%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE058+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 01:51:11 EDT 2022 % Result : Theorem 19.03s 6.32s % Output : Proof 19.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KLE058+1 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 16 14:06:41 EDT 2022 % 0.13/0.34 % CPUTime : % 0.58/0.61 ____ _ % 0.58/0.61 ___ / __ \_____(_)___ ________ __________ % 0.58/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.61 % 0.58/0.61 A Theorem Prover for First-Order Logic % 0.58/0.61 (ePrincess v.1.0) % 0.58/0.61 % 0.58/0.61 (c) Philipp Rümmer, 2009-2015 % 0.58/0.61 (c) Peter Backeman, 2014-2015 % 0.58/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.61 Bug reports to peter@backeman.se % 0.58/0.61 % 0.58/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.61 % 0.58/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.54/0.96 Prover 0: Preprocessing ... % 2.21/1.22 Prover 0: Constructing countermodel ... % 17.36/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.53/6.00 Prover 1: Preprocessing ... % 17.53/6.07 Prover 1: Constructing countermodel ... % 18.56/6.21 Prover 1: gave up % 18.56/6.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 18.56/6.23 Prover 2: Preprocessing ... % 18.56/6.27 Prover 2: Warning: ignoring some quantifiers % 18.56/6.27 Prover 2: Constructing countermodel ... % 18.56/6.31 Prover 2: proved (93ms) % 19.03/6.31 Prover 0: stopped % 19.03/6.31 % 19.03/6.32 No countermodel exists, formula is valid % 19.03/6.32 % SZS status Theorem for theBenchmark % 19.03/6.32 % 19.03/6.32 Generating proof ... Warning: ignoring some quantifiers % 19.94/6.53 found it (size 24) % 19.94/6.53 % 19.94/6.53 % SZS output start Proof for theBenchmark % 19.94/6.53 Assumed formulas after preprocessing and simplification: % 19.94/6.54 | (0) ? [v0] : ( ~ (v0 = one) & domain(one) = v0 & domain(zero) = zero & ! [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] : ( ~ (domain(v2) = v4) | ~ (domain(v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (domain(v6) = v5 & addition(v1, v2) = v6)) & ! [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 | ~ (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] : ! [v4] : ( ~ (domain(v2) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v5] : ? [v6] : (domain(v5) = v6 & domain(v4) = v6 & multiplication(v1, v2) = v5)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v1, v2) = v3) | ? [v4] : ( ~ (v4 = v2) & addition(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (domain(v3) = v2) | ~ (domain(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (multiplication(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (domain(v6) = v4 & domain(v3) = v4 & domain(v2) = v5 & multiplication(v1, v5) = v6)) & ! [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] : ? [v6] : (domain(v3) = v4 & domain(v2) = v6 & domain(v1) = v5 & addition(v5, v6) = 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 | ~ (multiplication(v1, zero) = v2)) & ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(zero, v1) = v2)) & ! [v1] : ! [v2] : ( ~ (domain(v1) = v2) | addition(v2, one) = one) & ! [v1] : ! [v2] : ( ~ (domain(v1) = v2) | ? [v3] : (multiplication(v2, v1) = v3 & addition(v1, v3) = v3)) & ! [v1] : ! [v2] : ( ~ (leq(v1, v2) = 0) | addition(v1, v2) = v2) & ! [v1] : ! [v2] : ( ~ (addition(v1, v2) = v2) | leq(v1, v2) = 0) & ? [v1] : ? [v2] : ? [v3] : leq(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : multiplication(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : addition(v2, v1) = v3 & ? [v1] : ? [v2] : domain(v1) = v2) % 19.94/6.57 | Instantiating (0) with all_0_0_0 yields: % 19.94/6.57 | (1) ~ (all_0_0_0 = one) & domain(one) = all_0_0_0 & domain(zero) = zero & ! [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] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) & ! [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 | ~ (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] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) & ! [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] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = 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 | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) & ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : domain(v0) = v1 % 19.94/6.58 | % 19.94/6.58 | Applying alpha-rule on (1) yields: % 19.94/6.58 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 19.94/6.58 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 19.94/6.58 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 19.94/6.58 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) % 19.94/6.58 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 19.94/6.58 | (7) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) % 19.94/6.58 | (8) domain(zero) = zero % 19.94/6.58 | (9) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) % 19.94/6.58 | (10) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 19.94/6.58 | (11) ~ (all_0_0_0 = one) % 19.94/6.58 | (12) ! [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)) % 19.94/6.58 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 19.94/6.58 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 19.94/6.58 | (15) ! [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)) % 19.94/6.58 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 19.94/6.58 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 19.94/6.58 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 