%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 : Thu Jul 14 15:37:32 EDT 2022 % Result : Theorem 4.14s 1.69s % Output : Proof 6.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n029.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 : 600 % 0.12/0.34 % DateTime : Wed Jun 8 06:45:36 EDT 2022 % 0.12/0.34 % CPUTime : % 0.65/0.63 ____ _ % 0.65/0.63 ___ / __ \_____(_)___ ________ __________ % 0.65/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.65/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.65/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.65/0.63 % 0.65/0.63 A Theorem Prover for First-Order Logic % 0.65/0.63 (ePrincess v.1.0) % 0.65/0.63 % 0.65/0.63 (c) Philipp Rümmer, 2009-2015 % 0.65/0.63 (c) Peter Backeman, 2014-2015 % 0.65/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.63 Bug reports to peter@backeman.se % 0.65/0.63 % 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.63 % 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.65/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/0.96 Prover 0: Preprocessing ... % 1.73/1.07 Prover 0: Warning: ignoring some quantifiers % 1.77/1.09 Prover 0: Constructing countermodel ... % 2.24/1.24 Prover 0: gave up % 2.24/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.24/1.25 Prover 1: Preprocessing ... % 2.40/1.33 Prover 1: Constructing countermodel ... % 2.68/1.37 Prover 1: gave up % 2.68/1.37 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.68/1.39 Prover 2: Preprocessing ... % 3.07/1.47 Prover 2: Warning: ignoring some quantifiers % 3.07/1.48 Prover 2: Constructing countermodel ... % 4.14/1.69 Prover 2: proved (314ms) % 4.14/1.69 % 4.14/1.69 No countermodel exists, formula is valid % 4.14/1.69 % SZS status Theorem for theBenchmark % 4.14/1.69 % 4.14/1.69 Generating proof ... Warning: ignoring some quantifiers % 6.61/2.30 found it (size 52) % 6.61/2.30 % 6.61/2.30 % SZS output start Proof for theBenchmark % 6.61/2.30 Assumed formulas after preprocessing and simplification: % 6.61/2.30 | (0) ? [v0] : ? [v1] : (a_vector_subspace_of(v0, v1) = 0 & a_vector_space(v1) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (lin_ind_subset(v4, v3) = v6) | ~ (vec_to_class(v2) = v5) | ~ (a_subset_of(v4, v5) = 0) | ? [v7] : (( ~ (v7 = 0) & a_vector_subspace_of(v2, v3) = v7) | (( ~ (v6 = 0) | (v7 = 0 & lin_ind_subset(v4, v2) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & lin_ind_subset(v4, v2) = v7))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (lin_ind_subset(v4, v3) = v5) | ~ (lin_ind_subset(v4, v2) = 0) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & vec_to_class(v2) = v6 & a_subset_of(v4, v6) = v7) | ( ~ (v6 = 0) & a_vector_subspace_of(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (lin_ind_subset(v4, v3) = 0) | ~ (lin_ind_subset(v4, v2) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & vec_to_class(v2) = v6 & a_subset_of(v4, v6) = v7) | ( ~ (v6 = 0) & a_vector_subspace_of(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (a_vector_subspace_of(v5, v4) = v3) | ~ (a_vector_subspace_of(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (union(v5, v4) = v3) | ~ (union(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (lin_ind_subset(v5, v4) = v3) | ~ (lin_ind_subset(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (basis_of(v5, v4) = v3) | ~ (basis_of(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (a_subset_of(v5, v4) = v3) | ~ (a_subset_of(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (a_vector_subspace_of(v2, v3) = 0) | ~ (lin_ind_subset(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & vec_to_class(v2) = v6 & a_subset_of(v4, v6) = v7) | (( ~ (v5 = 0) | (v6 = 0 & lin_ind_subset(v4, v2) = 0)) & (v5 = 0 | ( ~ (v6 = 0) & lin_ind_subset(v4, v2) = v6))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (a_vector_subspace_of(v2, v3) = 0) | ~ (lin_ind_subset(v4, v2) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & vec_to_class(v2) = v6 & a_subset_of(v4, v6) = v7) | (( ~ (v5 = 0) | (v6 = 0 & lin_ind_subset(v4, v3) = 0)) & (v5 = 0 | ( ~ (v6 = 0) & lin_ind_subset(v4, v3) = v6))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (a_vector_subspace_of(v2, v3) = 0) | ~ (vec_to_class(v2) = v5) | ~ (a_subset_of(v4, v5) = 0) | ? [v6] : ? [v7] : (((v7 = 0 & lin_ind_subset(v4, v3) = 0) | ( ~ (v6 = 0) & lin_ind_subset(v4, v2) = v6)) & ((v6 = 0 & lin_ind_subset(v4, v2) = 0) | ( ~ (v7 = 0) & lin_ind_subset(v4, v3) = v7)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vec_to_class(v3) = v4) | ~ (a_subset_of(v2, v4) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & lin_ind_subset(v2, v3) = 0) | ( ~ (v6 = 0) & basis_of(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (a_vector_space(v4) = v3) | ~ (a_vector_space(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (vec_to_class(v4) = v3) | ~ (vec_to_class(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & basis_of(v4, v1) = v5) | ( ~ (v5 = 0) & basis_of(v2, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (lin_ind_subset(v2, v4) = 0) | ~ (basis_of(v3, v4) = 0) | ? [v5] : ? [v6] : (union(v2, v5) = v6 & basis_of(v6, v4) = 0 & a_subset_of(v5, v3) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (lin_ind_subset(v2, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & vec_to_class(v3) = v5 & a_subset_of(v2, v5) = 0) | ( ~ (v5 = 0) & basis_of(v2, v3) = v5))) & ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v2, v3) = 0) | a_vector_space(v2) = 0) & ! [v2] : ! [v3] : ( ~ (basis_of(v2, v3) = 0) | ? [v4] : (lin_ind_subset(v2, v3) = 0 & vec_to_class(v3) = v4 & a_subset_of(v2, v4) = 0)) & ! [v2] : ( ~ (a_vector_space(v2) = 0) | ? [v3] : basis_of(v3, v2) = 0) & ? [v2] : ? [v3] : ? [v4] : a_vector_subspace_of(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : union(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : lin_ind_subset(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : basis_of(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : a_subset_of(v3, v2) = v4 & ? [v2] : ? [v3] : a_vector_space(v2) = v3 & ? [v2] : ? [v3] : vec_to_class(v2) = v3) % 6.95/2.34 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 6.95/2.34 | (1) a_vector_subspace_of(all_0_1_1, all_0_0_0) = 0 & a_vector_space(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (lin_ind_subset(v2, v1) = v4) | ~ (vec_to_class(v0) = v3) | ~ (a_subset_of(v2, v3) = 0) | ? [v5] : (( ~ (v5 = 0) & a_vector_subspace_of(v0, v1) = v5) | (( ~ (v4 = 0) | (v5 = 0 & lin_ind_subset(v2, v0) = 0)) & (v4 = 0 | ( ~ (v5 = 0) & lin_ind_subset(v2, v0) = v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lin_ind_subset(v2, v1) = v3) | ~ (lin_ind_subset(v2, v0) = 0) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | ( ~ (v4 = 0) & a_vector_subspace_of(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lin_ind_subset(v2, v1) = 0) | ~ (lin_ind_subset(v2, v0) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | ( ~ (v4 = 0) & a_vector_subspace_of(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_vector_subspace_of(v3, v2) = v1) | ~ (a_vector_subspace_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lin_ind_subset(v3, v2) = v1) | ~ (lin_ind_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (basis_of(v3, v2) = v1) | ~ (basis_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_subset_of(v3, v2) = v1) | ~ (a_subset_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | ~ (lin_ind_subset(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | (( ~ (v3 = 0) | (v4 = 0 & lin_ind_subset(v2, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & lin_ind_subset(v2, v0) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | ~ (lin_ind_subset(v2, v0) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | (( ~ (v3 = 0) | (v4 = 0 & lin_ind_subset(v2, v1) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & lin_ind_subset(v2, v1) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | ~ (vec_to_class(v0) = v3) | ~ (a_subset_of(v2, v3) = 0) | ? [v4] : ? [v5] : (((v5 = 0 & lin_ind_subset(v2, v1) = 0) | ( ~ (v4 = 0) & lin_ind_subset(v2, v0) = v4)) & ((v4 = 0 & lin_ind_subset(v2, v0) = 0) | ( ~ (v5 = 0) & lin_ind_subset(v2, v1) = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vec_to_class(v1) = v2) | ~ (a_subset_of(v0, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & lin_ind_subset(v0, v1) = 0) | ( ~ (v4 = 0) & basis_of(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_vector_space(v2) = v1) | ~ (a_vector_space(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vec_to_class(v2) = v1) | ~ (vec_to_class(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & basis_of(v2, all_0_0_0) = v3) | ( ~ (v3 = 0) & basis_of(v0, all_0_1_1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lin_ind_subset(v0, v2) = 0) | ~ (basis_of(v1, v2) = 0) | ? [v3] : ? [v4] : (union(v0, v3) = v4 & basis_of(v4, v2) = 0 & a_subset_of(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lin_ind_subset(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & vec_to_class(v1) = v3 & a_subset_of(v0, v3) = 0) | ( ~ (v3 = 0) & basis_of(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | a_vector_space(v0) = 0) & ! [v0] : ! [v1] : ( ~ (basis_of(v0, v1) = 0) | ? [v2] : (lin_ind_subset(v0, v1) = 0 & vec_to_class(v1) = v2 & a_subset_of(v0, v2) = 0)) & ! [v0] : ( ~ (a_vector_space(v0) = 0) | ? [v1] : basis_of(v1, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : a_vector_subspace_of(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : lin_ind_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : basis_of(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : a_subset_of(v1, v0) = v2 & ? [v0] : ? [v1] : a_vector_space(v0) = v1 & ? [v0] : ? [v1] : vec_to_class(v0) = v1 % 6.95/2.35 | % 6.95/2.35 | Applying alpha-rule on (1) yields: % 6.95/2.35 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (basis_of(v3, v2) = v1) | ~ (basis_of(v3, v2) = v0)) % 6.95/2.35 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 6.95/2.35 | (4) ? [v0] : ? [v1] : ? [v2] : a_subset_of(v1, v0) = v2 % 6.95/2.35 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_vector_space(v2) = v1) | ~ (a_vector_space(v2) = v0)) % 6.95/2.35 | (6) ? [v0] : ? [v1] : ? [v2] : basis_of(v1, v0) = v2 % 6.95/2.35 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_vector_subspace_of(v3, v2) = v1) | ~ (a_vector_subspace_of(v3, v2) = v0)) % 6.95/2.35 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_subset_of(v3, v2) = v1) | ~ (a_subset_of(v3, v2) = v0)) % 6.95/2.35 | (9) ! [v0] : ( ~ (a_vector_space(v0) = 0) | ? [v1] : basis_of(v1, v0) = 0) % 6.95/2.35 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (lin_ind_subset(v2, v1) = v4) | ~ (vec_to_class(v0) = v3) | ~ (a_subset_of(v2, v3) = 0) | ? [v5] : (( ~ (v5 = 0) & a_vector_subspace_of(v0, v1) = v5) | (( ~ (v4 = 0) | (v5 = 0 & lin_ind_subset(v2, v0) = 0)) & (v4 = 0 | ( ~ (v5 = 0) & lin_ind_subset(v2, v0) = v5))))) % 6.95/2.35 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vec_to_class(v2) = v1) | ~ (vec_to_class(v2) = v0)) % 6.95/2.35 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lin_ind_subset(v3, v2) = v1) | ~ (lin_ind_subset(v3, v2) = v0)) % 6.95/2.35 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | ~ (lin_ind_subset(v2, v0) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | (( ~ (v3 = 0) | (v4 = 0 & lin_ind_subset(v2, v1) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & lin_ind_subset(v2, v1) = v4))))) % 6.95/2.35 | (14) a_vector_space(all_0_0_0) = 0 % 6.95/2.36 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lin_ind_subset(v2, v1) = v3) | ~ (lin_ind_subset(v2, v0) = 0) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | ( ~ (v4 = 0) & a_vector_subspace_of(v0, v1) = v4))) % 6.95/2.36 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lin_ind_subset(v2, v1) = 0) | ~ (lin_ind_subset(v2, v0) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | ( ~ (v4 = 0) & a_vector_subspace_of(v0, v1) = v4))) % 6.95/2.36 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & basis_of(v2, all_0_0_0) = v3) | ( ~ (v3 = 0) & basis_of(v0, all_0_1_1) = v3))) % 6.95/2.36 | (18) a_vector_subspace_of(all_0_1_1, all_0_0_0) = 0 % 6.95/2.36 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (lin_ind_subset(v0, v2) = 0) | ~ (basis_of(v1, v2) = 0) | ? [v3] : ? [v4] : (union(v0, v3) = v4 & basis_of(v4, v2) = 0 & a_subset_of(v3, v1) = 0)) % 6.95/2.36 | (20) ? [v0] : ? [v1] : ? [v2] : a_vector_subspace_of(v1, v0) = v2 % 6.95/2.36 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vec_to_class(v1) = v2) | ~ (a_subset_of(v0, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & lin_ind_subset(v0, v1) = 0) | ( ~ (v4 = 0) & basis_of(v0, v1) = v4))) % 6.95/2.36 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | ~ (vec_to_class(v0) = v3) | ~ (a_subset_of(v2, v3) = 0) | ? [v4] : ? [v5] : (((v5 = 0 & lin_ind_subset(v2, v1) = 0) | ( ~ (v4 = 0) & lin_ind_subset(v2, v0) = v4)) & ((v4 = 0 & lin_ind_subset(v2, v0) = 0) | ( ~ (v5 = 0) & lin_ind_subset(v2, v1) = v5)))) % 6.95/2.36 | (23) ? [v0] : ? [v1] : ? [v2] : lin_ind_subset(v1, v0) = v2 % 6.95/2.36 | (24) ! [v0] : ! [v1] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | a_vector_space(v0) = 0) % 6.95/2.36 | (25) ! [v0] : ! [v1] : ( ~ (basis_of(v0, v1) = 0) | ? [v2] : (lin_ind_subset(v0, v1) = 0 & vec_to_class(v1) = v2 & a_subset_of(v0, v2) = 0)) % 6.95/2.36 | (26) ? [v0] : ? [v1] : a_vector_space(v0) = v1 % 6.95/2.36 | (27) ? [v0] : ? [v1] : vec_to_class(v0) = v1 % 6.95/2.36 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (lin_ind_subset(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & vec_to_class(v1) = v3 & a_subset_of(v0, v3) = 0) | ( ~ (v3 = 0) & basis_of(v0, v1) = v3))) % 6.95/2.36 | (29) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 % 6.95/2.36 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_vector_subspace_of(v0, v1) = 0) | ~ (lin_ind_subset(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & vec_to_class(v0) = v4 & a_subset_of(v2, v4) = v5) | (( ~ (v3 = 0) | (v4 = 0 & lin_ind_subset(v2, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & lin_ind_subset(v2, v0) = v4))))) % 6.95/2.36 | % 6.95/2.36 | Instantiating formula (24) with all_0_0_0, all_0_1_1 and discharging atoms a_vector_subspace_of(all_0_1_1, all_0_0_0) = 0, yields: % 6.95/2.36 | (31) a_vector_space(all_0_1_1) = 0 % 6.95/2.36 | % 6.95/2.36 | Instantiating formula (9) with all_0_0_0 and discharging atoms a_vector_space(all_0_0_0) = 0, yields: % 6.95/2.36 | (32) ? [v0] : basis_of(v0, all_0_0_0) = 0 % 6.95/2.36 | % 6.95/2.36 | Instantiating (32) with all_23_0_21 yields: % 6.95/2.36 | (33) basis_of(all_23_0_21, all_0_0_0) = 0 % 6.95/2.36 | % 6.95/2.36 | Instantiating formula (9) with all_0_1_1 and discharging atoms a_vector_space(all_0_1_1) = 0, yields: % 6.95/2.36 | (34) ? [v0] : basis_of(v0, all_0_1_1) = 0 % 6.95/2.36 | % 6.95/2.36 | Instantiating formula (25) with all_0_0_0, all_23_0_21 and discharging atoms basis_of(all_23_0_21, all_0_0_0) = 0, yields: % 6.95/2.36 | (35) ? [v0] : (lin_ind_subset(all_23_0_21, all_0_0_0) = 0 & vec_to_class(all_0_0_0) = v0 & a_subset_of(all_23_0_21, v0) = 0) % 6.95/2.36 | % 6.95/2.36 | Instantiating (35) with all_30_0_22 yields: % 6.95/2.36 | (36) lin_ind_subset(all_23_0_21, all_0_0_0) = 0 & vec_to_class(all_0_0_0) = all_30_0_22 & a_subset_of(all_23_0_21, all_30_0_22) = 0 % 6.95/2.36 | % 6.95/2.36 | Applying alpha-rule on (36) yields: % 6.95/2.36 | (37) lin_ind_subset(all_23_0_21, all_0_0_0) = 0 % 6.95/2.37 | (38) vec_to_class(all_0_0_0) = all_30_0_22 % 6.95/2.37 | (39) a_subset_of(all_23_0_21, all_30_0_22) = 0 % 6.95/2.37 | % 6.95/2.37 | Instantiating (34) with all_32_0_23 yields: % 6.95/2.37 | (40) basis_of(all_32_0_23, all_0_1_1) = 