%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG201+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 15:37:30 EDT 2022 % Result : Theorem 1.79s 0.98s % Output : Proof 2.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.08 % Problem : ALG201+1 : TPTP v8.1.0. Released v2.7.0. % 0.05/0.09 % 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 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Wed Jun 8 11:08:36 EDT 2022 % 0.08/0.28 % CPUTime : % 0.13/0.46 ____ _ % 0.13/0.46 ___ / __ \_____(_)___ ________ __________ % 0.13/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.46 % 0.13/0.46 A Theorem Prover for First-Order Logic % 0.13/0.46 (ePrincess v.1.0) % 0.13/0.46 % 0.13/0.46 (c) Philipp Rümmer, 2009-2015 % 0.13/0.46 (c) Peter Backeman, 2014-2015 % 0.13/0.46 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.46 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.46 Bug reports to peter@backeman.se % 0.13/0.46 % 0.13/0.46 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.46 % 0.13/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.51 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 0.99/0.73 Prover 0: Preprocessing ... % 1.43/0.88 Prover 0: Constructing countermodel ... % 1.79/0.97 Prover 0: proved (465ms) % 1.79/0.98 % 1.79/0.98 No countermodel exists, formula is valid % 1.79/0.98 % SZS status Theorem for theBenchmark % 1.79/0.98 % 1.79/0.98 Generating proof ... found it (size 30) % 2.33/1.15 % 2.33/1.15 % SZS output start Proof for theBenchmark % 2.33/1.15 Assumed formulas after preprocessing and simplification: % 2.33/1.15 | (0) ? [v0] : (op2(v0, v0) = 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] : ( ~ (op1(v1, 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] : ( ~ 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))))) % 2.38/1.19 | Instantiating (0) with all_0_0_0 yields: % 2.38/1.19 | (1) op2(all_0_0_0, all_0_0_0) = all_0_0_0 & 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] : ( ~ (op1(v0, 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] : ( ~ 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)))) % 2.38/1.19 | % 2.38/1.19 | Applying alpha-rule on (1) yields: % 2.38/1.19 | (2) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) % 2.38/1.19 | (3) sorti2(all_0_0_0) % 2.38/1.19 | (4) ! [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)))) % 2.38/1.19 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 2.38/1.19 | (6) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) % 2.38/1.20 | (7) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) % 2.38/1.20 | (8) ! [v0] : ( ~ (op1(v0, v0) = v0) | ~ sorti1(v0)) % 2.38/1.20 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 2.38/1.20 | (10) op2(all_0_0_0, all_0_0_0) = all_0_0_0 % 2.38/1.20 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 2.38/1.20 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) % 2.38/1.20 | (13) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) % 2.38/1.20 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) % 2.38/1.20 | (15) ! [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)))) % 2.38/1.20 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 2.38/1.20 | % 2.38/1.20 | Instantiating formula (7) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 2.38/1.20 | (17) ? [v0] : (j(all_0_0_0) = v0 & h(v0) = all_0_0_0) % 2.38/1.20 | % 2.38/1.20 | Instantiating formula (13) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 2.38/1.20 | (18) ? [v0] : (j(all_0_0_0) = v0 & sorti1(v0)) % 2.38/1.20 | % 2.38/1.20 | Instantiating formula (4) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 2.38/1.20 | (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))) % 2.38/1.20 | % 