%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN070+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 04:59:40 EDT 2022 % Result : Theorem 3.14s 1.50s % Output : Proof 4.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SYN070+1 : TPTP v8.1.0. Released v2.0.0. % 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n012.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 : Mon Jul 11 20:43:13 EDT 2022 % 0.13/0.34 % CPUTime : % 0.59/0.61 ____ _ % 0.59/0.61 ___ / __ \_____(_)___ ________ __________ % 0.59/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.61 % 0.59/0.61 A Theorem Prover for First-Order Logic % 0.59/0.62 (ePrincess v.1.0) % 0.59/0.62 % 0.59/0.62 (c) Philipp Rümmer, 2009-2015 % 0.59/0.62 (c) Peter Backeman, 2014-2015 % 0.59/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.62 Bug reports to peter@backeman.se % 0.59/0.62 % 0.59/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.62 % 0.59/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.38/0.96 Prover 0: Preprocessing ... % 1.52/1.03 Prover 0: Warning: ignoring some quantifiers % 1.52/1.05 Prover 0: Constructing countermodel ... % 2.21/1.26 Prover 0: gave up % 2.21/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.21/1.28 Prover 1: Preprocessing ... % 2.58/1.34 Prover 1: Constructing countermodel ... % 2.81/1.38 Prover 1: gave up % 2.81/1.38 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.81/1.39 Prover 2: Preprocessing ... % 2.81/1.44 Prover 2: Warning: ignoring some quantifiers % 2.81/1.45 Prover 2: Constructing countermodel ... % 3.14/1.49 Prover 2: proved (112ms) % 3.14/1.50 % 3.14/1.50 No countermodel exists, formula is valid % 3.14/1.50 % SZS status Theorem for theBenchmark % 3.14/1.50 % 3.14/1.50 Generating proof ... Warning: ignoring some quantifiers % 3.83/1.71 found it (size 56) % 3.83/1.71 % 3.83/1.71 % SZS output start Proof for theBenchmark % 3.83/1.72 Assumed formulas after preprocessing and simplification: % 3.83/1.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v1 = 0) & big_f(v0) = 0 & big_g(v0) = v1 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (big_j(v8, v7) = v6) | ~ (big_j(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (big_h(v8, v7) = v6) | ~ (big_h(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_f(v7) = v6) | ~ (big_f(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_g(v7) = v6) | ~ (big_g(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (big_h(v6, v5) = v7) | ? [v8] : ? [v9] : ((v8 = 0 & v7 = 0 & ~ (v9 = 0) & big_f(v6) = 0 & big_g(v6) = v9) | (v8 = 0 & big_g(v5) = 0) | ( ~ (v8 = 0) & big_f(v5) = v8))) & ! [v5] : ! [v6] : ( ~ (big_j(v6, v5) = 0) | ? [v7] : (( ~ (v7 = 0) & big_h(v5, v6) = v7) | ( ~ (v7 = 0) & big_f(v6) = v7) | ( ~ (v7 = 0) & big_f(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (big_h(v5, v6) = 0) | ? [v7] : (( ~ (v7 = 0) & big_j(v6, v5) = v7) | ( ~ (v7 = 0) & big_f(v6) = v7) | ( ~ (v7 = 0) & big_f(v5) = v7))) & ? [v5] : ? [v6] : ? [v7] : big_j(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : big_h(v6, v5) = v7 & ? [v5] : ? [v6] : big_f(v5) = v6 & ? [v5] : ? [v6] : big_g(v5) = v6 & ((v3 = 0 & ~ (v4 = 0) & big_f(v2) = 0 & big_g(v2) = v4 & ! [v5] : ! [v6] : (v6 = 0 | ~ (big_j(v2, v5) = v6) | ? [v7] : ((v7 = 0 & big_g(v5) = 0) | ( ~ (v7 = 0) & big_f(v5) = v7))) & ! [v5] : ! [v6] : (v6 = 0 | ~ (big_g(v5) = v6) | ? [v7] : ((v7 = 0 & big_j(v2, v5) = 0) | ( ~ (v7 = 0) & big_f(v5) = v7))) & ! [v5] : ( ~ (big_f(v5) = 0) | ? [v6] : ((v6 = 0 & big_j(v2, v5) = 0) | (v6 = 0 & big_g(v5) = 0)))) | ( ! [v5] : ! [v6] : (v6 = 0 | ~ (big_g(v5) = v6) | ? [v7] : ( ~ (v7 = 0) & big_f(v5) = v7)) & ! [v5] : ( ~ (big_f(v5) = 0) | big_g(v5) = 0)))) % 3.83/1.75 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.83/1.75 | (1) ~ (all_0_3_3 = 0) & big_f(all_0_4_4) = 0 & big_g(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_h(v1, v0) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & ~ (v4 = 0) & big_f(v1) = 0 & big_g(v1) = v4) | (v3 = 0 & big_g(v0) = 0) | ( ~ (v3 = 0) & big_f(v0) = v3))) & ! [v0] : ! [v1] : ( ~ (big_j(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & big_h(v0, v1) = v2) | ( ~ (v2 = 0) & big_f(v1) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (big_h(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & big_j(v1, v0) = v2) | ( ~ (v2 = 0) & big_f(v1) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ? [v0] : ? [v1] : ? [v2] : big_j(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : big_h(v1, v0) = v2 & ? [v0] : ? [v1] : big_f(v0) = v1 & ? [v0] : ? [v1] : big_g(v0) = v1 & ((all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & big_f(all_0_2_2) = 0 & big_g(all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(all_0_2_2, v0) = v1) | ? [v2] : ((v2 = 0 & big_g(v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ((v2 = 0 & big_j(all_0_2_2, v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_2_2, v0) = 0) | (v1 = 0 & big_g(v0) = 0)))) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2)) & ! [v0] : ( ~ (big_f(v0) = 0) | big_g(v0) = 0))) % 3.83/1.76 | % 3.83/1.76 | Applying alpha-rule on (1) yields: % 3.83/1.76 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = v0)) % 3.83/1.76 | (3) ~ (all_0_3_3 = 0) % 3.83/1.76 | (4) big_g(all_0_4_4) = all_0_3_3 % 3.83/1.76 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0)) % 3.83/1.76 | (6) ? [v0] : ? [v1] : big_f(v0) = v1 % 3.83/1.76 | (7) ? [v0] : ? [v1] : big_g(v0) = v1 % 3.83/1.76 | (8) ! [v0] : ! [v1] : ( ~ (big_j(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & big_h(v0, v1) = v2) | ( ~ (v2 = 0) & big_f(v1) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) % 3.83/1.76 | (9) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & big_f(all_0_2_2) = 0 & big_g(all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(all_0_2_2, v0) = v1) | ? [v2] : ((v2 = 0 & big_g(v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ((v2 = 0 & big_j(all_0_2_2, v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_2_2, v0) = 0) | (v1 = 0 & big_g(v0) = 0)))) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2)) & ! [v0] : ( ~ (big_f(v0) = 0) | big_g(v0) = 0)) % 3.83/1.76 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) % 3.83/1.76 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_h(v1, v0) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & ~ (v4 = 0) & big_f(v1) = 0 & big_g(v1) = v4) | (v3 = 0 & big_g(v0) = 0) | ( ~ (v3 = 0) & big_f(v0) = v3))) % 3.83/1.76 | (12) ? [v0] : ? [v1] : ? [v2] : big_h(v1, v0) = v2 % 3.83/1.76 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) % 3.83/1.76 | (14) ? [v0] : ? [v1] : ? [v2] : big_j(v1, v0) = v2 % 3.83/1.76 | (15) ! [v0] : ! [v1] : ( ~ (big_h(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & big_j(v1, v0) = v2) | ( ~ (v2 = 0) & big_f(v1) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) % 3.83/1.76 | (16) big_f(all_0_4_4) = 0 % 3.83/1.76 | % 3.83/1.76 +-Applying beta-rule and splitting (9), into two cases. % 3.83/1.76 |-Branch one: % 3.83/1.76 | (17) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & big_f(all_0_2_2) = 0 & big_g(all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(all_0_2_2, v0) = v1) | ? [v2] : ((v2 = 0 & big_g(v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ((v2 = 0 & big_j(all_0_2_2, v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_2_2, v0) = 0) | (v1 = 0 & big_g(v0) = 0))) % 3.83/1.76 | % 3.83/1.76 | Applying alpha-rule on (17) yields: % 3.83/1.76 | (18) ~ (all_0_0_0 = 0) % 3.83/1.76 | (19) all_0_1_1 = 0 % 3.83/1.76 | (20) big_g(all_0_2_2) = all_0_0_0 % 3.83/1.76 | (21) big_f(all_0_2_2) = 0 % 3.83/1.76 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ((v2 = 0 & big_j(all_0_2_2, v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) % 3.83/1.76 | (23) ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_2_2, v0) = 0) | (v1 = 0 & big_g(v0) = 0))) % 3.83/1.76 | (24) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(all_0_2_2, v0) = v1) | ? [v2] : ((v2 = 0 & big_g(v0) = 0) | ( ~ (v2 = 0) & big_f(v0) = v2))) % 3.83/1.77 | % 3.83/1.77 | Instantiating formula (22) with all_0_3_3, all_0_4_4 and discharging atoms big_g(all_0_4_4) = all_0_3_3, yields: % 3.83/1.77 | (25) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & big_j(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & big_f(all_0_4_4) = v0)) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (25), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (26) all_0_3_3 = 0 % 3.83/1.77 | % 3.83/1.77 | Equations (26) can reduce 3 to: % 3.83/1.77 | (27) $false % 3.83/1.77 | % 3.83/1.77 |-The branch is then unsatisfiable % 3.83/1.77 |-Branch two: % 3.83/1.77 | (3) ~ (all_0_3_3 = 0) % 3.83/1.77 | (29) ? [v0] : ((v0 = 0 & big_j(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & big_f(all_0_4_4) = v0)) % 3.83/1.77 | % 3.83/1.77 | Instantiating (29) with all_24_0_16 yields: % 3.83/1.77 | (30) (all_24_0_16 = 0 & big_j(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_24_0_16 = 0) & big_f(all_0_4_4) = all_24_0_16) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (30), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (31) all_24_0_16 = 0 & big_j(all_0_2_2, all_0_4_4) = 0 % 3.83/1.77 | % 3.83/1.77 | Applying alpha-rule on (31) yields: % 3.83/1.77 | (32) all_24_0_16 = 0 % 3.83/1.77 | (33) big_j(all_0_2_2, all_0_4_4) = 0 % 3.83/1.77 | % 3.83/1.77 | Instantiating formula (8) with all_0_2_2, all_0_4_4 and discharging atoms big_j(all_0_2_2, all_0_4_4) = 0, yields: % 3.83/1.77 | (34) ? [v0] : (( ~ (v0 = 0) & big_h(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & big_f(all_0_2_2) = v0) | ( ~ (v0 = 0) & big_f(all_0_4_4) = v0)) % 3.83/1.77 | % 3.83/1.77 | Instantiating formula (22) with all_0_0_0, all_0_2_2 and discharging atoms big_g(all_0_2_2) = all_0_0_0, yields: % 3.83/1.77 | (35) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & big_j(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & big_f(all_0_2_2) = v0)) % 3.83/1.77 | % 3.83/1.77 | Instantiating (34) with all_39_0_18 yields: % 3.83/1.77 | (36) ( ~ (all_39_0_18 = 0) & big_h(all_0_4_4, all_0_2_2) = all_39_0_18) | ( ~ (all_39_0_18 = 0) & big_f(all_0_2_2) = all_39_0_18) | ( ~ (all_39_0_18 = 0) & big_f(all_0_4_4) = all_39_0_18) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (35), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (37) all_0_0_0 = 0 % 3.83/1.77 | % 3.83/1.77 | Equations (37) can reduce 18 to: % 3.83/1.77 | (27) $false % 3.83/1.77 | % 3.83/1.77 |-The branch is then unsatisfiable % 3.83/1.77 |-Branch two: % 3.83/1.77 | (18) ~ (all_0_0_0 = 0) % 3.83/1.77 | (40) ? [v0] : ((v0 = 0 & big_j(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & big_f(all_0_2_2) = v0)) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (36), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (41) ( ~ (all_39_0_18 = 0) & big_h(all_0_4_4, all_0_2_2) = all_39_0_18) | ( ~ (all_39_0_18 = 0) & big_f(all_0_2_2) = all_39_0_18) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (41), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (42) ~ (all_39_0_18 = 0) & big_h(all_0_4_4, all_0_2_2) = all_39_0_18 % 3.83/1.77 | % 3.83/1.77 | Applying alpha-rule on (42) yields: % 3.83/1.77 | (43) ~ (all_39_0_18 = 0) % 3.83/1.77 | (44) big_h(all_0_4_4, all_0_2_2) = all_39_0_18 % 3.83/1.77 | % 3.83/1.77 | Instantiating formula (11) with all_39_0_18, all_0_4_4, all_0_2_2 and discharging atoms big_h(all_0_4_4, all_0_2_2) = all_39_0_18, yields: % 3.83/1.77 | (45) ? [v0] : ? [v1] : ((v0 = 0 & all_39_0_18 = 0 & ~ (v1 = 0) & big_f(all_0_4_4) = 0 & big_g(all_0_4_4) = v1) | (v0 = 0 & big_g(all_0_2_2) = 0) | ( ~ (v0 = 0) & big_f(all_0_2_2) = v0)) % 3.83/1.77 | % 3.83/1.77 | Instantiating (45) with all_60_0_20, all_60_1_21 yields: % 3.83/1.77 | (46) (all_60_1_21 = 0 & all_39_0_18 = 0 & ~ (all_60_0_20 = 0) & big_f(all_0_4_4) = 0 & big_g(all_0_4_4) = all_60_0_20) | (all_60_1_21 = 0 & big_g(all_0_2_2) = 0) | ( ~ (all_60_1_21 = 0) & big_f(all_0_2_2) = all_60_1_21) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (46), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (47) (all_60_1_21 = 0 & all_39_0_18 = 0 & ~ (all_60_0_20 = 0) & big_f(all_0_4_4) = 0 & big_g(all_0_4_4) = all_60_0_20) | (all_60_1_21 = 0 & big_g(all_0_2_2) = 0) % 3.83/1.77 | % 3.83/1.77 +-Applying beta-rule and splitting (47), into two cases. % 3.83/1.77 |-Branch one: % 3.83/1.77 | (48) all_60_1_21 = 0 & all_39_0_18 = 0 & ~ (all_60_0_20 = 0) & big_f(all_0_4_4) = 0 & big_g(all_0_4_4) = all_60_0_20 % 3.83/1.78 | % 3.83/1.78 | Applying alpha-rule on (48) yields: % 3.83/1.78 | (49) big_g(all_0_4_4) = all_60_0_20 % 3.83/1.78 | (50) ~ (all_60_0_20 = 0) % 3.83/1.78 | (51) all_60_1_21 = 0 % 3.83/1.78 | (52) all_39_0_18 = 0 % 3.83/1.78 | (16) big_f(all_0_4_4) = 0 % 3.83/1.78 | % 3.83/1.78 | Equations (52) can reduce 43 to: % 3.83/1.78 | (27) $false % 3.83/1.78 | % 3.83/1.78 |-The branch is then unsatisfiable % 3.83/1.78 |-Branch two: % 3.83/1.78 | (55) all_60_1_21 = 0 & big_g(all_0_2_2) = 0 % 3.83/1.78 | % 3.83/1.78 | Applying alpha-rule on (55) yields: % 3.83/1.78 | (51) all_60_1_21 = 0 % 3.83/1.78 | (57) big_g(all_0_2_2) = 0 % 3.83/1.78 | % 3.83/1.78 | Instantiating formula (10) with all_0_2_2, 0, all_0_0_0 and discharging atoms big_g(all_0_2_2) = all_0_0_0, big_g(all_0_2_2) = 0, yields: % 3.83/1.78 | (37) all_0_0_0 = 0 % 3.83/1.78 | % 3.83/1.78 | Equations (37) can reduce 18 to: % 3.83/1.78 | (27) $false % 3.83/1.78 | % 3.83/1.78 |-The branch is then unsatisfiable % 3.83/1.78 |-Branch two: % 3.83/1.78 | (60) ~ (all_60_1_21 = 0) & big_f(all_0_2_2) = all_60_1_21 % 3.83/1.78 | % 3.83/1.78 | Applying alpha-rule on (60) yields: % 3.83/1.78 | (61) ~ (all_60_1_21 = 0) % 3.83/1.78 | (62) big_f(all_0_2_2) = all_60_1_21 % 3.83/1.78 | % 3.83/1.78 | Instantiating formula (13) with all_0_2_2, all_60_1_21, 0 and discharging atoms big_f(all_0_2_2) = all_60_1_21, big_f(all_0_2_2) = 0, yields: % 3.83/1.78 | (51) all_60_1_21 = 0 % 3.83/1.78 | % 3.83/1.78 | Equations (51) can reduce 61 to: % 3.83/1.78 | (27) $false % 3.83/1.78 | % 3.83/1.78 |-The branch is then