%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 21 04:59:37 EDT 2022 % Result : Theorem 2.74s 1.40s % Output : Proof 4.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0. % 0.11/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n021.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jul 11 14:44:08 EDT 2022 % 0.14/0.34 % CPUTime : % 0.19/0.56 ____ _ % 0.19/0.56 ___ / __ \_____(_)___ ________ __________ % 0.19/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.56 % 0.19/0.56 A Theorem Prover for First-Order Logic % 0.19/0.56 (ePrincess v.1.0) % 0.19/0.56 % 0.19/0.56 (c) Philipp Rümmer, 2009-2015 % 0.19/0.56 (c) Peter Backeman, 2014-2015 % 0.19/0.56 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.56 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.56 Bug reports to peter@backeman.se % 0.19/0.56 % 0.19/0.56 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.56 % 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.62/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.23/0.87 Prover 0: Preprocessing ... % 1.41/0.95 Prover 0: Warning: ignoring some quantifiers % 1.41/0.97 Prover 0: Constructing countermodel ... % 1.52/1.05 Prover 0: gave up % 1.52/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.80/1.09 Prover 1: Preprocessing ... % 2.08/1.20 Prover 1: Constructing countermodel ... % 2.74/1.40 Prover 1: proved (350ms) % 2.74/1.40 % 2.74/1.40 No countermodel exists, formula is valid % 2.74/1.40 % SZS status Theorem for theBenchmark % 2.74/1.40 % 2.74/1.40 Generating proof ... found it (size 62) % 4.14/1.82 % 4.14/1.82 % SZS output start Proof for theBenchmark % 4.14/1.82 Assumed formulas after preprocessing and simplification: % 4.14/1.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (big_p(a) = v0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (big_r(v9, v8) = v7) | ~ (big_r(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (big_p(v8) = v7) | ~ (big_p(v8) = v6)) & ((v0 = 0 & big_p(v1) = v2 & ! [v6] : ! [v7] : ! [v8] : ( ~ (big_r(v6, v8) = 0) | ~ (big_p(v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & big_r(v10, v9) = 0 & big_r(v6, v10) = 0 & big_p(v9) = 0) | ( ~ (v9 = 0) & big_p(v8) = v9))) & ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7) | ? [v8] : ? [v9] : (big_r(v9, v8) = 0 & big_r(v6, v9) = 0 & big_p(v8) = 0)) & ! [v6] : ! [v7] : ( ~ (big_r(v1, v7) = 0) | ~ (big_p(v6) = 0) | ? [v8] : ( ~ (v8 = 0) & big_r(v7, v6) = v8)) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0 & big_r(v1, v3) = 0 & big_p(v3) = 0))) | (v0 = 0 & big_p(v1) = v2 & ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7) | ? [v8] : ? [v9] : (big_r(v9, v8) = 0 & big_r(v6, v9) = 0 & big_p(v8) = 0)) & ! [v6] : ! [v7] : ( ~ (big_r(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & big_r(v9, v8) = 0 & big_r(v6, v9) = 0 & big_p(v8) = 0) | ( ~ (v8 = 0) & big_p(v7) = v8))) & ! [v6] : ! [v7] : ( ~ (big_r(v1, v7) = 0) | ~ (big_p(v6) = 0) | ? [v8] : ( ~ (v8 = 0) & big_r(v7, v6) = v8)) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0 & big_r(v1, v3) = 0 & big_p(v3) = 0))))) % 4.14/1.85 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 4.14/1.85 | (1) big_p(a) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))) | (all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0)))) % 4.14/1.85 | % 4.14/1.85 | Applying alpha-rule on (1) yields: % 4.14/1.86 | (2) big_p(a) = all_0_5_5 % 4.14/1.86 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0)) % 4.14/1.86 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) % 4.14/1.86 | (5) (all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))) | (all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))) % 4.14/1.86 | % 4.14/1.86 +-Applying beta-rule and splitting (5), into two cases. % 4.14/1.86 |-Branch one: % 4.14/1.86 | (6) all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0)) % 4.14/1.86 | % 4.14/1.86 | Applying alpha-rule on (6) yields: % 4.14/1.86 | (7) all_0_5_5 = 0 % 4.14/1.86 | (8) ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0) % 4.14/1.86 | (9) big_p(all_0_4_4) = all_0_3_3 % 4.14/1.86 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) % 4.14/1.86 | (11) ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) % 4.14/1.86 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) % 4.14/1.86 | % 4.14/1.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4 and discharging atoms big_p(all_0_4_4) = all_0_3_3, yields: % 4.14/1.86 | (13) all_0_3_3 = 0 | ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) % 4.14/1.86 | % 4.14/1.86 +-Applying beta-rule and splitting (8), into two cases. % 4.14/1.86 |-Branch one: % 4.14/1.86 | (14) ~ (all_0_3_3 = 0) % 4.14/1.86 | % 4.14/1.86 +-Applying beta-rule and splitting (13), into two cases. % 4.14/1.86 |-Branch one: % 4.14/1.86 | (15) all_0_3_3 = 0 % 4.14/1.86 | % 4.14/1.86 | Equations (15) can reduce 14 to: % 4.14/1.86 | (16) $false % 4.14/1.86 | % 4.14/1.86 |-The branch is then unsatisfiable % 4.14/1.86 |-Branch two: % 4.14/1.86 | (14) ~ (all_0_3_3 = 0) % 4.14/1.87 | (18) ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) % 4.14/1.87 | % 4.14/1.87 | Instantiating (18) with all_22_0_6, all_22_1_7 yields: % 4.14/1.87 | (19) big_r(all_22_0_6, all_22_1_7) = 0 & big_r(all_0_4_4, all_22_0_6) = 0 & big_p(all_22_1_7) = 0 % 4.14/1.87 | % 4.14/1.87 | Applying alpha-rule on (19) yields: % 4.14/1.87 | (20) big_r(all_22_0_6, all_22_1_7) = 0 % 4.14/1.87 | (21) big_r(all_0_4_4, all_22_0_6) = 0 % 4.14/1.87 | (22) big_p(all_22_1_7) = 0 % 4.14/1.87 | % 4.14/1.87 | Instantiating formula (11) with all_22_0_6, all_22_1_7 and discharging atoms big_r(all_0_4_4, all_22_0_6) = 0, big_p(all_22_1_7) = 0, yields: % 4.14/1.87 | (23) ? [v0] : ( ~ (v0 = 0) & big_r(all_22_0_6, all_22_1_7) = v0) % 4.14/1.87 | % 4.14/1.87 | Instantiating (23) with all_29_0_8 yields: % 4.14/1.87 | (24) ~ (all_29_0_8 = 0) & big_r(all_22_0_6, all_22_1_7) = all_29_0_8 % 4.14/1.87 | % 4.14/1.87 | Applying alpha-rule on (24) yields: % 4.14/1.87 | (25) ~ (all_29_0_8 = 0) % 4.14/1.87 | (26) big_r(all_22_0_6, all_22_1_7) = all_29_0_8 % 4.14/1.87 | % 4.14/1.87 | Instantiating formula (3) with all_22_0_6, all_22_1_7, all_29_0_8, 0 and discharging atoms big_r(all_22_0_6, all_22_1_7) = all_29_0_8, big_r(all_22_0_6, all_22_1_7) = 0, yields: % 4.14/1.87 | (27) all_29_0_8 = 0 % 4.14/1.87 | % 