%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG019+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : ALG019+1 : TPTP v8.1.0. Released v2.7.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n019.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Wed Jun 8 20:28:25 EDT 2022 % 0.12/0.34 % CPUTime : % 0.60/0.59 ____ _ % 0.60/0.59 ___ / __ \_____(_)___ ________ __________ % 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.59 % 0.60/0.59 A Theorem Prover for First-Order Logic % 0.60/0.59 (ePrincess v.1.0) % 0.60/0.59 % 0.60/0.59 (c) Philipp Rümmer, 2009-2015 % 0.60/0.59 (c) Peter Backeman, 2014-2015 % 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.59 Bug reports to peter@backeman.se % 0.60/0.59 % 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.59 % 0.60/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.91 Prover 0: Preprocessing ... % 1.74/1.07 Prover 0: Constructing countermodel ... % 2.48/1.30 Prover 0: proved (657ms) % 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) % 4.48/1.80 % 4.48/1.80 % SZS output start Proof for theBenchmark % 4.48/1.80 Assumed formulas after preprocessing and simplification: % 4.48/1.80 | (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] : ! [v2] : (v2 = v0 | ~ (op2(v1, v1) = v2) | ~ 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] : ? [v3] : ( ~ (v3 = v1) & op1(v2, v2) = v3 & sorti1(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))))) % 4.54/1.83 | Instantiating (0) with all_0_0_0 yields: % 4.54/1.83 | (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] : ! [v1] : (v1 = all_0_0_0 | ~ (op2(v0, v0) = v1) | ~ 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] : ? [v2] : ( ~ (v2 = v0) & op1(v1, v1) = v2 & sorti1(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)))) % 4.54/1.84 | % 4.54/1.84 | Applying alpha-rule on (1) yields: % 4.54/1.84 | (2) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) % 4.54/1.84 | (3) ! [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)))) % 4.54/1.84 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) % 4.54/1.85 | (5) sorti2(all_0_0_0) % 4.54/1.85 | (6) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) % 4.54/1.85 | (7) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v0) & op1(v1, v1) = v2 & sorti1(v1))) % 4.54/1.85 | (8) ! [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)))) % 4.54/1.85 | (9) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (op2(v0, v0) = v1) | ~ sorti2(v0)) % 4.54/1.85 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 4.54/1.85 | (11) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) % 4.54/1.85 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) % 4.54/1.85 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 4.54/1.85 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 4.54/1.85 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 4.54/1.85 | (16) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) % 4.54/1.85 | % 4.54/1.85 | Instantiating formula (16) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 4.54/1.85 | (17) ? [v0] : (j(all_0_0_0) = v0 & h(v0) = all_0_0_0) % 4.54/1.85 | % 4.54/1.85 | Instantiating formula (2) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 4.54/1.85 | (18) ? [v0] : (j(all_0_0_0) = v0 & sorti1(v0)) % 4.54/1.85 | % 4.54/1.85 | Instantiating formula (8) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 4.54/1.85 | (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))) % 4.54/1.85 | % 4.54/1.85 | Instantiating (19) with