%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG177+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 15:37:05 EDT 2022 % Result : Theorem 2.65s 1.29s % Output : Proof 4.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG177+1 : TPTP v8.1.0. Released v2.7.0. % 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.32 % Computer : n018.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Thu Jun 9 02:29:07 EDT 2022 % 0.12/0.32 % CPUTime : % 0.58/0.57 ____ _ % 0.58/0.57 ___ / __ \_____(_)___ ________ __________ % 0.58/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.57 % 0.58/0.57 A Theorem Prover for First-Order Logic % 0.58/0.57 (ePrincess v.1.0) % 0.58/0.57 % 0.58/0.57 (c) Philipp Rümmer, 2009-2015 % 0.58/0.57 (c) Peter Backeman, 2014-2015 % 0.58/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.57 Bug reports to peter@backeman.se % 0.58/0.57 % 0.58/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.57 % 0.58/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.87 Prover 0: Preprocessing ... % 1.82/1.03 Prover 0: Constructing countermodel ... % 2.65/1.28 Prover 0: proved (665ms) % 2.65/1.29 % 2.65/1.29 No countermodel exists, formula is valid % 2.65/1.29 % SZS status Theorem for theBenchmark % 2.65/1.29 % 2.65/1.29 Generating proof ... found it (size 82) % 3.99/1.62 % 3.99/1.62 % SZS output start Proof for theBenchmark % 3.99/1.62 Assumed formulas after preprocessing and simplification: % 3.99/1.62 | (0) ? [v0] : (sorti1(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (op2(v4, v3) = v2) | ~ (op2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (op1(v4, v3) = v2) | ~ (op1(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (j(v3) = v2) | ~ (j(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (h(v3) = v2) | ~ (h(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (op2(v1, v2) = v3) | ~ sorti2(v2) | ~ sorti2(v1) | sorti2(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (op1(v1, v2) = v3) | ~ sorti1(v2) | ~ sorti1(v1) | sorti1(v3)) & ! [v1] : ( ~ (op1(v0, v1) = v1) | ~ sorti1(v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & h(v2) = v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & sorti1(v2))) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & ! [v3] : ( ~ sorti2(v3) | ? [v4] : ? [v5] : ? [v6] : (j(v4) = v5 & j(v3) = v6 & op2(v1, v3) = v4 & op1(v2, v6) = v5)))) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (op2(v1, v2) = v2 & sorti2(v2))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (j(v2) = v1 & h(v1) = v2)) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (h(v1) = v2 & sorti2(v2))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (h(v1) = v2 & ! [v3] : ( ~ sorti1(v3) | ? [v4] : ? [v5] : ? [v6] : (h(v4) = v5 & h(v3) = v6 & op2(v2, v6) = v5 & op1(v1, v3) = v4))))) % 3.99/1.65 | Instantiating (0) with all_0_0_0 yields: % 3.99/1.65 | (1) sorti1(all_0_0_0) & ! [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] : (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] : ( ~ (op1(all_0_0_0, v0) = v0) | ~ sorti1(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] : ( ~ sorti2(v0) | ? [v1] : (op2(v0, v1) = v1 & sorti2(v1))) & ! [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)))) % 3.99/1.66 | % 3.99/1.66 | Applying alpha-rule on (1) yields: % 3.99/1.66 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) % 3.99/1.66 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 3.99/1.66 | (4) sorti1(all_0_0_0) % 3.99/1.66 | (5) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) % 3.99/1.66 | (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)))) % 3.99/1.66 | (7) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (op2(v0, v1) = v1 & sorti2(v1))) % 3.99/1.66 | (8) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) % 3.99/1.66 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 3.99/1.66 | (10) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) % 3.99/1.66 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) % 3.99/1.66 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 3.99/1.66 | (13) ! [v0] : ( ~ (op1(all_0_0_0, v0) = v0) | ~ sorti1(v0)) % 3.99/1.66 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 3.99/1.66 | (15) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) % 3.99/1.66 | (16) ! [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)))) % 3.99/1.66 | % 3.99/1.66 | Instantiating formula (10) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 3.99/1.66 | (17) ? [v0] : (j(v0) = all_0_0_0 & h(all_0_0_0) = v0) % 3.99/1.66 | % 3.99/1.66 | Instantiating formula (15) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 3.99/1.66 | (18) ? [v0] : (h(all_0_0_0) = v0 & sorti2(v0)) % 3.99/1.66 | % 3.99/1.66 | Instantiating formula (16) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 3.99/1.66 | (19) ? [v0] : (h(all_0_0_0) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_0_0_0, v1) = v2))) % 3.99/1.66 | % 3.99/1.66 | Instantiating (19) with all_8_0_1 yields: % 3.99/1.66 | (20) h(all_0_0_0) = all_8_0_1 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_8_0_1, v3) = v2 & op1(all_0_0_0, v0) = v1)) % 3.99/1.66 | % 3.99/1.66 | Applying alpha-rule on (20) yields: % 3.99/1.66 | (21) h(all_0_0_0) = all_8_0_1 % 3.99/1.66 | (22) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_8_0_1, v3) = v2 & op1(all_0_0_0, v0) = v1)) % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 3.99/1.67 | (23) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_0_0) = v2 & op2(all_8_0_1, v2) = v1 & op1(all_0_0_0, all_0_0_0) = v0) % 3.99/1.67 | % 3.99/1.67 | Instantiating (18) with all_11_0_2 yields: % 3.99/1.67 | (24) h(all_0_0_0) = all_11_0_2 & sorti2(all_11_0_2) % 3.99/1.67 | % 3.99/1.67 | Applying alpha-rule on (24) yields: % 3.99/1.67 | (25) h(all_0_0_0) = all_11_0_2 % 3.99/1.67 | (26) sorti2(all_11_0_2) % 3.99/1.67 | % 3.99/1.67 | Instantiating (17) with all_13_0_3 yields: % 3.99/1.67 | (27) j(all_13_0_3) = all_0_0_0 & h(all_0_0_0) = all_13_0_3 % 3.99/1.67 | % 3.99/1.67 | Applying alpha-rule on (27) yields: % 3.99/1.67 | (28) j(all_13_0_3) = all_0_0_0 % 3.99/1.67 | (29) h(all_0_0_0) = all_13_0_3 % 3.99/1.67 | % 3.99/1.67 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields: % 3.99/1.67 | (30) h(all_15_2_6) = all_15_1_5 & h(all_0_0_0) = all_15_0_4 & op2(all_8_0_1, all_15_0_4) = all_15_1_5 & op1(all_0_0_0, all_0_0_0) = all_15_2_6 % 3.99/1.67 | % 3.99/1.67 | Applying alpha-rule on (30) yields: % 3.99/1.67 | (31) h(all_15_2_6) = all_15_1_5 % 3.99/1.67 | (32) h(all_0_0_0) = all_15_0_4 % 3.99/1.67 | (33) op2(all_8_0_1, all_15_0_4) = all_15_1_5 % 3.99/1.67 | (34) op1(all_0_0_0, all_0_0_0) = all_15_2_6 % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (12) with all_0_0_0, all_13_0_3, all_15_0_4 and discharging atoms h(all_0_0_0) = all_15_0_4, h(all_0_0_0) = all_13_0_3, yields: % 3.99/1.67 | (35) all_15_0_4 = all_13_0_3 % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (12) with all_0_0_0, all_11_0_2, all_15_0_4 and discharging atoms h(all_0_0_0) = all_15_0_4, h(all_0_0_0) = all_11_0_2, yields: % 3.99/1.67 | (36) all_15_0_4 = all_11_0_2 % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (12) with all_0_0_0, all_8_0_1, all_13_0_3 and discharging atoms h(all_0_0_0) = all_13_0_3, h(all_0_0_0) = all_8_0_1, yields: % 3.99/1.67 | (37) all_13_0_3 = all_8_0_1 % 3.99/1.67 | % 3.99/1.67 | Combining equations (35,36) yields a new equation: % 3.99/1.67 | (38) all_13_0_3 = all_11_0_2 % 3.99/1.67 | % 3.99/1.67 | Simplifying 38 yields: % 3.99/1.67 | (39) all_13_0_3 = all_11_0_2 % 3.99/1.67 | % 3.99/1.67 | Combining equations (37,39) yields a new equation: % 3.99/1.67 | (40) all_11_0_2 = all_8_0_1 % 3.99/1.67 | % 3.99/1.67 | Combining equations (40,39) yields a new equation: % 3.99/1.67 | (37) all_13_0_3 = all_8_0_1 % 3.99/1.67 | % 3.99/1.67 | Combining equations (40,36) yields a new equation: % 3.99/1.67 | (42) all_15_0_4 = all_8_0_1 % 3.99/1.67 | % 3.99/1.67 | From (37) and (28) follows: % 3.99/1.67 | (43) j(all_8_0_1) = all_0_0_0 % 3.99/1.67 | % 3.99/1.67 | From (42) and (33) follows: % 3.99/1.67 | (44) op2(all_8_0_1, all_8_0_1) = all_15_1_5 % 3.99/1.67 | % 3.99/1.67 | From (40) and (26) follows: % 3.99/1.67 | (45) sorti2(all_8_0_1) % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (2) with all_15_1_5, all_8_0_1, all_8_0_1 and discharging atoms op2(all_8_0_1, all_8_0_1) = all_15_1_5, sorti2(all_8_0_1), yields: % 3.99/1.67 | (46) sorti2(all_15_1_5) % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (6) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields: % 3.99/1.67 | (47) ? [v0] : (j(all_8_0_1) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_8_0_1, v1) = v2 & op1(v0, v4) = v3))) % 3.99/1.67 | % 3.99/1.67 | Instantiating formula (7) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields: % 3.99/1.67 | (48) ? [v0] : (op2(all_8_0_1, v0) = v0 & sorti2(v0)) % 3.99/1.67 | % 3.99/1.67 | Instantiating (48) with all_27_0_7 yields: % 3.99/1.67 | (49) op2(all_8_0_1, all_27_0_7) = all_27_0_7 & sorti2(all_27_0_7) % 3.99/1.67 | % 3.99/1.67 | Applying alpha-rule on (49) yields: % 3.99/1.67 | (50) op2(all_8_0_1, all_27_0_7) = all_27_0_7 % 3.99/1.67 | (51) sorti2(all_27_0_7) % 3.99/1.67 | % 3.99/1.67 | Instantiating (47) with all_29_0_8 yields: % 3.99/1.67 | (52) j(all_8_0_1) = all_29_0_8 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_8_0_1, v0) = v1 & op1(all_29_0_8, v3) = v2)) % 3.99/1.67 | % 3.99/1.67 | Applying alpha-rule on (52) yields: % 3.99/1.67 | (53) j(all_8_0_1) = all_29_0_8 % 3.99/1.67 | (54) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_8_0_1, v0) = v1 & op1(all_29_0_8, v3) = v2)) % 3.99/1.67 | % 3.99/1.68 | Instantiating formula (54) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields: % 3.99/1.68 | (55) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_8_0_1) = v2 & op2(all_8_0_1, all_8_0_1) = v0 & op1(all_29_0_8, v2) = v1) % 3.99/1.68 | % 3.99/1.68 | Instantiating (55) with all_32_0_9, all_32_1_10, all_32_2_11 yields: % 3.99/1.68 | (56) j(all_32_2_11) = all_32_1_10 & j(all_8_0_1) = all_32_0_9 & op2(all_8_0_1, all_8_0_1) = all_32_2_11 & op1(all_29_0_8, all_32_0_9) = all_32_1_10 % 3.99/1.68 | % 3.99/1.68 | Applying alpha-rule on (56) yields: % 3.99/1.68 | (57) j(all_32_2_11) = all_32_1_10 % 3.99/1.68 | (58) j(all_8_0_1) = all_32_0_9 % 3.99/1.68 | (59) op2(all_8_0_1, all_8_0_1) = all_32_2_11 % 3.99/1.68 | (60) op1(all_29_0_8, all_32_0_9) = all_32_1_10 % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (9) with all_8_0_1, all_32_0_9, all_0_0_0 and discharging atoms j(all_8_0_1) = all_32_0_9, j(all_8_0_1) = all_0_0_0, yields: % 3.99/1.68 | (61) all_32_0_9 = all_0_0_0 % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (9) with all_8_0_1, all_29_0_8, all_32_0_9 and discharging atoms j(all_8_0_1) = all_32_0_9, j(all_8_0_1) = all_29_0_8, yields: % 3.99/1.68 | (62) all_32_0_9 = all_29_0_8 % 3.99/1.68 | % 3.99/1.68 | Combining equations (61,62) yields a new equation: % 3.99/1.68 | (63) all_29_0_8 = all_0_0_0 % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (54) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields: % 3.99/1.68 | (64) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_27_0_7) = v2 & op2(all_8_0_1, all_27_0_7) = v0 & op1(all_29_0_8, v2) = v1) % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (5) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields: % 3.99/1.68 | (65) ? [v0] : (j(all_27_0_7) = v0 & h(v0) = all_27_0_7) % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (8) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields: % 3.99/1.68 | (66) ? [v0] : (j(all_27_0_7) = v0 & sorti1(v0)) % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (6) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields: % 3.99/1.68 | (67) ? [v0] : (j(all_27_0_7) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_27_0_7, v1) = v2 & op1(v0, v4) = v3))) % 3.99/1.68 | % 3.99/1.68 | Instantiating formula (6) with all_15_1_5 and discharging atoms sorti2(all_15_1_5), yields: % 3.99/1.68 | (68) ? [v0] : (j(all_15_1_5) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_15_1_5, v1) = v2 & op1(v0, v4) = v3))) % 3.99/1.68 | % 3.99/1.68 | Instantiating (68) with all_56_0_20 yields: % 3.99/1.68 | (69) j(all_15_1_5) = all_56_0_20 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_15_1_5, v0) = v1 & op1(all_56_0_20, v3) = v2)) % 3.99/1.68 | % 3.99/1.68 | Applying alpha-rule on (69) yields: % 3.99/1.68 | (70) j(all_15_1_5) = all_56_0_20 % 4.18/1.68 | (71) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_15_1_5, v0) = v1 & op1(all_56_0_20, v3) = v2)) % 4.18/1.68 | % 4.18/1.68 | Instantiating formula (71) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields: % 4.18/1.68 | (72) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_27_0_7) = v2 & op2(all_15_1_5, all_27_0_7) = v0 & op1(all_56_0_20, v2) = v1) % 4.18/1.68 | % 4.18/1.68 | Instantiating (67) with all_61_0_22 yields: % 4.18/1.68 | (73) j(all_27_0_7) = all_61_0_22 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_27_0_7, v0) = v1 & op1(all_61_0_22, v3) = v2)) % 4.18/1.68 | % 4.18/1.68 | Applying alpha-rule on (73) yields: % 4.18/1.68 | (74) j(all_27_0_7) = all_61_0_22 % 4.18/1.68 | (75) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_27_0_7, v0) = v1 & op1(all_61_0_22, v3) = v2)) % 4.18/1.68 | % 4.18/1.68 | Instantiating formula (75) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields: % 4.18/1.68 | (76) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_27_0_7) = v2 & op2(all_27_0_7, all_27_0_7) = v0 & op1(all_61_0_22, v2) = v1) % 4.18/1.68 | % 4.18/1.68 | Instantiating (65) with all_64_0_23 yields: % 4.18/1.68 | (77) j(all_27_0_7) = all_64_0_23 & h(all_64_0_23) = all_27_0_7 % 4.18/1.68 | % 4.18/1.68 | Applying alpha-rule on (77) yields: % 4.18/1.68 | (78) j(all_27_0_7) = all_64_0_23 % 4.18/1.68 | (79) h(all_64_0_23) = all_27_0_7 % 4.18/1.68 | % 4.18/1.68 | Instantiating (64) with all_66_0_24, all_66_1_25, all_66_2_26 yields: % 4.18/1.68 | (80) j(all_66_2_26) = all_66_1_25 & j(all_27_0_7) = all_66_0_24 & op2(all_8_0_1, all_27_0_7) = all_66_2_26 & op1(all_29_0_8, all_66_0_24) = all_66_1_25 % 4.18/1.68 | % 4.18/1.68 | Applying alpha-rule on (80) yields: % 4.18/1.68 | (81) j(all_66_2_26) = all_66_1_25 % 4.18/1.68 | (82) j(all_27_0_7) = all_66_0_24 % 4.18/1.68 | (83) op2(all_8_0_1, all_27_0_7) = all_66_2_26 % 4.18/1.69 | (84) op1(all_29_0_8, all_66_0_24) = all_66_1_25 % 4.18/1.69 | % 4.18/1.69 | Instantiating (66) with all_68_0_27 yields: % 4.18/1.69 | (85) j(all_27_0_7) = all_68_0_27 & sorti1(all_68_0_27) % 4.18/1.69 | % 4.18/1.69 | Applying alpha-rule on (85) yields: % 4.18/1.69 | (86) j(all_27_0_7) = all_68_0_27 % 4.18/1.69 | (87) sorti1(all_68_0_27) % 4.18/1.69 | % 4.18/1.69 | Instantiating (72) with all_78_0_40, all_78_1_41, all_78_2_42 yields: % 4.18/1.69 | (88) j(all_78_2_42) = all_78_1_41 & j(all_27_0_7) = all_78_0_40 & op2(all_15_1_5, all_27_0_7) = all_78_2_42 & op1(all_56_0_20, all_78_0_40) = all_78_1_41 % 4.18/1.69 | % 4.18/1.69 | Applying alpha-rule on (88) yields: % 4.18/1.69 | (89) j(all_78_2_42) = all_78_1_41 % 4.18/1.69 | (90) j(all_27_0_7) = all_78_0_40 % 4.18/1.69 | (91) op2(all_15_1_5, all_27_0_7) = all_78_2_42 % 4.18/1.69 | (92) op1(all_56_0_20, all_78_0_40) = all_78_1_41 % 4.18/1.69 | % 4.18/1.69 | Instantiating (76) with all_84_0_49, all_84_1_50, all_84_2_51 yields: % 4.18/1.69 | (93) j(all_84_2_51) = all_84_1_50 & j(all_27_0_7) = all_84_0_49 & op2(all_27_0_7, all_27_0_7) = all_84_2_51 & op1(all_61_0_22, all_84_0_49) = all_84_1_50 % 4.18/1.69 | % 4.18/1.69 | Applying alpha-rule on (93) yields: % 4.18/1.69 | (94) j(all_84_2_51) = all_84_1_50 % 4.18/1.69 | (95) j(all_27_0_7) = all_84_0_49 % 4.18/1.69 | (96) op2(all_27_0_7, all_27_0_7) = all_84_2_51 % 4.18/1.69 | (97) op1(all_61_0_22, all_84_0_49) = all_84_1_50 % 4.18/1.69 | % 4.18/1.69 | From (63) and (84) follows: % 4.18/1.69 | (98) op1(all_0_0_0, all_66_0_24) = all_66_1_25 % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (9) with all_27_0_7, all_78_0_40, all_84_0_49 and discharging atoms j(all_27_0_7) = all_84_0_49, j(all_27_0_7) = all_78_0_40, yields: % 4.18/1.69 | (99) all_84_0_49 = all_78_0_40 % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (9) with all_27_0_7, all_66_0_24, all_78_0_40 and discharging