4.14/1.87 | Equations (27) can reduce 25 to: % 4.14/1.87 | (16) $false % 4.14/1.87 | % 4.14/1.87 |-The branch is then unsatisfiable % 4.14/1.87 |-Branch two: % 4.14/1.87 | (15) all_0_3_3 = 0 % 4.14/1.87 | (30) all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0 % 4.14/1.87 | % 4.14/1.87 | Applying alpha-rule on (30) yields: % 4.14/1.87 | (31) all_0_0_0 = 0 % 4.14/1.87 | (32) all_0_1_1 = 0 % 4.14/1.87 | (33) big_r(all_0_4_4, all_0_2_2) = 0 % 4.14/1.87 | (34) big_p(all_0_2_2) = 0 % 4.14/1.87 | % 4.14/1.87 | From (15) and (9) follows: % 4.14/1.87 | (35) big_p(all_0_4_4) = 0 % 4.14/1.87 | % 4.14/1.87 | Instantiating formula (12) with all_0_2_2, 0, all_0_4_4 and discharging atoms big_r(all_0_4_4, all_0_2_2) = 0, big_p(all_0_4_4) = 0, yields: % 4.14/1.87 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) | ( ~ (v0 = 0) & big_p(all_0_2_2) = v0)) % 4.14/1.87 | % 4.14/1.87 | Instantiating (36) with all_27_0_17, all_27_1_18, all_27_2_19, all_27_3_20, all_27_4_21 yields: % 4.14/1.87 | (37) (all_27_0_17 = 0 & all_27_1_18 = 0 & all_27_2_19 = 0 & big_r(all_27_3_20, all_27_4_21) = 0 & big_r(all_0_4_4, all_27_3_20) = 0 & big_p(all_27_4_21) = 0) | ( ~ (all_27_4_21 = 0) & big_p(all_0_2_2) = all_27_4_21) % 4.14/1.87 | % 4.14/1.87 +-Applying beta-rule and splitting (37), into two cases. % 4.14/1.87 |-Branch one: % 4.14/1.87 | (38) all_27_0_17 = 0 & all_27_1_18 = 0 & all_27_2_19 = 0 & big_r(all_27_3_20, all_27_4_21) = 0 & big_r(all_0_4_4, all_27_3_20) = 0 & big_p(all_27_4_21) = 0 % 4.14/1.87 | % 4.14/1.87 | Applying alpha-rule on (38) yields: % 4.14/1.87 | (39) big_r(all_0_4_4, all_27_3_20) = 0 % 4.14/1.87 | (40) all_27_2_19 = 0 % 4.14/1.87 | (41) big_r(all_27_3_20, all_27_4_21) = 0 % 4.14/1.87 | (42) all_27_1_18 = 0 % 4.14/1.87 | (43) big_p(all_27_4_21) = 0 % 4.14/1.87 | (44) all_27_0_17 = 0 % 4.14/1.87 | % 4.14/1.87 | Instantiating formula (11) with all_27_3_20, all_27_4_21 and discharging atoms big_r(all_0_4_4, all_27_3_20) = 0, big_p(all_27_4_21) = 0, yields: % 4.14/1.87 | (45) ? [v0] : ( ~ (v0 = 0) & big_r(all_27_3_20, all_27_4_21) = v0) % 4.14/1.87 | % 4.14/1.87 | Instantiating (45) with all_39_0_23 yields: % 4.14/1.87 | (46) ~ (all_39_0_23 = 0) & big_r(all_27_3_20, all_27_4_21) = all_39_0_23 % 4.14/1.87 | % 4.14/1.87 | Applying alpha-rule on (46) yields: % 4.14/1.87 | (47) ~ (all_39_0_23 = 0) % 4.14/1.87 | (48) big_r(all_27_3_20, all_27_4_21) = all_39_0_23 % 4.14/1.87 | % 4.14/1.87 | Instantiating formula (3) with all_27_3_20, all_27_4_21, all_39_0_23, 0 and discharging atoms big_r(all_27_3_20, all_27_4_21) = all_39_0_23, big_r(all_27_3_20, all_27_4_21) = 0, yields: % 4.14/1.87 | (49) all_39_0_23 = 0 % 4.14/1.87 | % 4.14/1.87 | Equations (49) can reduce 47 to: % 4.14/1.87 | (16) $false % 4.14/1.87 | % 4.14/1.87 |-The branch is then unsatisfiable % 4.14/1.87 |-Branch two: % 4.14/1.87 | (51) ~ (all_27_4_21 = 0) & big_p(all_0_2_2) = all_27_4_21 % 4.14/1.87 | % 4.14/1.87 | Applying alpha-rule on (51) yields: % 4.14/1.87 | (52) ~ (all_27_4_21 = 0) % 4.14/1.87 | (53) big_p(all_0_2_2) = all_27_4_21 % 4.14/1.87 | % 4.14/1.87 | Instantiating formula (4) with all_0_2_2, all_27_4_21, 0 and discharging