%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX033+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 : Tue Apr 1 02:15:29 AM UTC 2025 % Result : Theorem 137.49s 18.71s % Output : Proof 138.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX033+1 : TPTP v9.1.0. Released v9.1.0. % 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n011.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 : Mon Mar 31 14:24:48 EDT 2025 % 0.12/0.33 % CPUTime : % 0.61/0.59 ________ _____ % 0.61/0.59 ___ __ \_________(_)________________________________ % 0.61/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.59 % 0.61/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.59 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.61 Running up to 7 provers in parallel. % 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.81/1.21 Prover 1: Preprocessing ... % 3.81/1.21 Prover 4: Preprocessing ... % 4.02/1.26 Prover 3: Preprocessing ... % 4.02/1.26 Prover 5: Preprocessing ... % 4.02/1.26 Prover 6: Preprocessing ... % 4.02/1.26 Prover 0: Preprocessing ... % 4.02/1.26 Prover 2: Preprocessing ... % 9.48/2.06 Prover 5: Proving ... % 9.48/2.07 Prover 4: Warning: ignoring some quantifiers % 10.08/2.08 Prover 6: Proving ... % 10.08/2.08 Prover 1: Warning: ignoring some quantifiers % 10.14/2.09 Prover 2: Proving ... % 10.14/2.09 Prover 3: Warning: ignoring some quantifiers % 10.35/2.12 Prover 3: Constructing countermodel ... % 10.35/2.13 Prover 1: Constructing countermodel ... % 10.35/2.15 Prover 4: Constructing countermodel ... % 10.35/2.22 Prover 0: Proving ... % 74.01/10.36 Prover 2: stopped % 74.01/10.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.63/10.48 Prover 7: Preprocessing ... % 76.28/10.65 Prover 7: Warning: ignoring some quantifiers % 76.28/10.66 Prover 7: Constructing countermodel ... % 101.34/13.95 Prover 5: stopped % 101.34/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 102.54/14.06 Prover 8: Preprocessing ... % 103.65/14.21 Prover 8: Warning: ignoring some quantifiers % 103.65/14.21 Prover 8: Constructing countermodel ... % 117.02/15.96 Prover 1: stopped % 117.02/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.60/16.02 Prover 9: Preprocessing ... % 119.24/16.21 Prover 9: Warning: ignoring some quantifiers % 119.24/16.22 Prover 9: Constructing countermodel ... % 131.70/17.88 Prover 6: stopped % 131.70/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.76/18.02 Prover 10: Preprocessing ... % 132.98/18.11 Prover 10: Warning: ignoring some quantifiers % 132.98/18.11 Prover 10: Constructing countermodel ... % 137.49/18.67 Prover 10: Found proof (size 36) % 137.49/18.70 Prover 10: proved (781ms) % 137.49/18.71 Prover 9: stopped % 137.49/18.71 Prover 3: stopped % 137.49/18.71 Prover 0: stopped % 137.49/18.71 Prover 8: stopped % 137.49/18.71 Prover 7: stopped % 137.49/18.71 Prover 4: stopped % 137.49/18.71 % 137.49/18.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 137.49/18.71 % 137.98/18.71 % SZS output start Proof for theBenchmark % 137.98/18.72 Assumptions after simplification: % 137.98/18.72 --------------------------------- % 137.98/18.72 % 137.98/18.72 (corollary-(plus:successor)) % 137.98/18.