%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE005+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%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 : 600s % DateTime : Sun Jul 17 01:50:47 EDT 2022 % Result : Theorem 4.45s 1.69s % Output : Proof 6.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KLE005+1 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n015.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Thu Jun 16 08:33:26 EDT 2022 % 0.12/0.34 % CPUTime : % 0.51/0.58 ____ _ % 0.51/0.58 ___ / __ \_____(_)___ ________ __________ % 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.58 % 0.51/0.58 A Theorem Prover for First-Order Logic % 0.51/0.58 (ePrincess v.1.0) % 0.51/0.58 % 0.51/0.58 (c) Philipp Rümmer, 2009-2015 % 0.51/0.58 (c) Peter Backeman, 2014-2015 % 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.58 Bug reports to peter@backeman.se % 0.51/0.58 % 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.58 % 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.51/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.38/0.92 Prover 0: Preprocessing ... % 2.24/1.18 Prover 0: Constructing countermodel ... % 2.62/1.33 Prover 0: gave up % 2.62/1.33 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.87/1.35 Prover 1: Preprocessing ... % 2.99/1.41 Prover 1: Constructing countermodel ... % 3.30/1.43 Prover 1: gave up % 3.30/1.43 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.30/1.45 Prover 2: Preprocessing ... % 3.48/1.53 Prover 2: Warning: ignoring some quantifiers % 3.48/1.53 Prover 2: Constructing countermodel ... % 4.45/1.69 Prover 2: proved (254ms) % 4.45/1.69 % 4.45/1.69 No countermodel exists, formula is valid % 4.45/1.69 % SZS status Theorem for theBenchmark % 4.45/1.69 % 4.45/1.69 Generating proof ... Warning: ignoring some quantifiers % 5.97/2.04 found it (size 61) % 5.97/2.04 % 5.97/2.04 % SZS output start Proof for theBenchmark % 5.97/2.04 Assumed formulas after preprocessing and simplification: % 5.97/2.04 | (0) ? [v0] : ( ~ (v0 = zero) & c(one) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v2, v3) = v5) | ~ (multiplication(v1, v3) = v4) | ~ (addition(v4, v5) = v6) | ? [v7] : (multiplication(v7, v3) = v6 & addition(v1, v2) = v7)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v1, v3) = v5) | ~ (multiplication(v1, v2) = v4) | ~ (addition(v4, v5) = v6) | ? [v7] : (multiplication(v1, v7) = v6 & addition(v2, v3) = v7)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v4, v3) = v5) | ~ (multiplication(v1, v2) = v4) | ? [v6] : (multiplication(v2, v3) = v6 & multiplication(v1, v6) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v4, v3) = v5) | ~ (addition(v1, v2) = v4) | ? [v6] : ? [v7] : (multiplication(v2, v3) = v7 & multiplication(v1, v3) = v6 & addition(v6, v7) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v2, v3) = v4) | ~ (multiplication(v1, v4) = v5) | ? [v6] : (multiplication(v6, v3) = v5 & multiplication(v1, v2) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v4) = v5) | ~ (addition(v2, v3) = v4) | ? [v6] : ? [v7] : (multiplication(v1, v3) = v7 & multiplication(v1, v2) = v6 & addition(v6, v7) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v4, v1) = v5) | ~ (addition(v3, v2) = v4) | ? [v6] : (addition(v3, v6) = v5 & addition(v2, v1) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v3, v4) = v5) | ~ (addition(v2, v1) = v4) | ? [v6] : (addition(v6, v1) = v5 & addition(v3, v2) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (complement(v4, v3) = v2) | ~ (complement(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (leq(v4, v3) = v2) | ~ (leq(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (multiplication(v4, v3) = v2) | ~ (multiplication(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (addition(v4, v3) = v2) | ~ (addition(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (complement(v2, v1) = v3) | ? [v4] : (( ~ (v4 = one) & addition(v1, v2) = v4) | ( ~ (v4 = zero) & multiplication(v2, v1) = v4) | ( ~ (v4 = zero) & multiplication(v1, v2) = v4))) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v1, v2) = v3) | ? [v4] : ( ~ (v4 = v2) & addition(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (c(v3) = v2) | ~ (c(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (test(v3) = v2) | ~ (test(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (test(v1) = v2) | ~ (complement(v3, v1) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (complement(v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & test(v1) = v4) | (( ~ (v3 = 0) | (v4 = v2 & c(v1) = v2)) & (v3 = 0 | ( ~ (v4 = v2) & c(v1) = v4))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (multiplication(v2, v1) = v3) | ? [v4] : ? [v5] : ((v5 = one & v4 = zero & v3 = zero & multiplication(v1, v2) = zero & addition(v1, v2) = one) | ( ~ (v4 = 0) & complement(v2, v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (multiplication(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = one & v4 = zero & v3 = zero & multiplication(v2, v1) = zero & addition(v1, v2) = one) | ( ~ (v4 = 0) & complement(v2, v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (addition(v2, v1) = v3) | addition(v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (addition(v1, v2) = v3) | addition(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (addition(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = zero & v4 = zero & v3 = one & multiplication(v2, v1) = zero & multiplication(v1, v2) = zero) | ( ~ (v4 = 0) & complement(v2, v1) = v4))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (multiplication(v1, one) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (multiplication(one, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v1, zero) = v2)) & ! [v1] : ! [v2] : (v2 = zero | ~ (c(v1) = v2) | test(v1) = 0) & ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, zero) = v2)) & ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(zero, v1) = v2)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (test(v1) = v2) | c(v1) = zero) & ! [v1] : ! [v2] : ( ~ (complement(v2, v1) = 0) | (multiplication(v2, v1) = zero & multiplication(v1, v2) = zero & addition(v1, v2) = one)) & ! [v1] : ! [v2] : ( ~ (leq(v1, v2) = 0) | addition(v1, v2) = v2) & ! [v1] : ! [v2] : ( ~ (multiplication(v2, v1) = zero) | ? [v3] : ((v3 = 0 & complement(v2, v1) = 0) | ( ~ (v3 = one) & addition(v1, v2) = v3) | ( ~ (v3 = zero) & multiplication(v1, v2) = v3))) & ! [v1] : ! [v2] : ( ~ (multiplication(v1, v2) = zero) | ? [v3] : ((v3 = 0 & complement(v2, v1) = 0) | ( ~ (v3 = one) & addition(v1, v2) = v3) | ( ~ (v3 = zero) & multiplication(v2, v1) = v3))) & ! [v1] : ! [v2] : ( ~ (addition(v1, v2) = v2) | leq(v1, v2) = 0) & ! [v1] : ! [v2] : ( ~ (addition(v1, v2) = one) | ? [v3] : ((v3 = 0 & complement(v2, v1) = 0) | ( ~ (v3 = zero) & multiplication(v2, v1) = v3) | ( ~ (v3 = zero) & multiplication(v1, v2) = v3))) & ! [v1] : ( ~ (test(v1) = 0) | ? [v2] : complement(v2, v1) = 0) & ? [v1] : ? [v2] : ? [v3] : complement(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : leq(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : multiplication(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : addition(v2, v1) = v3 & ? [v1] : ? [v2] : c(v1) = v2 & ? [v1] : ? [v2] : test(v1) = v2) % 6.05/2.09 | Instantiating (0) with all_0_0_0 yields: % 6.05/2.09 | (1) ~ (all_0_0_0 = zero) & c(one) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (complement(v1, v0) = v2) | ? [v3] : (( ~ (v3 = one) & addition(v0, v1) = v3) | ( ~ (v3 = zero) & multiplication(v1, v0) = v3) | ( ~ (v3 = zero) & multiplication(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (test(v0) = v1) | ~ (complement(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & test(v0) = v3) | (( ~ (v2 = 0) | (v3 = v1 & c(v0) = v1)) & (v2 = 0 | ( ~ (v3 = v1) & c(v0) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = one & v3 = zero & v2 = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) & complement(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = one & v3 = zero & v2 = zero & multiplication(v1, v0) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) & complement(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = zero & v3 = zero & v2 = one & multiplication(v1, v0) = zero & multiplication(v0, v1) = zero) | ( ~ (v3 = 0) & complement(v1, v0) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0) = 0) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (test(v0) = v1) | c(v0) = zero) & ! [v0] : ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | ? [v2] : ((v2 = 0 & complement(v1, v0) = 0) | ( ~ (v2 = one) & addition(v0, v1) = v2) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | ? [v2] : ((v2 = 0 & complement(v1, v0) = 0) | ( ~ (v2 = one) & addition(v0, v1) = v2) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2))) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | ? [v2] : ((v2 = 0 & complement(v1, v0) = 0) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2))) & ! [v0] : ( ~ (test(v0) = 0) | ? [v1] : complement(v1, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : complement(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : c(v0) = v1 & ? [v0] : ? [v1] : test(v0) = v1 % 6.05/2.10 | % 6.05/2.10 | Applying alpha-rule on (1) yields: % 6.05/2.10 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (test(v0) = v1) | c(v0) = zero) % 6.05/2.10 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 6.05/2.10 | (4) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 % 6.05/2.10 | (5) ? [v0] : ? [v1] : ? [v2] : complement(v1, v0) = v2 % 6.05/2.10 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 6.05/2.10 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 6.05/2.10 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 6.05/2.10 | (9) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 6.05/2.10 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 6.05/2.10 | (11) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | ? [v2] : ((v2 = 0 & complement(v1, v0) = 0) | ( ~ (v2 = one) & addition(v0, v1) = v2) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2))) % 6.05/2.10 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 6.05/2.10 | (13) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 % 6.05/2.10 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 6.05/2.10 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 6.05/2.11 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 6.05/2.11 | (17) ? [v0] : ? [v1] : c(v0) = v1 % 6.05/2.11 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & test(v0) = v3) | (( ~ (v2 = 0) | (v3 = v1 & c(v0) = v1)) & (v2 = 0 | ( ~ (v3 = v1) & c(v0) = v3))))) % 6.05/2.11 | (19) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) % 6.05/2.11 | (20) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 6.05/2.11 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 6.05/2.11 | (22) ~ (all_0_0_0 = zero) % 6.05/2.11 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (test(v0) = v1) | ~ (complement(v2, v0) = 0)) % 6.05/2.11 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = zero & v3 = zero & v2 = one & multiplication(v1, v0) = zero & multiplication(v0, v1) = zero) | ( ~ (v3 = 0) & complement(v1, v0) = v3))) % 6.05/2.11 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) % 6.05/2.11 | (26) ? [v0] : ? [v1] : test(v0) = v1 % 6.05/2.11 | (27) c(one) = all_0_0_0 % 6.05/2.11 | (28) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 % 6.05/2.11 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) % 6.05/2.11 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 6.05/2.11 | (31) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | ? [v2] : ((v2 = 0 & complement(v1, v0) = 0) | ( ~ (v2 = one) & addition(v0, v1) = v2) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2))) % 6.05/2.11 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 6.05/2.11 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0)) % 