%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRP665+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n014.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 : Thu Aug 31 01:12:59 EDT 2023 % Result : Theorem 7.62s 1.79s % Output : Proof 8.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP665+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n014.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 : Mon Aug 28 23:47:15 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.18/1.02 Prover 1: Preprocessing ... % 2.18/1.02 Prover 4: Preprocessing ... % 2.43/1.07 Prover 2: Preprocessing ... % 2.43/1.07 Prover 3: Preprocessing ... % 2.43/1.07 Prover 6: Preprocessing ... % 2.43/1.07 Prover 5: Preprocessing ... % 2.43/1.07 Prover 0: Preprocessing ... % 3.38/1.24 Prover 6: Constructing countermodel ... % 3.84/1.27 Prover 3: Constructing countermodel ... % 3.84/1.29 Prover 0: Proving ... % 3.84/1.29 Prover 4: Constructing countermodel ... % 3.84/1.30 Prover 1: Constructing countermodel ... % 3.84/1.32 Prover 5: Proving ... % 4.46/1.39 Prover 3: gave up % 4.46/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.46/1.41 Prover 7: Preprocessing ... % 4.46/1.42 Prover 6: gave up % 4.46/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.46/1.43 Prover 2: Proving ... % 5.08/1.43 Prover 8: Preprocessing ... % 5.08/1.47 Prover 1: gave up % 5.37/1.48 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.37/1.49 Prover 8: Warning: ignoring some quantifiers % 5.37/1.49 Prover 9: Preprocessing ... % 5.37/1.49 Prover 8: Constructing countermodel ... % 5.37/1.50 Prover 7: Constructing countermodel ... % 6.07/1.59 Prover 9: Constructing countermodel ... % 6.07/1.60 Prover 8: gave up % 6.07/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.57/1.64 Prover 10: Preprocessing ... % 6.82/1.69 Prover 10: Constructing countermodel ... % 7.34/1.75 Prover 10: gave up % 7.34/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.34/1.76 Prover 11: Preprocessing ... % 7.62/1.79 Prover 0: proved (1143ms) % 7.62/1.79 % 7.62/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.62/1.79 % 7.62/1.80 Prover 9: stopped % 7.62/1.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.62/1.80 Prover 2: stopped % 7.62/1.80 Prover 5: stopped % 7.62/1.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.62/1.81 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.62/1.82 Prover 11: Constructing countermodel ... % 7.62/1.82 Prover 13: Preprocessing ... % 7.62/1.82 Prover 19: Preprocessing ... % 7.62/1.82 Prover 16: Preprocessing ... % 7.62/1.83 Prover 4: Found proof (size 88) % 7.62/1.83 Prover 4: proved (1175ms) % 7.62/1.83 Prover 11: stopped % 8.05/1.83 Prover 7: stopped % 8.05/1.85 Prover 16: stopped % 8.05/1.85 Prover 13: stopped % 8.23/1.86 Prover 19: Warning: ignoring some quantifiers % 8.23/1.87 Prover 19: Constructing countermodel ... % 8.23/1.87 Prover 19: stopped % 8.23/1.87 % 8.23/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.23/1.87 % 8.23/1.91 % SZS output start Proof for theBenchmark % 8.23/1.91 Assumptions after simplification: % 8.23/1.91 --------------------------------- % 8.23/1.91 % 8.23/1.91 (f02) % 