%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE009+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 : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 05:34:10 EDT 2023 % Result : Theorem 13.79s 2.70s % Output : Proof 17.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE009+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n027.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 11:32:53 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.58 ________ _____ % 0.20/0.58 ___ __ \_________(_)________________________________ % 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.58 (2023-06-19) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2023 % 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.58 Amanda Stjerna. % 0.20/0.58 Free software under BSD-3-Clause. % 0.20/0.58 % 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.58 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.51/1.05 Prover 4: Preprocessing ... % 2.51/1.05 Prover 1: Preprocessing ... % 2.51/1.09 Prover 5: Preprocessing ... % 2.51/1.09 Prover 0: Preprocessing ... % 2.51/1.09 Prover 6: Preprocessing ... % 2.51/1.09 Prover 2: Preprocessing ... % 2.51/1.09 Prover 3: Preprocessing ... % 4.22/1.41 Prover 1: Constructing countermodel ... % 4.22/1.41 Prover 3: Constructing countermodel ... % 4.22/1.44 Prover 6: Proving ... % 4.99/1.48 Prover 5: Proving ... % 5.63/1.50 Prover 0: Proving ... % 5.63/1.52 Prover 4: Constructing countermodel ... % 5.63/1.56 Prover 2: Proving ... % 8.83/1.96 Prover 3: gave up % 8.83/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.18/2.05 Prover 7: Preprocessing ... % 10.71/2.21 Prover 7: Constructing countermodel ... % 13.79/2.68 Prover 0: proved (2075ms) % 13.79/2.69 % 13.79/2.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.79/2.70 % 13.79/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.26/2.72 Prover 6: stopped % 14.65/2.73 Prover 8: Preprocessing ... % 14.65/2.73 Prover 5: stopped % 14.65/2.73 Prover 2: stopped % 14.65/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.65/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.65/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.65/2.78 Prover 10: Preprocessing ... % 14.65/2.78 Prover 11: Preprocessing ... % 14.65/2.79 Prover 13: Preprocessing ... % 14.65/2.79 Prover 8: Warning: ignoring some quantifiers % 14.65/2.79 Prover 8: Constructing countermodel ... % 15.33/2.82 Prover 10: Constructing countermodel ... % 15.33/2.87 Prover 13: Warning: ignoring some quantifiers % 15.33/2.87 Prover 13: Constructing countermodel ... % 15.33/2.88 Prover 11: Constructing countermodel ... % 16.94/3.09 Prover 8: gave up % 16.94/3.10 Prover 10: Found proof (size 45) % 16.94/3.10 Prover 10: proved (353ms) % 16.94/3.10 Prover 13: Found proof (size 46) % 16.94/3.10 Prover 13: proved (321ms) % 16.94/3.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 16.94/3.10 Prover 7: stopped % 16.94/3.10 Prover 1: stopped % 16.94/3.10 Prover 11: stopped % 16.94/3.10 Prover 4: stopped % 16.94/3.11 Prover 16: Preprocessing ... % 17.60/3.13 Prover 16: stopped % 17.60/3.13 % 17.60/3.