19.94/6.58 | (19) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 % 19.94/6.58 | (20) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) % 19.94/6.58 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 19.94/6.58 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 19.94/6.58 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) % 19.94/6.58 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 19.94/6.58 | (25) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 % 19.94/6.59 | (26) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 19.94/6.59 | (27) ! [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)) % 19.94/6.59 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 19.94/6.59 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.94/6.59 | (30) ? [v0] : ? [v1] : domain(v0) = v1 % 19.94/6.59 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) % 19.94/6.59 | (32) ! [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)) % 19.94/6.59 | (33) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 % 19.94/6.59 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 19.94/6.59 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 19.94/6.59 | (36) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 19.94/6.59 | (37) domain(one) = all_0_0_0 % 19.94/6.59 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (7) with all_0_0_0, one and discharging atoms domain(one) = all_0_0_0, yields: % 19.94/6.59 | (39) addition(all_0_0_0, one) = one % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (20) with all_0_0_0, one and discharging atoms domain(one) = all_0_0_0, yields: % 19.94/6.59 | (40) ? [v0] : (multiplication(all_0_0_0, one) = v0 & addition(one, v0) = v0) % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (7) with zero, zero and discharging atoms domain(zero) = zero, yields: % 19.94/6.59 | (41) addition(zero, one) = one % 19.94/6.59 | % 19.94/6.59 | Instantiating (40) with all_19_0_13 yields: % 19.94/6.59 | (42) multiplication(all_0_0_0, one) = all_19_0_13 & addition(one, all_19_0_13) = all_19_0_13 % 19.94/6.59 | % 19.94/6.59 | Applying alpha-rule on (42) yields: % 19.94/6.59 | (43) multiplication(all_0_0_0, one) = all_19_0_13 % 19.94/6.59 | (44) addition(one, all_19_0_13) = all_19_0_13 % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (18) with all_19_0_13, all_0_0_0 and discharging atoms multiplication(all_0_0_0, one) = all_19_0_13, yields: % 19.94/6.59 | (45) all_19_0_13 = all_0_0_0 % 19.94/6.59 | % 19.94/6.59 | From (45)(45) and (44) follows: % 19.94/6.59 | (46) addition(one, all_0_0_0) = all_0_0_0 % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (35) with one, all_0_0_0, one and discharging atoms addition(all_0_0_0, one) = one, yields: % 19.94/6.59 | (47) addition(one, all_0_0_0) = one % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (2) with all_0_0_0, one, all_0_0_0, one, all_0_0_0 and discharging atoms addition(all_0_0_0, one) = one, addition(one, all_0_0_0) = all_0_0_0, yields: % 19.94/6.59 | (48) ? [v0] : (addition(all_0_0_0, v0) = all_0_0_0 & addition(one, all_0_0_0) = v0) % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (2) with all_0_0_0, one, zero, one, all_0_0_0 and discharging atoms addition(one, all_0_0_0) = all_0_0_0, addition(zero, one) = one, yields: % 19.94/6.59 | (49) ? [v0] : (addition(one, all_0_0_0) = v0 & addition(zero, v0) = all_0_0_0) % 19.94/6.59 | % 19.94/6.59 | Instantiating (49) with all_31_0_14 yields: % 19.94/6.59 | (50) addition(one, all_0_0_0) = all_31_0_14 & addition(zero, all_31_0_14) = all_0_0_0 % 19.94/6.59 | % 19.94/6.59 | Applying alpha-rule on (50) yields: % 19.94/6.59 | (51) addition(one, all_0_0_0) = all_31_0_14 % 19.94/6.59 | (52) addition(zero, all_31_0_14) = all_0_0_0 % 19.94/6.59 | % 19.94/6.59 | Instantiating (48) with all_49_0_29 yields: % 19.94/6.59 | (53) addition(all_0_0_0, all_49_0_29) = all_0_0_0 & addition(one, all_0_0_0) = all_49_0_29 % 19.94/6.59 | % 19.94/6.59 | Applying alpha-rule on (53) yields: % 19.94/6.59 | (54) addition(all_0_0_0, all_49_0_29) = all_0_0_0 % 19.94/6.59 | (55) addition(one, all_0_0_0) = all_49_0_29 % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (17) with one, all_0_0_0, all_49_0_29, all_0_0_0 and discharging atoms addition(one, all_0_0_0) = all_49_0_29, addition(one, all_0_0_0) = all_0_0_0, yields: % 19.94/6.59 | (56) all_49_0_29 = all_0_0_0 % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (17) with one, all_0_0_0, all_31_0_14, all_49_0_29 and discharging atoms addition(one, all_0_0_0) = all_49_0_29, addition(one, all_0_0_0) = all_31_0_14, yields: % 19.94/6.59 | (57) all_49_0_29 = all_31_0_14 % 19.94/6.59 | % 19.94/6.59 | Instantiating formula (17) with one, all_0_0_0, one, all_31_0_14 and discharging atoms addition(one, all_0_0_0) = all_31_0_14, addition(one, all_0_0_0) = one, yields: % 19.94/6.59 | (58) all_31_0_14 = one % 19.94/6.59 | % 19.94/6.60 | Combining equations (57,56) yields a new equation: % 19.94/6.60 | (59) all_31_0_14 = all_0_0_0 % 19.94/6.60 | % 19.94/6.60 | Simplifying 59 yields: % 19.94/6.60 | (60) all_31_0_14 = all_0_0_0 % 19.94/6.60 | % 19.94/6.60 | Combining equations (58,60) yields a new equation: % 19.94/6.60 | (61) all_0_0_0 = one % 19.94/6.60 | % 19.94/6.60 | Equations (61) can reduce 11 to: % 19.94/6.60 | (62) $false % 19.94/6.60 | % 19.94/6.60 |-The branch is then unsatisfiable % 19.94/6.60 % SZS output end Proof for theBenchmark % 19.94/6.60 % 20.40/6.60 5971ms %------------------------------------------------------------------------------