2.38/1.20 | Instantiating (19) with all_8_0_1 yields: % 2.38/1.20 | (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)) % 2.38/1.20 | % 2.38/1.20 | Applying alpha-rule on (20) yields: % 2.38/1.20 | (21) j(all_0_0_0) = all_8_0_1 % 2.38/1.20 | (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)) % 2.38/1.20 | % 2.38/1.20 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields: % 2.38/1.20 | (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) % 2.38/1.20 | % 2.38/1.20 | Instantiating (18) with all_11_0_2 yields: % 2.38/1.20 | (24) j(all_0_0_0) = all_11_0_2 & sorti1(all_11_0_2) % 2.38/1.20 | % 2.38/1.20 | Applying alpha-rule on (24) yields: % 2.38/1.20 | (25) j(all_0_0_0) = all_11_0_2 % 2.38/1.20 | (26) sorti1(all_11_0_2) % 2.38/1.20 | % 2.38/1.20 | Instantiating (17) with all_13_0_3 yields: % 2.38/1.20 | (27) j(all_0_0_0) = all_13_0_3 & h(all_13_0_3) = all_0_0_0 % 2.38/1.20 | % 2.38/1.20 | Applying alpha-rule on (27) yields: % 2.38/1.20 | (28) j(all_0_0_0) = all_13_0_3 % 2.38/1.20 | (29) h(all_13_0_3) = all_0_0_0 % 2.38/1.20 | % 2.38/1.20 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields: % 2.38/1.20 | (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 % 2.38/1.20 | % 2.38/1.20 | Applying alpha-rule on (30) yields: % 2.38/1.20 | (31) j(all_15_2_6) = all_15_1_5 % 2.38/1.20 | (32) j(all_0_0_0) = all_15_0_4 % 2.38/1.20 | (33) op2(all_0_0_0, all_0_0_0) = all_15_2_6 % 2.38/1.20 | (34) op1(all_8_0_1, all_15_0_4) = all_15_1_5 % 2.38/1.21 | % 2.38/1.21 | Instantiating formula (9) 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: % 2.38/1.21 | (35) all_15_0_4 = all_13_0_3 % 2.38/1.21 | % 2.38/1.21 | Instantiating formula (9) 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: % 2.38/1.21 | (36) all_15_0_4 = all_11_0_2 % 2.38/1.21 | % 2.38/1.21 | Instantiating formula (9) 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: % 2.38/1.21 | (37) all_13_0_3 = all_8_0_1 % 2.38/1.21 | % 2.38/1.21 | Instantiating formula (16) with all_0_0_0, all_0_0_0, all_15_2_6, all_0_0_0 and discharging atoms op2(all_0_0_0, all_0_0_0) = all_15_2_6, op2(all_0_0_0, all_0_0_0) = all_0_0_0, yields: % 2.38/1.21 | (38) all_15_2_6 = all_0_0_0 % 2.38/1.21 | % 2.38/1.21 | Combining equations (35,36) yields a new equation: % 2.38/1.21 | (39) all_13_0_3 = all_11_0_2 % 2.38/1.21 | % 2.38/1.21 | Simplifying 39 yields: % 2.38/1.21 | (40) all_13_0_3 = all_11_0_2 % 2.38/1.21 | % 2.38/1.21 | Combining equations (37,40) yields a new equation: % 2.38/1.21 | (41) all_11_0_2 = all_8_0_1 % 2.38/1.21 | % 2.38/1.21 | Combining equations (41,36) yields a new equation: % 2.38/1.21 | (42) all_15_0_4 = all_8_0_1 % 2.38/1.21 | % 2.38/1.21 | From (38) and (31) follows: % 2.38/1.21 | (43) j(all_0_0_0) = all_15_1_5 % 2.38/1.21 | % 2.38/1.21 | From (41) and (25) follows: % 2.38/1.21 | (21) j(all_0_0_0) = all_8_0_1 % 2.38/1.21 | % 2.38/1.21 | From (42) and (34) follows: % 2.38/1.21 | (45) op1(all_8_0_1, all_8_0_1) = all_15_1_5 % 2.38/1.21 | % 2.38/1.21 | From (41) and (26) follows: % 2.38/1.21 | (46) sorti1(all_8_0_1) % 2.38/1.21 | % 2.38/1.21 | Instantiating formula (9) 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: % 2.38/1.21 | (47) all_15_1_5 = all_8_0_1 % 2.38/1.21 | % 2.38/1.21 | From (47) and (45) follows: % 2.38/1.21 | (48) op1(all_8_0_1, all_8_0_1) = all_8_0_1 % 2.38/1.21 | % 2.38/1.21 | Instantiating formula (8) with all_8_0_1 and discharging atoms op1(all_8_0_1, all_8_0_1) = all_8_0_1, sorti1(all_8_0_1), yields: % 2.38/1.21 | (49) $false % 2.38/1.21 | % 2.38/1.21 |-The branch is then unsatisfiable % 2.38/1.21 % SZS output end Proof for theBenchmark % 2.38/1.21 % 2.38/1.21 738ms %------------------------------------------------------------------------------