%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 21 04:59:46 EDT 2022 % Result : Theorem 2.16s 1.21s % Output : Proof 2.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jul 11 12:24:09 EDT 2022 % 0.13/0.34 % CPUTime : % 0.55/0.60 ____ _ % 0.55/0.60 ___ / __ \_____(_)___ ________ __________ % 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.60 % 0.55/0.60 A Theorem Prover for First-Order Logic % 0.55/0.60 (ePrincess v.1.0) % 0.55/0.60 % 0.55/0.60 (c) Philipp Rümmer, 2009-2015 % 0.55/0.60 (c) Peter Backeman, 2014-2015 % 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.60 Bug reports to peter@backeman.se % 0.55/0.60 % 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.60 % 0.55/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.20/0.90 Prover 0: Preprocessing ... % 1.29/0.98 Prover 0: Warning: ignoring some quantifiers % 1.29/0.99 Prover 0: Constructing countermodel ... % 1.68/1.11 Prover 0: gave up % 1.68/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.68/1.12 Prover 1: Preprocessing ... % 1.68/1.17 Prover 1: Constructing countermodel ... % 2.16/1.21 Prover 1: proved (93ms) % 2.16/1.21 % 2.16/1.21 No countermodel exists, formula is valid % 2.16/1.21 % SZS status Theorem for theBenchmark % 2.16/1.21 % 2.16/1.21 Generating proof ... found it (size 25) % 2.46/1.38 % 2.46/1.38 % SZS output start Proof for theBenchmark % 2.46/1.38 Assumed formulas after preprocessing and simplification: % 2.46/1.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (f(v7) = v6) | ~ (f(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_p(v7) = v6) | ~ (big_p(v7) = v5)) & ((v4 = v0 & v3 = 0 & ~ (v1 = 0) & f(v2) = v0 & big_p(v2) = 0 & big_p(v0) = v1 & ! [v5] : ! [v6] : ( ~ (f(v5) = v6) | ? [v7] : ? [v8] : (big_p(v6) = v8 & big_p(v5) = v7 & ( ~ (v7 = 0) | v8 = 0)))) | (v1 = 0 & ~ (v3 = 0) & f(v0) = v2 & big_p(v2) = v3 & big_p(v0) = 0 & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (f(v7) = v5) | ~ (big_p(v5) = v6) | ? [v8] : ( ~ (v8 = 0) & big_p(v7) = v8))))) % 2.61/1.42 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 2.61/1.42 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((all_0_0_0 = all_0_4_4 & all_0_1_1 = 0 & ~ (all_0_3_3 = 0) & f(all_0_2_2) = all_0_4_4 & big_p(all_0_2_2) = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))) | (all_0_3_3 = 0 & ~ (all_0_1_1 = 0) & f(all_0_4_4) = all_0_2_2 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3)))) % 2.61/1.43 | % 2.61/1.43 | Applying alpha-rule on (1) yields: % 2.61/1.43 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) % 2.61/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) % 2.61/1.44 | (4) (all_0_0_0 = all_0_4_4 & all_0_1_1 = 0 & ~ (all_0_3_3 = 0) & f(all_0_2_2) = all_0_4_4 & big_p(all_0_2_2) = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))) | (all_0_3_3 = 0 & ~ (all_0_1_1 = 0) & f(all_0_4_4) = all_0_2_2 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3))) % 2.61/1.44 | % 2.61/1.44 +-Applying beta-rule and splitting (4), into two cases. % 2.61/1.44 |-Branch one: % 2.61/1.44 | (5) all_0_0_0 = all_0_4_4 & all_0_1_1 = 0 & ~ (all_0_3_3 = 0) & f(all_0_2_2) = all_0_4_4 & big_p(all_0_2_2) = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 2.61/1.44 | % 2.61/1.44 | Applying alpha-rule on (5) yields: % 2.61/1.44 | (6) all_0_1_1 = 0 % 2.61/1.44 | (7) big_p(all_0_4_4) = all_0_3_3 % 2.61/1.44 | (8) all_0_0_0 = all_0_4_4 % 2.61/1.45 | (9) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 2.61/1.45 | (10) big_p(all_0_2_2) = 0 % 2.61/1.45 | (11) f(all_0_2_2) = all_0_4_4 % 2.61/1.45 | (12) ~ (all_0_3_3 = 0) % 2.61/1.45 | % 2.61/1.45 | Instantiating formula (9) with all_0_4_4, all_0_2_2 and