unsatisfiable % 3.83/1.78 |-Branch two: % 3.83/1.78 | (65) ~ (all_39_0_18 = 0) & big_f(all_0_2_2) = all_39_0_18 % 3.83/1.78 | % 3.83/1.78 | Applying alpha-rule on (65) yields: % 3.83/1.78 | (43) ~ (all_39_0_18 = 0) % 3.83/1.78 | (67) big_f(all_0_2_2) = all_39_0_18 % 3.83/1.78 | % 3.83/1.78 | Instantiating formula (13) with all_0_2_2, all_39_0_18, 0 and discharging atoms big_f(all_0_2_2) = all_39_0_18, big_f(all_0_2_2) = 0, yields: % 3.83/1.78 | (52) all_39_0_18 = 0 % 3.83/1.78 | % 3.83/1.78 | Equations (52) can reduce 43 to: % 3.83/1.78 | (27) $false % 3.83/1.78 | % 3.83/1.78 |-The branch is then unsatisfiable % 3.83/1.78 |-Branch two: % 3.83/1.78 | (70) ~ (all_39_0_18 = 0) & big_f(all_0_4_4) = all_39_0_18 % 3.83/1.78 | % 3.83/1.78 | Applying alpha-rule on (70) yields: % 3.83/1.78 | (43) ~ (all_39_0_18 = 0) % 3.83/1.78 | (72) big_f(all_0_4_4) = all_39_0_18 % 3.83/1.78 | % 3.83/1.78 | Instantiating formula (13) with all_0_4_4, all_39_0_18, 0 and discharging atoms big_f(all_0_4_4) = all_39_0_18, big_f(all_0_4_4) = 0, yields: % 3.83/1.78 | (52) all_39_0_18 = 0 % 3.83/1.78 | % 3.83/1.78 | Equations (52) can reduce 43 to: % 3.83/1.78 | (27) $false % 4.11/1.78 | % 4.11/1.78 |-The branch is then unsatisfiable % 4.11/1.78 |-Branch two: % 4.11/1.78 | (75) ~ (all_24_0_16 = 0) & big_f(all_0_4_4) = all_24_0_16 % 4.11/1.78 | % 4.11/1.78 | Applying alpha-rule on (75) yields: % 4.11/1.78 | (76) ~ (all_24_0_16 = 0) % 4.11/1.78 | (77) big_f(all_0_4_4) = all_24_0_16 % 4.11/1.78 | % 4.11/1.78 | Instantiating formula (13) with all_0_4_4, all_24_0_16, 0 and discharging atoms big_f(all_0_4_4) = all_24_0_16, big_f(all_0_4_4) = 0, yields: % 4.11/1.78 | (32) all_24_0_16 = 0 % 4.11/1.78 | % 4.11/1.78 | Equations (32) can reduce 76 to: % 4.11/1.78 | (27) $false % 4.11/1.78 | % 4.11/1.78 |-The branch is then unsatisfiable % 4.11/1.78 |-Branch two: % 4.11/1.78 | (80) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2)) & ! [v0] : ( ~ (big_f(v0) = 0) | big_g(v0) = 0) % 4.11/1.78 | % 4.11/1.78 | Applying alpha-rule on (80) yields: % 4.11/1.78 | (81) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2)) % 4.11/1.78 | (82) ! [v0] : ( ~ (big_f(v0) = 0) | big_g(v0) = 0) % 4.11/1.78 | % 4.11/1.78 | Instantiating formula (82) with all_0_4_4 and discharging atoms big_f(all_0_4_4) = 0, yields: % 4.11/1.78 | (83) big_g(all_0_4_4) = 0 % 4.11/1.78 | % 4.11/1.78 | Instantiating formula (81) with all_0_3_3, all_0_4_4 and discharging atoms big_g(all_0_4_4) = all_0_3_3, yields: % 4.11/1.78 | (84) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & big_f(all_0_4_4) = v0) % 4.11/1.78 | % 4.11/1.78 +-Applying beta-rule and splitting (84), into two cases. % 4.11/1.78 |-Branch one: % 4.11/1.78 | (26) all_0_3_3 = 0 % 4.11/1.78 | % 4.11/1.78 | Equations (26) can reduce 3 to: % 4.11/1.78 | (27) $false % 4.11/1.78 | % 4.11/1.78 |-The branch is then unsatisfiable % 4.11/1.78 |-Branch two: % 4.11/1.78 | (3) ~ (all_0_3_3 = 0) % 4.11/1.78 | (88) ? [v0] : ( ~ (v0 = 0) & big_f(all_0_4_4) = v0) % 4.11/1.79 | % 4.11/1.79 | Instantiating formula (10) with all_0_4_4, 0, all_0_3_3 and discharging atoms big_g(all_0_4_4) = all_0_3_3, big_g(all_0_4_4) = 0, yields: % 4.11/1.79 | (26) all_0_3_3 = 0 % 4.11/1.79 | % 4.11/1.79 | Equations (26) can reduce 3 to: % 4.11/1.79 | (27) $false % 4.11/1.79 | % 4.11/1.79 |-The branch is then unsatisfiable % 4.11/1.79 % SZS output end Proof for theBenchmark % 4.11/1.79 % 4.11/1.79 1152ms %------------------------------------------------------------------------------