%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN374+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 05:01:54 EDT 2022 % Result : Theorem 2.28s 1.43s % Output : Proof 3.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.14/0.15 % Problem : SYN374+1 : TPTP v8.1.0. Released v2.0.0. % 0.14/0.16 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.37 % Computer : n027.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 600 % 0.15/0.37 % DateTime : Mon Jul 11 16:41:19 EDT 2022 % 0.15/0.37 % CPUTime : % 0.64/0.65 ____ _ % 0.64/0.65 ___ / __ \_____(_)___ ________ __________ % 0.64/0.65 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.64/0.65 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.64/0.65 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.64/0.65 % 0.64/0.65 A Theorem Prover for First-Order Logic % 0.64/0.65 (ePrincess v.1.0) % 0.64/0.65 % 0.64/0.65 (c) Philipp Rümmer, 2009-2015 % 0.64/0.65 (c) Peter Backeman, 2014-2015 % 0.64/0.65 (contributions by Angelo Brillout, Peter Baumgartner) % 0.64/0.65 Free software under GNU Lesser General Public License (LGPL). % 0.64/0.65 Bug reports to peter@backeman.se % 0.64/0.65 % 0.64/0.65 For more information, visit http://user.uu.se/~petba168/breu/ % 0.64/0.65 % 0.64/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.31/0.97 Prover 0: Preprocessing ... % 1.42/1.05 Prover 0: Warning: ignoring some quantifiers % 1.49/1.07 Prover 0: Constructing countermodel ... % 1.76/1.22 Prover 0: gave up % 1.76/1.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.76/1.24 Prover 1: Preprocessing ... % 2.18/1.31 Prover 1: Constructing countermodel ... % 2.28/1.43 Prover 1: proved (209ms) % 2.28/1.43 % 2.28/1.43 No countermodel exists, formula is valid % 2.28/1.43 % SZS status Theorem for theBenchmark % 2.28/1.43 % 2.28/1.43 Generating proof ... found it (size 43) % 2.98/1.65 % 2.98/1.65 % SZS output start Proof for theBenchmark % 2.98/1.66 Assumed formulas after preprocessing and simplification: % 2.98/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (big_p(v8) = v7) | ~ (big_p(v8) = v6)) & ((big_p(v4) = v5 & ! [v6] : ! [v7] : ( ~ (v5 = 0) | v7 = 0 | ~ (big_p(v6) = v7)) & ! [v6] : (v5 = 0 | ~ (big_p(v6) = 0)) & ((v3 = 0 & ~ (v1 = 0) & big_p(v2) = 0 & big_p(v0) = v1) | ( ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7)) & ! [v6] : ~ (big_p(v6) = 0)))) | ( ! [v6] : ! [v7] : ( ~ (big_p(v6) = v7) | ? [v8] : ? [v9] : (big_p(v8) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ((v1 = 0 & big_p(v0) = 0 & ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7))) | ( ~ (v1 = 0) & big_p(v0) = v1 & ! [v6] : ~ (big_p(v6) = 0)))))) % 3.09/1.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 3.09/1.70 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)))) | ( ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0))))) % 3.09/1.71 | % 3.09/1.71 | Applying alpha-rule on (1) yields: % 3.09/1.71 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) % 3.09/1.71 | (3) (big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)))) | ( ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0)))) % 3.09/1.71 | % 3.09/1.71 +-Applying beta-rule and splitting (3), into two cases. % 3.09/1.71 |-Branch one: % 3.09/1.71 | (4) big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0))) % 