all_8_0_1 yields: % 4.54/1.85 | (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)) % 4.54/1.85 | % 4.54/1.85 | Applying alpha-rule on (20) yields: % 4.54/1.85 | (21) j(all_0_0_0) = all_8_0_1 % 4.54/1.85 | (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)) % 4.54/1.85 | % 4.54/1.85 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 4.54/1.85 | (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) % 4.54/1.85 | % 4.54/1.85 | Instantiating (18) with all_11_0_2 yields: % 4.54/1.85 | (24) j(all_0_0_0) = all_11_0_2 & sorti1(all_11_0_2) % 4.54/1.85 | % 4.54/1.85 | Applying alpha-rule on (24) yields: % 4.54/1.85 | (25) j(all_0_0_0) = all_11_0_2 % 4.54/1.85 | (26) sorti1(all_11_0_2) % 4.54/1.85 | % 4.54/1.85 | Instantiating (17) with all_13_0_3 yields: % 4.54/1.85 | (27) j(all_0_0_0) = all_13_0_3 & h(all_13_0_3) = all_0_0_0 % 4.54/1.85 | % 4.54/1.85 | Applying alpha-rule on (27) yields: % 4.54/1.85 | (28) j(all_0_0_0) = all_13_0_3 % 4.54/1.85 | (29) h(all_13_0_3) = all_0_0_0 % 4.54/1.85 | % 4.54/1.85 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields: % 4.54/1.85 | (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 % 4.54/1.86 | % 4.54/1.86 | Applying alpha-rule on (30) yields: % 4.54/1.86 | (31) j(all_15_2_6) = all_15_1_5 % 4.54/1.86 | (32) j(all_0_0_0) = all_15_0_4 % 4.54/1.86 | (33) op2(all_0_0_0, all_0_0_0) = all_15_2_6 % 4.54/1.86 | (34) op1(all_8_0_1, all_15_0_4) = all_15_1_5 % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (10) 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: % 4.54/1.86 | (35) all_15_0_4 = all_13_0_3 % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (10) 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: % 4.54/1.86 | (36) all_15_0_4 = all_11_0_2 % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (10) 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: % 4.54/1.86 | (37) all_13_0_3 = all_8_0_1 % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (9) with all_15_2_6, all_0_0_0 and discharging atoms op2(all_0_0_0, all_0_0_0) = all_15_2_6, sorti2(all_0_0_0), yields: % 4.54/1.86 | (38) all_15_2_6 = all_0_0_0 % 4.54/1.86 | % 4.54/1.86 | Combining equations (35,36) yields a new equation: % 4.54/1.86 | (39) all_13_0_3 = all_11_0_2 % 4.54/1.86 | % 4.54/1.86 | Simplifying 39 yields: % 4.54/1.86 | (40) all_13_0_3 = all_11_0_2 % 4.54/1.86 | % 4.54/1.86 | Combining equations (37,40) yields a new equation: % 4.54/1.86 | (41) all_11_0_2 = all_8_0_1 % 4.54/1.86 | % 4.54/1.86 | From (38) and (31) follows: % 4.54/1.86 | (42) j(all_0_0_0) = all_15_1_5 % 4.54/1.86 | % 4.54/1.86 | From (41) and (25) follows: % 4.54/1.86 | (21) j(all_0_0_0) = all_8_0_1 % 4.54/1.86 | % 4.54/1.86 | From (41) and (26) follows: % 4.54/1.86 | (44) sorti1(all_8_0_1) % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (10) with all_0_0_0, all_15_1_5, all_8_0_1 and discharging atoms j(all_0_0_0) = all_15_1_5, j(all_0_0_0) = all_8_0_1, yields: % 4.54/1.86 | (45) all_15_1_5 = all_8_0_1 % 4.54/1.86 | % 4.54/1.86 | From (45) and (42) follows: % 4.54/1.86 | (21) j(all_0_0_0) = all_8_0_1 % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (7) with all_8_0_1 and discharging atoms sorti1(all_8_0_1), yields: % 4.54/1.86 | (47) ? [v0] : ? [v1] : ( ~ (v1 = all_8_0_1) & op1(v0, v0) = v1 & sorti1(v0)) % 4.54/1.86 | % 4.54/1.86 | Instantiating (47) with all_33_0_8, all_33_1_9 yields: % 4.54/1.86 | (48) ~ (all_33_0_8 = all_8_0_1) & op1(all_33_1_9, all_33_1_9) = all_33_0_8 & sorti1(all_33_1_9) % 4.54/1.86 | % 4.54/1.86 | Applying alpha-rule