atoms big_p(all_0_2_2) = all_27_4_21, big_p(all_0_2_2) = 0, yields: % 4.14/1.87 | (54) all_27_4_21 = 0 % 4.14/1.87 | % 4.14/1.87 | Equations (54) can reduce 52 to: % 4.14/1.87 | (16) $false % 4.14/1.87 | % 4.14/1.87 |-The branch is then unsatisfiable % 4.14/1.87 |-Branch two: % 4.14/1.87 | (56) all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0)) % 4.14/1.88 | % 4.14/1.88 | Applying alpha-rule on (56) yields: % 4.14/1.88 | (7) all_0_5_5 = 0 % 4.14/1.88 | (8) ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0) % 4.14/1.88 | (9) big_p(all_0_4_4) = all_0_3_3 % 4.14/1.88 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) % 4.14/1.88 | (61) ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) % 4.14/1.88 | (11) ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) % 4.14/1.88 | % 4.14/1.88 | Instantiating formula (10) with all_0_3_3, all_0_4_4 and discharging atoms big_p(all_0_4_4) = all_0_3_3, yields: % 4.14/1.88 | (13) all_0_3_3 = 0 | ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) % 4.14/1.88 | % 4.14/1.88 +-Applying beta-rule and splitting (8), into two cases. % 4.14/1.88 |-Branch one: % 4.14/1.88 | (14) ~ (all_0_3_3 = 0) % 4.14/1.88 | % 4.14/1.88 +-Applying beta-rule and splitting (13), into two cases. % 4.14/1.88 |-Branch one: % 4.14/1.88 | (15) all_0_3_3 = 0 % 4.14/1.88 | % 4.14/1.88 | Equations (15) can reduce 14 to: % 4.14/1.88 | (16) $false % 4.14/1.88 | % 4.14/1.88 |-The branch is then unsatisfiable % 4.14/1.88 |-Branch two: % 4.14/1.88 | (14) ~ (all_0_3_3 = 0) % 4.14/1.88 | (18) ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) % 4.14/1.88 | % 4.14/1.88 | Instantiating (18) with all_22_0_33, all_22_1_34 yields: % 4.14/1.88 | (69) big_r(all_22_0_33, all_22_1_34) = 0 & big_r(all_0_4_4, all_22_0_33) = 0 & big_p(all_22_1_34) = 0 % 4.14/1.88 | % 4.14/1.88 | Applying alpha-rule on (69) yields: % 4.14/1.88 | (70) big_r(all_22_0_33, all_22_1_34) = 0 % 4.14/1.88 | (71) big_r(all_0_4_4, all_22_0_33) = 0 % 4.14/1.88 | (72) big_p(all_22_1_34) = 0 % 4.14/1.88 | % 4.14/1.88 | Instantiating formula (11) with all_22_0_33, all_22_1_34 and discharging atoms big_r(all_0_4_4, all_22_0_33) = 0, big_p(all_22_1_34) = 0, yields: % 4.14/1.88 | (73) ? [v0] : ( ~ (v0 = 0) & big_r(all_22_0_33, all_22_1_34) = v0) % 4.14/1.88 | % 4.14/1.88 | Instantiating (73) with all_29_0_35 yields: % 4.14/1.88 | (74) ~ (all_29_0_35 = 0) & big_r(all_22_0_33, all_22_1_34) = all_29_0_35 % 4.14/1.88 | % 4.14/1.88 | Applying alpha-rule on (74) yields: % 4.14/1.88 | (75) ~ (all_29_0_35 = 0) % 4.14/1.88 | (76) big_r(all_22_0_33, all_22_1_34) = all_29_0_35 % 4.14/1.88 | % 4.14/1.88 | Instantiating formula (3) with all_22_0_33, all_22_1_34, all_29_0_35, 0 and discharging atoms big_r(all_22_0_33, all_22_1_34) = all_29_0_35, big_r(all_22_0_33, all_22_1_34) = 0, yields: % 4.14/1.88 | (77) all_29_0_35 = 0 % 4.14/1.88 | % 4.14/1.88 | Equations (77) can reduce 75 to: % 4.14/1.88 | (16) $false % 4.14/1.88 | % 4.14/1.88 |-The branch is then unsatisfiable % 4.14/1.88 |-Branch two: % 4.14/1.88 | (15) all_0_3_3 = 0 % 4.14/1.88 | (30) all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0 % 4.14/1.88 | % 4.14/1.88 | Applying alpha-rule on (30) yields: % 4.14/1.88 | (31) all_0_0_0 = 0 % 4.14/1.88 | (32) all_0_1_1 = 0 % 4.14/1.88 | (33) big_r(all_0_4_4, all_0_2_2) = 0 % 4.14/1.88 | (34) big_p(all_0_2_2) = 0 % 4.14/1.88 | % 4.14/1.88 | Instantiating formula (61) with all_0_2_2, all_0_4_4 and discharging atoms big_r(all_0_4_4, all_0_2_2) = 0, yields: % 4.14/1.88 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) | ( ~ (v0 = 0) & big_p(all_0_2_2) = v0)) % 4.14/1.88 | % 4.14/1.88 | Instantiating (36) with all_27_0_49, all_27_1_50, all_27_2_51, all_27_3_52, all_27_4_53 yields: % 4.14/1.88 | (86) (all_27_0_49 = 0 & all_27_1_50 = 0 & all_27_2_51 = 0 & big_r(all_27_3_52, all_27_4_53) = 0 & big_r(all_0_4_4, all_27_3_52) = 0 & big_p(all_27_4_53) = 0) | ( ~ (all_27_4_53 = 0) & big_p(all_0_2_2) = all_27_4_53) % 4.14/1.88 | % 4.14/1.88 +-Applying beta-rule and splitting (86), into two cases. % 4.14/1.88 |-Branch one: % 4.14/1.88 | (87) all_27_0_49 = 0 & all_27_1_50 = 0 & all_27_2_51 = 0 & big_r(all_27_3_52, all_27_4_53) = 0 & big_r(all_0_4_4, all_27_3_52) = 0 & big_p(all_27_4_53) = 0 % 4.14/1.88 | % 4.14/1.88 | Applying alpha-rule on (87) yields: % 4.14/1.88 | (88) big_r(all_27_3_52, all_27_4_53) = 0 % 4.14/1.88 | (89) all_27_2_51 = 0 % 4.14/1.88 | (90) all_27_0_49 = 0 % 4.14/1.88 | (91) all_27_1_50 = 0 % 4.14/1.88 | (92) big_p(all_27_4_53) = 0 % 4.14/1.88 | (93) big_r(all_0_4_4, all_27_3_52) = 0 % 4.14/1.89 | % 4.14/1.89 | Instantiating formula (11) with all_27_3_52, all_27_4_53 and discharging atoms big_r(all_0_4_4, all_27_3_52) = 0, big_p(all_27_4_53) = 0, yields: % 4.14/1.89 | (94) ? [v0] : ( ~ (v0 = 0) & big_r(all_27_3_52, all_27_4_53) = v0) % 4.14/1.89 | % 4.14/1.89 | Instantiating (94) with all_39_0_55 yields: % 4.14/1.89 | (95) ~ (all_39_0_55 = 0) & big_r(all_27_3_52, all_27_4_53) = all_39_0_55 % 4.14/1.89 | % 4.14/1.89 | Applying alpha-rule on (95) yields: % 4.14/1.89 | (96) ~ (all_39_0_55 = 0) % 4.14/1.89 | (97) big_r(all_27_3_52, all_27_4_53) = all_39_0_55 % 4.14/1.89 | % 4.14/1.89 | Instantiating formula (3) with all_27_3_52, all_27_4_53, all_39_0_55, 0 and discharging atoms big_r(all_27_3_52, all_27_4_53) = all_39_0_55, big_r(all_27_3_52, all_27_4_53) = 0, yields: % 4.14/1.89 | (98) all_39_0_55 = 0 % 4.14/1.89 | % 4.14/1.89 | Equations (98) can reduce 96 to: % 4.14/1.89 | (16) $false % 4.14/1.89 | % 4.14/1.89 |-The branch is then unsatisfiable % 4.14/1.89 |-Branch two: % 4.14/1.89 | (100) ~ (all_27_4_53 = 0) & big_p(all_0_2_2) = all_27_4_53 % 4.14/1.89 | % 4.14/1.89 | Applying alpha-rule on (100) yields: % 4.14/1.89 | (101) ~ (all_27_4_53 = 0) % 4.14/1.89 | (102) big_p(all_0_2_2) = all_27_4_53 % 4.14/1.89 | % 4.14/1.89 | Instantiating formula (4) with all_0_2_2, all_27_4_53, 0 and discharging atoms big_p(all_0_2_2) = all_27_4_53, big_p(all_0_2_2) = 0, yields: % 4.14/1.89 | (103) all_27_4_53 = 0 % 4.14/1.89 | % 4.14/1.89 | Equations (103) can reduce 101 to: % 4.14/1.89 | (16) $false % 4.14/1.89 | % 4.14/1.89 |-The branch is then unsatisfiable % 4.14/1.89 % SZS output end Proof for theBenchmark % 4.14/1.89 % 4.14/1.89 1317ms %------------------------------------------------------------------------------