0 % 6.95/2.37 | % 6.95/2.37 | Instantiating formula (19) with all_0_0_0, all_23_0_21, all_23_0_21 and discharging atoms lin_ind_subset(all_23_0_21, all_0_0_0) = 0, basis_of(all_23_0_21, all_0_0_0) = 0, yields: % 6.95/2.37 | (41) ? [v0] : ? [v1] : (union(all_23_0_21, v0) = v1 & basis_of(v1, all_0_0_0) = 0 & a_subset_of(v0, all_23_0_21) = 0) % 6.95/2.37 | % 6.95/2.37 | Instantiating formula (25) with all_0_1_1, all_32_0_23 and discharging atoms basis_of(all_32_0_23, all_0_1_1) = 0, yields: % 6.95/2.37 | (42) ? [v0] : (lin_ind_subset(all_32_0_23, all_0_1_1) = 0 & vec_to_class(all_0_1_1) = v0 & a_subset_of(all_32_0_23, v0) = 0) % 6.95/2.37 | % 6.95/2.37 | Instantiating (41) with all_40_0_25, all_40_1_26 yields: % 6.95/2.37 | (43) union(all_23_0_21, all_40_1_26) = all_40_0_25 & basis_of(all_40_0_25, all_0_0_0) = 0 & a_subset_of(all_40_1_26, all_23_0_21) = 0 % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (43) yields: % 6.95/2.37 | (44) union(all_23_0_21, all_40_1_26) = all_40_0_25 % 6.95/2.37 | (45) basis_of(all_40_0_25, all_0_0_0) = 0 % 6.95/2.37 | (46) a_subset_of(all_40_1_26, all_23_0_21) = 0 % 6.95/2.37 | % 6.95/2.37 | Instantiating (42) with all_43_0_29 yields: % 6.95/2.37 | (47) lin_ind_subset(all_32_0_23, all_0_1_1) = 0 & vec_to_class(all_0_1_1) = all_43_0_29 & a_subset_of(all_32_0_23, all_43_0_29) = 0 % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (47) yields: % 6.95/2.37 | (48) lin_ind_subset(all_32_0_23, all_0_1_1) = 0 % 6.95/2.37 | (49) vec_to_class(all_0_1_1) = all_43_0_29 % 6.95/2.37 | (50) a_subset_of(all_32_0_23, all_43_0_29) = 0 % 6.95/2.37 | % 6.95/2.37 | Instantiating formula (19) with all_0_0_0, all_40_0_25, all_23_0_21 and discharging atoms lin_ind_subset(all_23_0_21, all_0_0_0) = 0, basis_of(all_40_0_25, all_0_0_0) = 0, yields: % 6.95/2.37 | (51) ? [v0] : ? [v1] : (union(all_23_0_21, v0) = v1 & basis_of(v1, all_0_0_0) = 0 & a_subset_of(v0, all_40_0_25) = 0) % 6.95/2.37 | % 6.95/2.37 | Instantiating formula (22) with all_43_0_29, all_32_0_23, all_0_0_0, all_0_1_1 and discharging atoms a_vector_subspace_of(all_0_1_1, all_0_0_0) = 0, vec_to_class(all_0_1_1) = all_43_0_29, a_subset_of(all_32_0_23, all_43_0_29) = 0, yields: % 6.95/2.37 | (52) ? [v0] : ? [v1] : (((v1 = 0 & lin_ind_subset(all_32_0_23, all_0_0_0) = 0) | ( ~ (v0 = 0) & lin_ind_subset(all_32_0_23, all_0_1_1) = v0)) & ((v0 = 0 & lin_ind_subset(all_32_0_23, all_0_1_1) = 0) | ( ~ (v1 = 0) & lin_ind_subset(all_32_0_23, all_0_0_0) = v1))) % 6.95/2.37 | % 6.95/2.37 | Instantiating (52) with all_50_0_30, all_50_1_31 yields: % 6.95/2.37 | (53) ((all_50_0_30 = 0 & lin_ind_subset(all_32_0_23, all_0_0_0) = 0) | ( ~ (all_50_1_31 = 0) & lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31)) & ((all_50_1_31 = 0 & lin_ind_subset(all_32_0_23, all_0_1_1) = 0) | ( ~ (all_50_0_30 = 0) & lin_ind_subset(all_32_0_23, all_0_0_0) = all_50_0_30)) % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (53) yields: % 6.95/2.37 | (54) (all_50_0_30 = 0 & lin_ind_subset(all_32_0_23, all_0_0_0) = 0) | ( ~ (all_50_1_31 = 0) & lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31) % 6.95/2.37 | (55) (all_50_1_31 = 0 & lin_ind_subset(all_32_0_23, all_0_1_1) = 0) | ( ~ (all_50_0_30 = 0) & lin_ind_subset(all_32_0_23, all_0_0_0) = all_50_0_30) % 6.95/2.37 | % 6.95/2.37 | Instantiating (51) with all_52_0_33, all_52_1_34 yields: % 6.95/2.37 | (56) union(all_23_0_21, all_52_1_34) = all_52_0_33 & basis_of(all_52_0_33, all_0_0_0) = 0 & a_subset_of(all_52_1_34, all_40_0_25) = 0 % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (56) yields: % 6.95/2.37 | (57) union(all_23_0_21, all_52_1_34) = all_52_0_33 % 6.95/2.37 | (58) basis_of(all_52_0_33, all_0_0_0) = 0 % 6.95/2.37 | (59) a_subset_of(all_52_1_34, all_40_0_25) = 0 % 6.95/2.37 | % 6.95/2.37 +-Applying beta-rule and splitting (55), into two cases. % 6.95/2.37 |-Branch one: % 6.95/2.37 | (60) all_50_1_31 = 0 & lin_ind_subset(all_32_0_23, all_0_1_1) = 0 % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (60) yields: % 6.95/2.37 | (61) all_50_1_31 = 0 % 6.95/2.37 | (48) lin_ind_subset(all_32_0_23, all_0_1_1) = 0 % 6.95/2.37 | % 6.95/2.37 +-Applying beta-rule and splitting (54), into two cases. % 6.95/2.37 |-Branch one: % 6.95/2.37 | (63) all_50_0_30 = 0 & lin_ind_subset(all_32_0_23, all_0_0_0) = 0 % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (63) yields: % 6.95/2.37 | (64) all_50_0_30 = 0 % 6.95/2.37 | (65) lin_ind_subset(all_32_0_23, all_0_0_0) = 0 % 6.95/2.37 | % 6.95/2.37 | Instantiating formula (19) with all_0_0_0, all_52_0_33, all_32_0_23 and discharging atoms lin_ind_subset(all_32_0_23, all_0_0_0) = 0, basis_of(all_52_0_33, all_0_0_0) = 0, yields: % 6.95/2.37 | (66) ? [v0] : ? [v1] : (union(all_32_0_23, v0) = v1 & basis_of(v1, all_0_0_0) = 0 & a_subset_of(v0, all_52_0_33) = 0) % 6.95/2.37 | % 6.95/2.37 | Instantiating (66) with all_86_0_42, all_86_1_43 yields: % 6.95/2.37 | (67) union(all_32_0_23, all_86_1_43) = all_86_0_42 & basis_of(all_86_0_42, all_0_0_0) = 0 & a_subset_of(all_86_1_43, all_52_0_33) = 0 % 6.95/2.37 | % 6.95/2.37 | Applying alpha-rule on (67) yields: % 6.95/2.37 | (68) union(all_32_0_23, all_86_1_43) = all_86_0_42 % 6.95/2.37 | (69) basis_of(all_86_0_42, all_0_0_0) = 0 % 6.95/2.37 | (70) a_subset_of(all_86_1_43, all_52_0_33) = 0 % 6.95/2.37 | % 6.95/2.37 | Instantiating formula (17) with all_86_0_42, all_86_1_43, all_32_0_23 and discharging atoms union(all_32_0_23, all_86_1_43) = all_86_0_42, yields: % 6.95/2.37 | (71) ? [v0] : (( ~ (v0 = 0) & basis_of(all_86_0_42, all_0_0_0) = v0) | ( ~ (v0 = 0) & basis_of(all_32_0_23, all_0_1_1) = v0)) % 6.95/2.38 | % 6.95/2.38 | Instantiating (71) with all_150_0_93 yields: % 6.95/2.38 | (72) ( ~ (all_150_0_93 = 0) & basis_of(all_86_0_42, all_0_0_0) = all_150_0_93) | ( ~ (all_150_0_93 = 0) & basis_of(all_32_0_23, all_0_1_1) = all_150_0_93) % 6.95/2.38 | % 6.95/2.38 +-Applying beta-rule and splitting (72), into two cases. % 6.95/2.38 |-Branch one: % 6.95/2.38 | (73) ~ (all_150_0_93 = 0) & basis_of(all_86_0_42, all_0_0_0) = all_150_0_93 % 6.95/2.38 | % 6.95/2.38 | Applying alpha-rule on (73) yields: % 6.95/2.38 | (74) ~ (all_150_0_93 = 0) % 6.95/2.38 | (75) basis_of(all_86_0_42, all_0_0_0) = all_150_0_93 % 6.95/2.38 | % 6.95/2.38 | Instantiating formula (2) with