.17/1.63 1027ms %------------------------------------------------------------------------------