%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG018+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 15:33:46 EDT 2022 % Result : Theorem 2.48s 1.30s % Output : Proof 4.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG018+1 : TPTP v8.1.0. Released v2.7.0. % 0.13/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Thu Jun 9 02:06:19 EDT 2022 % 0.13/0.33 % CPUTime : % 0.20/0.57 ____ _ % 0.20/0.57 ___ / __ \_____(_)___ ________ __________ % 0.20/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.57 % 0.20/0.57 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 ... % 0.63/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/0.89 Prover 0: Preprocessing ... % 1.75/1.06 Prover 0: Constructing countermodel ... % 2.48/1.30 Prover 0: proved (674ms) % 2.48/1.30 % 2.48/1.30 No countermodel exists, formula is valid % 2.48/1.30 % SZS status Theorem for theBenchmark % 2.48/1.30 % 2.48/1.30 Generating proof ... found it (size 81) % 4.37/1.78 % 4.37/1.78 % SZS output start Proof for theBenchmark % 4.37/1.78 Assumed formulas after preprocessing and simplification: % 4.37/1.78 | (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] : ! [v2] : (v2 = v0 | ~ (op1(v1, v1) = v2) | ~ sorti1(v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ( ~ (v3 = v1) & op2(v2, v2) = v3 & sorti2(v2))) & ! [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))))) % 4.47/1.82 | Instantiating (0) with all_0_0_0 yields: % 4.47/1.82 | (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] : ! [v1] : (v1 = all_0_0_0 | ~ (op1(v0, v0) = v1) | ~ sorti1(v0)) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v0) & op2(v1, v1) = v2 & sorti2(v1))) & ! [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)))) % 4.52/1.82 | % 4.52/1.82 | Applying alpha-rule on (1) yields: % 4.52/1.82 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) % 4.52/1.82 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 4.52/1.82 | (4) sorti1(all_0_0_0) % 4.52/1.83 | (5) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) % 4.52/1.83 | (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)))) % 4.52/1.83 | (7) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) % 4.52/1.83 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 4.52/1.83 | (9) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v0) & op2(v1, v1) = v2 & sorti2(v1))) % 4.52/1.83 | (10) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) % 4.52/1.83 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) % 4.52/1.83 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 4.52/1.83 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 4.52/1.83 | (14) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) % 4.52/1.83 | (15) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (op1(v0, v0) = v1) | ~ sorti1(v0)) % 4.52/1.83 | (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)))) % 4.52/1.83 | % 4.52/1.83 | Instantiating formula (10) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 4.52/1.83 | (17) ? [v0] : (j(v0) = all_0_0_0 & h(all_0_0_0) = v0) % 4.52/1.83 | % 4.52/1.83 | Instantiating formula (14) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 4.52/1.83 | (18) ? [v0] : (h(all_0_0_0) = v0 & sorti2(v0)) % 4.52/1.83 | % 4.52/1.83 | Instantiating formula (16) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 4.52/1.83 | (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))) % 4.52/1.84 | % 4.52/1.84 | Instantiating (19) with all_8_0_1 yields: % 4.52/1.84 | (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)) % 4.52/1.84 | % 4.52/1.84 | Applying alpha-rule on (20) yields: % 4.52/1.84 | (21) h(all_0_0_0) = all_8_0_1 % 4.52/1.84 | (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)) % 4.52/1.84 | % 4.52/1.84 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 4.52/1.84 | (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) % 4.52/1.84 | % 4.52/1.84 | Instantiating (18) with all_11_0_2 yields: % 4.52/1.84 | (24) h(all_0_0_0) = all_11_0_2 & sorti2(all_11_0_2) % 4.52/1.84 | % 4.52/1.84 | Applying alpha-rule on (24) yields: % 4.52/1.84 | (25) h(all_0_0_0) = all_11_0_2 % 4.52/1.84 | (26) sorti2(all_11_0_2) % 4.52/1.84 | % 4.52/1.84 | Instantiating (17) with all_13_0_3 yields: % 4.52/1.84 | (27) j(all_13_0_3) = all_0_0_0 & h(all_0_0_0) = all_13_0_3 % 4.52/1.84 | % 4.52/1.84 | Applying alpha-rule on (27) yields: % 4.52/1.84 | (28) j(all_13_0_3) = all_0_0_0 % 4.52/1.84 | (29) h(all_0_0_0) = all_13_0_3 % 4.52/1.84 | % 4.52/1.84 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields: % 4.52/1.84 | (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 % 4.52/1.84 | % 4.52/1.84 | Applying alpha-rule on (30) yields: % 4.52/1.84 | (31) h(all_15_2_6) = all_15_1_5 % 4.52/1.84 | (32) h(all_0_0_0) = all_15_0_4 % 4.52/1.84 | (33) op2(all_8_0_1, all_15_0_4) = all_15_1_5 % 4.52/1.84 | (34) op1(all_0_0_0, all_0_0_0) = all_15_2_6 % 4.52/1.84 | % 4.52/1.84 | 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: % 4.52/1.84 | (35) all_15_0_4 = all_13_0_3 % 4.52/1.84 | % 4.52/1.84 | 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: % 4.52/1.84 | (36) all_15_0_4 = all_11_0_2 % 4.52/1.84 | % 4.52/1.84 | 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: % 4.52/1.84 | (37) all_13_0_3 = all_8_0_1 % 4.52/1.84 | % 4.52/1.84 | Instantiating formula (15) with all_15_2_6, all_0_0_0 and discharging atoms op1(all_0_0_0, all_0_0_0) = all_15_2_6, sorti1(all_0_0_0), yields: % 4.52/1.84 | (38) all_15_2_6 = all_0_0_0 % 4.52/1.84 | % 4.52/1.84 | Combining equations (35,36) yields a new equation: % 4.52/1.84 | (39) all_13_0_3 = all_11_0_2 % 4.52/1.84 | % 4.52/1.84 | Simplifying 39 yields: % 4.52/1.84 | (40) all_13_0_3 = all_11_0_2 % 4.52/1.84 | % 4.52/1.84 | Combining equations (37,40) yields a new equation: % 4.52/1.84 | (41) all_11_0_2 = all_8_0_1 % 4.52/1.84 | % 4.52/1.84 | From (38) and (31) follows: % 4.52/1.85 | (42) h(all_0_0_0) = all_15_1_5 % 4.52/1.85 | % 4.52/1.85 | From (41) and (25) follows: % 4.52/1.85 | (21) h(all_0_0_0) = all_8_0_1 % 4.52/1.85 | % 4.52/1.85 | From (41) and (26) follows: % 4.52/1.85 | (44) sorti2(all_8_0_1) % 4.52/1.85 | % 4.52/1.85 | Instantiating formula (12) with all_0_0_0, all_15_1_5, all_8_0_1 and discharging atoms h(all_0_0_0) = all_15_1_5, h(all_0_0_0) = all_8_0_1, yields: % 4.52/1.85 | (45) all_15_1_5 = all_8_0_1 % 4.52/1.85 | % 4.52/1.85 | From (45) and (42) follows: % 4.52/1.85 | (21) h(all_0_0_0) = all_8_0_1 % 4.52/1.85 | % 4.52/1.85 | Instantiating formula (9) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields: % 4.52/1.85 | (47) ? [v0] : ? [v1] : ( ~ (v1 = all_8_0_1) & op2(v0, v0) = v1 & sorti2(v0)) % 4.52/1.85 | % 4.52/1.85 | Instantiating (47) with all_33_0_8, all_33_1_9 yields: % 4.52/1.85 | (48) ~ (all_33_0_8 = all_8_0_1) & op2(all_33_1_9, all_33_1_9) = all_33_0_8 & sorti2(all_33_1_9) % 4.52/1.85 | % 4.52/1.85 | Applying alpha-rule on (48) yields: % 4.52/1.85 | (49) ~ (all_33_0_8 = all_8_0_1) % 