%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 08:46:48 EDT 2022 % Result : Theorem 16.47s 4.45s % Output : Proof 22.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jun 19 07:10:46 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.52 ____ _ % 0.19/0.52 ___ / __ \_____(_)___ ________ __________ % 0.19/0.52 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.52 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.52 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.52 % 0.19/0.52 A Theorem Prover for First-Order Logic % 0.19/0.52 (ePrincess v.1.0) % 0.19/0.52 % 0.19/0.52 (c) Philipp Rümmer, 2009-2015 % 0.19/0.52 (c) Peter Backeman, 2014-2015 % 0.19/0.52 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.52 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.52 Bug reports to peter@backeman.se % 0.19/0.52 % 0.19/0.52 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.52 % 0.19/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.58 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.40/0.88 Prover 0: Preprocessing ... % 1.74/1.04 Prover 0: Warning: ignoring some quantifiers % 1.74/1.05 Prover 0: Constructing countermodel ... % 2.40/1.22 Prover 0: gave up % 2.40/1.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.40/1.24 Prover 1: Preprocessing ... % 2.74/1.32 Prover 1: Warning: ignoring some quantifiers % 2.74/1.32 Prover 1: Constructing countermodel ... % 3.04/1.40 Prover 1: gave up % 3.04/1.40 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.04/1.41 Prover 2: Preprocessing ... % 3.45/1.49 Prover 2: Warning: ignoring some quantifiers % 3.45/1.50 Prover 2: Constructing countermodel ... % 3.61/1.56 Prover 2: gave up % 3.61/1.56 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.61/1.58 Prover 3: Preprocessing ... % 3.61/1.60 Prover 3: Warning: ignoring some quantifiers % 3.61/1.60 Prover 3: Constructing countermodel ... % 4.00/1.64 Prover 3: gave up % 4.00/1.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 4.00/1.65 Prover 4: Preprocessing ... % 4.43/1.72 Prover 4: Warning: ignoring some quantifiers % 4.43/1.72 Prover 4: Constructing countermodel ... % 9.24/2.80 Prover 4: gave up % 9.24/2.80 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 9.24/2.80 Prover 5: Preprocessing ... % 9.24/2.83 Prover 5: Warning: ignoring some quantifiers % 9.24/2.84 Prover 5: Constructing countermodel ... % 9.24/2.87 Prover 5: gave up % 9.24/2.88 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 9.24/2.88 Prover 6: Preprocessing ... % 9.79/2.92 Prover 6: Warning: ignoring some quantifiers % 9.79/2.92 Prover 6: Constructing countermodel ... % 9.82/2.95 Prover 6: gave up % 9.82/2.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 9.82/2.96 Prover 7: Preprocessing ... % 9.82/2.98 Prover 7: Proving ... % 16.47/4.45 Prover 7: proved (1494ms) % 16.47/4.45 % 16.47/4.45 % SZS status Theorem for theBenchmark % 16.47/4.45 % 16.47/4.45 Generating proof ... found it (size 57) % 22.14/5.89 % 22.14/5.89 % SZS output start Proof for theBenchmark % 22.14/5.89 Assumed formulas after preprocessing and simplification: % 22.14/5.89 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_difference(v4, v3) = v2) | ~ (set_difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v2)) & (in(v5, v4) | (in(v5, v1) & ~ in(v5, v2)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v1) & ~ in(v4, v2))) & ! [v4] : ( ~ in(v4, v1) | in(v4, v3) | in(v4, v2)))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_difference(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ~ in(v3, v1)) & (in(v3, v2) | in(v3, v1)))) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (in(v3, v1) & ~ in(v3, v2))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : (set_difference(v1, v2) = v3 & ((v3 = v0 & ~ subset(v1, v2)) | ( ~ (v3 = v0) & subset(v1, v2)))) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1)) % 22.60/5.91 | Instantiating (0) with all_0_0_0 yields: % 22.60/5.91 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : (set_difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1)))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 22.60/5.91 | % 22.60/5.91 | Applying alpha-rule on (1) yields: % 22.60/5.91 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) % 22.60/5.91 | (3) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) % 22.60/5.91 | (4) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) % 22.60/5.91 | (5) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) % 22.60/5.91 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 22.60/5.91 | (7) ? [v0] : ~ empty(v0) % 22.60/5.91 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 22.60/5.91 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) % 22.60/5.92 | (10) ! [v0] : subset(v0, v0) % 22.60/5.92 | (11) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 22.60/5.92 | (12) ? [v0] : ? [v1] : ? [v2] : (set_difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1)))) % 22.60/5.92 | (13) empty(all_0_0_0) % 22.60/5.92 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) % 22.60/5.92 | (15) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 22.60/5.92 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 22.60/5.92 | (17) ? [v0] : empty(v0) % 22.60/5.92 | (18) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 22.60/5.92 | % 22.60/5.92 | Instantiating (17) with all_3_0_1 yields: % 22.60/5.92 | (19) empty(all_3_0_1) % 22.60/5.92 | % 22.60/5.92 | Instantiating (12) with all_7_0_3, all_7_1_4, all_7_2_5 yields: % 22.60/5.92 | (20) set_difference(all_7_2_5, all_7_1_4) = all_7_0_3 & ((all_7_0_3 = all_0_0_0 & ~ subset(all_7_2_5, all_7_1_4)) | ( ~ (all_7_0_3 = all_0_0_0) & subset(all_7_2_5, all_7_1_4))) % 22.60/5.92 | % 22.60/5.92 | Applying alpha-rule on (20) yields: % 22.60/5.92 | (21) set_difference(all_7_2_5, all_7_1_4) = all_7_0_3 % 22.60/5.92 | (22) (all_7_0_3 = all_0_0_0 & ~ subset(all_7_2_5, all_7_1_4)) | ( ~ (all_7_0_3 = all_0_0_0) & subset(all_7_2_5, all_7_1_4)) % 22.60/5.92 | % 22.60/5.92 | Instantiating formula (8) with all_0_0_0, all_3_0_1 and discharging atoms empty(all_3_0_1), empty(all_0_0_0), yields: % 22.60/5.92 | (23) all_3_0_1 = all_0_0_0 % 22.60/5.92 | % 22.60/5.92 | Instantiating formula (2) with all_7_0_3, all_7_1_4, all_7_2_5 and discharging atoms set_difference(all_7_2_5, all_7_1_4) = all_7_0_3, yields: % 22.60/5.92 | (24) ! [v0] : (v0 = all_7_0_3 | ? [v1] : (( ~ in(v1, v0) | ~ in(v1, all_7_2_5) | in(v1, all_7_1_4)) & (in(v1, v0) | (in(v1, all_7_2_5) & ~ in(v1, all_7_1_4))))) % 22.60/5.92 | % 22.60/5.92 | Instantiating formula (9) with all_7_0_3, all_7_1_4, all_7_2_5 and discharging atoms set_difference(all_7_2_5, all_7_1_4) = all_7_0_3, yields: % 22.60/5.92 | (25) ! [v0] : ( ~ in(v0, all_7_0_3) | (in(v0, all_7_2_5) & ~ in(v0, all_7_1_4))) & ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_0_3) | in(v0, all_7_1_4)) % 22.60/5.92 | % 22.60/5.92 | Applying alpha-rule on (25) yields: % 22.60/5.92 | (26) ! [v0] : ( ~ in(v0, all_7_0_3) | (in(v0, all_7_2_5) & ~ in(v0, all_7_1_4))) % 22.60/5.92 | (27) ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_0_3) | in(v0, all_7_1_4)) % 22.60/5.92 | % 22.60/5.92 +-Applying beta-rule and splitting (22), into two cases. % 