%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 : Tue Jul 19 00:22:50 EDT 2022 % Result : Theorem 3.95s 1.67s % Output : Proof 5.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n029.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 : Sat Jul 9 20:16:00 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.57 ____ _ % 0.19/0.57 ___ / __ \_____(_)___ ________ __________ % 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.07/0.86 Prover 0: Preprocessing ... % 1.50/1.00 Prover 0: Warning: ignoring some quantifiers % 1.67/1.01 Prover 0: Constructing countermodel ... % 2.43/1.26 Prover 0: gave up % 2.43/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.43/1.29 Prover 1: Preprocessing ... % 2.73/1.35 Prover 1: Warning: ignoring some quantifiers % 2.73/1.36 Prover 1: Constructing countermodel ... % 2.97/1.45 Prover 1: gave up % 2.97/1.45 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.97/1.46 Prover 2: Preprocessing ... % 3.38/1.51 Prover 2: Warning: ignoring some quantifiers % 3.38/1.52 Prover 2: Constructing countermodel ... % 3.95/1.67 Prover 2: proved (223ms) % 3.95/1.67 % 3.95/1.67 No countermodel exists, formula is valid % 3.95/1.67 % SZS status Theorem for theBenchmark % 3.95/1.67 % 3.95/1.67 Generating proof ... Warning: ignoring some quantifiers % 4.82/1.87 found it (size 14) % 4.82/1.87 % 4.82/1.87 % SZS output start Proof for theBenchmark % 4.82/1.87 Assumed formulas after preprocessing and simplification: % 4.82/1.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v1 = v0) & empty(v6) = 0 & empty(v4) = v5 & singleton(v1) = v3 & singleton(v0) = v2 & set_union2(v2, v3) = v2 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v7) = v9) | ~ (set_union2(v9, v8) = v10) | ? [v11] : ((v11 = 0 & in(v7, v8) = 0) | ( ~ (v11 = 0) & subset(v10, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ (in(v9, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (in(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & subset(v11, v8) = v12 & singleton(v7) = v10 & set_union2(v10, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ? [v10] : ((v10 = 0 & empty(v7) = 0) | ( ~ (v10 = 0) & empty(v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : ((v10 = 0 & empty(v7) = 0) | ( ~ (v10 = 0) & empty(v9) = v10))) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : ? [v11] : (( ~ (v10 = v8) | ( ~ (v11 = 0) & in(v8, v7) = v11)) & (v10 = v8 | (v11 = 0 & in(v10, v7) = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : set_union2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8) % 4.82/1.90 | 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, all_0_6_6 yields: % 4.82/1.90 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_5_5 = all_0_6_6) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & singleton(all_0_5_5) = all_0_3_3 & singleton(all_0_6_6) = all_0_4_4 & set_union2(all_0_4_4, all_0_3_3) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ((v4 = 0 & in(v0, v1) = 0) | ( ~ (v4 = 0) & subset(v3, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v4, v1) = v5 & singleton(v0) = v3 & set_union2(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 % 5.18/1.91 | % 5.18/1.91 | Applying alpha-rule on (1) yields: % 5.18/1.91 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v4, v1) = v5 & singleton(v0) = v3 & set_union2(v3, v1) = v4)) % 5.18/1.91 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 5.18/1.91 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 5.18/1.91 | (5) ~ (all_0_5_5 = all_0_6_6) % 5.18/1.91 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 5.18/1.91 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 5.18/1.91 | (8) set_union2(all_0_4_4, all_0_3_3) = all_0_4_4 % 5.18/1.92 | (9) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 % 5.18/1.92 | (10) empty(all_0_0_0) = 0 % 5.18/1.92 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 5.18/1.92 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.18/1.92 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ((v4 = 0 & in(v0, v1) = 0) | ( ~ (v4 = 0) & subset(v3, v1) = v4))) % 5.18/1.92 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.18/1.92 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.18/1.92 | (16) ? [v0] : ? [v1] : singleton(v0) = v1 % 5.18/1.92 | (17) empty(all_0_2_2) = all_0_1_1 % 5.18/1.92 | (18) singleton(all_0_6_6) = all_0_4_4 % 5.18/1.92 | (19) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 5.18/1.92 | (20) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) % 5.18/1.92 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 5.18/1.92 | (22) ? [v0] : ? [v1] : empty(v0) = v1 % 5.18/1.92 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.18/1.92 | (24) singleton(all_0_5_5) = all_0_3_3 % 5.18/1.92 | (25) ~ (all_0_1_1 = 0) % 5.18/1.92 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 5.18/1.92 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.18/1.92 | (28) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 5.18/1.92 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 5.18/1.92 | (30) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 5.18/1.92 | (31) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 5.18/1.92 | % 5.18/1.92 | Instantiating formula (7) with all_0_4_4, all_0_4_4, all_0_3_3 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_4_4, yields: % 5.18/1.92 | (32) set_union2(all_0_3_3, all_0_4_4) = all_0_4_4 % 5.18/1.92 | % 5.18/1.92 | Instantiating formula (13) with all_0_4_4, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, set_union2(all_0_3_3, all_0_4_4) = all_0_4_4, yields: % 5.18/1.92 | (33) ? [v0] : ((v0 = 0 & in(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0)) % 5.18/1.92 | % 5.18/1.92 | Instantiating (33) with all_31_0_26 yields: % 5.18/1.92 | (34) (all_31_0_26 = 0 & in(all_0_5_5, all_0_4_4) = 0) | ( ~ (all_31_0_26 = 0) & subset(all_0_4_4, all_0_4_4) = all_31_0_26) % 5.18/1.93 | % 5.18/1.93 +-Applying beta-rule and splitting (34), into two cases. % 5.18/1.93 |-Branch one: % 5.18/1.93 | (35) all_31_0_26 = 0 & in(all_0_5_5, all_0_4_4) = 0 % 5.18/1.93 | % 5.18/1.93 | Applying alpha-rule on (35) yields: % 5.18/1.93 | (36) all_31_0_26 = 0 % 5.18/1.93 | (37) in(all_0_5_5, all_0_4_4) = 0 % 5.18/1.93 | % 5.18/1.93 | Instantiating formula (26) with all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, in(all_0_5_5, all_0_4_4) = 0, yields: % 5.18/1.93 | (38) all_0_5_5 = all_0_6_6 % 5.18/1.93 | % 5.18/1.93 | Equations (38) can reduce 5 to: % 5.18/1.93 | (39) $false % 5.18/1.93 | % 5.18/1.93 |-The branch is then unsatisfiable % 5.18/1.93 |-Branch two: % 5.18/1.93 | (40) ~ (all_31_0_26 = 0) & subset(all_0_4_4, all_0_4_4) = all_31_0_26 % 5.18/1.93 | % 5.18/1.93 | Applying alpha-rule on (40) yields: % 5.18/1.93 | (41) ~ (all_31_0_26 = 0) % 5.18/1.93 | (42) subset(all_0_4_4, all_0_4_4) = all_31_0_26 % 5.18/1.93 | % 5.18/1.93 | Instantiating formula (14) with all_31_0_26, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_4_4) = all_31_0_26, yields: % 5.18/1.93 | (36) all_31_0_26 = 0 % 5.18/1.93 | % 5.18/1.93 | Equations (36) can reduce 41 to: % 5.18/1.93 | (39) $false % 5.18/1.93 | % 5.18/1.93 |-The branch is then unsatisfiable % 5.18/1.93 % SZS output end Proof for theBenchmark % 5.18/1.93 % 5.18/1.93 1342ms %------------------------------------------------------------------------------