4.52/1.85 | (50) op2(all_33_1_9, all_33_1_9) = all_33_0_8 % 4.52/1.85 | (51) sorti2(all_33_1_9) % 4.52/1.85 | % 4.52/1.85 | Instantiating formula (5) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields: % 4.52/1.85 | (52) ? [v0] : (j(all_33_1_9) = v0 & h(v0) = all_33_1_9) % 4.52/1.85 | % 4.52/1.85 | Instantiating formula (7) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields: % 4.52/1.85 | (53) ? [v0] : (j(all_33_1_9) = v0 & sorti1(v0)) % 4.52/1.85 | % 4.52/1.85 | Instantiating formula (6) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields: % 4.52/1.85 | (54) ? [v0] : (j(all_33_1_9) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_33_1_9, v1) = v2 & op1(v0, v4) = v3))) % 4.52/1.85 | % 4.52/1.85 | Instantiating (54) with all_51_0_13 yields: % 4.52/1.85 | (55) j(all_33_1_9) = all_51_0_13 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_33_1_9, v0) = v1 & op1(all_51_0_13, v3) = v2)) % 4.52/1.85 | % 4.52/1.85 | Applying alpha-rule on (55) yields: % 4.52/1.85 | (56) j(all_33_1_9) = all_51_0_13 % 4.52/1.85 | (57) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_33_1_9, v0) = v1 & op1(all_51_0_13, v3) = v2)) % 4.52/1.85 | % 4.52/1.85 | Instantiating formula (57) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields: % 4.52/1.85 | (58) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_33_1_9) = v2 & op2(all_33_1_9, all_33_1_9) = v0 & op1(all_51_0_13, v2) = v1) % 4.52/1.85 | % 4.52/1.85 | Instantiating (53) with all_56_0_17 yields: % 4.52/1.85 | (59) j(all_33_1_9) = all_56_0_17 & sorti1(all_56_0_17) % 4.52/1.85 | % 4.52/1.85 | Applying alpha-rule on (59) yields: % 4.52/1.85 | (60) j(all_33_1_9) = all_56_0_17 % 4.52/1.85 | (61) sorti1(all_56_0_17) % 4.52/1.85 | % 4.52/1.85 | Instantiating (52) with all_58_0_18 yields: % 4.52/1.85 | (62) j(all_33_1_9) = all_58_0_18 & h(all_58_0_18) = all_33_1_9 % 4.52/1.86 | % 4.52/1.86 | Applying alpha-rule on (62) yields: % 4.52/1.86 | (63) j(all_33_1_9) = all_58_0_18 % 4.52/1.86 | (64) h(all_58_0_18) = all_33_1_9 % 4.52/1.86 | % 4.52/1.86 | Instantiating (58) with all_64_0_24, all_64_1_25, all_64_2_26 yields: % 4.52/1.86 | (65) j(all_64_2_26) = all_64_1_25 & j(all_33_1_9) = all_64_0_24 & op2(all_33_1_9, all_33_1_9) = all_64_2_26 & op1(all_51_0_13, all_64_0_24) = all_64_1_25 % 4.52/1.86 | % 4.52/1.86 | Applying alpha-rule on (65) yields: % 4.52/1.86 | (66) j(all_64_2_26) = all_64_1_25 % 4.52/1.86 | (67) j(all_33_1_9) = all_64_0_24 % 4.52/1.86 | (68) op2(all_33_1_9, all_33_1_9) = all_64_2_26 % 4.52/1.86 | (69) op1(all_51_0_13, all_64_0_24) = all_64_1_25 % 4.52/1.86 | % 4.52/1.86 | Instantiating formula (8) with all_33_1_9, all_58_0_18, all_64_0_24 and discharging atoms j(all_33_1_9) = all_64_0_24, j(all_33_1_9) = all_58_0_18, yields: % 4.52/1.86 | (70) all_64_0_24 = all_58_0_18 % 4.52/1.86 | % 4.52/1.86 | Instantiating formula (8) with all_33_1_9, all_56_0_17, all_58_0_18 and discharging atoms j(all_33_1_9) = all_58_0_18, j(all_33_1_9) = all_56_0_17, yields: % 4.52/1.86 | (71) all_58_0_18 = all_56_0_17 % 4.52/1.86 | % 4.52/1.86 | Instantiating formula (8) with all_33_1_9, all_51_0_13, all_64_0_24 and discharging atoms j(all_33_1_9) = all_64_0_24, j(all_33_1_9) = all_51_0_13, yields: % 4.52/1.86 | (72) all_64_0_24 = all_51_0_13 % 4.52/1.86 | % 4.52/1.86 | Instantiating formula (3) with all_33_1_9, all_33_1_9, all_64_2_26, all_33_0_8 and discharging atoms op2(all_33_1_9, all_33_1_9) = all_64_2_26, op2(all_33_1_9, all_33_1_9) = all_33_0_8, yields: % 4.52/1.86 | (73) all_64_2_26 = all_33_0_8 % 4.52/1.86 | % 4.52/1.86 | Combining equations (70,72) yields a new equation: % 4.52/1.86 | (74) all_58_0_18 = all_51_0_13 % 4.52/1.86 | % 4.52/1.86 | Simplifying 74 yields: % 4.52/1.86 | (75) all_58_0_18 = all_51_0_13 % 4.52/1.86 | % 4.52/1.86 | Combining equations (71,75) yields a new equation: % 4.52/1.86 | (76) all_56_0_17 = all_51_0_13 % 4.52/1.86 | % 4.52/1.86 | Simplifying 76 yields: % 4.52/1.86 | (77) all_56_0_17 = all_51_0_13 % 4.52/1.86 | % 4.52/1.86 | From (75) and (64) follows: % 4.52/1.86 | (78) h(all_51_0_13) = all_33_1_9 % 4.52/1.86 | % 4.52/1.86 | From (73) and (68) follows: % 4.52/1.86 | (50) op2(all_33_1_9, all_33_1_9) = all_33_0_8 % 4.52/1.86 | % 4.52/1.86 | From (77) and (61) follows: % 4.52/1.86 | (80) sorti1(all_51_0_13) % 4.52/1.86 | % 4.52/1.86 | Instantiating formula (22) with all_51_0_13 and discharging atoms sorti1(all_51_0_13), yields: % 4.52/1.86 | (81) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_51_0_13) = v2 & op2(all_8_0_1, v2) = v1 & op1(all_0_0_0, all_51_0_13) = v0) % 4.52/1.86 | % 4.52/1.86 | Instantiating formula (16) with all_51_0_13 and discharging atoms sorti1(all_51_0_13), yields: % 4.52/1.86 | (82) ? [v0] : (h(all_51_0_13) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_51_0_13, v1) = v2))) % 4.52/1.86 | % 4.52/1.86 | Instantiating (82) with all_89_0_32 yields: % 4.52/1.86 | (83) h(all_51_0_13) = all_89_0_32 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_89_0_32, v3) = v2 & op1(all_51_0_13, v0) = v1)) % 4.52/1.86 | % 4.52/1.86 | Applying alpha-rule on (83) yields: % 4.52/1.86 | (84) h(all_51_0_13) = all_89_0_32 % 4.52/1.86 | (85) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_89_0_32, v3) = v2 & op1(all_51_0_13, v0) = v1)) % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (85) with all_51_0_13 and discharging atoms sorti1(all_51_0_13), yields: % 4.52/1.87 | (86) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_51_0_13) = v2 & op2(all_89_0_32, v2) = v1 & op1(all_51_0_13, all_51_0_13) = v0) % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (85) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields: % 4.52/1.87 | (87) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_0_0) = v2 & op2(all_89_0_32, v2) = v1 & op1(all_51_0_13, all_0_0_0) = v0) % 4.52/1.87 | % 4.52/1.87 | Instantiating (81) with all_96_0_37, all_96_1_38, all_96_2_39 yields: % 4.52/1.87 | (88) h(all_96_2_39) = all_96_1_38 & h(all_51_0_13) = all_96_0_37 & op2(all_8_0_1, all_96_0_37) = all_96_1_38 & op1(all_0_0_0, all_51_0_13) = all_96_2_39 % 4.52/1.87 | % 4.52/1.87 | Applying alpha-rule on (88) yields: % 4.52/1.87 | (89) h(all_96_2_39) = all_96_1_38 % 4.52/1.87 | (90) h(all_51_0_13) = all_96_0_37 % 4.52/1.87 | (91) op2(all_8_0_1, all_96_0_37) = all_96_1_38 % 4.52/1.87 | (92) op1(all_0_0_0, all_51_0_13) = all_96_2_39 % 4.52/1.87 | % 4.52/1.87 | Instantiating (87) with all_117_0_64, all_117_1_65, all_117_2_66 yields: % 4.52/1.87 | (93) h(all_117_2_66) = all_117_1_65 & h(all_0_0_0) = all_117_0_64 & op2(all_89_0_32, all_117_0_64) = all_117_1_65 & op1(all_51_0_13, all_0_0_0) = all_117_2_66 % 4.52/1.87 | % 4.52/1.87 | Applying alpha-rule on (93) yields: % 4.52/1.87 | (94) h(all_117_2_66) = all_117_1_65 % 4.52/1.87 | (95) h(all_0_0_0) = all_117_0_64 % 4.52/1.87 | (96) op2(all_89_0_32, all_117_0_64) = all_117_1_65 % 4.52/1.87 | (97) op1(all_51_0_13, all_0_0_0) = all_117_2_66 % 