22.60/5.92 |-Branch one: % 22.60/5.92 | (28) all_7_0_3 = all_0_0_0 & ~ subset(all_7_2_5, all_7_1_4) % 22.60/5.92 | % 22.60/5.92 | Applying alpha-rule on (28) yields: % 22.60/5.92 | (29) all_7_0_3 = all_0_0_0 % 22.60/5.92 | (30) ~ subset(all_7_2_5, all_7_1_4) % 22.60/5.92 | % 22.60/5.92 | Introducing new symbol ex_29_1_7 defined by: % 22.60/5.92 | (31) ex_29_1_7 = all_7_2_5 % 22.60/5.92 | % 22.60/5.92 | Introducing new symbol ex_29_0_6 defined by: % 22.60/5.92 | (32) ex_29_0_6 = all_7_1_4 % 22.60/5.92 | % 22.60/5.92 | Instantiating formula (15) with ex_29_0_6, ex_29_1_7 yields: % 22.60/5.92 | (33) subset(ex_29_1_7, ex_29_0_6) | ? [v0] : (in(v0, ex_29_1_7) & ~ in(v0, ex_29_0_6)) % 22.60/5.92 | % 22.60/5.92 +-Applying beta-rule and splitting (33), into two cases. % 22.60/5.92 |-Branch one: % 22.60/5.92 | (34) subset(ex_29_1_7, ex_29_0_6) % 22.60/5.92 | % 22.60/5.92 | From (31)(32) and (34) follows: % 22.60/5.92 | (35) subset(all_7_2_5, all_7_1_4) % 22.60/5.92 | % 22.60/5.92 | Using (35) and (30) yields: % 22.60/5.92 | (36) $false % 22.60/5.92 | % 22.60/5.92 |-The branch is then unsatisfiable % 22.60/5.92 |-Branch two: % 22.60/5.92 | (37) ? [v0] : (in(v0, ex_29_1_7) & ~ in(v0, ex_29_0_6)) % 22.60/5.92 | % 22.60/5.92 | Instantiating (37) with all_31_0_8 yields: % 22.60/5.92 | (38) in(all_31_0_8, ex_29_1_7) & ~ in(all_31_0_8, ex_29_0_6) % 22.60/5.92 | % 22.60/5.92 | Applying alpha-rule on (38) yields: % 22.60/5.92 | (39) in(all_31_0_8, ex_29_1_7) % 22.60/5.92 | (40) ~ in(all_31_0_8, ex_29_0_6) % 22.60/5.92 | % 22.60/5.92 | Instantiating formula (11) with all_0_0_0, all_31_0_8 and discharging atoms empty(all_0_0_0), yields: % 22.60/5.92 | (41) ~ in(all_31_0_8, all_0_0_0) % 22.60/5.92 | % 22.60/5.93 | Instantiating formula (27) with all_31_0_8 yields: % 22.60/5.93 | (42) ~ in(all_31_0_8, all_7_2_5) | in(all_31_0_8, all_7_0_3) | in(all_31_0_8, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 +-Applying beta-rule and splitting (42), into two cases. % 22.60/5.93 |-Branch one: % 22.60/5.93 | (43) ~ in(all_31_0_8, all_7_2_5) % 22.60/5.93 | % 22.60/5.93 | From (31) and (39) follows: % 22.60/5.93 | (44) in(all_31_0_8, all_7_2_5) % 22.60/5.93 | % 22.60/5.93 | Using (44) and (43) yields: % 22.60/5.93 | (36) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 |-Branch two: % 22.60/5.93 | (46) in(all_31_0_8, all_7_0_3) | in(all_31_0_8, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 +-Applying beta-rule and splitting (46), into two cases. % 22.60/5.93 |-Branch one: % 22.60/5.93 | (47) in(all_31_0_8, all_7_0_3) % 22.60/5.93 | % 22.60/5.93 | From (29) and (47) follows: % 22.60/5.93 | (48) in(all_31_0_8, all_0_0_0) % 22.60/5.93 | % 22.60/5.93 | Using (48) and (41) yields: % 22.60/5.93 | (36) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 |-Branch two: % 22.60/5.93 | (50) in(all_31_0_8, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | From (32) and (40) follows: % 22.60/5.93 | (51) ~ in(all_31_0_8, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | Using (50) and (51) yields: % 22.60/5.93 | (36) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 |-Branch two: % 22.60/5.93 | (53) ~ (all_7_0_3 = all_0_0_0) & subset(all_7_2_5, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | Applying alpha-rule on (53) yields: % 22.60/5.93 | (54) ~ (all_7_0_3 = all_0_0_0) % 22.60/5.93 | (35) subset(all_7_2_5, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | Instantiating formula (3) with all_7_1_4, all_7_2_5 and discharging atoms subset(all_7_2_5, all_7_1_4), yields: % 22.60/5.93 | (56) ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_1_4)) % 