%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV570+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 : n015.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 02:02:56 AM UTC 2025 % Result : Theorem 97.62s 13.39s % Output : Proof 98.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEV570+1 : TPTP v9.1.0. Released v9.1.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.35 % Computer : n015.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Mon Mar 31 12:44:50 EDT 2025 % 0.12/0.35 % CPUTime : % 0.54/0.62 ________ _____ % 0.54/0.62 ___ __ \_________(_)________________________________ % 0.54/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.62 % 0.54/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.62 (2023-06-19) % 0.54/0.62 % 0.54/0.62 (c) Philipp Rümmer, 2009-2023 % 0.54/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.62 Amanda Stjerna. % 0.54/0.62 Free software under BSD-3-Clause. % 0.54/0.62 % 0.54/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.62 % 0.54/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.54/0.63 Running up to 7 provers in parallel. % 0.74/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.74/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.02/1.18 Prover 1: Preprocessing ... % 3.02/1.18 Prover 4: Preprocessing ... % 3.31/1.22 Prover 6: Preprocessing ... % 3.31/1.22 Prover 5: Preprocessing ... % 3.31/1.22 Prover 3: Preprocessing ... % 3.31/1.22 Prover 2: Preprocessing ... % 3.31/1.22 Prover 0: Preprocessing ... % 6.72/1.66 Prover 5: Proving ... % 6.72/1.67 Prover 2: Proving ... % 6.72/1.72 Prover 6: Proving ... % 7.38/1.77 Prover 1: Constructing countermodel ... % 7.72/1.81 Prover 3: Constructing countermodel ... % 8.62/1.95 Prover 4: Constructing countermodel ... % 8.96/1.96 Prover 0: Proving ... % 8.96/1.98 Prover 3: gave up % 8.96/1.99 Prover 1: gave up % 8.96/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.96/2.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.91/2.09 Prover 8: Preprocessing ... % 9.91/2.10 Prover 7: Preprocessing ... % 10.46/2.21 Prover 7: Warning: ignoring some quantifiers % 10.87/2.22 Prover 7: Constructing countermodel ... % 11.23/2.33 Prover 8: Warning: ignoring some quantifiers % 11.80/2.35 Prover 8: Constructing countermodel ... % 11.80/2.37 Prover 4: gave up % 11.80/2.37 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 12.05/2.41 Prover 9: Preprocessing ... % 12.62/2.51 Prover 8: gave up % 12.62/2.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.13/2.54 Prover 10: Preprocessing ... % 13.49/2.59 Prover 10: Warning: ignoring some quantifiers % 13.49/2.60 Prover 10: Constructing countermodel ... % 13.49/2.64 Prover 9: Constructing countermodel ... % 14.06/2.66 Prover 10: gave up % 14.06/2.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.33/2.72 Prover 11: Preprocessing ... % 15.71/2.90 Prover 11: Constructing countermodel ... % 16.48/3.03 Prover 11: gave up % 17.00/3.04 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 17.25/3.08 Prover 12: Preprocessing ... % 18.54/3.27 Prover 12: Proving ... % 39.00/5.88 Prover 12: stopped % 39.00/5.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 39.00/5.92 Prover 13: Preprocessing ... % 39.59/5.96 Prover 13: Warning: ignoring some quantifiers % 39.59/5.96 Prover 13: Constructing countermodel ... % 57.76/8.31 Prover 2: stopped % 57.76/8.31 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 58.38/8.35 Prover 14: Preprocessing ... % 60.05/8.58 Prover 14: Proving ... % 77.51/10.84 Prover 13: stopped % 77.51/10.86 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181 % 78.50/10.95 Prover 15: Preprocessing ... % 79.87/11.11 Prover 15: Proving ... % 97.62/13.38 Prover 7: Found proof (size 174) % 97.62/13.38 Prover 7: proved (11302ms) % 97.62/13.39 Prover 5: stopped % 97.62/13.39 Prover 15: stopped % 97.62/13.39 Prover 14: stopped % 97.62/13.39 Prover 6: stopped % 97.62/13.39 Prover 9: stopped % 97.62/13.39 Prover 0: stopped % 97.62/13.39 % 97.62/13.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 97.62/13.39 % 97.78/13.40 % SZS output start Proof for theBenchmark % 97.78/13.40 Assumptions after simplification: % 97.78/13.40 --------------------------------- % 97.78/13.40 % 97.78/13.40 (a_def) % 97.89/13.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) = v3) | % 97.89/13.43 ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & $i(v3))) & ! % 97.89/13.