%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n010.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 00:18:02 EDT 2022 % Result : Theorem 18.10s 5.43s % Output : Proof 34.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0. % 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.35 % Computer : n010.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 600 % 0.12/0.35 % DateTime : Mon Jul 11 02:38:30 EDT 2022 % 0.12/0.35 % CPUTime : % 0.61/0.60 ____ _ % 0.61/0.60 ___ / __ \_____(_)___ ________ __________ % 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic % 0.61/0.60 (ePrincess v.1.0) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2015 % 0.61/0.60 (c) Peter Backeman, 2014-2015 % 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.60 Bug reports to peter@backeman.se % 0.61/0.60 % 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/0.91 Prover 0: Preprocessing ... % 1.76/1.05 Prover 0: Warning: ignoring some quantifiers % 1.76/1.07 Prover 0: Constructing countermodel ... % 2.25/1.19 Prover 0: gave up % 2.25/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.25/1.21 Prover 1: Preprocessing ... % 2.42/1.29 Prover 1: Warning: ignoring some quantifiers % 2.42/1.29 Prover 1: Constructing countermodel ... % 2.68/1.32 Prover 1: gave up % 2.68/1.32 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.68/1.33 Prover 2: Preprocessing ... % 2.95/1.40 Prover 2: Warning: ignoring some quantifiers % 2.95/1.41 Prover 2: Constructing countermodel ... % 2.95/1.44 Prover 2: gave up % 2.95/1.45 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.95/1.46 Prover 3: Preprocessing ... % 3.34/1.48 Prover 3: Warning: ignoring some quantifiers % 3.34/1.48 Prover 3: Constructing countermodel ... % 3.44/1.51 Prover 3: gave up % 3.44/1.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 3.59/1.52 Prover 4: Preprocessing ... % 3.67/1.59 Prover 4: Warning: ignoring some quantifiers % 3.67/1.59 Prover 4: Constructing countermodel ... % 5.31/1.95 Prover 4: gave up % 5.31/1.95 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.31/1.96 Prover 5: Preprocessing ... % 5.31/1.99 Prover 5: Warning: ignoring some quantifiers % 5.31/1.99 Prover 5: Constructing countermodel ... % 5.67/2.01 Prover 5: gave up % 5.67/2.01 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.67/2.01 Prover 6: Preprocessing ... % 5.67/2.04 Prover 6: Warning: ignoring some quantifiers % 5.67/2.04 Prover 6: Constructing countermodel ... % 5.67/2.06 Prover 6: gave up % 5.67/2.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 5.67/2.07 Prover 7: Preprocessing ... % 6.06/2.09 Prover 7: Proving ... % 18.10/5.43 Prover 7: proved (3367ms) % 18.10/5.43 % 18.10/5.43 % SZS status Theorem for theBenchmark % 18.10/5.43 % 18.10/5.43 Generating proof ... found it (size 46) % 33.75/12.16 % 33.75/12.16 % SZS output start Proof for theBenchmark % 33.75/12.16 Assumed formulas after preprocessing and simplification: % 33.75/12.16 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (union(v4, v3) = v2) | ~ (union(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v1, v2) = v4) | ~ member(v3, v4) | member(v3, v2) | member(v3, v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | union(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ! [v4] : (member(v4, v3) | ( ~ member(v4, v2) & ~ member(v4, v1)))) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ member(v3, v2) | ~ member(v3, v1)) & (member(v3, v2) | member(v3, v1)))) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ member(v3, v1) | member(v3, v2))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ( ~ empty(v1) | ! [v2] : ~ member(v2, v1)) & ! [v1] : ~ member(v1, v0) & ! [v1] : (empty(v1) | ? [v2] : member(v2, v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ( ~ (v2 = v1) & union(v1, v0) = v2)) % 34.16/12.19 | Instantiating (0) with all_0_0_0 yields: % 34.16/12.19 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ member(v3, v1) & ~ member(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) & ! [v0] : ~ member(v0, all_0_0_0) & ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ( ~ (v1 = v0) & union(v0, all_0_0_0) = v1) % 34.27/12.19 | % 34.27/12.19 | Applying alpha-rule on (1) yields: % 34.27/12.19 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 34.27/12.19 | (3) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 34.27/12.19 | (4) ? [v0] : ? [v1] : ( ~ (v1 = v0) & union(v0, all_0_0_0) = v1) % 34.27/12.19 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ member(v3, v1) & ~ member(v3, v0)))) % 34.27/12.19 | (6) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 34.27/12.19 | (7) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 34.27/12.19 | (8) ! [v0] : subset(v0, v0) % 34.27/12.19 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 34.27/12.20 | (10) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) % 34.27/12.20 | (11) ! [v0] : ~ member(v0, all_0_0_0) % 34.27/12.20 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 34.27/12.20 | (13) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) % 34.27/12.20 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 34.27/12.20 | % 34.27/12.20 | Instantiating (4) with all_2_0_1, all_2_1_2 yields: % 34.27/12.20 | (15) ~ (all_2_0_1 = all_2_1_2) & union(all_2_1_2, all_0_0_0) = all_2_0_1 % 34.27/12.20 | % 34.27/12.20 | Applying alpha-rule on (15) yields: % 34.27/12.20 | (16) ~ (all_2_0_1 = all_2_1_2) % 34.27/12.20 | (17) union(all_2_1_2, all_0_0_0) = all_2_0_1 % 34.27/12.20 | % 34.27/12.20 | Instantiating formula (9) with all_2_0_1, all_0_0_0, all_2_1_2 and discharging atoms union(all_2_1_2, all_0_0_0) = all_2_0_1, yields: % 34.27/12.20 | (18) union(all_0_0_0, all_2_1_2) = all_2_0_1 % 34.27/12.20 | % 34.27/12.20 | Instantiating formula (5) with all_2_0_1, all_2_1_2, all_0_0_0 and discharging atoms union(all_0_0_0, all_2_1_2) = all_2_0_1, yields: % 34.27/12.20 | (19) ! [v0] : (member(v0, all_2_0_1) | ( ~ member(v0, all_2_1_2) & ~ member(v0, all_0_0_0))) % 34.27/12.20 | % 34.27/12.20 | Introducing new symbol ex_35_1_7 defined by: % 34.27/12.20 | (20) ex_35_1_7 = all_2_0_1 % 34.27/12.20 | % 34.27/12.20 | Introducing new symbol ex_35_0_6 defined by: % 34.27/12.20 | (21) ex_35_0_6 = all_2_1_2 % 34.27/12.20 | % 34.27/12.20 | Instantiating formula (3) with ex_35_0_6, ex_35_1_7 yields: % 34.27/12.20 | (22) ex_35_0_6 = ex_35_1_7 | ? [v0] : (( ~ member(v0, ex_35_0_6) | ~ member(v0, ex_35_1_7)) & (member(v0, ex_35_0_6) | member(v0, ex_35_1_7))) % 34.27/12.20 | % 34.27/12.20 +-Applying beta-rule and splitting (22), into two cases. % 34.27/12.20 |-Branch one: % 34.27/12.20 | (23) ex_35_0_6 = ex_35_1_7 % 34.27/12.20 | % 34.27/12.20 | Combining equations (21,23) yields a new equation: % 34.27/12.20 | (24) ex_35_1_7 = all_2_1_2 % 34.27/12.20 | % 34.27/12.20 | Combining equations (24,20) yields a new equation: % 34.27/12.20 | (25) all_2_0_1 = all_2_1_2 % 34.27/12.20 | % 34.27/12.20 | Equations (25) can reduce 16 to: % 34.27/12.20 | (26) $false % 34.27/12.20 | % 34.27/12.20 |-The branch is then unsatisfiable % 34.27/12.20 |-Branch two: % 34.27/12.20 | (27) ? [v0] : (( ~ member(v0, ex_35_0_6) | ~ member(v0, ex_35_1_7)) & (member(v0, ex_35_0_6) | member(v0, ex_35_1_7))) % 34.27/12.20 | % 34.27/12.20 | Instantiating (27) with all_38_0_8 yields: % 34.27/12.20 | (28) ( ~ member(all_38_0_8, ex_35_0_6) | ~ member(all_38_0_8, ex_35_1_7)) & (member(all_38_0_8, ex_35_0_6) | member(all_38_0_8, ex_35_1_7)) % 34.27/12.20 | % 34.27/12.20 | Applying alpha-rule on (28) yields: % 34.27/12.20 | (29) ~ member(all_38_0_8, ex_35_0_6) | ~ member(all_38_0_8, ex_35_1_7) % 34.27/12.20 | (30) member(all_38_0_8, ex_35_0_6) | member(all_38_0_8, ex_35_1_7) % 34.27/12.20 | % 34.27/12.20 +-Applying beta-rule and splitting (29), into two cases. % 34.27/12.20 |-Branch one: % 34.27/12.20 | (31) ~ member(all_38_0_8, ex_35_0_6) % 34.27/12.20 | % 34.27/12.20 +-Applying beta-rule and splitting (30), into two cases. % 34.27/12.20 |-Branch one: % 34.27/12.20 | (32) member(all_38_0_8, ex_35_0_6) % 34.27/12.20 | % 34.27/12.20 | Using (32) and (31) yields: % 34.27/12.20 | (33) $false % 34.27/12.20 | % 34.27/12.20 |-The branch is then unsatisfiable % 34.27/12.20 |-Branch two: % 34.27/12.20 | (34) member(all_38_0_8, ex_35_1_7) % 34.27/12.20 | % 34.27/12.20 | Instantiating formula (11) with all_38_0_8 yields: % 34.27/12.20 | (35) ~ member(all_38_0_8, all_0_0_0) % 34.27/12.20 | % 34.27/12.20 | Instantiating formula (14) with all_2_0_1, all_38_0_8, all_2_1_2, all_0_0_0 and discharging atoms union(all_0_0_0, all_2_1_2) = all_2_0_1, ~ member(all_38_0_8, all_0_0_0), yields: % 34.27/12.21 | (36) ~ member(all_38_0_8, all_2_0_1) | member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 +-Applying beta-rule and splitting (36), into two cases. % 34.27/12.21 |-Branch one: % 34.27/12.21 | (37) ~ member(all_38_0_8, all_2_0_1) % 34.27/12.21 | % 34.27/12.21 | From (20) and (34) follows: % 34.27/12.21 | (38) member(all_38_0_8, all_2_0_1) % 34.27/12.21 | % 34.27/12.21 | Using (38) and (37) yields: % 34.27/12.21 | (33) $false % 34.27/12.21 | % 34.27/12.21 |-The branch is then unsatisfiable % 34.27/12.21 |-Branch two: % 34.27/12.21 | (40) member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 | From (21) and (31) follows: % 34.27/12.21 | (41) ~ member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 | Using (40) and (41) yields: % 34.27/12.21 | (33) $false % 34.27/12.21 | % 34.27/12.21 |-The branch is then unsatisfiable % 34.27/12.21 |-Branch two: % 34.27/12.21 | (32) member(all_38_0_8, ex_35_0_6) % 34.27/12.21 | (44) ~ member(all_38_0_8, ex_35_1_7) % 34.27/12.21 | % 34.27/12.21 | Instantiating formula (11) with all_38_0_8 yields: % 34.27/12.21 | (35) ~ member(all_38_0_8, all_0_0_0) % 34.27/12.21 | % 34.27/12.21 | Instantiating formula (14) with all_2_0_1, all_38_0_8, all_2_1_2, all_0_0_0 and discharging atoms union(all_0_0_0, all_2_1_2) = all_2_0_1, ~ member(all_38_0_8, all_0_0_0), yields: % 34.27/12.21 | (36) ~ member(all_38_0_8, all_2_0_1) | member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 +-Applying beta-rule and splitting (36), into two cases. % 34.27/12.21 |-Branch one: % 34.27/12.21 | (37) ~ member(all_38_0_8, all_2_0_1) % 34.27/12.21 | % 34.27/12.21 | Introducing new symbol ex_86_0_27 defined by: % 34.27/12.21 | (48) ex_86_0_27 = all_38_0_8 % 34.27/12.21 | % 34.27/12.21 | Instantiating formula (19) with ex_86_0_27 yields: % 34.27/12.21 | (49) member(ex_86_0_27, all_2_0_1) | ( ~ member(ex_86_0_27, all_2_1_2) & ~ member(ex_86_0_27, all_0_0_0)) % 34.27/12.21 | % 34.27/12.21 +-Applying beta-rule and splitting (49), into two cases. % 34.27/12.21 |-Branch one: % 34.27/12.21 | (50) member(ex_86_0_27, all_2_0_1) % 34.27/12.21 | % 34.27/12.21 | From (48) and (50) follows: % 34.27/12.21 | (38) member(all_38_0_8, all_2_0_1) % 34.27/12.21 | % 34.27/12.21 | Using (38) and (37) yields: % 34.27/12.21 | (33) $false % 34.27/12.21 | % 34.27/12.21 |-The branch is then unsatisfiable % 34.27/12.21 |-Branch two: % 34.27/12.21 | (53) ~ member(ex_86_0_27, all_2_1_2) & ~ member(ex_86_0_27, all_0_0_0) % 34.27/12.21 | % 34.27/12.21 | Applying alpha-rule on (53) yields: % 34.27/12.21 | (54) ~ member(ex_86_0_27, all_2_1_2) % 34.27/12.21 | (55) ~ member(ex_86_0_27, all_0_0_0) % 34.27/12.21 | % 34.27/12.21 | From (21) and (32) follows: % 34.27/12.21 | (40) member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 | From (48) and (54) follows: % 34.27/12.21 | (41) ~ member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 | Using (40) and (41) yields: % 34.27/12.21 | (33) $false % 34.27/12.21 | % 34.27/12.21 |-The branch is then unsatisfiable % 34.27/12.21 |-Branch two: % 34.27/12.21 | (38) member(all_38_0_8, all_2_0_1) % 34.27/12.21 | (40) member(all_38_0_8, all_2_1_2) % 34.27/12.21 | % 34.27/12.21 | From (20) and (44) follows: % 34.27/12.21 | (37) ~ member(all_38_0_8, all_2_0_1) % 34.27/12.21 | % 34.27/12.21 | Using (38) and (37) yields: % 34.27/12.21 | (33) $false % 34.27/12.21 | % 34.27/12.21 |-The branch is then unsatisfiable % 34.27/12.21 % SZS output end Proof for theBenchmark % 34.27/12.21 % 34.27/12.21 11598ms %------------------------------------------------------------------------------