%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 15:34:14 EDT 2022 % Result : Theorem 2.41s 1.31s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n020.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 : Wed Jun 8 06:03:51 EDT 2022 % 0.12/0.33 % CPUTime : % 0.57/0.58 ____ _ % 0.57/0.58 ___ / __ \_____(_)___ ________ __________ % 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.58 % 0.57/0.58 A Theorem Prover for First-Order Logic % 0.57/0.58 (ePrincess v.1.0) % 0.57/0.58 % 0.57/0.58 (c) Philipp Rümmer, 2009-2015 % 0.57/0.58 (c) Peter Backeman, 2014-2015 % 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.58 Bug reports to peter@backeman.se % 0.57/0.58 % 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.58 % 0.57/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.93 Prover 0: Preprocessing ... % 1.87/1.13 Prover 0: Constructing countermodel ... % 2.41/1.30 Prover 0: proved (679ms) % 2.41/1.31 % 2.41/1.31 No countermodel exists, formula is valid % 2.41/1.31 % SZS status Theorem for theBenchmark % 2.41/1.31 % 2.41/1.31 Generating proof ... found it (size 118) % 4.07/1.74 % 4.07/1.74 % SZS output start Proof for theBenchmark % 4.07/1.74 Assumed formulas after preprocessing and simplification: % 4.07/1.74 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & op1(v1, v1) = v0 & op1(v0, v1) = v2 & op1(v0, v0) = v1 & sorti1(v1) & sorti1(v0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (op2(v6, v5) = v4) | ~ (op2(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (op1(v6, v5) = v4) | ~ (op1(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (op2(v3, v4) = v5) | ~ (op2(v3, v3) = v4) | ~ sorti2(v4) | ~ sorti2(v3) | ? [v6] : ( ~ (v6 = v3) & op2(v4, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (j(v5) = v4) | ~ (j(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (h(v5) = v4) | ~ (h(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (op2(v3, v4) = v5) | ~ sorti2(v4) | ~ sorti2(v3) | sorti2(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (op1(v3, v4) = v5) | ~ sorti1(v4) | ~ sorti1(v3) | sorti1(v5)) & ! [v3] : ! [v4] : ( ~ (op2(v4, v4) = v3) | ~ (op2(v3, v3) = v4) | ~ sorti2(v4) | ~ sorti2(v3) | op2(v3, v4) = v3) & ! [v3] : ( ~ sorti2(v3) | ? [v4] : (j(v3) = v4 & h(v4) = v3)) & ! [v3] : ( ~ sorti2(v3) | ? [v4] : (j(v3) = v4 & sorti1(v4))) & ! [v3] : ( ~ sorti2(v3) | ? [v4] : (j(v3) = v4 & ! [v5] : ( ~ sorti2(v5) | ? [v6] : ? [v7] : ? [v8] : (j(v6) = v7 & j(v5) = v8 & op2(v3, v5) = v6 & op1(v4, v8) = v7)))) & ! [v3] : ( ~ sorti1(v3) | ? [v4] : (j(v4) = v3 & h(v3) = v4)) & ! [v3] : ( ~ sorti1(v3) | ? [v4] : (h(v3) = v4 & sorti2(v4))) & ! [v3] : ( ~ sorti1(v3) | ? [v4] : (h(v3) = v4 & ! [v5] : ( ~ sorti1(v5) | ? [v6] : ? [v7] : ? [v8] : (h(v6) = v7 & h(v5) = v8 & op2(v4, v8) = v7 & op1(v3, v5) = v6))))) % 4.07/1.77 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.07/1.77 | (1) ~ (all_0_0_0 = all_0_2_2) & op1(all_0_1_1, all_0_1_1) = all_0_2_2 & op1(all_0_2_2, all_0_1_1) = all_0_0_0 & op1(all_0_2_2, all_0_2_2) = all_0_1_1 & sorti1(all_0_1_1) & sorti1(all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (op2(v0, v1) = v2) | ~ (op2(v0, v0) = v1) | ~ sorti2(v1) | ~ sorti2(v0) | ? [v3] : ( ~ (v3 = v0) & op2(v1, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) & ! [v0] : ! [v1] : ( ~ (op2(v1, v1) = v0) | ~ (op2(v0, v0) = v1) | ~ sorti2(v1) | ~ sorti2(v0) | op2(v0, v1) = v0) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & ! [v2] : ( ~ sorti2(v2) | ? [v3] : ? [v4] : ? [v5] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4)))) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & ! [v2] : ( ~ sorti1(v2) | ? [v3] : ? [v4] : ? [v5] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3)))) % 4.33/1.78 | % 4.33/1.78 | Applying alpha-rule on (1) yields: % 4.33/1.78 | (2) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) % 4.33/1.78 | (3) ~ (all_0_0_0 = all_0_2_2) % 4.33/1.78 | (4) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) % 4.33/1.78 | (5) sorti1(all_0_2_2) % 4.33/1.78 | (6) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & ! [v2] : ( ~ sorti2(v2) | ? [v3] : ? [v4] : ? [v5] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4)))) % 4.33/1.78 | (7) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & ! [v2] : ( ~ sorti1(v2) | ? [v3] : ? [v4] : ? [v5] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3)))) % 4.33/1.78 | (8) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) % 4.33/1.79 | (9) op1(all_0_1_1, all_0_1_1) = all_0_2_2 % 4.33/1.79 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) % 4.33/1.79 | (11) op1(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.33/1.79 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 4.33/1.79 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (op2(v0, v1) = v2) | ~ (op2(v0, v0) = v1) | ~ sorti2(v1) | ~ sorti2(v0) | ? [v3] : ( ~ (v3 = v0) & op2(v1, v1) = v3)) % 4.33/1.79 | (14) op1(all_0_2_2, all_0_2_2) = all_0_1_1 % 4.33/1.79 | (15) ! [v0] : ! [v1] : ( ~ (op2(v1, v1) = v0) | ~ (op2(v0, v0) = v1) | ~ sorti2(v1) | ~ sorti2(v0) | op2(v0, v1) = v0) % 4.33/1.79 | (16) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) % 4.33/1.79 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 4.33/1.79 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) % 4.33/1.79 | (19) sorti1(all_0_1_1) % 4.33/1.79 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 4.33/1.79 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 4.33/1.79 | % 4.33/1.79 | Instantiating formula (8) with all_0_1_1 and discharging atoms sorti1(all_0_1_1), yields: % 4.33/1.79 | (22) ? [v0] : (j(v0) = all_0_1_1 & h(all_0_1_1) = v0) % 4.33/1.79 | % 4.33/1.79 | Instantiating formula (4) with all_0_1_1 and discharging atoms sorti1(all_0_1_1), yields: % 4.33/1.79 | (23) ? [v0] : (h(all_0_1_1) = v0 & sorti2(v0)) % 4.33/1.79 | % 4.33/1.79 | Instantiating formula (7) with all_0_1_1 and discharging atoms sorti1(all_0_1_1), yields: % 4.33/1.79 | (24) ? [v0] : (h(all_0_1_1) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_0_1_1, v1) = v2))) % 4.33/1.79 | % 4.33/1.79 | Instantiating formula (8) with all_0_2_2 and discharging atoms sorti1(all_0_2_2), yields: % 4.33/1.79 | (25) ? [v0] : (j(v0) = all_0_2_2 & h(all_0_2_2) = v0) % 4.33/1.79 | % 4.33/1.79 | Instantiating formula (4) with all_0_2_2 and discharging atoms sorti1(all_0_2_2), yields: % 4.33/1.79 | (26) ? [v0] : (h(all_0_2_2) = v0 & sorti2(v0)) % 4.33/1.79 | % 4.33/1.79 | Instantiating formula (7) with all_0_2_2 and discharging atoms sorti1(all_0_2_2), yields: % 4.33/1.79 | (27) ? [v0] : (h(all_0_2_2) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_0_2_2, v1) = v2))) % 4.37/1.79 | % 4.37/1.79 | Instantiating (27) with all_9_0_3 yields: % 4.37/1.79 | (28) h(all_0_2_2) = all_9_0_3 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_9_0_3, v3) = v2 & op1(all_0_2_2, v0) = v1)) % 4.37/1.79 | % 4.37/1.79 | Applying alpha-rule on (28) yields: % 4.37/1.79 | (29) h(all_0_2_2) = all_9_0_3 % 4.37/1.79 | (30) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_9_0_3, v3) = v2 & op1(all_0_2_2, v0) = v1)) % 4.37/1.79 | % 4.37/1.79 | Instantiating formula (30) with all_0_1_1 and discharging atoms sorti1(all_0_1_1), yields: % 4.37/1.79 | (31) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_1_1) = v2 & op2(all_9_0_3, v2) = v1 & op1(all_0_2_2, all_0_1_1) = v0) % 4.37/1.79 | % 4.37/1.79 | Instantiating formula (30) with all_0_2_2 and discharging atoms sorti1(all_0_2_2), yields: % 4.37/1.79 | (32) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_2_2) = v2 & op2(all_9_0_3, v2) = v1 & op1(all_0_2_2, all_0_2_2) = v0) % 4.37/1.80 | % 4.37/1.80 | Instantiating (26) with all_12_0_4 yields: % 4.37/1.80 | (33) h(all_0_2_2) = all_12_0_4 & sorti2(all_12_0_4) % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (33) yields: % 4.37/1.80 | (34) h(all_0_2_2) = all_12_0_4 % 4.37/1.80 | (35) sorti2(all_12_0_4) % 4.37/1.80 | % 4.37/1.80 | Instantiating (23) with all_14_0_5 yields: % 4.37/1.80 | (36) h(all_0_1_1) = all_14_0_5 & sorti2(all_14_0_5) % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (36) yields: % 4.37/1.80 | (37) h(all_0_1_1) = all_14_0_5 % 4.37/1.80 | (38) sorti2(all_14_0_5) % 4.37/1.80 | % 4.37/1.80 | Instantiating (22) with all_16_0_6 yields: % 4.37/1.80 | (39) j(all_16_0_6) = all_0_1_1 & h(all_0_1_1) = all_16_0_6 % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (39) yields: % 4.37/1.80 | (40) j(all_16_0_6) = all_0_1_1 % 4.37/1.80 | (41) h(all_0_1_1) = all_16_0_6 % 4.37/1.80 | % 4.37/1.80 | Instantiating (25) with all_18_0_7 yields: % 4.37/1.80 | (42) j(all_18_0_7) = all_0_2_2 & h(all_0_2_2) = all_18_0_7 % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (42) yields: % 4.37/1.80 | (43) j(all_18_0_7) = all_0_2_2 % 4.37/1.80 | (44) h(all_0_2_2) = all_18_0_7 % 4.37/1.80 | % 4.37/1.80 | Instantiating (24) with all_20_0_8 yields: % 4.37/1.80 | (45) h(all_0_1_1) = all_20_0_8 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_20_0_8, v3) = v2 & op1(all_0_1_1, v0) = v1)) % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (45) yields: % 4.37/1.80 | (46) h(all_0_1_1) = all_20_0_8 % 4.37/1.80 | (47) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_20_0_8, v3) = v2 & op1(all_0_1_1, v0) = v1)) % 4.37/1.80 | % 4.37/1.80 | Instantiating formula (47) with all_0_1_1 and discharging atoms sorti1(all_0_1_1), yields: % 4.37/1.80 | (48) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_1_1) = v2 & op2(all_20_0_8, v2) = v1 & op1(all_0_1_1, all_0_1_1) = v0) % 4.37/1.80 | % 4.37/1.80 | Instantiating formula (47) with all_0_2_2 and discharging atoms sorti1(all_0_2_2), yields: % 4.37/1.80 | (49) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_2_2) = v2 & op2(all_20_0_8, v2) = v1 & op1(all_0_1_1, all_0_2_2) = v0) % 4.37/1.80 | % 4.37/1.80 | Instantiating (32) with all_23_0_9, all_23_1_10, all_23_2_11 yields: % 4.37/1.80 | (50) h(all_23_2_11) = all_23_1_10 & h(all_0_2_2) = all_23_0_9 & op2(all_9_0_3, all_23_0_9) = all_23_1_10 & op1(all_0_2_2, all_0_2_2) = all_23_2_11 % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (50) yields: % 4.37/1.80 | (51) h(all_23_2_11) = all_23_1_10 % 4.37/1.80 | (52) h(all_0_2_2) = all_23_0_9 % 4.37/1.80 | (53) op2(all_9_0_3, all_23_0_9) = all_23_1_10 % 4.37/1.80 | (54) op1(all_0_2_2, all_0_2_2) = all_23_2_11 % 4.37/1.80 | % 4.37/1.80 | Instantiating (31) with all_25_0_12, all_25_1_13, all_25_2_14 yields: % 4.37/1.80 | (55) h(all_25_2_14) = all_25_1_13 & h(all_0_1_1) = all_25_0_12 & op2(all_9_0_3, all_25_0_12) = all_25_1_13 & op1(all_0_2_2, all_0_1_1) = all_25_2_14 % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (55) yields: % 4.37/1.80 | (56) h(all_25_2_14) = all_25_1_13 % 4.37/1.80 | (57) h(all_0_1_1) = all_25_0_12 % 4.37/1.80 | (58) op2(all_9_0_3, all_25_0_12) = all_25_1_13 % 4.37/1.80 | (59) op1(all_0_2_2, all_0_1_1) = all_25_2_14 % 4.37/1.80 | % 4.37/1.80 | Instantiating (49) with all_27_0_15, all_27_1_16, all_27_2_17 yields: % 4.37/1.80 | (60) h(all_27_2_17) = all_27_1_16 & h(all_0_2_2) = all_27_0_15 & op2(all_20_0_8, all_27_0_15) = all_27_1_16 & op1(all_0_1_1, all_0_2_2) = all_27_2_17 % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (60) yields: % 4.37/1.80 | (61) h(all_27_2_17) = all_27_1_16 % 4.37/1.80 | (62) h(all_0_2_2) = all_27_0_15 % 4.37/1.80 | (63) op2(all_20_0_8, all_27_0_15) = all_27_1_16 % 4.37/1.80 | (64) op1(all_0_1_1, all_0_2_2) = all_27_2_17 % 4.37/1.80 | % 4.37/1.80 | Instantiating (48) with all_29_0_18, all_29_1_19, all_29_2_20 yields: % 4.37/1.80 | (65) h(all_29_2_20) = all_29_1_19 & h(all_0_1_1) = all_29_0_18 & op2(all_20_0_8, all_29_0_18) = all_29_1_19 & op1(all_0_1_1, all_0_1_1) = all_29_2_20 % 4.37/1.80 | % 4.37/1.80 | Applying alpha-rule on (65) yields: % 4.37/1.80 | (66) h(all_29_2_20) = all_29_1_19 % 4.37/1.80 | (67) h(all_0_1_1) = all_29_0_18 % 4.37/1.81 | (68) op2(all_20_0_8, all_29_0_18) = all_29_1_19 % 4.37/1.81 | (69) op1(all_0_1_1, all_0_1_1) = all_29_2_20 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_1_1, all_20_0_8, all_29_0_18 and discharging atoms h(all_0_1_1) = all_29_0_18, h(all_0_1_1) = all_20_0_8, yields: % 4.37/1.81 | (70) all_29_0_18 = all_20_0_8 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_1_1, all_20_0_8, all_25_0_12 and discharging atoms h(all_0_1_1) = all_25_0_12, h(all_0_1_1) = all_20_0_8, yields: % 4.37/1.81 | (71) all_25_0_12 = all_20_0_8 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_1_1, all_16_0_6, all_25_0_12 and discharging atoms h(all_0_1_1) = all_25_0_12, h(all_0_1_1) = all_16_0_6, yields: % 4.37/1.81 | (72) all_25_0_12 = all_16_0_6 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_1_1, all_14_0_5, all_29_0_18 and discharging atoms h(all_0_1_1) = all_29_0_18, h(all_0_1_1) = all_14_0_5, yields: % 4.37/1.81 | (73) all_29_0_18 = all_14_0_5 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_2_2, all_23_0_9, all_27_0_15 and discharging atoms h(all_0_2_2) = all_27_0_15, h(all_0_2_2) = all_23_0_9, yields: % 4.37/1.81 | (74) all_27_0_15 = all_23_0_9 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_2_2, all_18_0_7, all_23_0_9 and discharging atoms h(all_0_2_2) = all_23_0_9, h(all_0_2_2) = all_18_0_7, yields: % 4.37/1.81 | (75) all_23_0_9 = all_18_0_7 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_2_2, all_12_0_4, all_18_0_7 and discharging atoms h(all_0_2_2) = all_18_0_7, h(all_0_2_2) = all_12_0_4, yields: % 4.37/1.81 | (76) all_18_0_7 = all_12_0_4 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (17) with all_0_2_2, all_9_0_3, all_27_0_15 and discharging atoms h(all_0_2_2) = all_27_0_15, h(all_0_2_2) = all_9_0_3, yields: % 4.37/1.81 | (77) all_27_0_15 = all_9_0_3 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (20) with all_0_1_1, all_0_1_1, all_29_2_20, all_0_2_2 