8.23/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (mult(v1, v0) = v2) | ~ $i(v1) % 8.23/1.94 | ~ $i(v0) | ld(v1, v2) = v0) % 8.23/1.94 % 8.23/1.94 (f04) % 8.23/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (mult(v1, v0) = v2) | ~ $i(v1) % 8.23/1.94 | ~ $i(v0) | rd(v2, v0) = v1) % 8.23/1.94 % 8.23/1.94 (f07) % 8.23/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.23/1.94 $i] : ! [v6: $i] : ( ~ (rd(v3, v2) = v4) | ~ (mult(v4, v5) = v6) | ~ % 8.23/1.94 (mult(v2, v1) = v3) | ~ (mult(v2, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 8.23/1.94 $i(v0) | ? [v7: $i] : (mult(v2, v7) = v6 & mult(v1, v0) = v7 & $i(v7) & % 8.23/1.94 $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 8.23/1.94 $i] : ( ~ (mult(v2, v3) = v4) | ~ (mult(v1, v0) = v3) | ~ $i(v2) | ~ % 8.23/1.94 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (rd(v5, v2) = % 8.23/1.94 v6 & mult(v6, v7) = v4 & mult(v2, v1) = v5 & mult(v2, v0) = v7 & $i(v7) & % 8.23/1.94 $i(v6) & $i(v5) & $i(v4))) % 8.23/1.94 % 8.23/1.94 (f08) % 8.23/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.23/1.95 $i] : ! [v6: $i] : ( ~ (ld(v0, v4) = v5) | ~ (mult(v3, v5) = v6) | ~ % 8.23/1.95 (mult(v2, v0) = v3) | ~ (mult(v1, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 8.23/1.95 $i(v0) | ? [v7: $i] : (mult(v7, v0) = v6 & mult(v2, v1) = v7 & $i(v7) & % 8.23/1.95 $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 8.23/1.95 $i] : ( ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ~ $i(v2) | ~ % 8.23/1.95 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (ld(v0, v6) = % 8.23/1.95 v7 & mult(v5, v7) = v4 & mult(v2, v0) = v5 & mult(v1, v0) = v6 & $i(v7) & % 8.23/1.95 $i(v6) & $i(v5) & $i(v4))) % 8.23/1.95 % 8.23/1.95 (f09) % 8.23/1.95 $i(op_c) & ! [v0: $i] : ! [v1: $i] : ( ~ (mult(v0, op_c) = v1) | ~ $i(v0) | % 8.23/1.95 (mult(op_c, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 8.23/1.95 (mult(op_c, v0) = v1) | ~ $i(v0) | (mult(v0, op_c) = v1 & $i(v1))) % 8.23/1.95 % 8.23/1.95 (goals) % 8.23/1.95 $i(op_c) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 8.23/1.95 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 8.23/1.95 [v10: $i] : ? [v11: $i] : ? [v12: $i] : (mult(v6, v1) = v7 & mult(v4, v1) = % 8.23/1.95 v5 & mult(v2, op_c) = v10 & mult(v1, op_c) = v11 & mult(v0, v11) = v12 & % 8.23/1.95 mult(v0, v8) = v9 & mult(v0, v1) = v2 & mult(v0, op_c) = v6 & mult(op_c, v2) % 8.23/1.95 = v3 & mult(op_c, v1) = v8 & mult(op_c, v0) = v4 & $i(v12) & $i(v11) & % 8.23/1.95 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 8.23/1.95 $i(v2) & $i(v1) & $i(v0) & ( ~ (v12 = v10) | ~ (v9 = v7) | ~ (v5 = v3))) % 8.23/1.95 % 8.23/1.95 (function-axioms) % 8.23/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rd(v3, % 8.23/1.95 v2) = v1) | ~ (rd(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 8.23/1.95 $i] : ! [v3: $i] : (v1 = v0 | ~ (ld(v3, v2) = v1) | ~ (ld(v3, v2) = v0)) % 8.23/1.95 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.23/1.95 (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0)) % 8.23/1.95 % 8.23/1.95 Further assumptions not needed in the proof: % 8.23/1.95 -------------------------------------------- % 8.23/1.95 f01, f03, f05, f06 % 8.23/1.95 % 8.23/1.95 Those formulas are unsatisfiable: % 8.23/1.95 --------------------------------- % 8.23/1.95 % 8.23/1.95 Begin of proof % 8.23/1.96 | % 8.23/1.96 | ALPHA: (f07) implies: % 8.23/1.