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, v1) = v3) % 137.98/18.76 | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v0) | ? [v4: % 137.98/18.76 $i] : (@+(v0, v1) = v4 & s(v4) = v3 & $i(v4) & $i(v3))) % 137.98/18.76 % 137.98/18.76 (corollary-(plus:zero)) % 137.98/18.76 $i(0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ % 137.98/18.76 $i(v0)) % 137.98/18.76 % 137.98/18.76 (id2) % 137.98/18.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 137.98/18.76 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 137.98/18.76 % 137.98/18.76 (induction) % 137.98/18.77 $i(0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 137.98/18.77 ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v2) & $i(v1) & $i(v0) & ( ! [v7: $i] : % 137.98/18.77 ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v9 = v8 | ~ (@+(v7, v9) = % 137.98/18.77 v10) | ~ (@+(v7, v8) = v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ % 137.98/18.77 nat_succeeds(v7)) | (v4 = v3 & ~ (v2 = v1) & @+(v0, v2) = v3 & @+(v0, % 137.98/18.77 v1) = v3 & $i(v3) & (v0 = 0 | (v6 = v0 & s(v5) = v0 & nat_succeeds(v5) % 137.98/18.77 & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v8 = v7 | ~ (@+(v5, % 137.98/18.77 v8) = v9) | ~ (@+(v5, v7) = v9) | ~ $i(v8) | ~ $i(v7))))))) % 137.98/18.77 % 137.98/18.77 (lemma-(plus:injective:second)) % 137.98/18.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v2 = v1) & @+(v0, % 137.98/18.77 v2) = v3 & @+(v0, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 137.98/18.77 nat_succeeds(v0)) % 137.98/18.77 % 137.98/18.77 Further assumptions not needed in the proof: % 137.98/18.77 -------------------------------------------- % 137.98/18.77 (@*)/2, (@+)/2, corollary-(plus:types), id1, id10, id11, id12, id13, id14, id15, % 137.98/18.77 id16, id17, id18, id19, id20, id21, id22, id23, id24, id25, id26, id27, id28, % 137.98/18.77 id29, id3, id4, id5, id6, id7, id8, id9, lemma-(nat:ground), % 137.98/18.77 lemma-(nat:termination), lemma-(plus:existence), lemma-(plus:ground:1), % 137.98/18.77 lemma-(plus:ground:2), lemma-(plus:ground:3), lemma-(plus:successor), % 137.98/18.77 lemma-(plus:termination:1), lemma-(plus:termination:2), % 137.98/18.77 lemma-(plus:termination:3), lemma-(plus:types:1), lemma-(plus:types:2), % 137.98/18.77 lemma-(plus:types:3), lemma-(plus:uniqueness), lemma-(plus:zero), % 137.98/18.77 theorem-(plus:associative), theorem-(plus:commutative) % 137.98/18.77 % 137.98/18.77 Those formulas are unsatisfiable: % 137.98/18.77 --------------------------------- % 137.98/18.77 % 137.98/18.77 Begin of proof % 137.98/18.77 | % 137.98/18.77 | ALPHA: (corollary-(plus:zero)) implies: % 137.98/18.77 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ $i(v0)) % 137.98/18.77 | % 137.98/18.77 | ALPHA: (induction) implies: % 138.25/18.78 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 138.25/18.78 | ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v2) & $i(v1) & $i(v0) & ( ! % 138.25/18.78 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v9 = v8 | ~ % 138.25/18.78 | (@+(v7, v9) = v10) | ~ (@+(v7, v8) = v10) | ~ $i(v9) | ~ % 138.25/18.78 | $i(v8) | ~ $i(v7) | ~ nat_succeeds(v7)) | (v4 = v3 & ~ (v2 = % 138.25/18.78 | v1) & @+(v0, v2) = v3 & @+(v0, v1) = v3 & $i(v3) & (v0 = 0 | % 138.25/18.78 | (v6 = v0 & s(v5) = v0 & nat_succeeds(v5) & ! [v7: $i] : ! % 138.25/18.78 | [v8: $i] : ! [v9: $i] : (v8 = v7 | ~ (@+(v5, v8) = v9) | ~ % 138.25/18.78 | (@+(v5, v7) = v9) | ~ $i(v8) | ~ $i(v7))))))) % 138.25/18.78 | % 138.25/18.78 | DELTA: instantiating (lemma-(plus:injective:second)) with fresh symbols % 138.25/18.78 | all_64_0, all_64_1, all_64_2, all_64_3 gives: % 138.25/18.78 | (3) ~ (all_64_1 = all_64_2) & @+(all_64_3, all_64_1) = all_64_0 & % 138.25/18.78 | @+(all_64_3, all_64_2) = all_64_0 & $i(all_64_0) & $i(all_64_1) & % 138.25/18.78 | $i(all_64_2) & $i(all_64_3) & nat_succeeds(all_64_3) % 138.25/18.78 | % 138.25/18.78 | ALPHA: (3) implies: % 138.25/18.78 | (4) ~ (all_64_1 = all_64_2) % 138.25/18.78 | (5) nat_succeeds(all_64_3) % 138.25/18.78 | (6) $i(all_64_3) % 138.25/18.79 | (7) $i(all_64_2) % 138.25/18.79 | (8) $i(all_64_1) % 138.25/18.79 | (9) @+(all_64_3, all_64_2) = all_64_0 % 138.25/18.79 | (10) @+(all_64_3, all_64_1) = all_64_0 % 138.25/18.79 | % 138.25/18.79 | DELTA: instantiating (2) with fresh symbols all_79_0, all_79_1, all_79_2, % 138.25/18.79 | all_79_3, all_79_4, all_79_5, all_79_6 gives: % 138.25/18.79 | (11) $i(all_79_1) & $i(all_79_4) & $i(all_79_5) & $i(all_79_6) & ( ! [v0: % 138.25/18.79 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 138.25/18.79 | (@+(v0, v2) = v3) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 138.25/18.79 | ~ $i(v0) | ~ nat_succeeds(v0)) | (all_79_2 = all_79_3 & ~ % 138.25/18.79 | (all_79_4 = all_79_5) & @+(all_79_6, all_79_4) = all_79_3 & % 138.25/18.79 | @+(all_79_6, all_79_5) = all_79_3 & $i(all_79_3) & (all_79_6 = 0 | % 138.25/18.79 | (all_79_0 = all_79_6 & s(all_79_1) = all_79_6 & % 138.25/18.79 | nat_succeeds(all_79_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 138.25/18.79 | $i] : (v1 = v0 | ~ (@+(all_79_1, v1) = v2) | ~ % 138.25/18.79 | (@+(all_79_1, v0) = v2) | ~ $i(v1) | ~ $i(v0)))))) % 138.25/18.79 | % 138.25/18.79 | ALPHA: (11) implies: % 138.25/18.79 | (12) $i(all_79_5) % 138.25/18.79 | (13) $i(all_79_4) % 138.25/18.79 | (14) $i(all_79_1) % 138.25/18.80 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 138.25/18.80 | (@+(v0, v2) = v3) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 138.25/18.80 | ~ $i(v0) | ~ nat_succeeds(v0)) | (all_79_2 = all_79_3 & ~ % 138.25/18.80 | (all_79_4 = all_79_5) & @+(all_79_6, all_79_4) = all_79_3 & % 138.25/18.80 | @+(all_79_6, all_79_5) = all_79_3 & $i(all_79_3) & (all_79_6 = 0 | % 138.25/18.80 | (all_79_0 = all_79_6 & s(all_79_1) = all_79_6 & % 138.25/18.80 | nat_succeeds(all_79_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 138.25/18.80 | : (v1 = v0 | ~ (@+(all_79_1, v1) = v2) | ~ (@+(all_79_1, v0) = % 138.25/18.80 | v2) | ~ $i(v1) | ~ $i(v0))))) % 138.25/18.80 | % 138.25/18.80 | BETA: splitting (15) gives: % 138.25/18.80 | % 138.25/18.80 | Case 1: % 138.25/18.80 | | % 138.25/18.80 | | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | % 138.25/18.80 | | ~ (@+(v0, v2) = v3) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 138.25/18.80 | | | ~ $i(v0) | ~ nat_succeeds(v0)) % 138.25/18.80 | | % 138.25/18.80 | | GROUND_INST: instantiating (16) with all_64_3, all_64_2, all_64_1, all_64_0, % 138.25/18.80 | | simplifying with (5), (6), (7), (8), (9), (10) gives: % 138.25/18.80 | | (17) all_64_1 = all_64_2 % 138.25/18.80 | | % 138.25/18.80 | | REDUCE: (4), (17) imply: % 138.25/18.80 | | (18) $false % 138.25/18.80 | | % 138.25/18.80 | | CLOSE: (18) is inconsistent. % 138.25/18.80 | | % 138.25/18.80 | Case 2: % 138.25/18.80 | | % 138.25/18.80 | | (19) all_79_2 = all_79_3 & ~ (all_79_4 = all_79_5) & @+(all_79_6, % 138.25/18.80 | | all_79_4) = all_79_3 & @+(all_79_6, all_79_5) = all_79_3 & % 138.25/18.80 | | $i(all_79_3) & (all_79_6 = 0 | (all_79_0 = all_79_6 & s(all_79_1) = % 138.25/18.80 | | all_79_6 & nat_succeeds(all_79_1) & ! [v0: $i] : ! [v1: $i] : % 138.25/18.80 | | ! [v2: $i] : (v1 = v0 | ~ (@+(all_79_1, v1) = v2) | ~ % 138.25/18.80 | | (@+(all_79_1, v0) = v2) | ~ $i(v1) | ~ $i(v0)))) % 138.25/18.80 | | % 138.25/18.80 | | ALPHA: (19) implies: % 138.25/18.80 | | (20) ~ (all_79_4 = all_79_5) % 138.25/18.80 | | (21) @+(all_79_6, all_79_5) = all_79_3 % 138.25/18.80 | | (22) @+(all_79_6, all_79_4) = all_79_3 % 138.25/18.81 | | (23) all_79_6 = 0 | (all_79_0 = all_79_6 & s(all_79_1) = all_79_6 & % 138.25/18.81 | | nat_succeeds(all_79_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 138.25/18.81 | | (v1 = v0 | ~ (@+(all_79_1, v1) = v2) | ~ (@+(all_79_1, v0) = v2) % 138.25/18.81 | | | ~ $i(v1) | ~ $i(v0))) % 138.25/18.81 | | % 138.25/18.81 | | BETA: splitting (23) gives: % 138.25/18.81 | | % 138.25/18.81 | | Case 1: % 138.25/18.81 | | | % 138.25/18.81 | | | (24) all_79_6 = 0 % 138.25/18.81 | | | % 138.25/18.81 | | | REDUCE: (22), (24) imply: % 138.25/18.81 | | | (25) @+(0, all_79_4) = all_79_3 % 138.25/18.81 | | | % 138.25/18.81 | | | REDUCE: (21), (24) imply: % 138.25/18.81 | | | (26) @+(0, all_79_5) = all_79_3 % 138.25/18.81 | | | % 138.25/18.81 | | | GROUND_INST: instantiating (1) with all_79_5, all_79_3, simplifying with % 138.25/18.81 | | | (12), (26) gives: % 138.25/18.81 | | | (27) all_79_3 = all_79_5 % 138.25/18.81 | | | % 138.25/18.81 | | | GROUND_INST: instantiating (1) with all_79_4, all_79_3, simplifying with % 138.25/18.81 | | | (13), (25) gives: % 138.25/18.81 | | | (28) all_79_3 = all_79_4 % 138.25/18.81 | | | % 138.25/18.81 | | | COMBINE_EQS: (27), (28) imply: % 138.25/18.81 | | | (29) all_79_4 = all_79_5 % 138.25/18.81 | | | % 138.25/18.81 | | | SIMP: (29) implies: % 138.25/18.81 | | | (30) all_79_4 = all_79_5 % 138.25/18.81 | | | % 138.25/18.81 | | | REDUCE: (20), (30) imply: % 138.25/18.81 | | | (31) $false % 138.25/18.81 | | | % 138.25/18.81 | | | CLOSE: (31) is inconsistent. % 138.25/18.81 | | | % 138.25/18.81 | | Case 2: % 138.25/18.81 | | | % 138.25/18.81 | | | (32) all_79_0 = all_79_6 & s(all_79_1) = all_79_6 & % 138.25/18.81 | | | nat_succeeds(all_79_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 138.25/18.81 | | | (v1 = v0 | ~ (@+(all_79_1, v1) = v2) | ~ (@+(all_79_1, v0) = v2) % 