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.60/3.13 % 17.60/3.15 % SZS output start Proof for theBenchmark % 17.60/3.15 Assumptions after simplification: % 17.60/3.15 --------------------------------- % 17.60/3.15 % 17.60/3.15 (additive_associativity) % 17.60/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 17.60/3.19 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 17.60/3.19 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 & % 17.60/3.19 $i(v5) & $i(v4))) % 17.60/3.19 % 17.60/3.19 (additive_commutativity) % 17.60/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ % 17.60/3.19 $i(v1) | ~ $i(v0) | (addition(v1, v0) = v2 & $i(v2))) % 17.60/3.19 % 17.60/3.19 (goals) % 17.95/3.19 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 17.95/3.19 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.95/3.19 [v10: $i] : ( ~ (v10 = one) & c(v1) = v3 & c(v0) = v6 & multiplication(v6, v3) % 17.95/3.19 = v9 & multiplication(v6, v1) = v7 & multiplication(v0, v3) = v4 & % 17.95/3.19 multiplication(v0, v1) = v2 & addition(v8, v9) = v10 & addition(v5, v7) = v8 % 17.95/3.19 & addition(v2, v4) = v5 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.95/3.19 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & test(v1) & test(v0)) % 17.95/3.19 % 17.95/3.19 (left_distributivity) % 17.95/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.95/3.19 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 17.95/3.19 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 17.95/3.19 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) % 17.95/3.19 % 17.95/3.19 (multiplicative_right_identity) % 17.95/3.19 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 17.95/3.19 v1) | ~ $i(v0)) % 17.95/3.19 % 17.95/3.19 (right_distributivity) % 17.95/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.95/3.20 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 17.95/3.20 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 17.95/3.20 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) % 17.95/3.20 % 17.95/3.20 (test_2) % 17.95/3.20 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ % 17.95/3.20 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) & % 17.95/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ % 17.95/3.20 $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero % 17.95/3.20 & multiplication(v0, v1) = zero)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.95/3.20 (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0) | complement(v1, v0) | ? % 17.95/3.20 [v2: $i] : ? [v3: $i] : (( ~ (v3 = zero) & multiplication(v1, v0) = v3 & % 17.95/3.20 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2)))) % 17.95/3.20 % 17.95/3.20 (test_3) % 17.95/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (c(v0) = v2) | ~ % 17.95/3.20 $i(v1) | ~ $i(v0) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0: $i] : ! % 17.95/3.20 [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ test(v0) | % 17.95/3.20 complement(v0, v1)) % 17.95/3.20 % 17.95/3.20 (function-axioms) % 17.95/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.95/3.20 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 17.95/3.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 17.95/3.20 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.95/3.20 [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 17.95/3.20 % 17.95/3.20 Further assumptions not needed in the proof: % 17.95/3.20 -------------------------------------------- % 17.95/3.20 additive_idempotence, additive_identity, left_annihilation, % 17.95/3.20 multiplicative_associativity, multiplicative_left_identity, order, % 17.95/3.20 right_annihilation, test_1, test_4 % 17.95/3.20 % 17.95/3.20 Those formulas are unsatisfiable: % 17.95/3.20 --------------------------------- % 17.95/3.20 % 17.95/3.20 Begin of proof % 17.95/3.20 | % 17.95/3.20 | ALPHA: (multiplicative_right_identity) implies: % 17.95/3.20 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 17.95/3.20 | v1) | ~ $i(v0)) % 17.95/3.20 | % 17.95/3.20 | ALPHA: (test_2) implies: % 17.95/3.