3.09/1.72 | % 3.09/1.72 | Applying alpha-rule on (4) yields: % 3.09/1.72 | (5) big_p(all_0_1_1) = all_0_0_0 % 3.09/1.72 | (6) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) % 3.09/1.72 | (7) ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) % 3.09/1.72 | (8) (all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)) % 3.09/1.72 | % 3.09/1.72 +-Applying beta-rule and splitting (8), into two cases. % 3.09/1.72 |-Branch one: % 3.09/1.72 | (9) all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4 % 3.09/1.72 | % 3.09/1.72 | Applying alpha-rule on (9) yields: % 3.09/1.72 | (10) all_0_2_2 = 0 % 3.09/1.72 | (11) ~ (all_0_4_4 = 0) % 3.09/1.72 | (12) big_p(all_0_3_3) = 0 % 3.09/1.72 | (13) big_p(all_0_5_5) = all_0_4_4 % 3.09/1.72 | % 3.09/1.72 | Instantiating formula (2) with all_0_3_3, 0, all_0_0_0 and discharging atoms big_p(all_0_3_3) = 0, yields: % 3.09/1.72 | (14) all_0_0_0 = 0 | ~ (big_p(all_0_3_3) = all_0_0_0) % 3.09/1.72 | % 3.09/1.72 | Instantiating formula (7) with all_0_3_3 and discharging atoms big_p(all_0_3_3) = 0, yields: % 3.09/1.72 | (15) all_0_0_0 = 0 % 3.09/1.72 | % 3.09/1.72 +-Applying beta-rule and splitting (14), into two cases. % 3.09/1.72 |-Branch one: % 3.09/1.72 | (16) ~ (big_p(all_0_3_3) = all_0_0_0) % 3.09/1.72 | % 3.09/1.73 | From (15) and (16) follows: % 3.09/1.73 | (17) ~ (big_p(all_0_3_3) = 0) % 3.09/1.73 | % 3.09/1.73 | Using (12) and (17) yields: % 3.09/1.73 | (18) $false % 3.09/1.73 | % 3.09/1.73 |-The branch is then unsatisfiable % 3.09/1.73 |-Branch two: % 3.09/1.73 | (19) big_p(all_0_3_3) = all_0_0_0 % 3.09/1.73 | (15) all_0_0_0 = 0 % 3.09/1.73 | % 3.09/1.73 | Instantiating formula (6) with all_0_4_4, all_0_5_5 and discharging atoms big_p(all_0_5_5) = all_0_4_4, yields: % 3.09/1.73 | (21) ~ (all_0_0_0 = 0) | all_0_4_4 = 0 % 3.09/1.73 | % 3.09/1.73 +-Applying beta-rule and splitting (21), into two cases. % 3.09/1.73 |-Branch one: % 3.09/1.73 | (22) ~ (all_0_0_0 = 0) % 3.09/1.73 | % 3.09/1.73 | Equations (15) can reduce 22 to: % 3.09/1.73 | (23) $false % 3.09/1.73 | % 3.09/1.73 |-The branch is then unsatisfiable % 3.09/1.73 |-Branch two: % 3.09/1.73 | (15) all_0_0_0 = 0 % 3.09/1.73 | (25) all_0_4_4 = 0 % 3.09/1.73 | % 3.09/1.73 | Equations (25) can reduce 11 to: % 3.09/1.73 | (23) $false % 3.09/1.73 | % 3.09/1.73 |-The branch is then unsatisfiable % 3.09/1.73 |-Branch two: % 3.09/1.73 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0) % 3.09/1.73 | % 3.09/1.73 | Applying alpha-rule on (27) yields: % 3.09/1.73 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) % 3.09/1.73 | (29) ! [v0] : ~ (big_p(v0) = 0) % 3.09/1.73 | % 3.09/1.73 | Instantiating formula (29) with all_0_1_1 yields: % 3.09/1.73 | (30) ~ (big_p(all_0_1_1) = 0) % 3.09/1.73 | % 3.09/1.73 | Instantiating formula (28) with all_0_0_0, all_0_1_1 and discharging atoms big_p(all_0_1_1) = all_0_0_0, yields: % 3.09/1.73 | (15) all_0_0_0 = 0 % 3.09/1.73 | % 3.09/1.73 | From (15) and (5) follows: % 3.09/1.73 | (32) big_p(all_0_1_1) = 0 % 3.09/1.73 | % 3.09/1.73 | Using (32) and (30) yields: % 3.09/1.73 | (18) $false % 3.09/1.73 | % 3.09/1.73 |-The branch is then unsatisfiable % 3.09/1.73 |-Branch two: % 3.09/1.73 | (34) ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0))) % 3.09/1.74 | % 