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ $i(v1) | ~ % 97.89/13.43 $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & $i(v3) & $i(v2))) % 97.89/13.43 % 97.89/13.43 (e_ax) % 97.89/13.43 $i(e) & ! [v0: $i] : ( ~ $i(v0) | ~ mem(v0, e)) % 97.89/13.43 % 97.89/13.43 (n_def) % 97.89/13.44 ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = v1 & % 97.89/13.44 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (a(v0, v0) = v1) | ~ $i(v0) | % 97.89/13.44 (n(v0) = v1 & $i(v1))) % 97.89/13.44 % 97.89/13.44 (nsubq_1216_1152) % 97.89/13.44 $i(e) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.89/13.44 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 97.89/13.44 $i] : ? [v11: $i] : (n(v1) = v2 & n(v0) = v6 & n(e) = v0 & a(v10, v7) = v11 % 97.89/13.44 & a(v3, v4) = v5 & a(v1, v6) = v7 & u(v5, v8) = v9 & u(v0, v2) = v4 & s(v7) % 97.89/13.44 = v8 & s(v4) = v10 & s(v2) = v3 & s(v0) = v1 & $i(v11) & $i(v10) & $i(v9) & % 97.89/13.44 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 97.89/13.44 $i(v0) & subq(v9, v11)) % 97.89/13.44 % 97.89/13.44 (s_ax) % 97.89/13.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 97.89/13.44 $i(v1) | ~ $i(v0) | ~ mem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 97.89/13.44 (s(v0) = v1) | ~ $i(v0) | mem(v0, v1)) % 97.89/13.44 % 97.89/13.44 (subq_def) % 97.89/13.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 97.89/13.44 ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) & ? [v0: $i] : ? [v1: $i] % 97.89/13.44 : ( ~ $i(v1) | ~ $i(v0) | subq(v0, v1) | ? [v2: $i] : ($i(v2) & mem(v2, v0) % 97.89/13.44 & ~ mem(v2, v1))) % 97.89/13.44 % 97.89/13.44 (u_ax) % 97.89/13.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) = v3) | % 97.89/13.45 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v3) | mem(v0, v2) | mem(v0, % 97.89/13.45 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, % 97.89/13.45 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v2) | mem(v0, % 97.89/13.45 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, % 97.89/13.45 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v1) | mem(v0, % 97.89/13.45 v3)) % 97.89/13.45 % 97.89/13.45 (function-axioms) % 97.89/13.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3, % 97.89/13.45 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 97.89/13.45 $i] : ! [v3: $i] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & % 97.89/13.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (u(v3, % 97.89/13.45 v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 97.89/13.45 $i] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: $i] : ! [v1: % 97.89/13.45 $i] : ! [v2: $i] : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0: % 97.89/13.45 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = % 97.89/13.45 v0)) % 97.89/13.45 % 97.89/13.45 Further assumptions not needed in the proof: % 97.89/13.45 -------------------------------------------- % 97.89/13.45 atleast10p_def, atleast11p_def, atleast12p_def, atleast13p_def, atleast14p_def, % 97.89/13.45 atleast15p_def, atleast16p_def, atleast2p_def, atleast3p_def, atleast4p_def, % 97.89/13.45 atleast5p_def, atleast6p_def, atleast7p_def, atleast8p_def, atleast9p_def, % 97.89/13.45 disj_def, m_ax, p_ax, setext % 97.89/13.45 % 97.89/13.45 Those formulas are unsatisfiable: % 97.89/13.45 --------------------------------- % 97.89/13.45 % 97.89/13.45 Begin of proof % 97.89/13.45 | % 97.89/13.45 | ALPHA: (subq_def) implies: % 97.89/13.45 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 97.89/13.45 | $i(v0) | ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) % 97.89/13.46 | % 97.89/13.46 | ALPHA: (e_ax) implies: % 97.89/13.46 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ mem(v0, e)) % 97.89/13.46 | % 97.89/13.46 | ALPHA: (s_ax) implies: % 97.89/13.46 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (s(v0) = v1) | ~ $i(v0) | mem(v0, v1)) % 97.89/13.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 97.89/13.46 | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v2)) % 97.89/13.46 | % 97.89/13.46 | ALPHA: (u_ax) implies: % 97.89/13.46 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 97.89/13.46 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v1) | % 97.89/13.46 | mem(v0, v3)) % 97.89/13.46 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 97.89/13.46 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v2) | % 97.89/13.46 | mem(v0, v3)) % 97.89/13.46 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 97.89/13.46 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ mem(v0, v3) | % 97.89/13.46 | mem(v0, v2) | mem(v0, v1)) % 97.89/13.46 | % 97.89/13.46 | ALPHA: (a_def) implies: % 97.89/13.46 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ % 97.89/13.46 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & % 97.89/13.46 | $i(v3) & $i(v2))) % 97.89/13.46 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) % 97.89/13.46 | = v3) | ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & % 97.89/13.46 | $i(v3))) % 97.89/13.46 | % 97.89/13.46 | ALPHA: (n_def) implies: % 97.89/13.46 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) % 97.89/13.46 | = v1 & $i(v1))) % 97.89/13.46 | % 97.89/13.46 | ALPHA: (nsubq_1216_1152) implies: % 97.89/13.46 | (11) $i(e) % 97.89/13.47 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.89/13.47 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 