%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE072+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 : n031.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 05:34:27 EDT 2023 % Result : Theorem 6.80s 1.63s % Output : Proof 8.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE072+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n031.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 11:41:26 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.52/1.02 Prover 1: Preprocessing ... % 2.52/1.02 Prover 4: Preprocessing ... % 2.52/1.07 Prover 6: Preprocessing ... % 2.52/1.07 Prover 3: Preprocessing ... % 2.52/1.07 Prover 5: Preprocessing ... % 2.52/1.07 Prover 0: Preprocessing ... % 2.52/1.07 Prover 2: Preprocessing ... % 5.23/1.40 Prover 1: Constructing countermodel ... % 5.23/1.40 Prover 6: Constructing countermodel ... % 5.23/1.41 Prover 3: Constructing countermodel ... % 5.23/1.44 Prover 4: Constructing countermodel ... % 5.23/1.45 Prover 0: Proving ... % 5.23/1.46 Prover 5: Proving ... % 6.56/1.59 Prover 2: Proving ... % 6.80/1.63 Prover 3: proved (996ms) % 6.80/1.63 Prover 0: proved (1003ms) % 6.80/1.63 % 6.80/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.80/1.63 % 6.80/1.64 % 6.80/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.80/1.64 % 6.80/1.64 Prover 2: stopped % 6.80/1.64 Prover 5: stopped % 6.80/1.65 Prover 6: stopped % 6.80/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.80/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.80/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.80/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.80/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.80/1.68 Prover 7: Preprocessing ... % 6.80/1.69 Prover 10: Preprocessing ... % 6.80/1.70 Prover 8: Preprocessing ... % 6.80/1.70 Prover 11: Preprocessing ... % 7.37/1.71 Prover 13: Preprocessing ... % 7.37/1.77 Prover 8: Warning: ignoring some quantifiers % 7.37/1.78 Prover 8: Constructing countermodel ... % 8.00/1.78 Prover 7: Constructing countermodel ... % 8.00/1.80 Prover 4: Found proof (size 33) % 8.00/1.80 Prover 4: proved (1171ms) % 8.00/1.81 Prover 10: Constructing countermodel ... % 8.00/1.81 Prover 13: Warning: ignoring some quantifiers % 8.00/1.81 Prover 7: stopped % 8.00/1.81 Prover 1: Found proof (size 42) % 8.00/1.81 Prover 1: proved (1178ms) % 8.00/1.81 Prover 8: stopped % 8.00/1.81 Prover 10: stopped % 8.00/1.81 Prover 13: Constructing countermodel ... % 8.00/1.81 Prover 11: Constructing countermodel ... % 8.00/1.82 Prover 13: stopped % 8.00/1.82 Prover 11: stopped % 8.00/1.82 % 8.00/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.00/1.82 % 8.00/1.83 % SZS output start Proof for theBenchmark % 8.00/1.83 Assumptions after simplification: % 8.00/1.83 --------------------------------- % 8.00/1.83 % 8.00/1.83 (additive_commutativity) % 8.00/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 8.00/1.86 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 8.00/1.86 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 8.00/1.86 (addition(v1, v0) = v2 & $i(v2))) % 8.00/1.86 % 8.00/1.86 (domain2) % 8.00/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2) % 8.00/1.86 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 8.00/1.86 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = % 8.00/1.86 v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.00/1.86 (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 8.00/1.86 [v4: $i] : ? [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = % 8.00/1.86 v4 & multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3))) % 8.00/1.86 % 8.00/1.86 (domain5) % 8.00/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 8.00/1.87 (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ~ % 8.00/1.87 $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & addition(v0, v1) = v5 % 8.00/1.87 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.00/1.87 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] % 8.00/1.87 : ? [v5: $i] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & % 8.00/1.87 addition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 8.00/1.87 % 8.00/1.87 (goals) % 8.00/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.00/1.87 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 8.00/1.87 ? [v11: $i] : ( ~ (v11 = v6) & domain(v9) = v10 & domain(v7) = v8 & % 8.00/1.87 domain(v5) = v6 & domain(v2) = v4 & multiplication(v3, v4) = v5 & % 8.00/1.87 multiplication(v1, v4) = v9 & multiplication(v0, v4) = v7 & addition(v8, % 8.00/1.87 v10) = v11 & addition(v0, v1) = v3 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 8.00/1.87 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.00/1.87 % 8.00/1.87 (left_distributivity) % 8.00/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.00/1.87 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 8.00/1.87 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 8.00/1.87 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) & % 8.00/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 8.00/1.87 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~ % 8.00/1.87 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) = % 8.00/1.87 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 8.00/1.87 & $i(v4))) % 8.00/1.87 % 8.00/1.87 (function-axioms) % 8.00/1.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.00/1.88 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 8.00/1.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.00/1.88 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 8.00/1.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 8.00/1.88 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.00/1.88 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 8.00/1.88 % 8.00/1.88 Further assumptions not needed in the proof: % 8.00/1.88 -------------------------------------------- % 8.00/1.88 additive_associativity, additive_idempotence, additive_identity, domain1, % 8.00/1.88 domain3, domain4, left_annihilation, multiplicative_associativity, % 8.00/1.88 multiplicative_left_identity, multiplicative_right_identity, order, % 8.00/1.88 right_annihilation, right_distributivity % 8.00/1.88 % 8.00/1.88 Those formulas are unsatisfiable: % 8.00/1.88 --------------------------------- % 8.00/1.88 % 8.00/1.88 Begin of proof % 8.00/1.88 | % 8.00/1.88 | ALPHA: (additive_commutativity) implies: % 8.56/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 8.56/1.88 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 8.56/1.88 | % 8.56/1.88 | ALPHA: (left_distributivity) implies: % 8.56/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 8.56/1.88 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ % 8.56/1.88 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 8.56/1.88 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & % 8.56/1.88 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 8.56/1.88 | % 8.56/1.88 | ALPHA: (domain2) implies: % 8.56/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) = % 8.56/1.88 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.56/1.88 | $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & % 8.56/1.88 | multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3))) % 8.56/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) % 8.56/1.89 | = v2) | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 8.56/1.89 | ? [v4: $i] : ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & % 8.56/1.89 | multiplication(v0, v1) = v4 & $i(v5) & $i(v4))) % 8.56/1.89 | % 8.56/1.89 | ALPHA: (domain5) implies: % 8.56/1.89 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 8.56/1.89 | ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = % 8.56/1.89 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & % 8.56/1.89 | addition(v0, v1) = v5 & $i(v5) & $i(v4))) % 8.56/1.89 | % 8.56/1.89 | ALPHA: (function-axioms) implies: % 8.56/1.