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 8.23/1.96 | ~ (mult(v2, v3) = v4) | ~ (mult(v1, v0) = v3) | ~ $i(v2) | ~ % 8.23/1.96 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 8.23/1.96 | (rd(v5, v2) = v6 & mult(v6, v7) = v4 & mult(v2, v1) = v5 & mult(v2, % 8.23/1.96 | v0) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4))) % 8.23/1.96 | % 8.23/1.96 | ALPHA: (f08) implies: % 8.23/1.96 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 8.23/1.96 | ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ~ $i(v2) | ~ % 8.23/1.96 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 8.23/1.96 | (ld(v0, v6) = v7 & mult(v5, v7) = v4 & mult(v2, v0) = v5 & mult(v1, % 8.23/1.96 | v0) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4))) % 8.23/1.96 | % 8.23/1.96 | ALPHA: (f09) implies: % 8.23/1.96 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (mult(op_c, v0) = v1) | ~ $i(v0) | % 8.23/1.96 | (mult(v0, op_c) = v1 & $i(v1))) % 8.23/1.96 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (mult(v0, op_c) = v1) | ~ $i(v0) | % 8.23/1.96 | (mult(op_c, v0) = v1 & $i(v1))) % 8.23/1.96 | % 8.23/1.96 | ALPHA: (goals) implies: % 8.23/1.96 | (5) $i(op_c) % 8.23/1.96 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.23/1.96 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 8.23/1.96 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : (mult(v6, v1) = v7 & mult(v4, % 8.23/1.96 | v1) = v5 & mult(v2, op_c) = v10 & mult(v1, op_c) = v11 & mult(v0, % 8.23/1.96 | v11) = v12 & mult(v0, v8) = v9 & mult(v0, v1) = v2 & mult(v0, op_c) % 8.23/1.97 | = v6 & mult(op_c, v2) = v3 & mult(op_c, v1) = v8 & mult(op_c, v0) = % 8.23/1.97 | v4 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) % 8.23/1.97 | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v12 = % 8.23/1.97 | v10) | ~ (v9 = v7) | ~ (v5 = v3))) % 8.23/1.97 | % 8.23/1.97 | ALPHA: (function-axioms) implies: % 8.23/1.97 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.23/1.97 | (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0)) % 8.23/1.97 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.23/1.97 | (ld(v3, v2) = v1) | ~ (ld(v3, v2) = v0)) % 8.23/1.97 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.23/1.97 | (rd(v3, v2) = v1) | ~ (rd(v3, v2) = v0)) % 8.23/1.97 | % 8.23/1.97 | DELTA: instantiating (6) with fresh symbols all_13_0, all_13_1, all_13_2, % 8.23/1.97 | all_13_3, all_13_4, all_13_5, all_13_6, all_13_7, all_13_8, all_13_9, % 8.23/1.97 | all_13_10, all_13_11, all_13_12 gives: % 8.23/1.97 | (10) mult(all_13_6, all_13_11) = all_13_5 & mult(all_13_8, all_13_11) = % 8.23/1.97 | all_13_7 & mult(all_13_10, op_c) = all_13_2 & mult(all_13_11, op_c) = % 8.23/1.97 | all_13_1 & mult(all_13_12, all_13_1) = all_13_0 & mult(all_13_12, % 8.23/1.97 | all_13_4) = all_13_3 & mult(all_13_12, all_13_11) = all_13_10 & % 8.23/1.97 | mult(all_13_12, op_c) = all_13_6 & mult(op_c, all_13_10) = all_13_9 & % 8.23/1.97 | mult(op_c, all_13_11) = all_13_4 & mult(op_c, all_13_12) = all_13_8 & % 8.23/1.97 | $i(all_13_0) & $i(all_13_1) & $i(all_13_2) & $i(all_13_3) & % 8.23/1.97 | $i(all_13_4) & $i(all_13_5) & $i(all_13_6) & $i(all_13_7) & % 8.23/1.97 | $i(all_13_8) & $i(all_13_9) & $i(all_13_10) & $i(all_13_11) & % 8.23/1.97 | $i(all_13_12) & ( ~ (all_13_0 = all_13_2) | ~ (all_13_3 = all_13_5) | % 8.23/1.97 | ~ (all_13_7 = all_13_9)) % 8.23/1.97 | % 8.23/1.97 | ALPHA: (10) implies: % 8.23/1.97 | (11) $i(all_13_12) % 8.23/1.97 | (12) $i(all_13_11) % 8.23/1.97 | (13) $i(all_13_10) % 8.23/1.97 | (14) mult(op_c, all_13_12) = all_13_8 % 8.23/1.97 | (15) mult(op_c, all_13_11) = all_13_4 % 8.23/1.97 | (16) mult(op_c, all_13_10) = all_13_9 % 8.23/1.97 | (17) mult(all_13_12, op_c) = all_13_6 % 8.23/1.97 | (18) mult(all_13_12, all_13_11) = all_13_10 % 8.23/1.97 | (19) mult(all_13_12, all_13_4) = all_13_3 % 8.23/1.97 | (20) mult(all_13_12, all_13_1) = all_13_0 % 8.23/1.97 | (21) mult(all_13_11, op_c) = all_13_1 % 8.23/1.97 | (22) mult(all_13_10, op_c) = all_13_2 % 8.23/1.97 | (23) mult(all_13_8, all_13_11) = all_13_7 % 8.23/1.97 | (24) mult(all_13_6, all_13_11) = all_13_5 % 8.23/1.97 | (25) ~ (all_13_0 = all_13_2) | ~ (all_13_3 = all_13_5) | ~ (all_13_7 = % 8.23/1.97 | all_13_9) % 8.23/1.97 | % 8.23/1.97 | GROUND_INST: instantiating (3) with all_13_12, all_13_8, simplifying with % 8.23/1.97 | (11), (14) gives: % 8.23/1.97 | (26) mult(all_13_12, op_c) = all_13_8 & $i(all_13_8) % 8.23/1.97 | % 8.23/1.97 | ALPHA: (26) implies: % 8.23/1.97 | (27) mult(all_13_12, op_c) = all_13_8 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (3) with all_13_11, all_13_4, simplifying with % 8.23/1.98 | (12), (15) gives: % 8.23/1.98 | (28) mult(all_13_11, op_c) = all_13_4 & $i(all_13_4) % 8.23/1.98 | % 8.23/1.98 | ALPHA: (28) implies: % 8.23/1.98 | (29) mult(all_13_11, op_c) = all_13_4 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (f02) with all_13_11, op_c, all_13_4, simplifying % 8.23/1.98 | with (5), (12), (15) gives: % 8.23/1.98 | (30) ld(op_c, all_13_4) = all_13_11 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (3) with all_13_10, all_13_9, simplifying with % 8.23/1.98 | (13), (16) gives: % 8.23/1.98 | (31) mult(all_13_10, op_c) = all_13_9 & $i(all_13_9) % 8.23/1.98 | % 8.23/1.98 | ALPHA: (31) implies: % 8.23/1.98 | (32) mult(all_13_10, op_c) = all_13_9 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (4) with all_13_12, all_13_6, simplifying with % 8.23/1.98 | (11), (17) gives: % 8.23/1.98 | (33) mult(op_c, all_13_12) = all_13_6 & $i(all_13_6) % 8.23/1.98 | % 8.23/1.98 | ALPHA: (33) implies: % 8.23/1.98 | (34) mult(op_c, all_13_12) = all_13_6 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (f04) with op_c, all_13_12, all_13_6, simplifying % 8.23/1.98 | with (5), (11), (17) gives: % 8.23/1.98 | (35) rd(all_13_6, op_c) = all_13_12 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (1) with all_13_11, all_13_12, op_c, all_13_10, % 8.23/1.98 | all_13_9, simplifying with (5), (11), (12), (16), (18) gives: % 8.23/1.98 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (rd(v0, op_c) = v1 & % 8.23/1.98 | mult(v1, v2) = all_13_9 & mult(op_c, all_13_11) = v2 & mult(op_c, % 8.23/1.98 | all_13_12) = v0 & $i(v2) & $i(v1) & $i(v0) & $i(all_13_9)) % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (1) with all_13_11, op_c, all_13_12, all_13_4, % 8.23/1.98 | all_13_3, simplifying with (5), (11), (12), (15), (19) gives: % 8.23/1.98 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (rd(v0, all_13_12) = v1 & % 8.23/1.98 | mult(v1, v2) = all_13_3 & mult(all_13_12, all_13_11) = v2 & % 8.23/1.98 | mult(all_13_12, op_c) = v0 & $i(v2) & $i(v1) & $i(v0) & % 8.23/1.98 | $i(all_13_3)) % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (1) with op_c, all_13_11, all_13_12, all_13_1, % 8.23/1.98 | all_13_0, simplifying with (5), (11), (12), (20), (21) gives: % 8.23/1.98 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (rd(v0, all_13_12) = v1 & % 8.23/1.98 | mult(v1, v2) = all_13_0 & mult(all_13_12, all_13_11) = v0 & % 8.23/1.98 | mult(all_13_12, op_c) = v2 & $i(v2) & $i(v1) & $i(v0) & % 8.23/1.98 | $i(all_13_0)) % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (4) with all_13_11, all_13_1, simplifying with % 8.23/1.98 | (12), (21) gives: % 8.23/1.98 | (39) mult(op_c, all_13_11) = all_13_1 & $i(all_13_1) % 8.23/1.98 | % 8.23/1.98 | ALPHA: (39) implies: % 8.23/1.98 | (40) mult(op_c, all_13_11) = all_13_1 % 8.23/1.98 | % 8.23/1.98 | GROUND_INST: instantiating (2) with op_c, all_13_11, all_13_12, all_13_10, % 8.23/1.98 | all_13_2, simplifying with (5), (11), (12), (18), (22) gives: % 8.23/1.98 | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ld(op_c, v1) = v2 & % 8.23/1.98 | mult(v0, v2) = all_13_2 & mult(all_13_11, op_c) = v1 & % 8.23/1.98 | mult(all_13_12, op_c) = v0 & $i(v2) & $i(v1) & $i(v0) & % 8.23/1.98 | $i(all_13_2)) % 8.23/1.98 | % 8.23/1.99 | GROUND_INST: instantiating (2) with all_13_11, all_13_12, op_c, all_13_8, % 8.23/1.99 | all_13_7, simplifying with (5), (11), (12), (14), (23) gives: % 8.23/1.99 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ld(all_13_11, v1) = v2 & % 8.23/1.99 | mult(v0, v2) = all_13_7 & mult(all_13_12, all_13_11) = v1 & % 8.23/1.99 | mult(op_c, all_13_11) = v0 & $i(v2) & $i(v1) & $i(v0) & % 8.23/1.99 | $i(all_13_7)) % 8.23/1.99 | % 8.23/1.99 | GROUND_INST: instantiating (2) with all_13_11, op_c, all_13_12, all_13_6, % 8.23/1.99 | all_13_5, simplifying with (5), (11), (12), (17), (24) gives: % 8.23/1.99 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ld(all_13_11, v1) = v2 & % 8.23/1.99 | mult(v0, v2) = all_13_5 & mult(all_13_12, all_13_11) = v0 & % 8.23/1.99 | mult(op_c, all_13_11) = v1 & $i(v2) & $i(v1) & $i(v0) & % 8.23/1.99 | $i(all_13_5)) % 8.23/1.99 | % 8.23/1.99 | DELTA: instantiating (36) with fresh symbols all_21_0, all_21_1, all_21_2 % 8.23/1.99 | gives: % 8.23/1.99 | (44) rd(all_21_2, op_c) = all_21_1 & mult(all_21_1, all_21_0) = all_13_9 & % 8.23/1.99 | mult(op_c, all_13_11) = all_21_0 & mult(op_c, all_13_12) = all_21_2 & % 8.23/1.99 | $i(all_21_0) & $i(all_21_1) & $i(all_21_2) & $i(all_13_9) % 8.23/1.99 | % 8.23/1.99 | ALPHA: (44) implies: % 8.23/1.99 | (45) mult(op_c, all_13_12) = all_21_2 % 8.23/1.99 | (46) mult(op_c, all_13_11) = all_21_0 % 8.23/1.99 | (47) mult(all_21_1, all_21_0) = all_13_9 % 8.23/1.99 | (48) rd(all_21_2, op_c) = all_21_1 % 