and discharging atoms op1(all_0_1_1, all_0_1_1) = all_29_2_20, op1(all_0_1_1, all_0_1_1) = all_0_2_2, yields: % 4.37/1.81 | (78) all_29_2_20 = all_0_2_2 % 4.37/1.81 | % 4.37/1.81 | Instantiating formula (20) with all_0_2_2, all_0_1_1, all_25_2_14, all_0_0_0 and discharging atoms op1(all_0_2_2, all_0_1_1) = all_25_2_14, op1(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.37/1.81 | (79) all_25_2_14 = all_0_0_0 % 4.37/1.81 | % 4.44/1.81 | Instantiating formula (20) with all_0_2_2, all_0_2_2, all_23_2_11, all_0_1_1 and discharging atoms op1(all_0_2_2, all_0_2_2) = all_23_2_11, op1(all_0_2_2, all_0_2_2) = all_0_1_1, yields: % 4.44/1.81 | (80) all_23_2_11 = all_0_1_1 % 4.44/1.81 | % 4.44/1.81 | Combining equations (70,73) yields a new equation: % 4.44/1.81 | (81) all_20_0_8 = all_14_0_5 % 4.44/1.81 | % 4.44/1.81 | Simplifying 81 yields: % 4.44/1.81 | (82) all_20_0_8 = all_14_0_5 % 4.44/1.81 | % 4.44/1.81 | Combining equations (74,77) yields a new equation: % 4.44/1.81 | (83) all_23_0_9 = all_9_0_3 % 4.44/1.81 | % 4.44/1.81 | Simplifying 83 yields: % 4.44/1.81 | (84) all_23_0_9 = all_9_0_3 % 4.44/1.81 | % 4.44/1.81 | Combining equations (71,72) yields a new equation: % 4.44/1.81 | (85) all_20_0_8 = all_16_0_6 % 4.44/1.81 | % 4.44/1.81 | Simplifying 85 yields: % 4.44/1.81 | (86) all_20_0_8 = all_16_0_6 % 4.44/1.81 | % 4.44/1.81 | Combining equations (75,84) yields a new equation: % 4.44/1.81 | (87) all_18_0_7 = all_9_0_3 % 4.44/1.81 | % 4.44/1.81 | Simplifying 87 yields: % 4.44/1.81 | (88) all_18_0_7 = all_9_0_3 % 4.44/1.81 | % 4.44/1.81 | Combining equations (82,86) yields a new equation: % 4.44/1.81 | (89) all_16_0_6 = all_14_0_5 % 4.44/1.81 | % 4.44/1.81 | Combining equations (76,88) yields a new equation: % 4.44/1.81 | (90) all_12_0_4 = all_9_0_3 % 4.44/1.81 | % 4.44/1.81 | Simplifying 90 yields: % 4.44/1.81 | (91) all_12_0_4 = all_9_0_3 % 4.44/1.81 | % 4.44/1.81 | Combining equations (89,86) yields a new equation: % 4.44/1.81 | (82) all_20_0_8 = all_14_0_5 % 4.44/1.81 | % 4.44/1.81 | From (88) and (43) follows: % 4.44/1.81 | (93) j(all_9_0_3) = all_0_2_2 % 4.44/1.81 | % 4.44/1.81 | From (89) and (40) follows: % 4.44/1.81 | (94) j(all_14_0_5) = all_0_1_1 % 4.44/1.81 | % 4.44/1.81 | From (78) and (66) follows: % 4.46/1.81 | (95) h(all_0_2_2) = all_29_1_19 % 4.46/1.81 | % 4.46/1.81 | From (80) and (51) follows: % 4.46/1.81 | (96) h(all_0_1_1) = all_23_1_10 % 4.46/1.81 | % 4.46/1.81 | From (89) and (41) follows: % 4.46/1.82 | (37) h(all_0_1_1) = all_14_0_5 % 4.46/1.82 | % 4.46/1.82 | From (91) and (34) follows: % 4.46/1.82 | (29) h(all_0_2_2) = all_9_0_3 % 4.46/1.82 | % 4.46/1.82 | From (82)(73) and (68) follows: % 4.46/1.82 | (99) op2(all_14_0_5, all_14_0_5) = all_29_1_19 % 4.46/1.82 | % 4.46/1.82 | From (84) and (53) follows: % 4.46/1.82 | (100) op2(all_9_0_3, all_9_0_3) = all_23_1_10 % 4.46/1.82 | % 4.46/1.82 | From (78) and (69) follows: % 4.46/1.82 | (9) op1(all_0_1_1, all_0_1_1) = all_0_2_2 % 4.46/1.82 | % 4.46/1.82 | From (79) and (59) follows: % 4.46/1.82 | (11) op1(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.46/1.82 | % 4.46/1.82 | From (91) and (35) follows: % 4.46/1.82 | (103) sorti2(all_9_0_3) % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (17) with all_0_1_1, all_23_1_10, all_14_0_5 and discharging atoms h(all_0_1_1) = all_23_1_10, h(all_0_1_1) = all_14_0_5, yields: % 4.46/1.82 | (104) all_23_1_10 = all_14_0_5 % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (17) with all_0_2_2, all_29_1_19, all_9_0_3 and discharging atoms h(all_0_2_2) = all_29_1_19, h(all_0_2_2) = all_9_0_3, yields: % 4.46/1.82 | (105) all_29_1_19 = all_9_0_3 % 4.46/1.82 | % 4.46/1.82 | From (105) and (99) follows: % 4.46/1.82 | (106) op2(all_14_0_5, all_14_0_5) = all_9_0_3 % 4.46/1.82 | % 4.46/1.82 | From (104) and (100) follows: % 4.46/1.82 | (107) op2(all_9_0_3, all_9_0_3) = all_14_0_5 % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (6) with all_14_0_5 and discharging atoms sorti2(all_14_0_5), yields: % 4.46/1.82 | (108) ? [v0] : (j(all_14_0_5) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_14_0_5, v1) = v2 & op1(v0, v4) = v3))) % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (15) with all_14_0_5, all_9_0_3 and discharging atoms op2(all_14_0_5, all_14_0_5) = all_9_0_3, op2(all_9_0_3, all_9_0_3) = all_14_0_5, sorti2(all_14_0_5), sorti2(all_9_0_3), yields: % 4.46/1.82 | (109) op2(all_9_0_3, all_14_0_5) = all_9_0_3 % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (6) with all_9_0_3 and discharging atoms sorti2(all_9_0_3), yields: % 4.46/1.82 | (110) ? [v0] : (j(all_9_0_3) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_9_0_3, v1) = v2 & op1(v0, v4) = v3))) % 4.46/1.82 | % 4.46/1.82 | Instantiating (108) with all_54_0_27 yields: % 4.46/1.82 | (111) j(all_14_0_5) = all_54_0_27 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_14_0_5, v0) = v1 & op1(all_54_0_27, v3) = v2)) % 4.46/1.82 | % 4.46/1.82 | Applying alpha-rule on (111) yields: % 4.46/1.82 | (112) j(all_14_0_5) = all_54_0_27 % 4.46/1.82 | (113) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_14_0_5, v0) = v1 & op1(all_54_0_27, v3) = v2)) % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (113) with all_14_0_5 and discharging atoms sorti2(all_14_0_5), yields: % 4.46/1.82 | (114) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_14_0_5) = v2 & op2(all_14_0_5, all_14_0_5) = v0 & op1(all_54_0_27, v2) = v1) % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (113) with all_9_0_3 and discharging atoms sorti2(all_9_0_3), yields: % 4.46/1.82 | (115) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_9_0_3) = v2 & op2(all_14_0_5, all_9_0_3) = v0 & op1(all_54_0_27, v2) = v1) % 4.46/1.82 | % 4.46/1.82 | Instantiating (110) with all_59_0_31 yields: % 4.46/1.82 | (116) j(all_9_0_3) = all_59_0_31 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_9_0_3, v0) = v1 & op1(all_59_0_31, v3) = v2)) % 4.46/1.82 | % 4.46/1.82 | Applying alpha-rule on (116) yields: % 4.46/1.82 | (117) j(all_9_0_3) = all_59_0_31 % 4.46/1.82 | (118) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_9_0_3, v0) = v1 & op1(all_59_0_31, v3) = v2)) % 4.46/1.82 | % 4.46/1.82 | Instantiating formula (118) with all_14_0_5 and discharging atoms sorti2(all_14_0_5), yields: % 4.46/1.82 | (119) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_14_0_5) = v2 & op2(all_9_0_3, all_14_0_5) = v0 & op1(all_59_0_31, v2) = v1) % 4.46/1.82 | % 4.46/1.83 | Instantiating formula (118) with all_9_0_3 and discharging atoms sorti2(all_9_0_3), yields: % 4.46/1.83 | (120) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_9_0_3) = v2 & op2(all_9_0_3, all_9_0_3) = v0 & op1(all_59_0_31, v2) = v1) % 4.46/1.83 | % 4.46/1.83 | Instantiating (115) with all_68_0_41, all_68_1_42, all_68_2_43 yields: % 4.46/1.83 | (121) j(all_68_2_43) = all_68_1_42 & j(all_9_0_3) = all_68_0_41 & op2(all_14_0_5, all_9_0_3) = all_68_2_43 & op1(all_54_0_27, all_68_0_41) = all_68_1_42 % 4.46/1.83 | % 4.46/1.83 | Applying alpha-rule on (121) yields: % 4.46/1.83 | (122) j(all_68_2_43) = all_68_1_42 % 4.46/1.83 | (123) j(all_9_0_3) = all_68_0_41 % 4.46/1.83 | (124) op2(all_14_0_5, all_9_0_3) = all_68_2_43 % 4.46/1.83 | (125) op1(all_54_0_27, all_68_0_41) = all_68_1_42 % 4.46/1.83 | % 4.46/1.83 | Instantiating (114) with all_70_0_44, all_70_1_45, all_70_2_46 yields: % 4.46/1.83 | (126) j(all_70_2_46) = all_70_1_45 & j(all_14_0_5) = all_70_0_44 & op2(all_14_0_5, all_14_0_5) = all_70_2_46 & op1(all_54_0_27, all_70_0_44) = all_70_1_45 % 4.46/1.83 | % 4.46/1.83 | Applying alpha-rule on (126) yields: % 4.46/1.83 | (127) j(all_70_2_46) = all_70_1_45 % 4.46/1.83 | (128) j(all_14_0_5) = all_70_0_44 % 4.46/1.83 | (129) op2(all_14_0_5, all_14_0_5) = all_70_2_46 % 4.46/1.83 | (130) op1(all_54_0_27, all_70_0_44) = all_70_1_45 % 4.46/1.83 | % 4.46/1.83 | Instantiating (120) with all_72_0_47, all_72_1_48, all_72_2_49 yields: % 4.46/1.83 | (131) j(all_72_2_49) = all_72_1_48 & j(all_9_0_3) = all_72_0_47 & op2(all_9_0_3, all_9_0_3) = all_72_2_49 & op1(all_59_0_31, all_72_0_47) = all_72_1_48 % 4.46/1.83 | % 4.46/1.83 | Applying alpha-rule on (131) yields: % 4.46/1.83 | (132) j(all_72_2_49) = all_72_1_48 % 4.46/1.83 | (133) j(all_9_0_3) = all_72_0_47 % 4.46/1.83 | (134) op2(all_9_0_3, all_9_0_3) = all_72_2_49 % 4.46/1.83 | (135) op1(all_59_0_31, all_72_0_47) = all_72_1_48 % 4.46/1.83 | % 4.46/1.83 | Instantiating (119) with all_74_0_50, all_74_1_51, all_74_2_52 yields: % 4.46/1.83 | (136) j(all_74_2_52) = all_74_1_51 & j(all_14_0_5) = all_74_0_50 & op2(all_9_0_3, all_14_0_5) = all_74_2_52 & op1(all_59_0_31, all_74_0_50) = all_74_1_51 % 4.46/1.83 | % 4.46/1.83 | Applying alpha-rule on (136) yields: % 4.46/1.83 | (137) j(all_74_2_52) = all_74_1_51 % 4.46/1.83 | (138) j(all_14_0_5) = all_74_0_50 % 4.46/1.83 | (139) op2(all_9_0_3, all_14_0_5) = all_74_2_52 % 4.46/1.83 | (140) op1(all_59_0_31, all_74_0_50) = all_74_1_51 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (12) with all_14_0_5, all_70_0_44, all_0_1_1 and discharging atoms j(all_14_0_5) = all_70_0_44, j(all_14_0_5) = all_0_1_1, yields: % 4.46/1.83 | (141) all_70_0_44 = all_0_1_1 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (12) with all_14_0_5, all_70_0_44, all_74_0_50 and discharging atoms j(all_14_0_5) = all_74_0_50, j(all_14_0_5) = all_70_0_44, yields: % 4.46/1.83 | (142) all_74_0_50 = all_70_0_44 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (12) with all_14_0_5, all_54_0_27, all_74_0_50 and discharging atoms j(all_14_0_5) = all_74_0_50, j(all_14_0_5) = all_54_0_27, yields: % 4.46/1.83 | (143) all_74_0_50 = all_54_0_27 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (12) with all_9_0_3, all_72_0_47, all_0_2_2 and discharging atoms j(all_9_0_3) = all_72_0_47, j(all_9_0_3) = all_0_2_2, yields: % 4.46/1.83 | (144) all_72_0_47 = all_0_2_2 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (12) with all_9_0_3, all_68_0_41, all_72_0_47 and discharging atoms j(all_9_0_3) = all_72_0_47, j(all_9_0_3) = all_68_0_41, yields: % 4.46/1.83 | (145) all_72_0_47 = all_68_0_41 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (12) with all_9_0_3, all_59_0_31, all_68_0_41 and discharging atoms j(all_9_0_3) = all_68_0_41, j(all_9_0_3) = all_59_0_31, yields: % 4.46/1.83 | (146) all_68_0_41 = all_59_0_31 