6.05/2.11 | (34) ! [v0] : ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 6.05/2.11 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) % 6.05/2.11 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 6.05/2.11 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (complement(v1, v0) = v2) | ? [v3] : (( ~ (v3 = one) & addition(v0, v1) = v3) | ( ~ (v3 = zero) & multiplication(v1, v0) = v3) | ( ~ (v3 = zero) & multiplication(v0, v1) = v3))) % 6.05/2.11 | (38) ! [v0] : ( ~ (test(v0) = 0) | ? [v1] : complement(v1, v0) = 0) % 6.05/2.11 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 6.05/2.12 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 6.05/2.12 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = v0)) % 6.05/2.12 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = one & v3 = zero & v2 = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) & complement(v1, v0) = v3))) % 6.32/2.12 | (43) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 6.32/2.12 | (44) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | ? [v2] : ((v2 = 0 & complement(v1, v0) = 0) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2))) % 6.32/2.12 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 6.32/2.12 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) % 6.32/2.12 | (47) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0) = 0) % 6.32/2.12 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = one & v3 = zero & v2 = zero & multiplication(v1, v0) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) & complement(v1, v0) = v3))) % 6.32/2.12 | % 6.32/2.12 | Instantiating formula (47) with all_0_0_0, one and discharging atoms c(one) = all_0_0_0, yields: % 6.32/2.12 | (49) all_0_0_0 = zero | test(one) = 0 % 6.32/2.12 | % 6.32/2.12 +-Applying beta-rule and splitting (49), into two cases. % 6.32/2.12 |-Branch one: % 6.32/2.12 | (50) test(one) = 0 % 6.32/2.12 | % 6.32/2.12 | Instantiating formula (38) with one and discharging atoms test(one) = 0, yields: % 6.32/2.12 | (51) ? [v0] : complement(v0, one) = 0 % 6.32/2.12 | % 6.32/2.12 | Instantiating (51) with all_27_0_17 yields: % 6.32/2.12 | (52) complement(all_27_0_17, one) = 0 % 6.32/2.12 | % 6.32/2.12 | Instantiating formula (34) with all_27_0_17, one and discharging atoms complement(all_27_0_17, one) = 0, yields: % 6.32/2.12 | (53) multiplication(all_27_0_17, one) = zero & multiplication(one, all_27_0_17) = zero & addition(one, all_27_0_17) = one % 6.32/2.12 | % 6.32/2.12 | Applying alpha-rule on (53) yields: % 6.32/2.12 | (54) multiplication(all_27_0_17, one) = zero % 6.32/2.12 | (55) multiplication(one, all_27_0_17) = zero % 6.32/2.12 | (56) addition(one, all_27_0_17) = one % 6.32/2.12 | % 6.32/2.12 | Instantiating formula (30) with zero, all_27_0_17 and discharging atoms multiplication(one, all_27_0_17) = zero, yields: % 6.32/2.12 | (57) all_27_0_17 = zero % 6.32/2.12 | % 6.32/2.12 | From (57) and (52) follows: % 6.32/2.12 | (58) complement(zero, one) = 0 % 6.32/2.12 | % 6.32/2.12 | From (57) and (54) follows: % 6.32/2.12 | (59) multiplication(zero, one) = zero % 6.32/2.12 | % 6.32/2.12 | From (57) and (55) follows: % 6.32/2.12 | (60) multiplication(one, zero) = zero % 6.32/2.12 | % 6.32/2.12 | From (57) and (56) follows: % 6.32/2.12 | (61) addition(one, zero) = one % 6.32/2.12 | % 6.32/2.12 | Instantiating formula (31) with one, zero and discharging atoms multiplication(one, zero) = zero, yields: % 6.32/2.12 | (62) ? [v0] : ((v0 = 0 & complement(one, zero) = 0) | ( ~ (v0 = one) & addition(zero, one) = v0) | ( ~ (v0 = zero) & multiplication(zero, one) = v0)) % 6.32/2.13 | % 6.32/2.13 | Instantiating formula (11) with one, zero and discharging atoms multiplication(zero, one) = zero, yields: % 6.32/2.13 | (63) ? [v0] : ((v0 = 0 & complement(one, zero) = 0) | ( ~ (v0 = one) & addition(zero, one) = v0) | ( ~ (v0 = zero) & multiplication(one, zero) = v0)) % 6.32/2.13 | % 6.32/2.13 | Instantiating formula (48) with zero, one, zero and discharging