8.23/1.99 | % 8.23/1.99 | DELTA: instantiating (41) with fresh symbols all_23_0, all_23_1, all_23_2 % 8.23/1.99 | gives: % 8.23/1.99 | (49) ld(op_c, all_23_1) = all_23_0 & mult(all_23_2, all_23_0) = all_13_2 & % 8.23/1.99 | mult(all_13_11, op_c) = all_23_1 & mult(all_13_12, op_c) = all_23_2 & % 8.23/1.99 | $i(all_23_0) & $i(all_23_1) & $i(all_23_2) & $i(all_13_2) % 8.23/1.99 | % 8.23/1.99 | ALPHA: (49) implies: % 8.23/1.99 | (50) mult(all_13_12, op_c) = all_23_2 % 8.23/1.99 | (51) mult(all_13_11, op_c) = all_23_1 % 8.23/1.99 | (52) mult(all_23_2, all_23_0) = all_13_2 % 8.23/1.99 | (53) ld(op_c, all_23_1) = all_23_0 % 8.23/1.99 | % 8.23/1.99 | DELTA: instantiating (42) with fresh symbols all_25_0, all_25_1, all_25_2 % 8.23/1.99 | gives: % 8.23/1.99 | (54) ld(all_13_11, all_25_1) = all_25_0 & mult(all_25_2, all_25_0) = % 8.23/1.99 | all_13_7 & mult(all_13_12, all_13_11) = all_25_1 & mult(op_c, % 8.23/1.99 | all_13_11) = all_25_2 & $i(all_25_0) & $i(all_25_1) & $i(all_25_2) & % 8.23/1.99 | $i(all_13_7) % 8.23/1.99 | % 8.23/1.99 | ALPHA: (54) implies: % 8.23/1.99 | (55) mult(op_c, all_13_11) = all_25_2 % 8.23/1.99 | % 8.23/1.99 | DELTA: instantiating (37) with fresh symbols all_27_0, all_27_1, all_27_2 % 8.23/1.99 | gives: % 8.23/1.99 | (56) rd(all_27_2, all_13_12) = all_27_1 & mult(all_27_1, all_27_0) = % 8.23/1.99 | all_13_3 & mult(all_13_12, all_13_11) = all_27_0 & mult(all_13_12, % 8.23/1.99 | op_c) = all_27_2 & $i(all_27_0) & $i(all_27_1) & $i(all_27_2) & % 8.23/1.99 | $i(all_13_3) % 8.23/1.99 | % 8.23/1.99 | ALPHA: (56) implies: % 8.23/1.99 | (57) mult(all_13_12, op_c) = all_27_2 % 8.23/1.99 | % 8.23/1.99 | DELTA: instantiating (43) with fresh symbols all_29_0, all_29_1, all_29_2 % 8.23/1.99 | gives: % 8.23/1.99 | (58) ld(all_13_11, all_29_1) = all_29_0 & mult(all_29_2, all_29_0) = % 8.23/1.99 | all_13_5 & mult(all_13_12, all_13_11) = all_29_2 & mult(op_c, % 8.23/1.99 | all_13_11) = all_29_1 & $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & % 8.23/1.99 | $i(all_13_5) % 8.23/1.99 | % 8.23/1.99 | ALPHA: (58) implies: % 8.23/1.99 | (59) mult(op_c, all_13_11) = all_29_1 % 8.23/1.99 | % 8.23/1.99 | DELTA: instantiating (38) with fresh symbols all_31_0, all_31_1, all_31_2 % 8.23/1.99 | gives: % 8.23/1.99 | (60) rd(all_31_2, all_13_12) = all_31_1 & mult(all_31_1, all_31_0) = % 8.23/1.99 | all_13_0 & mult(all_13_12, all_13_11) = all_31_2 & mult(all_13_12, % 8.23/1.99 | op_c) = all_31_0 & $i(all_31_0) & $i(all_31_1) & $i(all_31_2) & % 8.23/2.00 | $i(all_13_0) % 8.23/2.00 | % 8.23/2.00 | ALPHA: (60) implies: % 8.23/2.00 | (61) mult(all_13_12, op_c) = all_31_0 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_8, all_21_2, all_13_12, op_c, % 8.23/2.00 | simplifying with (14), (45) gives: % 8.23/2.00 | (62) all_21_2 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_6, all_21_2, all_13_12, op_c, % 8.23/2.00 | simplifying with (34), (45) gives: % 8.23/2.00 | (63) all_21_2 = all_13_6 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_4, all_29_1, all_13_11, op_c, % 8.23/2.00 | simplifying with (15), (59) gives: % 8.23/2.00 | (64) all_29_1 = all_13_4 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_25_2, all_29_1, all_13_11, op_c, % 