%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG069+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 15:34:13 EDT 2022 % Result : Theorem 2.17s 1.12s % Output : Proof 3.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.08 % Problem : ALG069+1 : TPTP v8.1.0. Released v2.7.0. % 0.02/0.08 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.27 % Computer : n032.cluster.edu % 0.08/0.27 % Model : x86_64 x86_64 % 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.27 % Memory : 8042.1875MB % 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.27 % CPULimit : 300 % 0.08/0.27 % WCLimit : 600 % 0.08/0.27 % DateTime : Wed Jun 8 16:46:06 EDT 2022 % 0.08/0.27 % CPUTime : % 0.12/0.46 ____ _ % 0.12/0.46 ___ / __ \_____(_)___ ________ __________ % 0.12/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.12/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.12/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.12/0.46 % 0.12/0.46 A Theorem Prover for First-Order Logic % 0.12/0.47 (ePrincess v.1.0) % 0.12/0.47 % 0.12/0.47 (c) Philipp Rümmer, 2009-2015 % 0.12/0.47 (c) Peter Backeman, 2014-2015 % 0.12/0.47 (contributions by Angelo Brillout, Peter Baumgartner) % 0.12/0.47 Free software under GNU Lesser General Public License (LGPL). % 0.12/0.47 Bug reports to peter@backeman.se % 0.12/0.47 % 0.12/0.47 For more information, visit http://user.uu.se/~petba168/breu/ % 0.12/0.47 % 0.12/0.47 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.12/0.51 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.10/0.73 Prover 0: Preprocessing ... % 1.44/0.88 Prover 0: Constructing countermodel ... % 2.17/1.12 Prover 0: proved (609ms) % 2.17/1.12 % 2.17/1.12 No countermodel exists, formula is valid % 2.17/1.12 % SZS status Theorem for theBenchmark % 2.17/1.12 % 2.17/1.12 Generating proof ... found it (size 90) % 3.23/1.46 % 3.23/1.46 % SZS output start Proof for theBenchmark % 3.23/1.46 Assumed formulas after preprocessing and simplification: % 3.50/1.47 | (0) ? [v0] : (sorti2(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] : ( ~ (op2(v1, v1) = v0) | ~ sorti2(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] : ( ~ 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)))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (op1(v2, v2) = v1 & sorti1(v2)))) % 3.51/1.50 | Instantiating (0) with all_0_0_0 yields: % 3.51/1.50 | (1) sorti2(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] : ( ~ (op2(v0, v0) = all_0_0_0) | ~ sorti2(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)))) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (op1(v1, v1) = v0 & sorti1(v1))) % 3.58/1.51 | % 3.58/1.51 | Applying alpha-rule on (1) yields: % 3.58/1.51 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) % 3.58/1.51 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 3.58/1.51 | (4) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) % 3.58/1.51 | (5) ! [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)))) % 3.58/1.51 | (6) sorti2(all_0_0_0) % 3.58/1.51 | (7) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) % 3.58/1.51 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 3.58/1.51 | (9) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) % 3.58/1.51 | (10) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (op1(v1, v1) = v0 & sorti1(v1))) % 3.58/1.51 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) % 3.58/1.51 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 3.58/1.51 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 3.58/1.51 | (14) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) % 3.58/1.51 | (15) ! [v0] : ( ~ (op2(v0, v0) = all_0_0_0) | ~ sorti2(v0)) % 3.58/1.51 | (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)))) % 3.58/1.51 | % 3.58/1.51 | Instantiating formula (4) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 3.58/1.52 | (17) ? [v0] : (j(all_0_0_0) = v0 & h(v0) = all_0_0_0) % 3.58/1.52 | % 3.58/1.52 | Instantiating formula (7) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 3.58/1.52 | (18) ? [v0] : (j(all_0_0_0) = v0 & sorti1(v0)) % 3.58/1.52 | % 3.58/1.52 | Instantiating formula (5) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 3.58/1.52 | (19) ? [v0] : (j(all_0_0_0) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_0_0, v1) = v2 & op1(v0, v4) = v3))) % 3.58/1.52 | % 3.58/1.52 | Instantiating (19) with all_8_0_1 yields: % 3.58/1.52 | (20) j(all_0_0_0) = all_8_0_1 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_0_0, v0) = v1 & op1(all_8_0_1, v3) = v2)) % 3.58/1.52 | % 3.58/1.52 | Applying alpha-rule on (20) yields: % 3.58/1.52 | (21) j(all_0_0_0) = all_8_0_1 % 3.58/1.52 | (22) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_0_0, v0) = v1 & op1(all_8_0_1, v3) = v2)) % 3.58/1.52 | % 3.58/1.52 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 3.58/1.52 | (23) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_0_0_0) = v2 & op2(all_0_0_0, all_0_0_0) = v0 & op1(all_8_0_1, v2) = v1) % 3.58/1.52 | % 3.58/1.52 | Instantiating (18) with all_11_0_2 yields: % 3.58/1.52 | (24) j(all_0_0_0) = all_11_0_2 & sorti1(all_11_0_2) % 3.58/1.52 | % 3.58/1.52 | Applying alpha-rule on (24) yields: % 3.58/1.52 | (25) j(all_0_0_0) = all_11_0_2 % 3.58/1.52 | (26) sorti1(all_11_0_2) % 3.58/1.52 | % 3.58/1.52 | Instantiating (17) with all_13_0_3 yields: % 3.58/1.52 | (27) j(all_0_0_0) = all_13_0_3 & h(all_13_0_3) = all_0_0_0 % 3.58/1.52 | % 3.58/1.52 | Applying alpha-rule on (27) yields: % 3.58/1.52 | (28) j(all_0_0_0) = all_13_0_3 % 3.58/1.52 | (29) h(all_13_0_3) = all_0_0_0 % 3.58/1.52 | % 3.58/1.52 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields: % 3.58/1.52 | (30) j(all_15_2_6) = all_15_1_5 & j(all_0_0_0) = all_15_0_4 & op2(all_0_0_0, all_0_0_0) = all_15_2_6 & op1(all_8_0_1, all_15_0_4) = all_15_1_5 % 3.58/1.52 | % 3.58/1.52 | Applying alpha-rule on (30) yields: % 3.58/1.52 | (31) j(all_15_2_6) = all_15_1_5 % 3.58/1.52 | (32) j(all_0_0_0) = all_15_0_4 % 3.58/1.52 | (33) op2(all_0_0_0, all_0_0_0) = all_15_2_6 % 3.58/1.52 | (34) op1(all_8_0_1, all_15_0_4) = all_15_1_5 % 3.58/1.52 | % 3.58/1.52 | Instantiating formula (8) with all_0_0_0, all_13_0_3, all_15_0_4 and discharging atoms j(all_0_0_0) = all_15_0_4, j(all_0_0_0) = all_13_0_3, yields: % 3.58/1.52 | (35) all_15_0_4 = all_13_0_3 % 3.58/1.52 | % 3.58/1.52 | Instantiating formula (8) with all_0_0_0, all_11_0_2, all_15_0_4 and discharging atoms j(all_0_0_0) = all_15_0_4, j(all_0_0_0) = all_11_0_2, yields: % 3.58/1.52 | (36) all_15_0_4 = all_11_0_2 % 3.58/1.52 | % 3.58/1.52 | Instantiating formula (8) with all_0_0_0, all_8_0_1, all_13_0_3 and discharging atoms j(all_0_0_0) = all_13_0_3, j(all_0_0_0) = all_8_0_1, yields: % 3.58/1.52 | (37) all_13_0_3 = all_8_0_1 % 3.58/1.52 | % 3.58/1.52 | Combining equations (35,36) yields a new equation: % 3.58/1.52 | (38) all_13_0_3 = all_11_0_2 % 3.58/1.52 | % 3.58/1.52 | Simplifying 38 yields: % 3.58/1.52 | (39) all_13_0_3 = all_11_0_2 % 3.58/1.52 | % 3.58/1.52 | Combining equations (37,39) yields a new equation: % 3.58/1.52 | (40) all_11_0_2 = all_8_0_1 % 3.58/1.52 | % 3.58/1.52 | Combining equations (40,39) yields a new equation: % 3.58/1.52 | (37) all_13_0_3 = all_8_0_1 % 3.58/1.52 | % 3.58/1.52 | Combining equations (40,36) yields a new equation: % 3.58/1.52 | (42) all_15_0_4 = all_8_0_1 % 3.58/1.52 | % 3.58/1.52 | From (37) and (29) follows: % 3.58/1.52 | (43) h(all_8_0_1) = all_0_0_0 % 3.58/1.52 | % 3.58/1.52 | From (42) and (34) follows: % 3.58/1.52 | (44) op1(all_8_0_1, all_8_0_1) = all_15_1_5 % 3.58/1.53 | % 3.58/1.53 | From (40) and (26) follows: % 3.58/1.53 | (45) sorti1(all_8_0_1) % 3.58/1.53 | % 3.58/1.53 | Instantiating formula (11) with all_15_1_5, all_8_0_1, all_8_0_1 and discharging atoms op1(all_8_0_1, all_8_0_1) = all_15_1_5, sorti1(all_8_0_1), yields: % 3.58/1.53 | (46) sorti1(all_15_1_5) % 3.58/1.53 | % 3.58/1.53 | Instantiating formula (16) with all_8_0_1 and discharging atoms sorti1(all_8_0_1), yields: % 3.58/1.53 | (47) ? [v0] : (h(all_8_0_1) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_8_0_1, v1) = v2))) % 3.58/1.53 | % 3.58/1.53 | Instantiating formula (10) with all_8_0_1 and discharging atoms sorti1(all_8_0_1), yields: % 3.58/1.53 | (48) ? [v0] : (op1(v0, v0) = all_8_0_1 & sorti1(v0)) % 3.58/1.53 | % 3.64/1.53 | Instantiating (48) with all_27_0_7 yields: % 3.64/1.53 | (49) op1(all_27_0_7, all_27_0_7) = all_8_0_1 & sorti1(all_27_0_7) % 3.64/1.53 | % 3.64/1.53 | Applying alpha-rule on (49) yields: % 3.64/1.53 | (50) op1(all_27_0_7, all_27_0_7) = all_8_0_1 % 3.64/1.53 | (51) sorti1(all_27_0_7) % 3.64/1.53 | % 3.64/1.53 | Instantiating (47) with all_29_0_8 yields: % 3.64/1.53 | (52) h(all_8_0_1) = all_29_0_8 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_29_0_8, v3) = v2 & op1(all_8_0_1, v0) = v1)) % 3.64/1.53 | % 3.64/1.53 | Applying alpha-rule on (52) yields: % 3.64/1.53 | (53) h(all_8_0_1) = all_29_0_8 % 3.64/1.53 | (54) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_29_0_8, v3) = v2 & op1(all_8_0_1, v0) = v1)) % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (54) with all_8_0_1 and discharging atoms sorti1(all_8_0_1), yields: % 3.64/1.53 | (55) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_8_0_1) = v2 & op2(all_29_0_8, v2) = v1 & op1(all_8_0_1, all_8_0_1) = v0) % 3.64/1.53 | % 3.64/1.53 | Instantiating (55) with all_32_0_9, all_32_1_10, all_32_2_11 yields: % 3.64/1.53 | (56) h(all_32_2_11) = all_32_1_10 & h(all_8_0_1) = all_32_0_9 & op2(all_29_0_8, all_32_0_9) = all_32_1_10 & op1(all_8_0_1, all_8_0_1) = all_32_2_11 % 3.64/1.53 | % 3.64/1.53 | Applying alpha-rule on (56) yields: % 3.64/1.53 | (57) h(all_32_2_11) = all_32_1_10 % 3.64/1.53 | (58) h(all_8_0_1) = all_32_0_9 % 3.64/1.53 | (59) op2(all_29_0_8, all_32_0_9) = all_32_1_10 % 3.64/1.53 | (60) op1(all_8_0_1, all_8_0_1) = all_32_2_11 % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (12) with all_8_0_1, all_32_0_9, all_0_0_0 and discharging atoms h(all_8_0_1) = all_32_0_9, h(all_8_0_1) = all_0_0_0, yields: % 3.64/1.53 | (61) all_32_0_9 = all_0_0_0 % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (12) with all_8_0_1, all_29_0_8, all_32_0_9 and discharging atoms h(all_8_0_1) = all_32_0_9, h(all_8_0_1) = all_29_0_8, yields: % 3.64/1.53 | (62) all_32_0_9 = all_29_0_8 % 3.64/1.53 | % 3.64/1.53 | Combining equations (61,62) yields a new equation: % 3.64/1.53 | (63) all_29_0_8 = all_0_0_0 % 3.64/1.53 | % 3.64/1.53 | From (63) and (53) follows: % 3.64/1.53 | (43) h(all_8_0_1) = all_0_0_0 % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (54) with all_27_0_7 and discharging atoms sorti1(all_27_0_7), yields: % 3.64/1.53 | (65) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_27_0_7) = v2 & op2(all_29_0_8, v2) = v1 & op1(all_8_0_1, all_27_0_7) = v0) % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (9) with all_27_0_7 and discharging atoms sorti1(all_27_0_7), yields: % 3.64/1.53 | (66) ? [v0] : (j(v0) = all_27_0_7 & h(all_27_0_7) = v0) % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (14) with all_27_0_7 and discharging atoms sorti1(all_27_0_7), yields: % 3.64/1.53 | (67) ? [v0] : (h(all_27_0_7) = v0 & sorti2(v0)) % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (16) with all_27_0_7 and discharging atoms sorti1(all_27_0_7), yields: % 3.64/1.53 | (68) ? [v0] : (h(all_27_0_7) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_27_0_7, v1) = v2))) % 3.64/1.53 | % 3.64/1.53 | Instantiating formula (16) with all_15_1_5 and discharging atoms sorti1(all_15_1_5), yields: % 3.64/1.53 | (69) ? [v0] : (h(all_15_1_5) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_15_1_5, v1) = v2))) % 3.64/1.54 | % 3.64/1.54 | Instantiating (68) with all_53_0_17 yields: % 3.64/1.54 | (70) h(all_27_0_7) = all_53_0_17 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_53_0_17, v3) = v2 & op1(all_27_0_7, v0) = v1)) % 3.64/1.54 | % 3.64/1.54 | Applying alpha-rule on (70) yields: % 3.64/1.54 | (71) h(all_27_0_7) = all_53_0_17 % 3.64/1.54 | (72) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_53_0_17, v3) = v2 & op1(all_27_0_7, v0) = v1)) % 3.64/1.54 | % 3.64/1.54 | Instantiating formula (72) with all_27_0_7 and discharging atoms sorti1(all_27_0_7), yields: % 3.64/1.54 | (73) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_27_0_7) = v2 & op2(all_53_0_17, v2) = v1 & op1(all_27_0_7, all_27_0_7) = v0) % 3.64/1.54 | % 3.64/1.54 | Instantiating formula (72) with all_8_0_1 and discharging atoms sorti1(all_8_0_1), yields: % 3.64/1.54 | (74) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_8_0_1) = v2 & op2(all_53_0_17, v2) = v1 & op1(all_27_0_7, all_8_0_1) = v0) % 3.64/1.54 | % 3.64/1.54 | Instantiating (69) with all_56_0_18 yields: % 3.64/1.54 | (75) h(all_15_1_5) = all_56_0_18 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_56_0_18, v3) = v2 & op1(all_15_1_5, v0) = v1)) % 3.64/1.54 | % 3.64/1.54 | Applying alpha-rule on (75) yields: % 3.64/1.54 | (76) h(all_15_1_5) = all_56_0_18 % 3.64/1.54 | (77) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_56_0_18, v3) = v2 & op1(all_15_1_5, v0) = v1)) % 3.64/1.54 | % 3.64/1.54 | Instantiating formula (77) with all_27_0_7 and discharging atoms sorti1(all_27_0_7), yields: % 3.64/1.54 | (78) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_27_0_7) = v2 & op2(all_56_0_18, v2) = v1 & op1(all_15_1_5, all_27_0_7) = v0) % 3.64/1.54 | % 3.64/1.54 | Instantiating formula (77) with all_8_0_1 and discharging atoms sorti1(all_8_0_1), yields: % 3.64/1.54 | (79) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_8_0_1) = v2 & op2(all_56_0_18, v2) = v1 & op1(all_15_1_5, all_8_0_1) = v0) % 3.64/1.54 | % 3.64/1.54 | Instantiating (67) with all_59_0_19 yields: % 3.64/1.54 | (80) h(all_27_0_7) = all_59_0_19 & sorti2(all_59_0_19) % 3.64/1.54 | % 3.64/1.54 | Applying alpha-rule on (80) yields: % 3.64/1.54 | (81) h(all_27_0_7) = all_59_0_19 % 3.64/1.54 | (82) sorti2(all_59_0_19) % 3.64/1.54 | % 3.64/1.54 | Instantiating (66) with all_61_0_20 yields: % 3.64/1.54 | (83) j(all_61_0_20) = all_27_0_7 & h(all_27_0_7) = all_61_0_20 % 3.64/1.54 | % 3.64/1.54 | Applying alpha-rule on (83) yields: % 3.64/1.54 | (84) j(all_61_0_20) = all_27_0_7 % 3.64/1.54 | (85) h(all_27_0_7) = all_61_0_20 % 3.64/1.54 | % 3.64/1.54 | Instantiating (65) with all_68_0_25, all_68_1_26, all_68_2_27 yields: % 3.64/1.54 | (86) h(all_68_2_27) = all_68_1_26 & h(all_27_0_7) = all_68_0_25 & op2(all_29_0_8, all_68_0_25) = all_68_1_26 & op1(all_8_0_1, all_27_0_7) = all_68_2_27 % 3.64/1.54 | % 3.64/1.54 | Applying alpha-rule on (86) yields: % 3.64/1.54 | (87) h(all_68_2_27) = all_68_1_26 % 3.64/1.54 | (88) h(all_27_0_7) = all_68_0_25 % 3.64/1.54 | (89) op2(all_29_0_8, all_68_0_25) = all_68_1_26 % 3.64/1.54 | (90) op1(all_8_0_1, all_27_0_7) = all_68_2_27 % 3.64/1.54 | % 3.64/1.54 | Instantiating (74) with all_70_0_28, all_70_1_29, all_70_2_30 yields: % 3.64/1.54 | (91) h(all_70_2_30) = all_70_1_29 & h(all_8_0_1) = all_70_0_28 & op2(all_53_0_17, all_70_0_28) = all_70_1_29 & op1(all_27_0_7, all_8_0_1) = all_70_2_30 % 3.64/1.54 | % 3.64/1.54 | Applying alpha-rule on (91) yields: % 3.64/1.54 | (92) h(all_70_2_30) = all_70_1_29 % 3.64/1.54 | (93) h(all_8_0_1) = all_70_0_28 % 3.64/1.54 | (94) op2(all_53_0_17, all_70_0_28) = all_70_1_29 % 3.64/1.54 | (95) op1(all_27_0_7, all_8_0_1) = all_70_2_30 % 3.64/1.55 | % 3.64/1.55 | Instantiating (73) with all_74_0_34, all_74_1_35, all_74_2_36 yields: % 3.64/1.55 | (96) h(all_74_2_36) = all_74_1_35 & h(all_27_0_7) = all_74_0_34 & op2(all_53_0_17, all_74_0_34) = all_74_1_35 & op1(all_27_0_7, all_27_0_7) = all_74_2_36 % 3.64/1.55 | % 3.64/1.55 | Applying alpha-rule on (96) yields: % 3.64/1.55 | (97) h(all_74_2_36) = all_74_1_35 % 3.64/1.55 | (98) h(all_27_0_7) = all_74_0_34 % 3.64/1.55 | (99) op2(all_53_0_17, all_74_0_34) = all_74_1_35 % 3.64/1.55 | (100) op1(all_27_0_7, all_27_0_7) = all_74_2_36 % 3.64/1.55 | % 3.64/1.55 | Instantiating (79) with all_76_0_37, all_76_1_38, all_76_2_39 yields: % 3.64/1.55 | (101) h(all_76_2_39) = all_76_1_38 & h(all_8_0_1) = all_76_0_37 & op2(all_56_0_18, all_76_0_37) = all_76_1_38 & op1(all_15_1_5, all_8_0_1) = all_76_2_39 % 3.64/1.55 | % 3.64/1.55 | Applying alpha-rule on (101) yields: % 3.64/1.55 | (102) h(all_76_2_39) = all_76_1_38 % 3.64/1.55 | (103) h(all_8_0_1) = all_76_0_37 % 3.64/1.55 | (104) op2(all_56_0_18, all_76_0_37) = all_76_1_38 % 3.64/1.55 | (105) op1(all_15_1_5, all_8_0_1) = all_76_2_39 % 3.64/1.55 | % 3.64/1.55 | Instantiating (78) with all_80_0_43, all_80_1_44, all_80_2_45 yields: % 3.64/1.55 | (106) h(all_80_2_45) = all_80_1_44 & h(all_27_0_7) = all_80_0_43 & op2(all_56_0_18, all_80_0_43) = all_80_1_44 & op1(all_15_1_5, all_27_0_7) = all_80_2_45 % 3.64/1.55 | % 3.64/1.55 | Applying alpha-rule on (106) yields: % 3.64/1.55 | (107) h(all_80_2_45) = all_80_1_44 % 3.64/1.55 | (108) h(all_27_0_7) = all_80_0_43 % 3.64/1.55 | (109) op2(all_56_0_18, all_80_0_43) = all_80_1_44 % 3.64/1.55 | (110) op1(all_15_1_5, all_27_0_7) = all_80_2_45 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_27_0_7, all_68_0_25, all_74_0_34 and discharging atoms h(all_27_0_7) = all_74_0_34, h(all_27_0_7) = all_68_0_25, yields: % 3.64/1.55 | (111) all_74_0_34 = all_68_0_25 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_27_0_7, all_61_0_20, all_80_0_43 and discharging atoms h(all_27_0_7) = all_80_0_43, h(all_27_0_7) = all_61_0_20, yields: % 3.64/1.55 | (112) all_80_0_43 = all_61_0_20 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_27_0_7, all_61_0_20, all_68_0_25 and discharging atoms h(all_27_0_7) = all_68_0_25, h(all_27_0_7) = all_61_0_20, yields: % 3.64/1.55 | (113) all_68_0_25 = all_61_0_20 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_27_0_7, all_59_0_19, all_80_0_43 and discharging atoms h(all_27_0_7) = all_80_0_43, h(all_27_0_7) = all_59_0_19, yields: % 3.64/1.55 | (114) all_80_0_43 = all_59_0_19 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_27_0_7, all_53_0_17, all_74_0_34 