all_86_0_42, all_0_0_0, all_150_0_93, 0 and discharging atoms basis_of(all_86_0_42, all_0_0_0) = all_150_0_93, basis_of(all_86_0_42, all_0_0_0) = 0, yields: % 6.95/2.38 | (76) all_150_0_93 = 0 % 6.95/2.38 | % 6.95/2.38 | Equations (76) can reduce 74 to: % 6.95/2.38 | (77) $false % 6.95/2.38 | % 6.95/2.38 |-The branch is then unsatisfiable % 6.95/2.38 |-Branch two: % 6.95/2.38 | (78) ~ (all_150_0_93 = 0) & basis_of(all_32_0_23, all_0_1_1) = all_150_0_93 % 6.95/2.38 | % 6.95/2.38 | Applying alpha-rule on (78) yields: % 6.95/2.38 | (74) ~ (all_150_0_93 = 0) % 6.95/2.38 | (80) basis_of(all_32_0_23, all_0_1_1) = all_150_0_93 % 6.95/2.38 | % 6.95/2.38 | Instantiating formula (2) with all_32_0_23, all_0_1_1, all_150_0_93, 0 and discharging atoms basis_of(all_32_0_23, all_0_1_1) = all_150_0_93, basis_of(all_32_0_23, all_0_1_1) = 0, yields: % 6.95/2.38 | (76) all_150_0_93 = 0 % 6.95/2.38 | % 6.95/2.38 | Equations (76) can reduce 74 to: % 6.95/2.38 | (77) $false % 6.95/2.38 | % 6.95/2.38 |-The branch is then unsatisfiable % 6.95/2.38 |-Branch two: % 6.95/2.38 | (83) ~ (all_50_1_31 = 0) & lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31 % 6.95/2.38 | % 6.95/2.38 | Applying alpha-rule on (83) yields: % 6.95/2.38 | (84) ~ (all_50_1_31 = 0) % 6.95/2.38 | (85) lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31 % 6.95/2.38 | % 6.95/2.38 | Equations (61) can reduce 84 to: % 6.95/2.38 | (77) $false % 6.95/2.38 | % 6.95/2.38 |-The branch is then unsatisfiable % 6.95/2.38 |-Branch two: % 6.95/2.38 | (87) ~ (all_50_0_30 = 0) & lin_ind_subset(all_32_0_23, all_0_0_0) = all_50_0_30 % 6.95/2.38 | % 6.95/2.38 | Applying alpha-rule on (87) yields: % 6.95/2.38 | (88) ~ (all_50_0_30 = 0) % 6.95/2.38 | (89) lin_ind_subset(all_32_0_23, all_0_0_0) = all_50_0_30 % 6.95/2.38 | % 6.95/2.38 +-Applying beta-rule and splitting (54), into two cases. % 6.95/2.38 |-Branch one: % 6.95/2.38 | (63) all_50_0_30 = 0 & lin_ind_subset(all_32_0_23, all_0_0_0) = 0 % 6.95/2.38 | % 6.95/2.38 | Applying alpha-rule on (63) yields: % 6.95/2.38 | (64) all_50_0_30 = 0 % 6.95/2.38 | (65) lin_ind_subset(all_32_0_23, all_0_0_0) = 0 % 6.95/2.38 | % 6.95/2.38 | Equations (64) can reduce 88 to: % 6.95/2.38 | (77) $false % 6.95/2.38 | % 6.95/2.38 |-The branch is then unsatisfiable % 6.95/2.38 |-Branch two: % 6.95/2.38 | (83) ~ (all_50_1_31 = 0) & lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31 % 6.95/2.38 | % 6.95/2.38 | Applying alpha-rule on (83) yields: % 6.95/2.38 | (84) ~ (all_50_1_31 = 0) % 6.95/2.38 | (85) lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31 % 6.95/2.38 | % 6.95/2.38 | Instantiating formula (12) with all_32_0_23, all_0_1_1, all_50_1_31, 0 and discharging atoms lin_ind_subset(all_32_0_23, all_0_1_1) = all_50_1_31, lin_ind_subset(all_32_0_23, all_0_1_1) = 0, yields: % 6.95/2.38 | (61) all_50_1_31 = 0 % 6.95/2.38 | % 6.95/2.38 | Equations (61) can reduce 84 to: % 6.95/2.38 | (77) $false % 6.95/2.38 | % 6.95/2.38 |-The branch is then unsatisfiable % 6.95/2.38 % SZS output end Proof for theBenchmark % 6.95/2.38 % 6.95/2.38 1740ms %------------------------------------------------------------------------------