on (48) yields: % 4.54/1.86 | (49) ~ (all_33_0_8 = all_8_0_1) % 4.54/1.86 | (50) op1(all_33_1_9, all_33_1_9) = all_33_0_8 % 4.54/1.86 | (51) sorti1(all_33_1_9) % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (6) with all_33_1_9 and discharging atoms sorti1(all_33_1_9), yields: % 4.54/1.86 | (52) ? [v0] : (j(v0) = all_33_1_9 & h(all_33_1_9) = v0) % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (11) with all_33_1_9 and discharging atoms sorti1(all_33_1_9), yields: % 4.54/1.86 | (53) ? [v0] : (h(all_33_1_9) = v0 & sorti2(v0)) % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (3) with all_33_1_9 and discharging atoms sorti1(all_33_1_9), yields: % 4.54/1.86 | (54) ? [v0] : (h(all_33_1_9) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_33_1_9, v1) = v2))) % 4.54/1.86 | % 4.54/1.86 | Instantiating (54) with all_51_0_13 yields: % 4.54/1.86 | (55) h(all_33_1_9) = all_51_0_13 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_51_0_13, v3) = v2 & op1(all_33_1_9, v0) = v1)) % 4.54/1.86 | % 4.54/1.86 | Applying alpha-rule on (55) yields: % 4.54/1.86 | (56) h(all_33_1_9) = all_51_0_13 % 4.54/1.86 | (57) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_51_0_13, v3) = v2 & op1(all_33_1_9, v0) = v1)) % 4.54/1.86 | % 4.54/1.86 | Instantiating formula (57) with all_33_1_9 and discharging atoms sorti1(all_33_1_9), yields: % 4.54/1.86 | (58) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_33_1_9) = v2 & op2(all_51_0_13, v2) = v1 & op1(all_33_1_9, all_33_1_9) = v0) % 4.54/1.86 | % 4.54/1.86 | Instantiating (53) with all_56_0_17 yields: % 4.54/1.86 | (59) h(all_33_1_9) = all_56_0_17 & sorti2(all_56_0_17) % 4.54/1.86 | % 4.54/1.86 | Applying alpha-rule on (59) yields: % 4.54/1.86 | (60) h(all_33_1_9) = all_56_0_17 % 4.54/1.86 | (61) sorti2(all_56_0_17) % 4.54/1.86 | % 4.54/1.86 | Instantiating (52) with all_58_0_18 yields: % 4.54/1.86 | (62) j(all_58_0_18) = all_33_1_9 & h(all_33_1_9) = all_58_0_18 % 4.54/1.86 | % 4.54/1.87 | Applying alpha-rule on (62) yields: % 4.54/1.87 | (63) j(all_58_0_18) = all_33_1_9 % 4.54/1.87 | (64) h(all_33_1_9) = all_58_0_18 % 4.54/1.87 | % 4.54/1.87 | Instantiating (58) with all_64_0_24, all_64_1_25, all_64_2_26 yields: % 4.54/1.87 | (65) h(all_64_2_26) = all_64_1_25 & h(all_33_1_9) = all_64_0_24 & op2(all_51_0_13, all_64_0_24) = all_64_1_25 & op1(all_33_1_9, all_33_1_9) = all_64_2_26 % 4.54/1.87 | % 4.54/1.87 | Applying alpha-rule on (65) yields: % 4.54/1.87 | (66) h(all_64_2_26) = all_64_1_25 % 4.54/1.87 | (67) h(all_33_1_9) = all_64_0_24 % 4.54/1.87 | (68) op2(all_51_0_13, all_64_0_24) = all_64_1_25 % 4.54/1.87 | (69) op1(all_33_1_9, all_33_1_9) = all_64_2_26 % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (15) with all_33_1_9, all_58_0_18, all_64_0_24 and discharging atoms h(all_33_1_9) = all_64_0_24, h(all_33_1_9) = all_58_0_18, yields: % 4.54/1.87 | (70) all_64_0_24 = all_58_0_18 % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (15) with all_33_1_9, all_56_0_17, all_58_0_18 and discharging atoms h(all_33_1_9) = all_58_0_18, h(all_33_1_9) = all_56_0_17, yields: % 4.54/1.87 | (71) all_58_0_18 = all_56_0_17 % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (15) with all_33_1_9, all_51_0_13, all_64_0_24 and discharging atoms h(all_33_1_9) = all_64_0_24, h(all_33_1_9) = all_51_0_13, yields: % 4.54/1.87 | (72) all_64_0_24 = all_51_0_13 % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (13) with all_33_1_9, all_33_1_9, all_64_2_26, all_33_0_8 and discharging atoms