138.25/18.81 | | | | ~ $i(v1) | ~ $i(v0)) % 138.25/18.81 | | | % 138.25/18.81 | | | ALPHA: (32) implies: % 138.25/18.81 | | | (33) nat_succeeds(all_79_1) % 138.25/18.81 | | | (34) s(all_79_1) = all_79_6 % 138.25/18.81 | | | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 138.25/18.81 | | | (@+(all_79_1, v1) = v2) | ~ (@+(all_79_1, v0) = v2) | ~ $i(v1) % 138.25/18.81 | | | | ~ $i(v0)) % 138.25/18.81 | | | % 138.25/18.81 | | | GROUND_INST: instantiating (corollary-(plus:successor)) with all_79_1, % 138.25/18.81 | | | all_79_4, all_79_6, all_79_3, simplifying with (13), (14), % 138.25/18.81 | | | (22), (33), (34) gives: % 138.25/18.81 | | | (36) ? [v0: $i] : (@+(all_79_1, all_79_4) = v0 & s(v0) = all_79_3 & % 138.25/18.81 | | | $i(v0) & $i(all_79_3)) % 138.25/18.81 | | | % 138.25/18.82 | | | GROUND_INST: instantiating (corollary-(plus:successor)) with all_79_1, % 138.25/18.82 | | | all_79_5, all_79_6, all_79_3, simplifying with (12), (14), % 138.25/18.82 | | | (21), (33), (34) gives: % 138.25/18.82 | | | (37) ? [v0: $i] : (@+(all_79_1, all_79_5) = v0 & s(v0) = all_79_3 & % 138.25/18.82 | | | $i(v0) & $i(all_79_3)) % 138.25/18.82 | | | % 138.25/18.82 | | | DELTA: instantiating (36) with fresh symbol all_375_0 gives: % 138.25/18.82 | | | (38) @+(all_79_1, all_79_4) = all_375_0 & s(all_375_0) = all_79_3 & % 138.25/18.82 | | | $i(all_375_0) & $i(all_79_3) % 138.25/18.82 | | | % 138.25/18.82 | | | ALPHA: (38) implies: % 138.25/18.82 | | | (39) $i(all_375_0) % 138.25/18.82 | | | (40) s(all_375_0) = all_79_3 % 138.25/18.82 | | | (41) @+(all_79_1, all_79_4) = all_375_0 % 138.25/18.82 | | | % 138.25/18.82 | | | DELTA: instantiating (37) with fresh symbol all_377_0 gives: % 138.25/18.82 | | | (42) @+(all_79_1, all_79_5) = all_377_0 & s(all_377_0) = all_79_3 & % 138.25/18.82 | | | $i(all_377_0) & $i(all_79_3) % 138.25/18.82 | | | % 138.25/18.82 | | | ALPHA: (42) implies: % 138.25/18.82 | | | (43) $i(all_377_0) % 138.25/18.82 | | | (44) s(all_377_0) = all_79_3 % 138.25/18.82 | | | (45) @+(all_79_1, all_79_5) = all_377_0 % 138.25/18.82 | | | % 138.25/18.82 | | | GROUND_INST: instantiating (id2) with all_375_0, all_377_0, all_79_3, % 138.25/18.82 | | | simplifying with (39), (40), (43), (44) gives: % 138.25/18.82 | | | (46) all_377_0 = all_375_0 % 138.25/18.82 | | | % 138.25/18.82 | | | REDUCE: (45), (46) imply: % 138.25/18.82 | | | (47) @+(all_79_1, all_79_5) = all_375_0 % 138.25/18.82 | | | % 138.25/18.82 | | | GROUND_INST: instantiating (35) with all_79_4, all_79_5, all_375_0, % 138.25/18.82 | | | simplifying with (12), (13), (41), (47) gives: % 138.25/18.82 | | | (48) all_79_4 = all_79_5 % 138.25/18.82 | | | % 138.25/18.82 | | | REDUCE: (20), (48) imply: % 138.25/18.82 | | | (49) $false % 138.25/18.82 | | | % 138.25/18.82 | | | CLOSE: (49) is inconsistent. % 138.25/18.82 | | | % 138.25/18.82 | | End of split % 138.25/18.82 | | % 138.25/18.82 | End of split % 138.25/18.82 | % 138.25/18.82 End of proof % 138.25/18.82 % SZS output end Proof for theBenchmark % 138.25/18.82 % 138.25/18.82 18225ms %------------------------------------------------------------------------------