atoms j(all_27_0_7) = all_78_0_40, j(all_27_0_7) = all_66_0_24, yields: % 4.18/1.69 | (100) all_78_0_40 = all_66_0_24 % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (9) with all_27_0_7, all_66_0_24, all_68_0_27 and discharging atoms j(all_27_0_7) = all_68_0_27, j(all_27_0_7) = all_66_0_24, yields: % 4.18/1.69 | (101) all_68_0_27 = all_66_0_24 % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (9) with all_27_0_7, all_64_0_23, all_84_0_49 and discharging atoms j(all_27_0_7) = all_84_0_49, j(all_27_0_7) = all_64_0_23, yields: % 4.18/1.69 | (102) all_84_0_49 = all_64_0_23 % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (9) with all_27_0_7, all_61_0_22, all_68_0_27 and discharging atoms j(all_27_0_7) = all_68_0_27, j(all_27_0_7) = all_61_0_22, yields: % 4.18/1.69 | (103) all_68_0_27 = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (3) with all_8_0_1, all_27_0_7, all_66_2_26, all_27_0_7 and discharging atoms op2(all_8_0_1, all_27_0_7) = all_66_2_26, op2(all_8_0_1, all_27_0_7) = all_27_0_7, yields: % 4.18/1.69 | (104) all_66_2_26 = all_27_0_7 % 4.18/1.69 | % 4.18/1.69 | Combining equations (99,102) yields a new equation: % 4.18/1.69 | (105) all_78_0_40 = all_64_0_23 % 4.18/1.69 | % 4.18/1.69 | Simplifying 105 yields: % 4.18/1.69 | (106) all_78_0_40 = all_64_0_23 % 4.18/1.69 | % 4.18/1.69 | Combining equations (100,106) yields a new equation: % 4.18/1.69 | (107) all_66_0_24 = all_64_0_23 % 4.18/1.69 | % 4.18/1.69 | Simplifying 107 yields: % 4.18/1.69 | (108) all_66_0_24 = all_64_0_23 % 4.18/1.69 | % 4.18/1.69 | Combining equations (101,103) yields a new equation: % 4.18/1.69 | (109) all_66_0_24 = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | Simplifying 109 yields: % 4.18/1.69 | (110) all_66_0_24 = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | Combining equations (110,108) yields a new equation: % 4.18/1.69 | (111) all_64_0_23 = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | Combining equations (111,108) yields a new equation: % 4.18/1.69 | (110) all_66_0_24 = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | From (104) and (81) follows: % 4.18/1.69 | (113) j(all_27_0_7) = all_66_1_25 % 4.18/1.69 | % 4.18/1.69 | From (111) and (78) follows: % 4.18/1.69 | (74) j(all_27_0_7) = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | From (110) and (98) follows: % 4.18/1.69 | (115) op1(all_0_0_0, all_61_0_22) = all_66_1_25 % 4.18/1.69 | % 4.18/1.69 | From (103) and (87) follows: % 4.18/1.69 | (116) sorti1(all_61_0_22) % 4.18/1.69 | % 4.18/1.69 | Instantiating formula (9) with all_27_0_7, all_66_1_25, all_61_0_22 and discharging atoms j(all_27_0_7) = all_66_1_25, j(all_27_0_7) = all_61_0_22, yields: % 4.18/1.69 | (117) all_66_1_25 = all_61_0_22 % 4.18/1.69 | % 4.18/1.69 | From (117) and (115) follows: % 4.18/1.70 | (118) op1(all_0_0_0, all_61_0_22) = all_61_0_22 % 4.18/1.70 | % 4.18/1.70 | Instantiating formula (13) with all_61_0_22 and discharging atoms op1(all_0_0_0, all_61_0_22) = all_61_0_22, sorti1(all_61_0_22), yields: % 4.18/1.70 | (119) $false % 4.18/1.70 | % 4.18/1.70 |-The branch is then unsatisfiable % 4.18/1.70 % SZS output end Proof for theBenchmark % 4.18/1.70 % 4.18/1.70 1114ms 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