atoms multiplication(zero, one) = zero, yields: % 6.32/2.13 | (64) ? [v0] : ? [v1] : ((v1 = one & v0 = zero & multiplication(one, zero) = zero & addition(zero, one) = one) | ( ~ (v0 = 0) & complement(one, zero) = v0)) % 6.32/2.13 | % 6.32/2.13 | Instantiating formula (40) with one, one, zero and discharging atoms addition(one, zero) = one, yields: % 6.32/2.13 | (65) addition(zero, one) = one % 6.32/2.13 | % 6.32/2.13 | Instantiating (63) with all_48_0_21 yields: % 6.32/2.13 | (66) (all_48_0_21 = 0 & complement(one, zero) = 0) | ( ~ (all_48_0_21 = one) & addition(zero, one) = all_48_0_21) | ( ~ (all_48_0_21 = zero) & multiplication(one, zero) = all_48_0_21) % 6.32/2.13 | % 6.32/2.13 | Instantiating (64) with all_49_0_22, all_49_1_23 yields: % 6.32/2.13 | (67) (all_49_0_22 = one & all_49_1_23 = zero & multiplication(one, zero) = zero & addition(zero, one) = one) | ( ~ (all_49_1_23 = 0) & complement(one, zero) = all_49_1_23) % 6.32/2.13 | % 6.32/2.13 | Instantiating (62) with all_57_0_30 yields: % 6.32/2.13 | (68) (all_57_0_30 = 0 & complement(one, zero) = 0) | ( ~ (all_57_0_30 = one) & addition(zero, one) = all_57_0_30) | ( ~ (all_57_0_30 = zero) & multiplication(zero, one) = all_57_0_30) % 6.32/2.13 | % 6.32/2.13 +-Applying beta-rule and splitting (66), into two cases. % 6.32/2.13 |-Branch one: % 6.32/2.13 | (69) (all_48_0_21 = 0 & complement(one, zero) = 0) | ( ~ (all_48_0_21 = one) & addition(zero, one) = all_48_0_21) % 6.32/2.13 | % 6.32/2.13 +-Applying beta-rule and splitting (69), into two cases. % 6.32/2.13 |-Branch one: % 6.32/2.13 | (70) all_48_0_21 = 0 & complement(one, zero) = 0 % 6.32/2.13 | % 6.32/2.13 | Applying alpha-rule on (70) yields: % 6.32/2.13 | (71) all_48_0_21 = 0 % 6.32/2.13 | (72) complement(one, zero) = 0 % 6.32/2.13 | % 6.32/2.13 +-Applying beta-rule and splitting (68), into two cases. % 6.32/2.13 |-Branch one: % 6.32/2.13 | (73) (all_57_0_30 = 0 & complement(one, zero) = 0) | ( ~ (all_57_0_30 = one) & addition(zero, one) = all_57_0_30) % 6.32/2.13 | % 6.32/2.13 +-Applying beta-rule and splitting (73), into two cases. % 6.32/2.13 |-Branch one: % 6.32/2.13 | (74) all_57_0_30 = 0 & complement(one, zero) = 0 % 6.32/2.13 | % 6.32/2.13 | Applying alpha-rule on (74) yields: % 6.32/2.13 | (75) all_57_0_30 = 0 % 6.32/2.13 | (72) complement(one, zero) = 0 % 6.32/2.13 | % 6.32/2.13 | Instantiating formula (18) with 0, zero, one and discharging atoms complement(one, zero) = 0, yields: % 6.32/2.13 | (77) ? [v0] : ((v0 = zero & c(one) = zero) | ( ~ (v0 = 0) & test(one) = v0)) % 6.32/2.13 | % 6.32/2.13 | Instantiating (77) with all_94_0_41 yields: % 6.32/2.13 | (78) (all_94_0_41 = zero & c(one) = zero) | ( ~ (all_94_0_41 = 0) & test(one) = all_94_0_41) % 6.32/2.13 | % 6.32/2.13 +-Applying beta-rule and splitting (78), into two cases. % 6.32/2.13 |-Branch one: % 6.32/2.13 | (79) all_94_0_41 = zero & c(one) = zero % 6.32/2.13 | % 6.32/2.13 | Applying alpha-rule on (79) yields: % 6.32/2.13 | (80) all_94_0_41 = zero % 6.32/2.13 | (81) c(one) = zero % 6.32/2.13 | % 6.32/2.13 | Instantiating formula (36) with one, zero, all_0_0_0 and discharging atoms c(one) = all_0_0_0, c(one) = zero, yields: % 6.32/2.13 | (82) all_0_0_0 = zero % 6.32/2.13 | % 6.32/2.13 | Equations (82) can reduce 22 to: % 6.32/2.13 | (83) $false % 6.32/2.13 | % 6.32/2.13 |-The branch is then unsatisfiable % 6.32/2.13 |-Branch two: % 6.32/2.13 | (84) ~ (all_94_0_41 = 0) & test(one) = all_94_0_41 % 6.32/2.13 | % 6.32/2.13 | Applying alpha-rule on (84) yields: % 6.32/2.13 | (85) ~ (all_94_0_41 = 0) % 6.32/2.13 | (86) test(one) = all_94_0_41 % 6.32/2.13 | % 6.32/2.13 | Instantiating formula (23) with zero, all_94_0_41, one and discharging atoms test(one) = all_94_0_41, complement(zero, one) = 0, yields: % 6.32/2.14 | (87) all_94_0_41 = 0 % 6.32/2.14 | % 6.32/2.14 | Equations (87) can reduce 85 to: % 6.32/2.14 | (83) $false % 6.32/2.14 | % 6.32/2.14 |-The branch is then unsatisfiable % 6.32/2.14 |-Branch two: % 6.32/2.14 | (89) ~ (all_57_0_30 = one) & addition(zero, one) = all_57_0_30 % 6.32/2.14 | % 6.32/2.14 | Applying alpha-rule on (89) yields: % 6.32/2.14 | (90) ~ (all_57_0_30 = one) % 6.32/2.14 | (91) addition(zero, one) = all_57_0_30 % 6.32/2.14 | % 6.32/2.14 +-Applying beta-rule and splitting (67), into two cases. % 6.32/2.14 |-Branch one: % 6.32/2.14 | (92) all_49_0_22 = one & all_49_1_23 = zero & multiplication(one, zero) = zero & addition(zero, one) = one % 6.32/2.14 | % 6.32/2.14 | Applying alpha-rule on (92) yields: % 6.32/2.14 | (93) all_49_0_22 = one % 6.32/2.14 | (94) all_49_1_23 = zero % 6.32/2.14 | (60) multiplication(one, zero) = zero % 6.32/2.14 | (65) addition(zero, one) = one % 6.32/2.14 | % 6.32/2.14 | Instantiating formula (6) with zero, one, all_57_0_30, one and discharging atoms addition(zero, one) = all_57_0_30, addition(zero, one) = one, yields: % 6.32/2.14 | (97) all_57_0_30 = one % 6.32/2.14 | % 6.32/2.14 | Equations (97) can reduce 90 to: % 6.32/2.14 | (83) $false % 6.32/2.14 | % 6.32/2.14 |-The branch is then unsatisfiable % 6.32/2.14 |-Branch two: % 6.32/2.14 | (99) ~ (all_49_1_23 = 0) & complement(one, zero) = all_49_1_23 % 6.32/2.14 | % 6.32/2.14 | Applying alpha-rule on (99) yields: % 6.32/2.14 | (100) ~ (all_49_1_23 = 0) % 6.32/2.14 | (101) complement(one, zero) = all_49_1_23 % 6.32/2.14 | % 6.32/2.14 | Instantiating formula (41) with one, zero, 0, all_49_1_23 and discharging atoms complement(one, zero) = all_49_1_23, complement(one, zero) = 0, yields: % 6.32/2.14 | (102) all_49_1_23 = 0 % 6.32/2.14 | % 6.32/2.14 | Equations (102) can reduce 100 to: % 6.32/2.14 | (83) $false % 6.32/2.14 | % 6.32/2.14 |-The branch is then unsatisfiable % 6.32/2.14 |-Branch two: % 6.32/2.14 | (104) ~ (all_57_0_30 = zero) & multiplication(zero, one) = all_57_0_30 % 6.32/2.14 | % 6.32/2.14 | Applying alpha-rule on (104) yields: % 6.32/2.14 | (105) ~ (all_57_0_30 = zero) % 6.32/2.14 | (106) multiplication(zero, one) = all_57_0_30 % 6.32/2.14 | % 6.32/2.14 | Instantiating formula (10) with all_57_0_30, zero and discharging atoms multiplication(zero, one) = all_57_0_30, yields: % 6.32/2.14 | (107) all_57_0_30 = zero % 6.32/2.14 | % 6.32/2.14 | Equations (107) can reduce 105 to: % 6.32/2.14 | (83) $false % 6.32/2.14 | % 6.32/2.14 |-The branch is then unsatisfiable % 6.32/2.14 |-Branch two: % 6.32/2.14 | (109) ~ (all_48_0_21 = one) & addition(zero, one) = all_48_0_21 % 6.32/2.14 | % 6.32/2.14 | Applying alpha-rule on (109) yields: % 6.32/2.14 | (110) ~ (all_48_0_21 = one) % 6.32/2.14 | (111) addition(zero, one) = all_48_0_21 % 6.32/2.14 | % 6.32/2.14 | Instantiating formula (6) with zero, one, all_48_0_21, one and discharging atoms addition(zero, one) = all_48_0_21, addition(zero, one) = one, yields: % 6.32/2.14 | (112) all_48_0_21 = one % 6.32/2.14 | % 6.32/2.14 | Equations (112) can reduce 110 to: % 6.32/2.14 | (83) $false % 6.32/2.14 | % 6.32/2.14 |-The branch is then unsatisfiable % 6.32/2.14 |-Branch two: % 6.32/2.14 | (114) ~ (all_48_0_21 = zero) & multiplication(one, zero) = all_48_0_21 % 6.32/2.14 | % 6.32/2.14 | Applying alpha-rule on (114) yields: % 6.32/2.14 | (115) ~ (all_48_0_21 = zero) % 6.32/2.14 | (116) multiplication(one, zero) = all_48_0_21 % 6.32/2.14 | % 6.32/2.14 | Instantiating formula (30) with all_48_0_21, zero and discharging atoms multiplication(one, zero) = all_48_0_21, yields: % 6.32/2.14 | (117) all_48_0_21 = zero % 6.32/2.15 | % 6.32/2.15 | Equations (117) can reduce 115 to: % 6.32/2.15 | (83) $false % 6.32/2.15 | % 6.32/2.15 |-The branch is then unsatisfiable % 6.32/2.15 |-Branch two: % 6.32/2.15 | (119) ~ (test(one) = 0) % 6.32/2.15 | (82) all_0_0_0 = zero % 6.32/2.15 | % 6.32/2.15 | Equations (82) can reduce 22 to: % 6.32/2.15 | (83) $false % 6.32/2.15 | % 6.32/2.15 |-The branch is then unsatisfiable % 6.32/2.15 % SZS output end Proof for theBenchmark % 6.32/2.15 % 6.32/2.15 1556ms %------------------------------------------------------------------------------