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) = % 8.56/1.89 | v1) | ~ (domain(v2) = v0)) % 8.56/1.89 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.56/1.89 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 8.56/1.89 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.56/1.89 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 8.56/1.89 | % 8.56/1.89 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2, % 8.56/1.89 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9, % 8.56/1.89 | all_20_10, all_20_11 gives: % 8.56/1.89 | (9) ~ (all_20_0 = all_20_5) & domain(all_20_2) = all_20_1 & % 8.56/1.89 | domain(all_20_4) = all_20_3 & domain(all_20_6) = all_20_5 & % 8.56/1.89 | domain(all_20_9) = all_20_7 & multiplication(all_20_8, all_20_7) = % 8.56/1.89 | all_20_6 & multiplication(all_20_10, all_20_7) = all_20_2 & % 8.56/1.89 | multiplication(all_20_11, all_20_7) = all_20_4 & addition(all_20_3, % 8.56/1.89 | all_20_1) = all_20_0 & addition(all_20_11, all_20_10) = all_20_8 & % 8.56/1.89 | $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & % 8.56/1.89 | $i(all_20_4) & $i(all_20_5) & $i(all_20_6) & $i(all_20_7) & % 8.56/1.89 | $i(all_20_8) & $i(all_20_9) & $i(all_20_10) & $i(all_20_11) % 8.56/1.89 | % 8.56/1.89 | ALPHA: (9) implies: % 8.62/1.89 | (10) ~ (all_20_0 = all_20_5) % 8.62/1.89 | (11) $i(all_20_11) % 8.62/1.89 | (12) $i(all_20_10) % 8.62/1.89 | (13) $i(all_20_9) % 8.62/1.89 | (14) $i(all_20_7) % 8.62/1.89 | (15) $i(all_20_4) % 8.62/1.89 | (16) $i(all_20_2) % 8.62/1.89 | (17) addition(all_20_11, all_20_10) = all_20_8 % 8.62/1.89 | (18) addition(all_20_3, all_20_1) = all_20_0 % 8.62/1.89 | (19) multiplication(all_20_11, all_20_7) = all_20_4 % 8.62/1.90 | (20) multiplication(all_20_10, all_20_7) = all_20_2 % 8.62/1.90 | (21) multiplication(all_20_8, all_20_7) = all_20_6 % 8.62/1.90 | (22) domain(all_20_9) = all_20_7 % 8.62/1.90 | (23) domain(all_20_6) = all_20_5 % 8.62/1.90 | (24) domain(all_20_4) = all_20_3 % 8.62/1.90 | (25) domain(all_20_2) = all_20_1 % 8.62/1.90 | % 8.62/1.90 | GROUND_INST: instantiating (1) with all_20_10, all_20_11, all_20_8, % 8.62/1.90 | simplifying with (11), (12), (17) gives: % 8.62/1.90 | (26) addition(all_20_10, all_20_11) = all_20_8 & $i(all_20_8) % 8.62/1.90 | % 8.62/1.90 | ALPHA: (26) implies: % 8.62/1.90 | (27) $i(all_20_8) % 8.62/1.90 | % 8.62/1.90 | GROUND_INST: instantiating (2) with all_20_11, all_20_10, all_20_7, all_20_8, % 8.62/1.90 | all_20_6, simplifying with (11), (12), (14), (17), (21) gives: % 8.62/1.90 | (28) ? [v0: $i] : ? [v1: $i] : (multiplication(all_20_10, all_20_7) = v1 % 8.62/1.90 | & multiplication(all_20_11, all_20_7) = v0 & addition(v0, v1) = % 8.62/1.90 | all_20_6 & $i(v1) & $i(v0) & $i(all_20_6)) % 8.62/1.90 | % 8.62/1.90 | GROUND_INST: instantiating (3) with all_20_8, all_20_7, all_20_6, simplifying % 8.62/1.90 | with (14), (21), (27) gives: % 8.62/1.90 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 & % 8.62/1.90 | domain(all_20_6) = v0 & domain(all_20_7) = v1 & % 8.62/1.90 | multiplication(all_20_8, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 8.62/1.90 | % 8.62/1.90 | GROUND_INST: instantiating (4) with all_20_8, all_20_9, all_20_7, all_20_6, % 8.62/1.90 | simplifying with (13), (21), (22), (27) gives: % 8.62/1.90 | (30) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_6) = v1 & % 8.62/1.90 | multiplication(all_20_8, all_20_9) = v0 & $i(v1) & $i(v0)) % 8.62/1.90 | % 8.62/1.90 | GROUND_INST: instantiating (5) with