22.60/5.93 | % 22.60/5.93 | Introducing new symbol ex_59_0_17 defined by: % 22.60/5.93 | (57) ex_59_0_17 = all_3_0_1 % 22.60/5.93 | % 22.60/5.93 | Instantiating formula (24) with ex_59_0_17 yields: % 22.60/5.93 | (58) ex_59_0_17 = all_7_0_3 | ? [v0] : (( ~ in(v0, ex_59_0_17) | ~ in(v0, all_7_2_5) | in(v0, all_7_1_4)) & (in(v0, ex_59_0_17) | (in(v0, all_7_2_5) & ~ in(v0, all_7_1_4)))) % 22.60/5.93 | % 22.60/5.93 +-Applying beta-rule and splitting (58), into two cases. % 22.60/5.93 |-Branch one: % 22.60/5.93 | (59) ex_59_0_17 = all_7_0_3 % 22.60/5.93 | % 22.60/5.93 | Combining equations (59,57) yields a new equation: % 22.60/5.93 | (60) all_7_0_3 = all_3_0_1 % 22.60/5.93 | % 22.60/5.93 | Simplifying 60 yields: % 22.60/5.93 | (61) all_7_0_3 = all_3_0_1 % 22.60/5.93 | % 22.60/5.93 | Combining equations (23,61) yields a new equation: % 22.60/5.93 | (29) all_7_0_3 = all_0_0_0 % 22.60/5.93 | % 22.60/5.93 | Equations (29) can reduce 54 to: % 22.60/5.93 | (63) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 |-Branch two: % 22.60/5.93 | (64) ? [v0] : (( ~ in(v0, ex_59_0_17) | ~ in(v0, all_7_2_5) | in(v0, all_7_1_4)) & (in(v0, ex_59_0_17) | (in(v0, all_7_2_5) & ~ in(v0, all_7_1_4)))) % 22.60/5.93 | % 22.60/5.93 | Instantiating (64) with all_62_0_18 yields: % 22.60/5.93 | (65) ( ~ in(all_62_0_18, ex_59_0_17) | ~ in(all_62_0_18, all_7_2_5) | in(all_62_0_18, all_7_1_4)) & (in(all_62_0_18, ex_59_0_17) | (in(all_62_0_18, all_7_2_5) & ~ in(all_62_0_18, all_7_1_4))) % 22.60/5.93 | % 22.60/5.93 | Applying alpha-rule on (65) yields: % 22.60/5.93 | (66) ~ in(all_62_0_18, ex_59_0_17) | ~ in(all_62_0_18, all_7_2_5) | in(all_62_0_18, all_7_1_4) % 22.60/5.93 | (67) in(all_62_0_18, ex_59_0_17) | (in(all_62_0_18, all_7_2_5) & ~ in(all_62_0_18, all_7_1_4)) % 22.60/5.93 | % 22.60/5.93 +-Applying beta-rule and splitting (66), into two cases. % 22.60/5.93 |-Branch one: % 22.60/5.93 | (68) ~ in(all_62_0_18, ex_59_0_17) % 22.60/5.93 | % 22.60/5.93 +-Applying beta-rule and splitting (67), into two cases. % 22.60/5.93 |-Branch one: % 22.60/5.93 | (69) in(all_62_0_18, ex_59_0_17) % 22.60/5.93 | % 22.60/5.93 | Using (69) and (68) yields: % 22.60/5.93 | (36) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 |-Branch two: % 22.60/5.93 | (71) in(all_62_0_18, all_7_2_5) & ~ in(all_62_0_18, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | Applying alpha-rule on (71) yields: % 22.60/5.93 | (72) in(all_62_0_18, all_7_2_5) % 22.60/5.93 | (73) ~ in(all_62_0_18, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | Instantiating formula (56) with all_62_0_18 and discharging atoms in(all_62_0_18, all_7_2_5), ~ in(all_62_0_18, all_7_1_4), yields: % 22.60/5.93 | (36) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 |-Branch two: % 22.60/5.93 | (69) in(all_62_0_18, ex_59_0_17) % 22.60/5.93 | (76) ~ in(all_62_0_18, all_7_2_5) | in(all_62_0_18, all_7_1_4) % 22.60/5.93 | % 22.60/5.93 | Instantiating formula (11) with all_0_0_0, all_62_0_18 and discharging atoms empty(all_0_0_0), yields: % 22.60/5.93 | (77) ~ in(all_62_0_18, all_0_0_0) % 22.60/5.93 | % 22.60/5.93 | Combining equations (23,57) yields a new equation: % 22.60/5.93 | (78) ex_59_0_17 = all_0_0_0 % 22.60/5.93 | % 22.60/5.93 | From (78) and (69) follows: % 22.60/5.93 | (79) in(all_62_0_18, all_0_0_0) % 22.60/5.93 | % 22.60/5.93 | Using (79) and (77) yields: % 22.60/5.93 | (36) $false % 22.60/5.93 | % 22.60/5.93 |-The branch is then unsatisfiable % 22.60/5.93 % SZS output end Proof for theBenchmark % 22.60/5.93 % 22.60/5.93 5398ms %------------------------------------------------------------------------------