discharging atoms f(all_0_2_2) = all_0_4_4, yields: % 2.61/1.45 | (13) ? [v0] : ? [v1] : (big_p(all_0_2_2) = v0 & big_p(all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 2.61/1.45 | % 2.61/1.45 | Instantiating (13) with all_12_0_5, all_12_1_6 yields: % 2.61/1.45 | (14) big_p(all_0_2_2) = all_12_1_6 & big_p(all_0_4_4) = all_12_0_5 & ( ~ (all_12_1_6 = 0) | all_12_0_5 = 0) % 2.61/1.46 | % 2.61/1.46 | Applying alpha-rule on (14) yields: % 2.61/1.46 | (15) big_p(all_0_2_2) = all_12_1_6 % 2.61/1.46 | (16) big_p(all_0_4_4) = all_12_0_5 % 2.61/1.46 | (17) ~ (all_12_1_6 = 0) | all_12_0_5 = 0 % 2.61/1.46 | % 2.61/1.46 | Instantiating formula (3) with all_0_2_2, all_12_1_6, 0 and discharging atoms big_p(all_0_2_2) = all_12_1_6, big_p(all_0_2_2) = 0, yields: % 2.61/1.46 | (18) all_12_1_6 = 0 % 2.61/1.46 | % 2.61/1.46 | Instantiating formula (3) with all_0_4_4, all_12_0_5, all_0_3_3 and discharging atoms big_p(all_0_4_4) = all_12_0_5, big_p(all_0_4_4) = all_0_3_3, yields: % 2.61/1.46 | (19) all_12_0_5 = all_0_3_3 % 2.61/1.46 | % 2.61/1.46 +-Applying beta-rule and splitting (17), into two cases. % 2.61/1.46 |-Branch one: % 2.61/1.46 | (20) ~ (all_12_1_6 = 0) % 2.61/1.46 | % 2.61/1.46 | Equations (18) can reduce 20 to: % 2.61/1.46 | (21) $false % 2.61/1.46 | % 2.83/1.46 |-The branch is then unsatisfiable % 2.83/1.46 |-Branch two: % 2.83/1.46 | (18) all_12_1_6 = 0 % 2.83/1.46 | (23) all_12_0_5 = 0 % 2.83/1.46 | % 2.83/1.47 | Combining equations (23,19) yields a new equation: % 2.83/1.47 | (24) all_0_3_3 = 0 % 2.83/1.47 | % 2.83/1.47 | Equations (24) can reduce 12 to: % 2.83/1.47 | (21) $false % 2.83/1.47 | % 2.83/1.47 |-The branch is then unsatisfiable % 2.83/1.47 |-Branch two: % 2.83/1.47 | (26) all_0_3_3 = 0 & ~ (all_0_1_1 = 0) & f(all_0_4_4) = all_0_2_2 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3)) % 2.83/1.47 | % 2.83/1.47 | Applying alpha-rule on (26) yields: % 2.83/1.47 | (27) ~ (all_0_1_1 = 0) % 2.83/1.47 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3)) % 2.83/1.47 | (29) big_p(all_0_2_2) = all_0_1_1 % 2.83/1.47 | (30) f(all_0_4_4) = all_0_2_2 % 2.83/1.47 | (24) all_0_3_3 = 0 % 2.83/1.47 | (32) big_p(all_0_4_4) = 0 % 2.83/1.47 | % 2.83/1.47 | Instantiating formula (28) with all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms f(all_0_4_4) = all_0_2_2, big_p(all_0_2_2) = all_0_1_1, yields: % 2.83/1.47 | (33) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & big_p(all_0_4_4) = v0) % 2.83/1.47 | % 2.83/1.47 +-Applying beta-rule and splitting (33), into two cases. % 2.83/1.47 |-Branch one: % 2.83/1.47 | (6) all_0_1_1 = 0 % 2.83/1.47 | % 2.83/1.47 | Equations (6) can reduce 27 to: % 2.83/1.47 | (21) $false % 2.83/1.47 | % 2.83/1.47 |-The branch is then unsatisfiable % 2.83/1.47 |-Branch two: % 2.83/1.47 | (27) ~ (all_0_1_1 = 0) % 2.83/1.47 | (37) ? [v0] : ( ~ (v0 = 0) & big_p(all_0_4_4) = v0) % 2.83/1.47 | % 2.83/1.47 | Instantiating (37) with all_18_0_7 yields: % 2.83/1.47 | (38) ~ (all_18_0_7 = 0) & big_p(all_0_4_4) = all_18_0_7 % 2.83/1.47 | % 2.83/1.47 | Applying alpha-rule on (38) yields: % 2.83/1.47 | (39) ~ (all_18_0_7 = 0) % 2.83/1.47 | (40) big_p(all_0_4_4) = all_18_0_7 % 2.85/1.47 | % 2.85/1.47 | Instantiating formula (3) with all_0_4_4, all_18_0_7, 0 and discharging atoms big_p(all_0_4_4) = all_18_0_7, big_p(all_0_4_4) = 0, yields: % 2.85/1.47 | (41) all_18_0_7 = 0 % 2.85/1.47 | % 2.85/1.47 | Equations (41) can reduce 39 to: % 2.85/1.47 | (21) $false % 2.85/1.47 | % 2.85/1.47 |-The branch is then unsatisfiable % 2.85/1.47 % SZS output end Proof for theBenchmark % 2.85/1.47 % 2.85/1.47 862ms %------------------------------------------------------------------------------