all_20_4, all_20_2, all_20_3, all_20_1, % 8.62/1.90 | all_20_0, simplifying with (15), (16), (18), (24), (25) gives: % 8.62/1.90 | (31) ? [v0: $i] : (domain(v0) = all_20_0 & addition(all_20_4, all_20_2) = % 8.62/1.90 | v0 & $i(v0) & $i(all_20_0)) % 8.62/1.90 | % 8.62/1.90 | DELTA: instantiating (31) with fresh symbol all_38_0 gives: % 8.62/1.90 | (32) domain(all_38_0) = all_20_0 & addition(all_20_4, all_20_2) = all_38_0 % 8.62/1.90 | & $i(all_38_0) & $i(all_20_0) % 8.62/1.90 | % 8.62/1.90 | ALPHA: (32) implies: % 8.62/1.90 | (33) addition(all_20_4, all_20_2) = all_38_0 % 8.62/1.90 | (34) domain(all_38_0) = all_20_0 % 8.62/1.90 | % 8.62/1.90 | DELTA: instantiating (30) with fresh symbols all_44_0, all_44_1 gives: % 8.62/1.90 | (35) domain(all_44_1) = all_44_0 & domain(all_20_6) = all_44_0 & % 8.62/1.90 | multiplication(all_20_8, all_20_9) = all_44_1 & $i(all_44_0) & % 8.62/1.90 | $i(all_44_1) % 8.62/1.90 | % 8.62/1.90 | ALPHA: (35) implies: % 8.62/1.90 | (36) domain(all_20_6) = all_44_0 % 8.62/1.90 | % 8.62/1.90 | DELTA: instantiating (28) with fresh symbols all_46_0, all_46_1 gives: % 8.62/1.91 | (37) multiplication(all_20_10, all_20_7) = all_46_0 & % 8.62/1.91 | multiplication(all_20_11, all_20_7) = all_46_1 & addition(all_46_1, % 8.62/1.91 | all_46_0) = all_20_6 & $i(all_46_0) & $i(all_46_1) & $i(all_20_6) % 8.62/1.91 | % 8.62/1.91 | ALPHA: (37) implies: % 8.62/1.91 | (38) addition(all_46_1, all_46_0) = all_20_6 % 8.62/1.91 | (39) multiplication(all_20_11, all_20_7) = all_46_1 % 8.62/1.91 | (40) multiplication(all_20_10, all_20_7) = all_46_0 % 8.62/1.91 | % 8.62/1.91 | DELTA: instantiating (29) with fresh symbols all_50_0, all_50_1, all_50_2 % 8.62/1.91 | gives: % 8.62/1.91 | (41) domain(all_50_0) = all_50_2 & domain(all_20_6) = all_50_2 & % 8.62/1.91 | domain(all_20_7) = all_50_1 & multiplication(all_20_8, all_50_1) = % 8.62/1.91 | all_50_0 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) % 8.62/1.91 | % 8.62/1.91 | ALPHA: (41) implies: % 8.62/1.91 | (42) domain(all_20_6) = all_50_2 % 8.62/1.91 | % 8.62/1.91 | GROUND_INST: instantiating (8) with all_20_4, all_46_1, all_20_7, all_20_11, % 8.62/1.91 | simplifying with (19), (39) gives: % 8.62/1.91 | (43) all_46_1 = all_20_4 % 8.62/1.91 | % 8.62/1.91 | GROUND_INST: instantiating (8) with all_20_2, all_46_0, all_20_7, all_20_10, % 8.62/1.91 | simplifying with (20), (40) gives: % 8.62/1.91 | (44) all_46_0 = all_20_2 % 8.62/1.91 | % 8.62/1.91 | GROUND_INST: instantiating (6) with all_20_5, all_50_2, all_20_6, simplifying % 8.62/1.91 | with (23), (42) gives: % 8.62/1.91 | (45) all_50_2 = all_20_5 % 8.62/1.91 | % 8.62/1.91 | GROUND_INST: instantiating (6) with all_44_0, all_50_2, all_20_6, simplifying % 8.62/1.91 | with (36), (42) gives: % 8.62/1.91 | (46) all_50_2 = all_44_0 % 8.62/1.91 | % 8.62/1.91 | COMBINE_EQS: (45), (46) imply: % 8.62/1.91 | (47) all_44_0 = all_20_5 % 8.62/1.91 | % 8.62/1.91 | REDUCE: (38), (43), (44) imply: % 8.62/1.91 | (48) addition(all_20_4, all_20_2) = all_20_6 % 8.62/1.91 | % 8.62/1.91 | GROUND_INST: instantiating (7) with all_38_0, all_20_6, all_20_2, all_20_4, % 8.62/1.91 | simplifying with (33), (48) gives: % 8.62/1.91 | (49) all_38_0 = all_20_6 % 8.62/1.91 | % 8.62/1.91 | REDUCE: (34), (49) imply: % 8.62/1.91 | (50) domain(all_20_6) = all_20_0 % 8.62/1.91 | % 8.62/1.91 | GROUND_INST: instantiating (6) with all_20_5, all_20_0, all_20_6, simplifying % 8.62/1.91 | with (23), (50) gives: % 8.62/1.91 | (51) all_20_0 = all_20_5 % 8.62/1.91 | % 8.62/1.91 | REDUCE: (10), (51) imply: % 8.62/1.91 | (52) $false % 8.62/1.91 | % 8.62/1.91 | CLOSE: (52) is inconsistent. % 8.62/1.91 | % 8.62/1.91 End of proof % 8.62/1.91 % SZS output end Proof for theBenchmark % 8.62/1.91 % 8.62/1.91 1302ms %------------------------------------------------------------------------------