op1(all_33_1_9, all_33_1_9) = all_64_2_26, op1(all_33_1_9, all_33_1_9) = all_33_0_8, yields: % 4.54/1.87 | (73) all_64_2_26 = all_33_0_8 % 4.54/1.87 | % 4.54/1.87 | Combining equations (70,72) yields a new equation: % 4.54/1.87 | (74) all_58_0_18 = all_51_0_13 % 4.54/1.87 | % 4.54/1.87 | Simplifying 74 yields: % 4.54/1.87 | (75) all_58_0_18 = all_51_0_13 % 4.54/1.87 | % 4.54/1.87 | Combining equations (71,75) yields a new equation: % 4.54/1.87 | (76) all_56_0_17 = all_51_0_13 % 4.54/1.87 | % 4.54/1.87 | Simplifying 76 yields: % 4.54/1.87 | (77) all_56_0_17 = all_51_0_13 % 4.54/1.87 | % 4.54/1.87 | From (75) and (63) follows: % 4.54/1.87 | (78) j(all_51_0_13) = all_33_1_9 % 4.54/1.87 | % 4.54/1.87 | From (73) and (69) follows: % 4.54/1.87 | (50) op1(all_33_1_9, all_33_1_9) = all_33_0_8 % 4.54/1.87 | % 4.54/1.87 | From (77) and (61) follows: % 4.54/1.87 | (80) sorti2(all_51_0_13) % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (22) with all_51_0_13 and discharging atoms sorti2(all_51_0_13), yields: % 4.54/1.87 | (81) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_51_0_13) = v2 & op2(all_0_0_0, all_51_0_13) = v0 & op1(all_8_0_1, v2) = v1) % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (8) with all_51_0_13 and discharging atoms sorti2(all_51_0_13), yields: % 4.54/1.87 | (82) ? [v0] : (j(all_51_0_13) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_51_0_13, v1) = v2 & op1(v0, v4) = v3))) % 4.54/1.87 | % 4.54/1.87 | Instantiating (82) with all_104_0_48 yields: % 4.54/1.87 | (83) j(all_51_0_13) = all_104_0_48 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_51_0_13, v0) = v1 & op1(all_104_0_48, v3) = v2)) % 4.54/1.87 | % 4.54/1.87 | Applying alpha-rule on (83) yields: % 4.54/1.87 | (84) j(all_51_0_13) = all_104_0_48 % 4.54/1.87 | (85) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_51_0_13, v0) = v1 & op1(all_104_0_48, v3) = v2)) % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (85) with all_51_0_13 and discharging atoms sorti2(all_51_0_13), yields: % 4.54/1.87 | (86) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_51_0_13) = v2 & op2(all_51_0_13, all_51_0_13) = v0 & op1(all_104_0_48, v2) = v1) % 4.54/1.87 | % 4.54/1.87 | Instantiating formula (85) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 4.54/1.87 | (87) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_0_0_0) = v2 & op2(all_51_0_13, all_0_0_0) = v0 & op1(all_104_0_48, v2) = v1) % 4.54/1.87 | % 4.54/1.87 | Instantiating (81) with all_107_0_49, all_107_1_50, all_107_2_51 yields: % 4.54/1.87 | (88) j(all_107_2_51) = all_107_1_50 & j(all_51_0_13) = all_107_0_49 & op2(all_0_0_0, all_51_0_13) = all_107_2_51 & op1(all_8_0_1, all_107_0_49) = all_107_1_50 % 4.54/1.87 | % 4.54/1.87 | Applying alpha-rule on (88) yields: % 4.54/1.87 | (89) j(all_107_2_51) = all_107_1_50 % 4.54/1.87 | (90) j(all_51_0_13) = all_107_0_49 % 4.54/1.87 | (91) op2(all_0_0_0, all_51_0_13) = all_107_2_51 % 4.54/1.87 | (92) op1(all_8_0_1, all_107_0_49) = all_107_1_50 % 4.54/1.87 | % 4.54/1.88 | Instantiating (87) with all_125_0_76, all_125_1_77, all_125_2_78 yields: % 4.54/1.88 | (93) j(all_125_2_78) = all_125_1_77 & j(all_0_0_0) = all_125_0_76 & op2(all_51_0_13, all_0_0_0) = all_125_2_78 & op1(all_104_0_48, all_125_0_76) = all_125_1_77 % 4.54/1.88 | % 4.54/1.88 | Applying alpha-rule on (93) yields: % 4.54/1.88 | (94) j(all_125_2_78) = all_125_1_77 % 4.54/1.88 | (95) j(all_0_0_0) = all_125_0_76 % 4.54/1.88 | (96) op2(all_51_0_13, all_0_0_0) = all_125_2_78 % 4.54/1.88 | (97) op1(all_104_0_48, all_125_0_76) = all_125_1_77 % 4.54/1.88 | % 4.54/1.88 | Instantiating (86) with all_127_0_79, all_127_1_80, all_127_2_81 yields: % 4.54/1.88 | (98) j(all_127_2_81) = all_127_1_80 & j(all_51_0_13) = all_127_0_79 & op2(all_51_0_13, all_51_0_13) = all_127_2_81 & op1(all_104_0_48, all_127_0_79) = all_127_1_80 % 4.54/1.88 | % 4.54/1.88 | Applying alpha-rule on (98) yields: % 4.54/1.88 | (99) j(all_127_2_81) = all_127_1_80 % 4.54/1.88 | (100) j(all_51_0_13) = all_127_0_79 % 4.54/1.88 | (101) op2(all_51_0_13, all_51_0_13) = all_127_2_81 % 4.54/1.88 | (102) op1(all_104_0_48, all_127_0_79) = all_127_1_80 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (10) with all_51_0_13, all_107_0_49, all_33_1_9 and discharging atoms j(all_51_0_13) = all_107_0_49, j(all_51_0_13) = all_33_1_9, yields: % 4.54/1.88 | (103) all_107_0_49 = all_33_1_9 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (10) with all_51_0_13, all_107_0_49, all_127_0_79 and discharging atoms j(all_51_0_13) = all_127_0_79, j(all_51_0_13) = all_107_0_49, yields: % 4.54/1.88 | (104) all_127_0_79 = all_107_0_49 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (10) with all_51_0_13, all_104_0_48, all_127_0_79 and discharging atoms j(all_51_0_13) = all_127_0_79, j(all_51_0_13) = all_104_0_48, yields: % 4.54/1.88 | (105) all_127_0_79 = all_104_0_48 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (10) with all_0_0_0, all_125_0_76, all_8_0_1 and discharging atoms j(all_0_0_0) = all_125_0_76, j(all_0_0_0) = all_8_0_1, yields: % 4.54/1.88 | (106) all_125_0_76 = all_8_0_1 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (9) with all_127_2_81, all_51_0_13 and discharging atoms op2(all_51_0_13, all_51_0_13) = all_127_2_81, sorti2(all_51_0_13), yields: % 4.54/1.88 | (107) all_127_2_81 = all_0_0_0 % 4.54/1.88 | % 4.54/1.88 | Combining equations (104,105) yields a new equation: % 4.54/1.88 | (108) all_107_0_49 = all_104_0_48 % 4.54/1.88 | % 4.54/1.88 | Simplifying 108 yields: % 4.54/1.88 | (109) all_107_0_49 = all_104_0_48 % 4.54/1.88 | % 4.54/1.88 | Combining equations (103,109) yields a new equation: % 4.54/1.88 | (110) all_104_0_48 = all_33_1_9 % 4.54/1.88 | % 4.54/1.88 | Combining equations (110,105) yields a new equation: % 4.54/1.88 | (111) all_127_0_79 = all_33_1_9 % 4.54/1.88 | % 4.54/1.88 | From (107) and (99) follows: % 4.54/1.88 | (112) j(all_0_0_0) = all_127_1_80 % 4.54/1.88 | % 4.54/1.88 | From (106) and (95) follows: % 4.54/1.88 | (21) j(all_0_0_0) = all_8_0_1 % 4.54/1.88 | % 4.54/1.88 | From (110)(111) and (102) follows: % 4.54/1.88 | (114) op1(all_33_1_9, all_33_1_9) = all_127_1_80 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (10) with all_0_0_0, all_127_1_80, all_8_0_1 and discharging atoms j(all_0_0_0) = all_127_1_80, j(all_0_0_0) = all_8_0_1, yields: % 4.54/1.88 | (115) all_127_1_80 = all_8_0_1 % 4.54/1.88 | % 4.54/1.88 | Instantiating formula (13) with all_33_1_9, all_33_1_9, all_127_1_80, all_33_0_8 and discharging atoms op1(all_33_1_9, all_33_1_9) = all_127_1_80, op1(all_33_1_9, all_33_1_9) = all_33_0_8, yields: % 4.54/1.88 | (116) all_127_1_80 = all_33_0_8 % 4.54/1.88 | % 4.54/1.88 | Combining equations (115,116) yields a new equation: % 4.54/1.88 | (117) all_33_0_8 = all_8_0_1 % 4.54/1.88 | % 4.54/1.88 | Equations (117) can reduce 49 to: % 4.54/1.88 | (118) $false % 4.54/1.88 | % 4.54/1.88 |-The branch is then unsatisfiable % 4.54/1.88 % SZS output end Proof for theBenchmark % 4.54/1.88 % 4.54/1.88 1279ms %------------------------------------------------------------------------------