8.23/2.00 | simplifying with (55), (59) gives: % 8.23/2.00 | (65) all_29_1 = all_25_2 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_21_0, all_29_1, all_13_11, op_c, % 8.23/2.00 | simplifying with (46), (59) gives: % 8.23/2.00 | (66) all_29_1 = all_21_0 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_1, all_29_1, all_13_11, op_c, % 8.23/2.00 | simplifying with (40), (59) gives: % 8.23/2.00 | (67) all_29_1 = all_13_1 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_23_2, all_27_2, op_c, all_13_12, % 8.23/2.00 | simplifying with (50), (57) gives: % 8.23/2.00 | (68) all_27_2 = all_23_2 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_27_2, all_31_0, op_c, all_13_12, % 8.23/2.00 | simplifying with (57), (61) gives: % 8.23/2.00 | (69) all_31_0 = all_27_2 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_8, all_31_0, op_c, all_13_12, % 8.23/2.00 | simplifying with (27), (61) gives: % 8.23/2.00 | (70) all_31_0 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_4, all_23_1, op_c, all_13_11, % 8.23/2.00 | simplifying with (29), (51) gives: % 8.23/2.00 | (71) all_23_1 = all_13_4 % 8.23/2.00 | % 8.23/2.00 | GROUND_INST: instantiating (7) with all_13_2, all_13_9, op_c, all_13_10, % 8.23/2.00 | simplifying with (22), (32) gives: % 8.23/2.00 | (72) all_13_2 = all_13_9 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (69), (70) imply: % 8.23/2.00 | (73) all_27_2 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | SIMP: (73) implies: % 8.23/2.00 | (74) all_27_2 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (65), (67) imply: % 8.23/2.00 | (75) all_25_2 = all_13_1 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (65), (66) imply: % 8.23/2.00 | (76) all_25_2 = all_21_0 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (64), (65) imply: % 8.23/2.00 | (77) all_25_2 = all_13_4 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (68), (74) imply: % 8.23/2.00 | (78) all_23_2 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | SIMP: (78) implies: % 8.23/2.00 | (79) all_23_2 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (75), (76) imply: % 8.23/2.00 | (80) all_21_0 = all_13_1 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (76), (77) imply: % 8.23/2.00 | (81) all_21_0 = all_13_4 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (80), (81) imply: % 8.23/2.00 | (82) all_13_1 = all_13_4 % 8.23/2.00 | % 8.23/2.00 | COMBINE_EQS: (62), (63) imply: % 8.23/2.00 | (83) all_13_6 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | SIMP: (83) implies: % 8.23/2.00 | (84) all_13_6 = all_13_8 % 8.23/2.00 | % 8.23/2.00 | REDUCE: (48), (62) imply: % 8.23/2.01 | (85) rd(all_13_8, op_c) = all_21_1 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (35), (84) imply: % 8.23/2.01 | (86) rd(all_13_8, op_c) = all_13_12 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (53), (71) imply: % 8.23/2.01 | (87) ld(op_c, all_13_4) = all_23_0 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (52), (72), (79) imply: % 8.23/2.01 | (88) mult(all_13_8, all_23_0) = all_13_9 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (47), (81) imply: % 8.23/2.01 | (89) mult(all_21_1, all_13_4) = all_13_9 