3.09/1.74 | Applying alpha-rule on (34) yields: % 3.09/1.74 | (35) ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 3.09/1.74 | (36) (all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0)) % 3.09/1.74 | % 3.09/1.74 +-Applying beta-rule and splitting (36), into two cases. % 3.09/1.74 |-Branch one: % 3.09/1.74 | (37) all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) % 3.09/1.74 | % 3.09/1.74 | Applying alpha-rule on (37) yields: % 3.09/1.74 | (25) all_0_4_4 = 0 % 3.09/1.74 | (39) big_p(all_0_5_5) = 0 % 3.09/1.74 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) % 3.09/1.74 | % 3.09/1.74 | Instantiating formula (35) with 0, all_0_5_5 and discharging atoms big_p(all_0_5_5) = 0, yields: % 3.09/1.74 | (41) ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_p(v0) = v1) % 3.09/1.74 | % 3.09/1.74 | Instantiating (41) with all_16_0_6, all_16_1_7 yields: % 3.09/1.74 | (42) ~ (all_16_0_6 = 0) & big_p(all_16_1_7) = all_16_0_6 % 3.09/1.74 | % 3.09/1.74 | Applying alpha-rule on (42) yields: % 3.09/1.74 | (43) ~ (all_16_0_6 = 0) % 3.09/1.74 | (44) big_p(all_16_1_7) = all_16_0_6 % 3.09/1.74 | % 3.09/1.74 | Instantiating formula (28) with all_16_0_6, all_16_1_7 and discharging atoms big_p(all_16_1_7) = all_16_0_6, yields: % 3.09/1.74 | (45) all_16_0_6 = 0 % 3.09/1.74 | % 3.09/1.74 | Equations (45) can reduce 43 to: % 3.09/1.74 | (23) $false % 3.09/1.74 | % 3.09/1.74 |-The branch is then unsatisfiable % 3.09/1.74 |-Branch two: % 3.09/1.74 | (47) ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0) % 3.09/1.74 | % 3.09/1.74 | Applying alpha-rule on (47) yields: % 3.09/1.74 | (11) ~ (all_0_4_4 = 0) % 3.09/1.74 | (13) big_p(all_0_5_5) = all_0_4_4 % 3.09/1.74 | (29) ! [v0] : ~ (big_p(v0) = 0) % 3.09/1.74 | % 3.09/1.74 | Instantiating formula (35) with all_0_4_4, all_0_5_5 and discharging atoms big_p(all_0_5_5) = all_0_4_4, yields: % 3.09/1.74 | (51) ? [v0] : ? [v1] : (big_p(v0) = v1 & ( ~ (v1 = 0) | ~ (all_0_4_4 = 0)) & (v1 = 0 | all_0_4_4 = 0)) % 3.09/1.74 | % 3.09/1.74 | Instantiating (51) with all_16_0_8, all_16_1_9 yields: % 3.09/1.74 | (52) big_p(all_16_1_9) = all_16_0_8 & ( ~ (all_16_0_8 = 0) | ~ (all_0_4_4 = 0)) & (all_16_0_8 = 0 | all_0_4_4 = 0) % 3.09/1.74 | % 3.09/1.74 | Applying alpha-rule on (52) yields: % 3.09/1.74 | (53) big_p(all_16_1_9) = all_16_0_8 % 3.09/1.74 | (54) ~ (all_16_0_8 = 0) | ~ (all_0_4_4 = 0) % 3.09/1.74 | (55) all_16_0_8 = 0 | all_0_4_4 = 0 % 3.09/1.74 | % 3.09/1.75 +-Applying beta-rule and splitting (55), into two cases. % 3.09/1.75 |-Branch one: % 3.09/1.75 | (56) all_16_0_8 = 0 % 3.09/1.75 | % 3.09/1.75 | From (56) and (53) follows: % 3.09/1.75 | (57) big_p(all_16_1_9) = 0 % 3.09/1.75 | % 3.09/1.75 | Instantiating formula (29) with all_16_1_9 and discharging atoms big_p(all_16_1_9) = 0, yields: % 3.09/1.75 | (18) $false % 3.09/1.75 | % 3.09/1.75 |-The branch is then unsatisfiable % 3.09/1.75 |-Branch two: % 3.09/1.75 | (59) ~ (all_16_0_8 = 0) % 3.09/1.75 | (25) all_0_4_4 = 0 % 3.09/1.75 | % 3.09/1.75 | Equations (25) can reduce 11 to: % 3.09/1.75 | (23) $false % 3.09/1.75 | % 3.09/1.75 |-The branch is then unsatisfiable % 3.09/1.75 % SZS output end Proof for theBenchmark % 3.09/1.75 % 3.09/1.75 1083ms %------------------------------------------------------------------------------