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (21) with all_14_0_5, all_14_0_5, all_70_2_46, all_9_0_3 and discharging atoms op2(all_14_0_5, all_14_0_5) = all_70_2_46, op2(all_14_0_5, all_14_0_5) = all_9_0_3, yields: % 4.46/1.83 | (147) all_70_2_46 = all_9_0_3 % 4.46/1.83 | % 4.46/1.83 | Instantiating formula (21) with all_9_0_3, all_14_0_5, all_9_0_3, all_74_2_52 and discharging atoms op2(all_9_0_3, all_14_0_5) = all_74_2_52, op2(all_9_0_3, all_14_0_5) = all_9_0_3, yields: % 4.46/1.83 | (148) all_74_2_52 = all_9_0_3 % 4.46/1.83 | % 4.46/1.83 | Combining equations (142,143) yields a new equation: % 4.46/1.83 | (149) all_70_0_44 = all_54_0_27 % 4.46/1.83 | % 4.46/1.83 | Simplifying 149 yields: % 4.46/1.83 | (150) all_70_0_44 = all_54_0_27 % 4.46/1.83 | % 4.46/1.83 | Combining equations (145,144) yields a new equation: % 4.46/1.83 | (151) all_68_0_41 = all_0_2_2 % 4.46/1.84 | % 4.46/1.84 | Simplifying 151 yields: % 4.46/1.84 | (152) all_68_0_41 = all_0_2_2 % 4.46/1.84 | % 4.46/1.84 | Combining equations (141,150) yields a new equation: % 4.46/1.84 | (153) all_54_0_27 = all_0_1_1 % 4.46/1.84 | % 4.46/1.84 | Combining equations (146,152) yields a new equation: % 4.46/1.84 | (154) all_59_0_31 = all_0_2_2 % 4.46/1.84 | % 4.46/1.84 | Simplifying 154 yields: % 4.46/1.84 | (155) all_59_0_31 = all_0_2_2 % 4.46/1.84 | % 4.46/1.84 | Combining equations (153,150) yields a new equation: % 4.46/1.84 | (141) all_70_0_44 = all_0_1_1 % 4.46/1.84 | % 4.46/1.84 | Combining equations (153,143) yields a new equation: % 4.46/1.84 | (157) all_74_0_50 = all_0_1_1 % 4.46/1.84 | % 4.46/1.84 | From (148) and (137) follows: % 4.46/1.84 | (158) j(all_9_0_3) = all_74_1_51 % 4.46/1.84 | % 4.46/1.84 | From (147) and (127) follows: % 4.46/1.84 | (159) j(all_9_0_3) = all_70_1_45 % 4.46/1.84 | % 4.46/1.84 | From (155)(157) and (140) follows: % 4.46/1.84 | (160) op1(all_0_2_2, all_0_1_1) = all_74_1_51 % 4.46/1.84 | % 4.46/1.84 | From (153)(141) and (130) follows: % 4.46/1.84 | (161) op1(all_0_1_1, all_0_1_1) = all_70_1_45 % 4.46/1.84 | % 4.46/1.84 | Instantiating formula (12) with all_9_0_3, all_70_1_45, all_74_1_51 and discharging atoms j(all_9_0_3) = all_74_1_51, j(all_9_0_3) = all_70_1_45, yields: % 4.46/1.84 | (162) all_74_1_51 = all_70_1_45 % 4.46/1.84 | % 4.46/1.84 | Instantiating formula (20) with all_0_1_1, all_0_1_1, all_70_1_45, all_0_2_2 and discharging atoms op1(all_0_1_1, all_0_1_1) = all_70_1_45, op1(all_0_1_1, all_0_1_1) = all_0_2_2, yields: % 4.46/1.84 | (163) all_70_1_45 = all_0_2_2 % 4.46/1.84 | % 4.46/1.84 | Instantiating formula (20) with all_0_2_2, all_0_1_1, all_74_1_51, all_0_0_0 and discharging atoms op1(all_0_2_2, all_0_1_1) = all_74_1_51, op1(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.46/1.84 | (164) all_74_1_51 = all_0_0_0 % 4.46/1.84 | % 4.46/1.84 | Combining equations (162,164) yields a new equation: % 4.46/1.84 | (165) all_70_1_45 = all_0_0_0 % 4.46/1.84 | % 4.46/1.84 | Simplifying 165 yields: % 4.46/1.84 | (166) all_70_1_45 = all_0_0_0 % 4.46/1.84 | % 4.46/1.84 | Combining equations (163,166) yields a new equation: % 4.46/1.84 | (167) all_0_0_0 = all_0_2_2 % 4.46/1.84 | % 4.46/1.84 | Equations (167) can reduce 3 to: % 4.46/1.84 | (168) $false % 4.46/1.84 | % 4.46/1.84 |-The branch is then unsatisfiable % 4.46/1.84 % SZS output end Proof for theBenchmark % 4.46/1.84 % 4.46/1.84 1255ms %------------------------------------------------------------------------------