and discharging atoms h(all_27_0_7) = all_74_0_34, h(all_27_0_7) = all_53_0_17, yields: % 3.64/1.55 | (115) all_74_0_34 = all_53_0_17 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_8_0_1, all_76_0_37, all_0_0_0 and discharging atoms h(all_8_0_1) = all_76_0_37, h(all_8_0_1) = all_0_0_0, yields: % 3.64/1.55 | (116) all_76_0_37 = all_0_0_0 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (12) with all_8_0_1, all_70_0_28, all_76_0_37 and discharging atoms h(all_8_0_1) = all_76_0_37, h(all_8_0_1) = all_70_0_28, yields: % 3.64/1.55 | (117) all_76_0_37 = all_70_0_28 % 3.64/1.55 | % 3.64/1.55 | Instantiating formula (13) with all_27_0_7, all_27_0_7, all_74_2_36, all_8_0_1 and discharging atoms op1(all_27_0_7, all_27_0_7) = all_74_2_36, op1(all_27_0_7, all_27_0_7) = all_8_0_1, yields: % 3.64/1.55 | (118) all_74_2_36 = all_8_0_1 % 3.64/1.55 | % 3.64/1.55 | Combining equations (112,114) yields a new equation: % 3.64/1.55 | (119) all_61_0_20 = all_59_0_19 % 3.64/1.55 | % 3.64/1.55 | Simplifying 119 yields: % 3.64/1.55 | (120) all_61_0_20 = all_59_0_19 % 3.64/1.55 | % 3.64/1.55 | Combining equations (116,117) yields a new equation: % 3.64/1.55 | (121) all_70_0_28 = all_0_0_0 % 3.64/1.55 | % 3.64/1.55 | Combining equations (111,115) yields a new equation: % 3.64/1.55 | (122) all_68_0_25 = all_53_0_17 % 3.64/1.55 | % 3.64/1.55 | Simplifying 122 yields: % 3.64/1.55 | (123) all_68_0_25 = all_53_0_17 % 3.64/1.55 | % 3.64/1.55 | Combining equations (113,123) yields a new equation: % 3.64/1.55 | (124) all_61_0_20 = all_53_0_17 % 3.64/1.55 | % 3.64/1.55 | Simplifying 124 yields: % 3.64/1.55 | (125) all_61_0_20 = all_53_0_17 % 3.64/1.55 | % 3.64/1.55 | Combining equations (125,120) yields a new equation: % 3.64/1.55 | (126) all_59_0_19 = all_53_0_17 % 3.64/1.55 | % 3.64/1.55 | From (118) and (97) follows: % 3.64/1.55 | (127) h(all_8_0_1) = all_74_1_35 % 3.64/1.55 | % 3.64/1.55 | From (121) and (93) follows: % 3.64/1.55 | (43) h(all_8_0_1) = all_0_0_0 % 3.64/1.55 | % 3.64/1.55 | From (115) and (99) follows: % 3.64/1.55 | (129) op2(all_53_0_17, all_53_0_17) = all_74_1_35 % 3.64/1.55 | % 3.64/1.55 | From (126) and (82) follows: % 3.64/1.56 | (130) sorti2(all_53_0_17) % 3.64/1.56 | % 3.64/1.56 | Instantiating formula (12) with all_8_0_1, all_74_1_35, all_0_0_0 and discharging atoms h(all_8_0_1) = all_74_1_35, h(all_8_0_1) = all_0_0_0, yields: % 3.64/1.56 | (131) all_74_1_35 = all_0_0_0 % 3.64/1.56 | % 3.64/1.56 | From (131) and (129) follows: % 3.64/1.56 | (132) op2(all_53_0_17, all_53_0_17) = all_0_0_0 % 3.64/1.56 | % 3.64/1.56 | Instantiating formula (15) with all_53_0_17 and discharging atoms op2(all_53_0_17, all_53_0_17) = all_0_0_0, sorti2(all_53_0_17), yields: % 3.64/1.56 | (133) $false % 3.64/1.56 | % 3.64/1.56 |-The branch is then unsatisfiable % 3.64/1.56 % SZS output end Proof for theBenchmark % 3.64/1.56 % 3.64/1.56 1081ms %------------------------------------------------------------------------------