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (24), (84) imply: % 8.23/2.01 | (90) mult(all_13_8, all_13_11) = all_13_5 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (20), (82) imply: % 8.23/2.01 | (91) mult(all_13_12, all_13_4) = all_13_0 % 8.23/2.01 | % 8.23/2.01 | GROUND_INST: instantiating (7) with all_13_3, all_13_0, all_13_4, all_13_12, % 8.23/2.01 | simplifying with (19), (91) gives: % 8.23/2.01 | (92) all_13_0 = all_13_3 % 8.23/2.01 | % 8.23/2.01 | GROUND_INST: instantiating (7) with all_13_7, all_13_5, all_13_11, all_13_8, % 8.23/2.01 | simplifying with (23), (90) gives: % 8.23/2.01 | (93) all_13_5 = all_13_7 % 8.23/2.01 | % 8.23/2.01 | GROUND_INST: instantiating (8) with all_13_11, all_23_0, all_13_4, op_c, % 8.23/2.01 | simplifying with (30), (87) gives: % 8.23/2.01 | (94) all_23_0 = all_13_11 % 8.23/2.01 | % 8.23/2.01 | GROUND_INST: instantiating (9) with all_13_12, all_21_1, op_c, all_13_8, % 8.23/2.01 | simplifying with (85), (86) gives: % 8.23/2.01 | (95) all_21_1 = all_13_12 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (89), (95) imply: % 8.23/2.01 | (96) mult(all_13_12, all_13_4) = all_13_9 % 8.23/2.01 | % 8.23/2.01 | REDUCE: (88), (94) imply: % 8.23/2.01 | (97) mult(all_13_8, all_13_11) = all_13_9 % 8.23/2.01 | % 8.23/2.01 | GROUND_INST: instantiating (7) with all_13_3, all_13_9, all_13_4, all_13_12, % 8.23/2.01 | simplifying with (19), (96) gives: % 8.23/2.01 | (98) all_13_3 = all_13_9 % 8.23/2.01 | % 8.23/2.01 | GROUND_INST: instantiating (7) with all_13_7, all_13_9, all_13_11, all_13_8, % 8.23/2.01 | simplifying with (23), (97) gives: % 8.23/2.01 | (99) all_13_7 = all_13_9 % 8.23/2.01 | % 8.23/2.01 | COMBINE_EQS: (93), (99) imply: % 8.23/2.01 | (100) all_13_5 = all_13_9 % 8.23/2.01 | % 8.23/2.01 | COMBINE_EQS: (92), (98) imply: % 8.23/2.01 | (101) all_13_0 = all_13_9 % 8.23/2.01 | % 8.23/2.01 | BETA: splitting (25) gives: % 8.23/2.01 | % 8.23/2.01 | Case 1: % 8.23/2.01 | | % 8.23/2.01 | | (102) ~ (all_13_0 = all_13_2) % 8.23/2.01 | | % 8.23/2.01 | | REDUCE: (72), (101), (102) imply: % 8.23/2.01 | | (103) $false % 8.23/2.01 | | % 8.23/2.01 | | CLOSE: (103) is inconsistent. % 8.23/2.01 | | % 8.23/2.01 | Case 2: % 8.23/2.01 | | % 8.23/2.01 | | (104) ~ (all_13_3 = all_13_5) | ~ (all_13_7 = all_13_9) % 8.23/2.01 | | % 8.23/2.01 | | BETA: splitting (104) gives: % 8.23/2.01 | | % 8.23/2.01 | | Case 1: % 8.23/2.01 | | | % 8.23/2.01 | | | (105) ~ (all_13_3 = all_13_5) % 8.23/2.01 | | | % 8.23/2.01 | | | REDUCE: (98), (100), (105) imply: % 8.23/2.01 | | | (106) $false % 8.23/2.01 | | | % 8.23/2.01 | | | CLOSE: (106) is inconsistent. % 8.23/2.01 | | | % 8.23/2.01 | | Case 2: % 8.23/2.01 | | | % 8.23/2.01 | | | (107) ~ (all_13_7 = all_13_9) % 8.23/2.01 | | | % 8.23/2.01 | | | REDUCE: (99), (107) imply: % 8.23/2.01 | | | (108) $false % 8.23/2.01 | | | % 8.23/2.01 | | | CLOSE: (108) is inconsistent. % 8.23/2.01 | | | % 8.23/2.01 | | End of split % 8.23/2.01 | | % 8.23/2.01 | End of split % 8.23/2.01 | % 8.23/2.01 End of proof % 8.23/2.01 % SZS output end Proof for theBenchmark % 8.23/2.01 % 8.23/2.01 1391ms %------------------------------------------------------------------------------