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ (addition(v0, % 17.95/3.20 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) % 17.95/3.20 | % 17.95/3.20 | ALPHA: (test_3) implies: % 17.95/3.20 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | % 17.95/3.20 | ~ test(v0) | complement(v0, v1)) % 17.95/3.20 | % 17.95/3.20 | ALPHA: (goals) implies: % 17.95/3.21 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.95/3.21 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.95/3.21 | [v10: $i] : ( ~ (v10 = one) & c(v1) = v3 & c(v0) = v6 & % 17.95/3.21 | multiplication(v6, v3) = v9 & multiplication(v6, v1) = v7 & % 17.95/3.21 | multiplication(v0, v3) = v4 & multiplication(v0, v1) = v2 & % 17.95/3.21 | addition(v8, v9) = v10 & addition(v5, v7) = v8 & addition(v2, v4) = % 17.95/3.21 | v5 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.95/3.21 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & test(v1) & test(v0)) % 17.95/3.21 | % 17.95/3.21 | ALPHA: (function-axioms) implies: % 17.95/3.21 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.95/3.21 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 17.95/3.21 | % 17.95/3.21 | DELTA: instantiating (4) with fresh symbols all_20_0, all_20_1, all_20_2, % 17.95/3.21 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9, % 17.95/3.21 | all_20_10 gives: % 17.95/3.21 | (6) ~ (all_20_0 = one) & c(all_20_9) = all_20_7 & c(all_20_10) = all_20_4 % 17.95/3.21 | & multiplication(all_20_4, all_20_7) = all_20_1 & % 17.95/3.21 | multiplication(all_20_4, all_20_9) = all_20_3 & % 17.95/3.21 | multiplication(all_20_10, all_20_7) = all_20_6 & % 17.95/3.21 | multiplication(all_20_10, all_20_9) = all_20_8 & addition(all_20_2, % 17.95/3.21 | all_20_1) = all_20_0 & addition(all_20_5, all_20_3) = all_20_2 & % 17.95/3.21 | addition(all_20_8, all_20_6) = all_20_5 & $i(all_20_0) & $i(all_20_1) & % 17.95/3.21 | $i(all_20_2) & $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & % 17.95/3.21 | $i(all_20_6) & $i(all_20_7) & $i(all_20_8) & $i(all_20_9) & % 17.95/3.21 | $i(all_20_10) & test(all_20_9) & test(all_20_10) % 17.95/3.21 | % 17.95/3.21 | ALPHA: (6) implies: % 17.95/3.21 | (7) ~ (all_20_0 = one) % 17.95/3.21 | (8) test(all_20_10) % 17.95/3.21 | (9) test(all_20_9) % 17.95/3.21 | (10) $i(all_20_10) % 17.95/3.21 | (11) $i(all_20_9) % 17.95/3.21 | (12) $i(all_20_8) % 17.95/3.21 | (13) $i(all_20_7) % 17.95/3.21 | (14) $i(all_20_6) % 17.95/3.21 | (15) $i(all_20_4) % 17.95/3.21 | (16) $i(all_20_3) % 17.95/3.21 | (17) $i(all_20_1) % 17.95/3.21 | (18) addition(all_20_8, all_20_6) = all_20_5 % 17.95/3.21 | (19) addition(all_20_5, all_20_3) = all_20_2 % 17.95/3.21 | (20) addition(all_20_2, all_20_1) = all_20_0 % 17.95/3.21 | (21) multiplication(all_20_10, all_20_9) = all_20_8 % 17.95/3.21 | (22) multiplication(all_20_10, all_20_7) = all_20_6 % 17.95/3.21 | (23) multiplication(all_20_4, all_20_9) = all_20_3 % 17.95/3.21 | (24) multiplication(all_20_4, all_20_7) = all_20_1 % 17.95/3.21 | (25) c(all_20_10) = all_20_4 % 17.95/3.21 | (26) c(all_20_9) = all_20_7 % 17.95/3.21 | % 17.95/3.21 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_20_6, % 17.95/3.21 | all_20_5, simplifying with (12), (14), (18) gives: % 17.95/3.21 | (27) addition(all_20_6, all_20_8) = all_20_5 & $i(all_20_5) % 17.95/3.21 | % 17.95/3.21 | ALPHA: (27) implies: % 17.95/3.21 | (28) $i(all_20_5) % 17.95/3.21 | (29) addition(all_20_6, all_20_8) = all_20_5 % 17.95/3.21 | % 17.95/3.21 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_3, % 17.95/3.21 | all_20_5, all_20_2, all_20_0, simplifying with (16), (17), (19), % 17.95/3.21 | (20), (28) gives: % 17.95/3.22 | (30) ? [v0: $i] : (addition(all_20_3, all_20_1) = v0 & addition(all_20_5, % 17.95/3.22 | v0) = all_20_0 & $i(v0) & $i(all_20_0)) % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (right_distributivity) with all_20_10, all_20_9, % 17.95/3.22 | all_20_7, all_20_8, all_20_6, all_20_5, simplifying with (10), % 17.95/3.22 | (11), (13), (18), (21), (22) gives: % 17.95/3.22 | (31) ? [v0: $i] : (multiplication(all_20_10, v0) = all_20_5 & % 17.95/3.22 | addition(all_20_9, all_20_7) = v0 & $i(v0) & $i(all_20_5)) % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (3) with all_20_10, all_20_4, simplifying with (8), % 17.95/3.22 | (10), (15), (25) gives: % 17.95/3.22 | (32) complement(all_20_10, all_20_4) % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (3) with all_20_9, all_20_7, simplifying with (9), % 17.95/3.22 | (11), (13), (26) gives: % 17.95/3.22 | (33) complement(all_20_9, all_20_7) % 17.95/3.22 | % 17.95/3.22 | DELTA: instantiating (30) with fresh symbol all_32_0 gives: % 17.95/3.22 | (34) addition(all_20_3, all_20_1) = all_32_0 & addition(all_20_5, all_32_0) % 17.95/3.22 | = all_20_0 & $i(all_32_0) & $i(all_20_0) % 17.95/3.22 | % 17.95/3.22 | ALPHA: (34) implies: % 17.95/3.22 | (35) $i(all_32_0) % 17.95/3.22 | (36) addition(all_20_5, all_32_0) = all_20_0 % 17.95/3.22 | (37) addition(all_20_3, all_20_1) = all_32_0 % 17.95/3.22 | % 17.95/3.22 | DELTA: instantiating (31) with fresh symbol all_34_0 gives: % 17.95/3.22 | (38) multiplication(all_20_10, all_34_0) = all_20_5 & addition(all_20_9, % 17.95/3.22 | all_20_7) = all_34_0 & $i(all_34_0) & $i(all_20_5) % 17.95/3.22 | % 17.95/3.22 | ALPHA: (38) implies: % 17.95/3.22 | (39) addition(all_20_9, all_20_7) = all_34_0 % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (additive_commutativity) with all_20_9, all_20_7, % 17.95/3.22 | all_34_0, simplifying with (11), (13), (39) gives: % 17.95/3.22 | (40) addition(all_20_7, all_20_9) = all_34_0 & $i(all_34_0) % 17.95/3.22 | % 17.95/3.22 | ALPHA: (40) implies: % 17.95/3.22 | (41) addition(all_20_7, all_20_9) = all_34_0 % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (right_distributivity) with all_20_10, all_20_7, % 17.95/3.22 | all_20_9, all_20_6, all_20_8, all_20_5, simplifying with (10), % 17.95/3.22 | (11), (13), (21), (22), (29) gives: % 17.95/3.22 | (42) ? [v0: $i] : (multiplication(all_20_10, v0) = all_20_5 & % 17.95/3.22 | addition(all_20_7, all_20_9) = v0 & $i(v0) & $i(all_20_5)) % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (additive_commutativity) with all_20_5, all_32_0, % 17.95/3.22 | all_20_0, simplifying with (28), (35), (36) gives: % 17.95/3.22 | (43) addition(all_32_0, all_20_5) = all_20_0 & $i(all_20_0) % 17.95/3.22 | % 17.95/3.22 | ALPHA: (43) implies: % 17.95/3.22 | (44) addition(all_32_0, all_20_5) = all_20_0 % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (right_distributivity) with all_20_4, all_20_9, % 17.95/3.22 | all_20_7, all_20_3, all_20_1, all_32_0, simplifying with (11), % 17.95/3.22 | (13), (15), (23), (24), (37) gives: % 17.95/3.22 | (45) ? [v0: $i] : (multiplication(all_20_4, v0) = all_32_0 & % 17.95/3.22 | addition(all_20_9, all_20_7) = v0 & $i(v0) & $i(all_32_0)) % 17.95/3.22 | % 17.95/3.22 | DELTA: instantiating (45) with fresh symbol all_48_0 gives: % 17.95/3.22 | (46) multiplication(all_20_4, all_48_0) = all_32_0 & addition(all_20_9, % 17.95/3.22 | all_20_7) = all_48_0 & $i(all_48_0) & $i(all_32_0) % 17.95/3.22 | % 17.95/3.22 | ALPHA: (46) implies: % 17.95/3.22 | (47) $i(all_48_0) % 17.95/3.22 | (48) addition(all_20_9, all_20_7) = all_48_0 % 17.95/3.22 | (49) multiplication(all_20_4, all_48_0) = all_32_0 % 17.95/3.22 | % 17.95/3.22 | DELTA: instantiating (42) with fresh symbol all_54_0 gives: % 17.95/3.22 | (50) multiplication(all_20_10, all_54_0) = all_20_5 & addition(all_20_7, % 17.95/3.22 | all_20_9) = all_54_0 & $i(all_54_0) & $i(all_20_5) % 17.95/3.22 | % 17.95/3.22 | ALPHA: (50) implies: % 17.95/3.22 | (51) addition(all_20_7, all_20_9) = all_54_0 % 17.95/3.22 | (52) multiplication(all_20_10, all_54_0) = all_20_5 % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (5) with all_34_0, all_48_0, all_20_7, all_20_9, % 17.95/3.22 | simplifying with (39), (48) gives: % 17.95/3.22 | (53) all_48_0 = all_34_0 % 17.95/3.22 | % 17.95/3.22 | GROUND_INST: instantiating (5) with all_34_0, all_54_0, all_20_9, all_20_7, % 17.95/3.22 | simplifying with (41), (51) gives: % 17.95/3.23 | (54) all_54_0 = all_34_0 % 17.95/3.23 | % 17.95/3.23 | REDUCE: (49), (53) imply: % 17.95/3.23 | (55) multiplication(all_20_4, all_34_0) = all_32_0 % 17.95/3.23 | % 17.95/3.23 | REDUCE: (52), (54) imply: % 17.95/3.23 | (56) multiplication(all_20_10, all_34_0) = all_20_5 % 17.95/3.23 | % 17.95/3.23 | REDUCE: (47), (53) imply: % 17.95/3.23 | (57) $i(all_34_0) % 17.95/3.23 | % 17.95/3.23 | GROUND_INST: instantiating (2) with all_20_7, all_20_9, all_34_0, simplifying % 17.95/3.23 | with (11), (13), (33), (41) gives: % 17.95/3.23 | (58) all_34_0 = one % 17.95/3.23 | % 17.95/3.23 | GROUND_INST: instantiating (left_distributivity) with all_20_4, all_20_10, % 17.95/3.23 | all_34_0, all_32_0, all_20_5, all_20_0, simplifying with (10), % 17.95/3.23 | (15), (44), (55), (56), (57) gives: % 17.95/3.23 | (59) ? [v0: $i] : (multiplication(v0, all_34_0) = all_20_0 & % 17.95/3.23 | addition(all_20_4, all_20_10) = v0 & $i(v0) & $i(all_20_0)) % 17.95/3.23 | % 17.95/3.23 | DELTA: instantiating (59) with fresh symbol all_78_0 gives: % 17.95/3.23 | (60) multiplication(all_78_0, all_34_0) = all_20_0 & addition(all_20_4, % 17.95/3.23 | all_20_10) = all_78_0 & $i(all_78_0) & $i(all_20_0) % 17.95/3.23 | % 17.95/3.23 | ALPHA: (60) implies: % 17.95/3.23 | (61) addition(all_20_4, all_20_10) = all_78_0 % 17.95/3.23 | (62) multiplication(all_78_0, all_34_0) = all_20_0 % 17.95/3.23 | % 17.95/3.23 | REDUCE: (58), (62) imply: % 17.95/3.23 | (63) multiplication(all_78_0, one) = all_20_0 % 17.95/3.23 | % 17.95/3.23 | GROUND_INST: instantiating (2) with all_20_4, all_20_10, all_78_0, simplifying % 17.95/3.23 | with (10), (15), (32), (61) gives: % 17.95/3.23 | (64) all_78_0 = one % 17.95/3.23 | % 17.95/3.23 | GROUND_INST: instantiating (additive_commutativity) with all_20_4, all_20_10, % 17.95/3.23 | all_78_0, simplifying with (10), (15), (61) gives: % 17.95/3.23 | (65) addition(all_20_10, all_20_4) = all_78_0 & $i(all_78_0) % 17.95/3.23 | % 17.95/3.23 | ALPHA: (65) implies: % 17.95/3.23 | (66) $i(all_78_0) % 17.95/3.23 | % 17.95/3.23 | GROUND_INST: instantiating (1) with all_78_0, all_20_0, simplifying with (63), % 17.95/3.23 | (66) gives: % 17.95/3.23 | (67) all_78_0 = all_20_0 % 17.95/3.23 | % 17.95/3.23 | COMBINE_EQS: (64), (67) imply: % 17.95/3.23 | (68) all_20_0 = one % 17.95/3.23 | % 17.95/3.23 | REDUCE: (7), (68) imply: % 17.95/3.23 | (69) $false % 17.95/3.23 | % 17.95/3.23 | CLOSE: (69) is inconsistent. % 17.95/3.23 | % 17.95/3.23 End of proof % 17.95/3.23 % SZS output end Proof for theBenchmark % 17.95/3.23 % 17.95/3.23 2646ms %------------------------------------------------------------------------------