97.89/13.47 | ? [v10: $i] : ? [v11: $i] : (n(v1) = v2 & n(v0) = v6 & n(e) = v0 & % 97.89/13.47 | a(v10, v7) = v11 & a(v3, v4) = v5 & a(v1, v6) = v7 & u(v5, v8) = v9 % 97.89/13.47 | & u(v0, v2) = v4 & s(v7) = v8 & s(v4) = v10 & s(v2) = v3 & s(v0) = % 97.89/13.47 | v1 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 97.89/13.47 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & subq(v9, v11)) % 97.89/13.47 | % 97.89/13.47 | ALPHA: (function-axioms) implies: % 97.89/13.47 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 97.89/13.47 | ~ (s(v2) = v0)) % 97.89/13.47 | % 97.89/13.47 | DELTA: instantiating (12) with fresh symbols all_31_0, all_31_1, all_31_2, % 97.89/13.47 | all_31_3, all_31_4, all_31_5, all_31_6, all_31_7, all_31_8, all_31_9, % 97.89/13.47 | all_31_10, all_31_11 gives: % 97.89/13.47 | (14) n(all_31_10) = all_31_9 & n(all_31_11) = all_31_5 & n(e) = all_31_11 & % 97.89/13.47 | a(all_31_1, all_31_4) = all_31_0 & a(all_31_8, all_31_7) = all_31_6 & % 97.89/13.47 | a(all_31_10, all_31_5) = all_31_4 & u(all_31_6, all_31_3) = all_31_2 & % 97.89/13.47 | u(all_31_11, all_31_9) = all_31_7 & s(all_31_4) = all_31_3 & % 97.89/13.47 | s(all_31_7) = all_31_1 & s(all_31_9) = all_31_8 & s(all_31_11) = % 97.89/13.47 | all_31_10 & $i(all_31_0) & $i(all_31_1) & $i(all_31_2) & $i(all_31_3) % 97.89/13.47 | & $i(all_31_4) & $i(all_31_5) & $i(all_31_6) & $i(all_31_7) & % 97.89/13.47 | $i(all_31_8) & $i(all_31_9) & $i(all_31_10) & $i(all_31_11) & % 97.89/13.47 | subq(all_31_2, all_31_0) % 97.89/13.47 | % 97.89/13.47 | ALPHA: (14) implies: % 97.89/13.47 | (15) subq(all_31_2, all_31_0) % 97.89/13.47 | (16) $i(all_31_11) % 97.89/13.47 | (17) $i(all_31_10) % 97.89/13.47 | (18) $i(all_31_9) % 97.89/13.47 | (19) $i(all_31_8) % 97.89/13.47 | (20) $i(all_31_7) % 97.89/13.47 | (21) $i(all_31_6) % 97.89/13.47 | (22) $i(all_31_5) % 97.89/13.47 | (23) $i(all_31_4) % 97.89/13.47 | (24) $i(all_31_1) % 97.89/13.47 | (25) s(all_31_11) = all_31_10 % 97.89/13.47 | (26) s(all_31_9) = all_31_8 % 97.89/13.47 | (27) s(all_31_7) = all_31_1 % 97.89/13.47 | (28) s(all_31_4) = all_31_3 % 97.89/13.47 | (29) u(all_31_11, all_31_9) = all_31_7 % 97.89/13.47 | (30) u(all_31_6, all_31_3) = all_31_2 % 97.89/13.47 | (31) a(all_31_10, all_31_5) = all_31_4 % 97.89/13.47 | (32) a(all_31_8, all_31_7) = all_31_6 % 97.89/13.47 | (33) a(all_31_1, all_31_4) = all_31_0 % 97.89/13.47 | (34) n(e) = all_31_11 % 97.89/13.47 | (35) n(all_31_11) = all_31_5 % 97.89/13.47 | (36) n(all_31_10) = all_31_9 % 97.89/13.47 | % 97.89/13.47 | GROUND_INST: instantiating (3) with all_31_11, all_31_10, simplifying with % 97.89/13.47 | (16), (25) gives: % 97.89/13.47 | (37) mem(all_31_11, all_31_10) % 97.89/13.47 | % 97.89/13.47 | GROUND_INST: instantiating (3) with all_31_9, all_31_8, simplifying with (18), % 97.89/13.47 | (26) gives: % 97.89/13.47 | (38) mem(all_31_9, all_31_8) % 97.89/13.47 | % 97.89/13.47 | GROUND_INST: instantiating (3) with all_31_7, all_31_1, simplifying with (20), % 97.89/13.47 | (27) gives: % 97.89/13.47 | (39) mem(all_31_7, all_31_1) % 97.89/13.47 | % 97.89/13.47 | GROUND_INST: instantiating (3) with all_31_4, all_31_3, simplifying with (23), % 97.89/13.47 | (28) gives: % 97.89/13.47 | (40) mem(all_31_4, all_31_3) % 97.89/13.47 | % 97.89/13.47 | GROUND_INST: instantiating (9) with all_31_6, all_31_4, all_31_3, all_31_2, % 97.89/13.47 | simplifying with (21), (23), (28), (30) gives: % 97.89/13.47 | (41) a(all_31_6, all_31_4) = all_31_2 & $i(all_31_2) % 97.89/13.47 | % 97.89/13.47 | ALPHA: (41) implies: % 97.89/13.47 | (42) $i(all_31_2) % 97.89/13.47 | % 97.89/13.47 | GROUND_INST: instantiating (8) with all_31_10, all_31_5, all_31_4, simplifying % 97.89/13.47 | with (17), (22), (31) gives: % 97.89/13.48 | (43) ? [v0: $i] : (u(all_31_10, v0) = all_31_4 & s(all_31_5) = v0 & $i(v0) % 97.89/13.48 | & $i(all_31_4)) % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (8) with all_31_8, all_31_7, all_31_6, simplifying % 97.89/13.48 | with (19), (20), (32) gives: % 97.89/13.48 | (44) ? [v0: $i] : (u(all_31_8, v0) = all_31_6 & s(all_31_7) = v0 & $i(v0) % 97.89/13.48 | & $i(all_31_6)) % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (8) with all_31_1, all_31_4, all_31_0, simplifying % 97.89/13.48 | with (23), (24), (33) gives: % 97.89/13.48 | (45) ? [v0: $i] : (u(all_31_1, v0) = all_31_0 & s(all_31_4) = v0 & $i(v0) % 97.89/13.48 | & $i(all_31_0)) % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (10) with e, all_31_11, simplifying with (11), (34) % 97.89/13.48 | gives: % 97.89/13.48 | (46) a(e, e) = all_31_11 & $i(all_31_11) % 97.89/13.48 | % 97.89/13.48 | ALPHA: (46) implies: % 97.89/13.48 | (47) a(e, e) = all_31_11 % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (10) with all_31_11, all_31_5, simplifying with % 97.89/13.48 | (16), (35) gives: % 97.89/13.48 | (48) a(all_31_11, all_31_11) = all_31_5 & $i(all_31_5) % 