4.52/1.87 | % 4.52/1.87 | Instantiating (86) with all_119_0_67, all_119_1_68, all_119_2_69 yields: % 4.52/1.87 | (98) h(all_119_2_69) = all_119_1_68 & h(all_51_0_13) = all_119_0_67 & op2(all_89_0_32, all_119_0_67) = all_119_1_68 & op1(all_51_0_13, all_51_0_13) = all_119_2_69 % 4.52/1.87 | % 4.52/1.87 | Applying alpha-rule on (98) yields: % 4.52/1.87 | (99) h(all_119_2_69) = all_119_1_68 % 4.52/1.87 | (100) h(all_51_0_13) = all_119_0_67 % 4.52/1.87 | (101) op2(all_89_0_32, all_119_0_67) = all_119_1_68 % 4.52/1.87 | (102) op1(all_51_0_13, all_51_0_13) = all_119_2_69 % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (12) with all_51_0_13, all_119_0_67, all_33_1_9 and discharging atoms h(all_51_0_13) = all_119_0_67, h(all_51_0_13) = all_33_1_9, yields: % 4.52/1.87 | (103) all_119_0_67 = all_33_1_9 % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (12) with all_51_0_13, all_96_0_37, all_119_0_67 and discharging atoms h(all_51_0_13) = all_119_0_67, h(all_51_0_13) = all_96_0_37, yields: % 4.52/1.87 | (104) all_119_0_67 = all_96_0_37 % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (12) with all_51_0_13, all_89_0_32, all_96_0_37 and discharging atoms h(all_51_0_13) = all_96_0_37, h(all_51_0_13) = all_89_0_32, yields: % 4.52/1.87 | (105) all_96_0_37 = all_89_0_32 % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (12) with all_0_0_0, all_117_0_64, all_8_0_1 and discharging atoms h(all_0_0_0) = all_117_0_64, h(all_0_0_0) = all_8_0_1, yields: % 4.52/1.87 | (106) all_117_0_64 = all_8_0_1 % 4.52/1.87 | % 4.52/1.87 | Instantiating formula (15) with all_119_2_69, all_51_0_13 and discharging atoms op1(all_51_0_13, all_51_0_13) = all_119_2_69, sorti1(all_51_0_13), yields: % 4.52/1.88 | (107) all_119_2_69 = all_0_0_0 % 4.52/1.88 | % 4.52/1.88 | Combining equations (104,103) yields a new equation: % 4.52/1.88 | (108) all_96_0_37 = all_33_1_9 % 4.52/1.88 | % 4.52/1.88 | Simplifying 108 yields: % 4.52/1.88 | (109) all_96_0_37 = all_33_1_9 % 4.52/1.88 | % 4.52/1.88 | Combining equations (105,109) yields a new equation: % 4.52/1.88 | (110) all_89_0_32 = all_33_1_9 % 4.52/1.88 | % 4.52/1.88 | Simplifying 110 yields: % 4.52/1.88 | (111) all_89_0_32 = all_33_1_9 % 4.52/1.88 | % 4.52/1.88 | From (107) and (99) follows: % 4.52/1.88 | (112) h(all_0_0_0) = all_119_1_68 % 4.52/1.88 | % 4.52/1.88 | From (106) and (95) follows: % 4.52/1.88 | (21) h(all_0_0_0) = all_8_0_1 % 4.52/1.88 | % 4.52/1.88 | From (111)(103) and (101) follows: % 4.52/1.88 | (114) op2(all_33_1_9, all_33_1_9) = all_119_1_68 % 4.52/1.88 | % 4.52/1.88 | Instantiating formula (12) with all_0_0_0, all_119_1_68, all_8_0_1 and discharging atoms h(all_0_0_0) = all_119_1_68, h(all_0_0_0) = all_8_0_1, yields: % 4.52/1.88 | (115) all_119_1_68 = all_8_0_1 % 4.52/1.88 | % 4.52/1.88 | Instantiating formula (3) with all_33_1_9, all_33_1_9, all_119_1_68, all_33_0_8 and discharging atoms op2(all_33_1_9, all_33_1_9) = all_119_1_68, op2(all_33_1_9, all_33_1_9) = all_33_0_8, yields: % 4.52/1.88 | (116) all_119_1_68 = all_33_0_8 % 4.52/1.88 | % 4.52/1.88 | Combining equations (115,116) yields a new equation: % 4.52/1.88 | (117) all_33_0_8 = all_8_0_1 % 4.52/1.88 | % 4.52/1.88 | Equations (117) can reduce 49 to: % 4.52/1.88 | (118) $false % 4.52/1.88 | % 4.52/1.88 |-The branch is then unsatisfiable % 4.52/1.88 % SZS output end Proof for theBenchmark % 4.52/1.88 % 4.52/1.88 1298ms %------------------------------------------------------------------------------