97.89/13.48 | % 97.89/13.48 | ALPHA: (48) implies: % 97.89/13.48 | (49) a(all_31_11, all_31_11) = all_31_5 % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (10) with all_31_10, all_31_9, simplifying with % 97.89/13.48 | (17), (36) gives: % 97.89/13.48 | (50) a(all_31_10, all_31_10) = all_31_9 & $i(all_31_9) % 97.89/13.48 | % 97.89/13.48 | ALPHA: (50) implies: % 97.89/13.48 | (51) a(all_31_10, all_31_10) = all_31_9 % 97.89/13.48 | % 97.89/13.48 | DELTA: instantiating (44) with fresh symbol all_39_0 gives: % 97.89/13.48 | (52) u(all_31_8, all_39_0) = all_31_6 & s(all_31_7) = all_39_0 & % 97.89/13.48 | $i(all_39_0) & $i(all_31_6) % 97.89/13.48 | % 97.89/13.48 | ALPHA: (52) implies: % 97.89/13.48 | (53) $i(all_39_0) % 97.89/13.48 | (54) s(all_31_7) = all_39_0 % 97.89/13.48 | (55) u(all_31_8, all_39_0) = all_31_6 % 97.89/13.48 | % 97.89/13.48 | DELTA: instantiating (43) with fresh symbol all_41_0 gives: % 97.89/13.48 | (56) u(all_31_10, all_41_0) = all_31_4 & s(all_31_5) = all_41_0 & % 97.89/13.48 | $i(all_41_0) & $i(all_31_4) % 97.89/13.48 | % 97.89/13.48 | ALPHA: (56) implies: % 97.89/13.48 | (57) $i(all_41_0) % 97.89/13.48 | (58) s(all_31_5) = all_41_0 % 97.89/13.48 | (59) u(all_31_10, all_41_0) = all_31_4 % 97.89/13.48 | % 97.89/13.48 | DELTA: instantiating (45) with fresh symbol all_43_0 gives: % 97.89/13.48 | (60) u(all_31_1, all_43_0) = all_31_0 & s(all_31_4) = all_43_0 & % 97.89/13.48 | $i(all_43_0) & $i(all_31_0) % 97.89/13.48 | % 97.89/13.48 | ALPHA: (60) implies: % 97.89/13.48 | (61) $i(all_31_0) % 97.89/13.48 | (62) $i(all_43_0) % 97.89/13.48 | (63) s(all_31_4) = all_43_0 % 97.89/13.48 | (64) u(all_31_1, all_43_0) = all_31_0 % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (13) with all_31_1, all_39_0, all_31_7, simplifying % 97.89/13.48 | with (27), (54) gives: % 97.89/13.48 | (65) all_39_0 = all_31_1 % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (13) with all_31_3, all_43_0, all_31_4, simplifying % 97.89/13.48 | with (28), (63) gives: % 97.89/13.48 | (66) all_43_0 = all_31_3 % 97.89/13.48 | % 97.89/13.48 | REDUCE: (64), (66) imply: % 97.89/13.48 | (67) u(all_31_1, all_31_3) = all_31_0 % 97.89/13.48 | % 97.89/13.48 | REDUCE: (55), (65) imply: % 97.89/13.48 | (68) u(all_31_8, all_31_1) = all_31_6 % 97.89/13.48 | % 97.89/13.48 | REDUCE: (62), (66) imply: % 97.89/13.48 | (69) $i(all_31_3) % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (2) with all_31_11, simplifying with (16) gives: % 97.89/13.48 | (70) ~ mem(all_31_11, e) % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (5) with all_31_7, all_31_6, all_31_3, all_31_2, % 97.89/13.48 | simplifying with (20), (21), (30), (69) gives: % 97.89/13.48 | (71) ~ mem(all_31_7, all_31_6) | mem(all_31_7, all_31_2) % 97.89/13.48 | % 97.89/13.48 | GROUND_INST: instantiating (4) with all_31_4, all_31_9, all_31_8, simplifying % 97.89/13.48 | with (18), (23), (26) gives: % 97.89/13.48 | (72) all_31_4 = all_31_9 | ~ mem(all_31_4, all_31_8) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (7) with all_31_4, all_31_8, all_31_1, all_31_6, % 97.89/13.49 | simplifying with (19), (23), (24), (68) gives: % 97.89/13.49 | (73) ~ mem(all_31_4, all_31_6) | mem(all_31_4, all_31_1) | mem(all_31_4, % 97.89/13.49 | all_31_8) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (6) with all_31_4, all_31_8, all_31_3, all_31_6, % 97.89/13.49 | simplifying with (19), (23), (40), (69) gives: % 97.89/13.49 | (74) ~ (u(all_31_8, all_31_3) = all_31_6) | mem(all_31_4, all_31_6) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (6) with all_31_7, all_31_8, all_31_1, all_31_6, % 97.89/13.49 | simplifying with (19), (20), (24), (39), (68) gives: % 97.89/13.49 | (75) mem(all_31_7, all_31_6) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (5) with all_31_9, all_31_8, all_31_1, all_31_6, % 97.89/13.49 | simplifying with (18), (19), (24), (38), (68) gives: % 97.89/13.49 | (76) mem(all_31_9, all_31_6) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (8) with e, e, all_31_11, simplifying with (11), % 97.89/13.49 | (47) gives: % 97.89/13.49 | (77) ? [v0: $i] : (u(e, v0) = all_31_11 & s(e) = v0 & $i(v0) & % 97.89/13.49 | $i(all_31_11)) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (8) with all_31_11, all_31_11, all_31_5, % 97.89/13.49 | simplifying with (16), (49) gives: % 97.89/13.49 | (78) ? [v0: $i] : (u(all_31_11, v0) = all_31_5 & s(all_31_11) = v0 & % 97.89/13.49 | $i(v0) & $i(all_31_5)) % 97.89/13.49 | % 97.89/13.49 | GROUND_INST: instantiating (8) with all_31_10, all_31_10, all_31_9, % 97.89/13.49 | simplifying with (17), (51) gives: % 97.89/13.49 | (79) ? [v0: $i] : (u(all_31_10, v0) = all_31_9 & s(all_31_10) = v0 & % 97.89/13.49 | $i(v0) & $i(all_31_9)) % 97.89/13.49 | % 97.89/13.49 | DELTA: instantiating (79) with fresh symbol all_55_0 gives: % 97.89/13.49 | (80) u(all_31_10, all_55_0) = all_31_9 & s(all_31_10) = all_55_0 & % 97.89/13.49 | $i(all_55_0) & $i(all_31_9) % 97.89/13.49 | % 97.89/13.49 | ALPHA: (80) implies: % 97.89/13.49 | (81) $i(all_55_0) % 97.89/13.49 | (82) s(all_31_10) = all_55_0 % 97.89/13.49 | (83) u(all_31_10, all_55_0) = all_31_9 % 97.89/13.49 | % 97.89/13.49 | DELTA: instantiating (78) with fresh symbol all_57_0 gives: % 97.89/13.49 | (84) u(all_31_11, all_57_0) = all_31_5 & s(all_31_11) = all_57_0 & % 97.89/13.49 | $i(all_57_0) & $i(all_31_5) % 97.89/13.49 | % 97.89/13.49 | ALPHA: (84) implies: % 97.89/13.49 | (85) $i(all_57_0) % 97.89/13.49 | (86) s(all_31_11) = all_57_0 % 97.89/13.49 | (87) u(all_31_11, all_57_0) = all_31_5 % 97.89/13.49 | % 97.89/13.49 | DELTA: instantiating (77) with fresh symbol all_59_0 gives: % 97.89/13.49 | (88) u(e, all_59_0) = all_31_11 & s(e) = all_59_0 & $i(all_59_0) & % 97.89/13.49 | $i(all_31_11) % 97.89/13.49 | % 97.89/13.49 | ALPHA: (88) implies: % 97.89/13.49 | (89) $i(all_59_0) % 97.89/13.49 | (90) s(e) = all_59_0 % 97.89/13.49 | (91) u(e, all_59_0) = all_31_11 % 97.89/13.49 | % 97.89/13.49 | BETA: splitting (71) gives: % 97.89/13.49 | % 97.89/13.49 | Case 1: % 97.89/13.49 | | % 97.89/13.49 | | (92) ~ mem(all_31_7, all_31_6) % 97.89/13.49 | | % 97.89/13.49 | | PRED_UNIFY: (75), (92) imply: % 97.89/13.49 | | (93) $false % 97.89/13.49 | | % 97.89/13.49 | | CLOSE: (93) is inconsistent. % 97.89/13.49 | | % 97.89/13.50 | Case 2: % 97.89/13.50 | | % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (13) with all_31_10, all_57_0, all_31_11, % 97.89/13.50 | | simplifying with (25), (86) gives: % 97.89/13.50 | | (94) all_57_0 = all_31_10 % 97.89/13.50 | | % 97.89/13.50 | | PRED_UNIFY: (37), (70) imply: % 97.89/13.50 | | (95) ~ (all_31_10 = e) % 97.89/13.50 | | % 97.89/13.50 | | REDUCE: (87), (94) imply: % 97.89/13.50 | | (96) u(all_31_11, all_31_10) = all_31_5 % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (6) with all_31_11, all_31_11, all_31_9, % 97.89/13.50 | | all_31_7, simplifying with (16), (18), (29) gives: % 97.89/13.50 | | (97) ~ mem(all_31_11, all_31_9) | mem(all_31_11, all_31_7) % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (5) with all_31_9, all_31_6, all_31_3, all_31_2, % 97.89/13.50 | | simplifying with (18), (21), (30), (69), (76) gives: % 97.89/13.50 | | (98) mem(all_31_9, all_31_2) % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (4) with all_31_4, all_31_7, all_31_1, % 97.89/13.50 | | simplifying with (20), (23), (27) gives: % 97.89/13.50 | | (99) all_31_4 = all_31_7 | ~ mem(all_31_4, all_31_1) % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (3) with e, all_59_0, simplifying with (11), (90) % 97.89/13.50 | | gives: % 97.89/13.50 | | (100) mem(e, all_59_0) % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (4) with all_31_7, all_31_10, all_31_1, % 97.89/13.50 | | simplifying with (17), (20), (39) gives: % 97.89/13.50 | | (101) all_31_7 = all_31_10 | ~ (s(all_31_10) = all_31_1) % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (3) with all_31_10, all_55_0, simplifying with % 97.89/13.50 | | (17), (82) gives: % 97.89/13.50 | | (102) mem(all_31_10, all_55_0) % 97.89/13.50 | | % 97.89/13.50 | | GROUND_INST: instantiating (5) with all_31_11, all_31_10, all_55_0, % 97.89/13.50 | | all_31_9, simplifying with (16), (17), (37), (81), (83) gives: % 97.89/13.50 | | (103) mem(all_31_11, all_31_9) % 97.89/13.50 | | % 97.89/13.50 | | BETA: splitting (97) gives: % 97.89/13.50 | | % 97.89/13.50 | | Case 1: % 97.89/13.50 | | | % 97.89/13.50 | | | (104) ~ mem(all_31_11, all_31_9) % 97.89/13.50 | | | % 97.89/13.50 | | | PRED_UNIFY: (103), (104) imply: % 97.89/13.50 | | | (105) $false % 97.89/13.50 | | | % 97.89/13.50 | | | CLOSE: (105) is inconsistent. % 97.89/13.50 | | | % 97.89/13.50 | | Case 2: % 97.89/13.50 | | | % 97.89/13.50 | | | (106) mem(all_31_11, all_31_7) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (7) with e, all_31_10, all_55_0, all_31_9, % 97.89/13.50 | | | simplifying with (11), (17), (81), (83) gives: % 97.89/13.50 | | | (107) ~ mem(e, all_31_9) | mem(e, all_55_0) | mem(e, all_31_10) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (5) with e, all_31_11, all_31_9, all_31_7, % 97.89/13.50 | | | simplifying with (11), (16), (18), (29) gives: % 97.89/13.50 | | | (108) ~ mem(e, all_31_11) | mem(e, all_31_7) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (5) with e, all_31_11, all_31_10, all_31_5, % 97.89/13.50 | | | simplifying with (11), (16), (17), (96) gives: % 97.89/13.50 | | | (109) ~ mem(e, all_31_11) | mem(e, all_31_5) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (6) with e, e, all_59_0, all_31_11, simplifying % 97.89/13.50 | | | with (11), (89), (91), (100) gives: % 97.89/13.50 | | | (110) mem(e, all_31_11) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (4) with e, all_31_10, all_55_0, simplifying % 97.89/13.50 | | | with (11), (17), (82) gives: % 97.89/13.50 | | | (111) all_31_10 = e | ~ mem(e, all_55_0) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (4) with e, all_31_11, all_31_10, simplifying % 97.89/13.50 | | | with (11), (16), (25) gives: % 97.89/13.50 | | | (112) all_31_11 = e | ~ mem(e, all_31_10) % 97.89/13.50 | | | % 97.89/13.50 | | | GROUND_INST: instantiating (2) with e, simplifying with (11) gives: % 97.89/13.50 | | | (113) ~ mem(e, e) % 97.89/13.50 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (4) with all_31_11, e, all_31_7, simplifying % 97.89/13.51 | | | with (11), (16), (106) gives: % 97.89/13.51 | | | (114) all_31_11 = e | ~ (s(e) = all_31_7) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (6) with all_31_10, all_31_10, all_55_0, % 97.89/13.51 | | | all_31_9, simplifying with (17), (81), (83), (102) gives: % 97.89/13.51 | | | (115) mem(all_31_10, all_31_9) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (7) with all_31_10, all_31_10, all_41_0, % 97.89/13.51 | | | all_31_4, simplifying with (17), (57), (59) gives: % 97.89/13.51 | | | (116) ~ mem(all_31_10, all_31_4) | mem(all_31_10, all_41_0) | % 97.89/13.51 | | | mem(all_31_10, all_31_10) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (6) with all_31_10, all_31_11, all_31_9, % 97.89/13.51 | | | all_31_7, simplifying with (16), (17), (18), (29) gives: % 97.89/13.51 | | | (117) ~ mem(all_31_10, all_31_9) | mem(all_31_10, all_31_7) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (4) with all_31_10, all_31_5, all_41_0, % 97.89/13.51 | | | simplifying with (17), (22), (58) gives: % 97.89/13.51 | | | (118) all_31_5 = all_31_10 | ~ mem(all_31_10, all_41_0) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (4) with all_31_10, all_31_11, all_31_10, % 97.89/13.51 | | | simplifying with (16), (17), (25) gives: % 97.89/13.51 | | | (119) all_31_10 = all_31_11 | ~ mem(all_31_10, all_31_10) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (4) with all_31_9, all_31_4, all_31_3, % 97.89/13.51 | | | simplifying with (18), (23), (28) gives: % 97.89/13.51 | | | (120) all_31_4 = all_31_9 | ~ mem(all_31_9, all_31_3) % 97.89/13.51 | | | % 97.89/13.51 | | | GROUND_INST: instantiating (1) with all_31_2, all_31_0, all_31_9, % 97.89/13.51 | | | simplifying with (15), (18), (42), (61), (98) gives: % 97.89/13.51 | | | (121) mem(all_31_9, all_31_0) % 97.89/13.51 | | | % 97.89/13.51 | | | BETA: splitting (109) gives: % 97.89/13.51 | | | % 97.89/13.51 | | | Case 1: % 97.89/13.51 | | | | % 97.89/13.51 | | | | (122) ~ mem(e, all_31_11) % 97.89/13.51 | | | | % 97.89/13.51 | | | | PRED_UNIFY: (110), (122) imply: % 97.89/13.51 | | | | (123) $false % 97.89/13.51 | | | | % 97.89/13.51 | | | | CLOSE: (123) is inconsistent. % 97.89/13.51 | | | | % 97.89/13.51 | | | Case 2: % 97.89/13.51 | | | | % 97.89/13.51 | | | | (124) mem(e, all_31_5) % 97.89/13.51 | | | | % 97.89/13.51 | | | | BETA: splitting (117) gives: % 97.89/13.51 | | | | % 97.89/13.51 | | | | Case 1: % 97.89/13.51 | | | | | % 97.89/13.51 | | | | | (125) ~ mem(all_31_10, all_31_9) % 97.89/13.51 | | | | | % 97.89/13.51 | | | | | PRED_UNIFY: (115), (125) imply: % 97.89/13.51 | | | | | (126) $false % 97.89/13.51 | | | | | % 97.89/13.51 | | | | | CLOSE: (126) is inconsistent. % 97.89/13.51 | | | | | % 97.89/13.51 | | | | Case 2: % 97.89/13.51 | | | | | % 97.89/13.51 | | | | | (127) mem(all_31_10, all_31_7) % 97.89/13.51 | | | | | % 97.89/13.51 | | | | | BETA: splitting (108) gives: % 97.89/13.51 | | | | | % 97.89/13.51 | | | | | Case 1: % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | | (128) ~ mem(e, all_31_11) % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | | PRED_UNIFY: (110), (128) imply: % 97.89/13.51 | | | | | | (129) $false % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | | CLOSE: (129) is inconsistent. % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | Case 2: % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | | (130) mem(e, all_31_7) % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | | BETA: splitting (111) gives: % 97.89/13.51 | | | | | | % 97.89/13.51 | | | | | | Case 1: % 97.89/13.51 | | | | | | | % 97.89/13.51 | | | | | | | (131) ~ mem(e, all_55_0) % 97.89/13.51 | | | | | | | % 97.89/13.51 | | | | | | | PRED_UNIFY: (110), (113) imply: % 97.89/13.51 | | | | | | | (132) ~ (all_31_11 = e) % 97.89/13.51 | | | | | | | % 97.89/13.51 | | | | | | | BETA: splitting (112) gives: % 97.89/13.51 | | | | | | | % 97.89/13.51 | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | % 97.89/13.51 | | | | | | | | (133) ~ mem(e, all_31_10) % 97.89/13.51 | | | | | | | | % 97.89/13.51 | | | | | | | | BETA: splitting (107) gives: % 97.89/13.51 | | | | | | | | % 97.89/13.51 | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | % 97.89/13.51 | | | | | | | | | (134) ~ mem(e, all_31_9) % 97.89/13.51 | | | | | | | | | % 97.89/13.51 | | | | | | | | | BETA: splitting (114) gives: % 97.89/13.51 | | | | | | | | | % 97.89/13.51 | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | PRED_UNIFY: (124), (133) imply: % 97.89/13.51 | | | | | | | | | | (135) ~ (all_31_5 = all_31_10) % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | PRED_UNIFY: (130), (133) imply: % 97.89/13.51 | | | | | | | | | | (136) ~ (all_31_7 = all_31_10) % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | PRED_UNIFY: (110), (133) imply: % 97.89/13.51 | | | | | | | | | | (137) ~ (all_31_10 = all_31_11) % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | PRED_UNIFY: (130), (134) imply: % 97.89/13.51 | | | | | | | | | | (138) ~ (all_31_7 = all_31_9) % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | BETA: splitting (118) gives: % 97.89/13.51 | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | (139) ~ mem(all_31_10, all_41_0) % 97.89/13.51 | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | BETA: splitting (119) gives: % 97.89/13.51 | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | (140) ~ mem(all_31_10, all_31_10) % 97.89/13.51 | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | BETA: splitting (116) gives: % 97.89/13.51 | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | (141) ~ mem(all_31_10, all_31_4) % 97.89/13.51 | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | BETA: splitting (101) gives: % 97.89/13.51 | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | PRED_UNIFY: (127), (141) imply: % 97.89/13.51 | | | | | | | | | | | | | | (142) ~ (all_31_4 = all_31_7) % 97.89/13.51 | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | PRED_UNIFY: (115), (141) imply: % 97.89/13.51 | | | | | | | | | | | | | | (143) ~ (all_31_4 = all_31_9) % 97.89/13.51 | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | BETA: splitting (99) gives: % 97.89/13.51 | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | (144) ~ mem(all_31_4, all_31_1) % 97.89/13.51 | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 97.89/13.51 | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | (145) ~ mem(all_31_9, all_31_3) % 97.89/13.51 | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 97.89/13.51 | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | (146) ~ mem(all_31_4, all_31_8) % 97.89/13.51 | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 97.89/13.51 | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | | (147) ~ mem(all_31_4, all_31_6) % 97.89/13.51 | | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 97.89/13.51 | | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | | Case 1: % 97.89/13.51 | | | | | | | | | | | | | | | | | | | % 97.89/13.51 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_31_9, all_31_1, % 97.89/13.52 | | | | | | | | | | | | | | | | | | | all_31_3, all_31_0, simplifying with (18), (24), % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (67), (69), (121), (145) gives: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (148) mem(all_31_9, all_31_1) % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_31_9, all_31_7, % 97.89/13.52 | | | | | | | | | | | | | | | | | | | all_31_1, simplifying with (18), (20), (27), (148) % 97.89/13.52 | | | | | | | | | | | | | | | | | | | gives: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (149) all_31_7 = all_31_9 % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | REDUCE: (138), (149) imply: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (150) $false % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (151) mem(all_31_4, all_31_6) % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (147), (151) imply: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (152) $false % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | (153) mem(all_31_4, all_31_1) | mem(all_31_4, all_31_8) % 97.89/13.52 | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives: % 97.89/13.52 | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | Case 1: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (154) mem(all_31_4, all_31_1) % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (144), (154) imply: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (155) $false % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (156) mem(all_31_4, all_31_8) % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (146), (156) imply: % 97.89/13.52 | | | | | | | | | | | | | | | | | | | (157) $false % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | (158) all_31_4 = all_31_9 % 97.89/13.52 | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | REDUCE: (143), (158) imply: % 97.89/13.52 | | | | | | | | | | | | | | | | | (159) $false % 97.89/13.52 | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | (160) all_31_4 = all_31_9 % 97.89/13.52 | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | REDUCE: (143), (160) imply: % 97.89/13.52 | | | | | | | | | | | | | | | | (161) $false % 97.89/13.52 | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | (162) all_31_4 = all_31_7 % 97.89/13.52 | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | REDUCE: (142), (162) imply: % 97.89/13.52 | | | | | | | | | | | | | | | (163) $false % 97.89/13.52 | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | (164) all_31_7 = all_31_10 % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | REDUCE: (136), (164) imply: % 97.89/13.52 | | | | | | | | | | | | | | (165) $false % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | CLOSE: (165) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | (166) mem(all_31_10, all_41_0) | mem(all_31_10, % 97.89/13.52 | | | | | | | | | | | | | all_31_10) % 97.89/13.52 | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | BETA: splitting (166) gives: % 97.89/13.52 | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | Case 1: % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | (167) mem(all_31_10, all_41_0) % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | PRED_UNIFY: (139), (167) imply: % 97.89/13.52 | | | | | | | | | | | | | | (168) $false % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | (169) mem(all_31_10, all_31_10) % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | PRED_UNIFY: (140), (169) imply: % 97.89/13.52 | | | | | | | | | | | | | | (170) $false % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | (171) all_31_10 = all_31_11 % 97.89/13.52 | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | REDUCE: (137), (171) imply: % 97.89/13.52 | | | | | | | | | | | | (172) $false % 97.89/13.52 | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 97.89/13.52 | | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | (173) all_31_5 = all_31_10 % 97.89/13.52 | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | REDUCE: (135), (173) imply: % 97.89/13.52 | | | | | | | | | | | (174) $false % 97.89/13.52 | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | | CLOSE: (174) is inconsistent. % 97.89/13.52 | | | | | | | | | | | % 97.89/13.52 | | | | | | | | | | End of split % 97.89/13.52 | | | | | | | | | | % 97.89/13.52 | | | | | | | | | Case 2: % 97.89/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | (175) all_31_11 = e % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | REDUCE: (132), (175) imply: % 98.37/13.52 | | | | | | | | | | (176) $false % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | CLOSE: (176) is inconsistent. % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | End of split % 98.37/13.52 | | | | | | | | | % 98.37/13.52 | | | | | | | | Case 2: % 98.37/13.52 | | | | | | | | | % 98.37/13.52 | | | | | | | | | (177) mem(e, all_55_0) | mem(e, all_31_10) % 98.37/13.52 | | | | | | | | | % 98.37/13.52 | | | | | | | | | BETA: splitting (177) gives: % 98.37/13.52 | | | | | | | | | % 98.37/13.52 | | | | | | | | | Case 1: % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | (178) mem(e, all_55_0) % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | PRED_UNIFY: (131), (178) imply: % 98.37/13.52 | | | | | | | | | | (179) $false % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | CLOSE: (179) is inconsistent. % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | Case 2: % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | (180) mem(e, all_31_10) % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | PRED_UNIFY: (133), (180) imply: % 98.37/13.52 | | | | | | | | | | (181) $false % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | | CLOSE: (181) is inconsistent. % 98.37/13.52 | | | | | | | | | | % 98.37/13.52 | | | | | | | | | End of split % 98.37/13.52 | | | | | | | | | % 98.37/13.52 | | | | | | | | End of split % 98.37/13.52 | | | | | | | | % 98.37/13.52 | | | | | | | Case 2: % 98.37/13.52 | | | | | | | | % 98.37/13.52 | | | | | | | | (182) all_31_11 = e % 98.37/13.52 | | | | | | | | % 98.37/13.52 | | | | | | | | REDUCE: (132), (182) imply: % 98.37/13.52 | | | | | | | | (183) $false % 98.37/13.52 | | | | | | | | % 98.37/13.52 | | | | | | | | CLOSE: (183) is inconsistent. % 98.37/13.52 | | | | | | | | % 98.37/13.52 | | | | | | | End of split % 98.37/13.52 | | | | | | | % 98.37/13.52 | | | | | | Case 2: % 98.37/13.52 | | | | | | | % 98.37/13.52 | | | | | | | (184) all_31_10 = e % 98.37/13.52 | | | | | | | % 98.37/13.52 | | | | | | | REDUCE: (95), (184) imply: % 98.37/13.52 | | | | | | | (185) $false % 98.37/13.52 | | | | | | | % 98.37/13.52 | | | | | | | CLOSE: (185) is inconsistent. % 98.37/13.52 | | | | | | | % 98.37/13.52 | | | | | | End of split % 98.37/13.52 | | | | | | % 98.37/13.52 | | | | | End of split % 98.37/13.52 | | | | | % 98.37/13.52 | | | | End of split % 98.37/13.52 | | | | % 98.37/13.52 | | | End of split % 98.37/13.52 | | | % 98.37/13.52 | | End of split % 98.37/13.52 | | % 98.37/13.52 | End of split % 98.37/13.52 | % 98.37/13.52 End of proof % 98.37/13.52 % SZS output end Proof for theBenchmark % 98.37/13.52 % 98.37/13.52 12902ms %------------------------------------------------------------------------------