%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU137+1 : TPTP v8.1.0. Released v3.3.0. % 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 : Tue Jul 19 08:46:52 EDT 2022 % Result : Theorem 30.49s 9.72s % Output : Proof 37.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU137+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n027.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 22:48:39 EDT 2022 % 0.12/0.34 % CPUTime : % 0.49/0.58 ____ _ % 0.49/0.58 ___ / __ \_____(_)___ ________ __________ % 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.58 % 0.49/0.58 A Theorem Prover for First-Order Logic % 0.49/0.59 (ePrincess v.1.0) % 0.49/0.59 % 0.49/0.59 (c) Philipp Rümmer, 2009-2015 % 0.49/0.59 (c) Peter Backeman, 2014-2015 % 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.59 Bug reports to peter@backeman.se % 0.49/0.59 % 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.59 % 0.49/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.52/0.94 Prover 0: Preprocessing ... % 2.02/1.13 Prover 0: Warning: ignoring some quantifiers % 2.02/1.15 Prover 0: Constructing countermodel ... % 2.88/1.37 Prover 0: gave up % 2.88/1.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.88/1.39 Prover 1: Preprocessing ... % 3.27/1.48 Prover 1: Warning: ignoring some quantifiers % 3.27/1.49 Prover 1: Constructing countermodel ... % 3.75/1.64 Prover 1: gave up % 3.75/1.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.08/1.66 Prover 2: Preprocessing ... % 4.58/1.76 Prover 2: Warning: ignoring some quantifiers % 4.70/1.77 Prover 2: Constructing countermodel ... % 5.11/1.89 Prover 2: gave up % 5.11/1.89 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.11/1.90 Prover 3: Preprocessing ... % 5.46/1.93 Prover 3: Warning: ignoring some quantifiers % 5.46/1.93 Prover 3: Constructing countermodel ... % 5.65/1.99 Prover 3: gave up % 5.65/1.99 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 5.65/2.00 Prover 4: Preprocessing ... % 6.10/2.08 Prover 4: Warning: ignoring some quantifiers % 6.10/2.08 Prover 4: Constructing countermodel ... % 10.13/3.04 Prover 4: gave up % 10.13/3.04 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 10.13/3.05 Prover 5: Preprocessing ... % 10.47/3.09 Prover 5: Warning: ignoring some quantifiers % 10.47/3.09 Prover 5: Constructing countermodel ... % 10.87/3.19 Prover 5: gave up % 10.87/3.19 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 10.96/3.20 Prover 6: Preprocessing ... % 11.10/3.24 Prover 6: Warning: ignoring some quantifiers % 11.19/3.24 Prover 6: Constructing countermodel ... % 11.57/3.33 Prover 6: gave up % 11.57/3.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 11.57/3.34 Prover 7: Preprocessing ... % 11.57/3.36 Prover 7: Proving ... % 30.49/9.72 Prover 7: proved (6383ms) % 30.49/9.72 % 30.49/9.72 % SZS status Theorem for theBenchmark % 30.49/9.72 % 30.49/9.72 Generating proof ... found it (size 36) % 37.60/11.85 % 37.60/11.85 % SZS output start Proof for theBenchmark % 37.60/11.85 Assumed formulas after preprocessing and simplification: % 37.60/11.85 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_difference(v4, v3) = v2) | ~ (set_difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_union2(v4, v3) = v2) | ~ (set_union2(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] : ! [v3] : ( ~ (set_union2(v2, v1) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | set_union2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ( ~ in(v5, v2) & ~ in(v5, v1))) & (in(v5, v4) | in(v5, v2) | in(v5, v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | in(v4, v2) | in(v4, v1)) & ! [v4] : (in(v4, v3) | ( ~ in(v4, v2) & ~ in(v4, v1))))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_difference(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(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] : ? [v4] : ( ~ (v4 = v2) & set_difference(v2, v1) = v3 & set_union2(v1, v3) = v4 & subset(v1, v2)) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1)) % 37.60/11.87 | Instantiating (0) with all_0_0_0 yields: % 37.60/11.87 | (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] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(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] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(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] : ? [v3] : ( ~ (v3 = v1) & set_difference(v1, v0) = v2 & set_union2(v0, v2) = v3 & subset(v0, v1)) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 37.78/11.88 | % 37.78/11.88 | Applying alpha-rule on (1) yields: % 37.78/11.88 | (2) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 37.78/11.88 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 37.78/11.88 | (4) ! [v0] : subset(v0, v0) % 37.78/11.88 | (5) ? [v0] : ~ empty(v0) % 37.78/11.88 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) % 37.78/11.88 | (7) ! [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)))) % 37.78/11.88 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 37.78/11.88 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 37.78/11.88 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1)) % 37.78/11.88 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 37.78/11.88 | (12) empty(all_0_0_0) % 37.78/11.88 | (13) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 37.78/11.88 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) % 37.78/11.89 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 37.78/11.89 | (16) ! [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)))))) % 37.78/11.89 | (17) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v1) & set_difference(v1, v0) = v2 & set_union2(v0, v2) = v3 & subset(v0, v1)) % 37.78/11.89 | (18) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 37.78/11.89 | (19) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) % 37.78/11.89 | (20) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 37.78/11.89 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) % 37.78/11.89 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 37.78/11.89 | (23) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) % 37.78/11.89 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 37.78/11.89 | (25) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) % 37.78/11.89 | (26) ? [v0] : empty(v0) % 37.78/11.89 | % 37.78/11.89 | Instantiating (17) with all_7_0_3, all_7_1_4, all_7_2_5, all_7_3_6 yields: % 37.78/11.89 | (27) ~ (all_7_0_3 = all_7_2_5) & set_difference(all_7_2_5, all_7_3_6) = all_7_1_4 & set_union2(all_7_3_6, all_7_1_4) = all_7_0_3 & subset(all_7_3_6, all_7_2_5) % 37.78/11.89 | % 37.78/11.89 | Applying alpha-rule on (27) yields: % 37.78/11.89 | (28) ~ (all_7_0_3 = all_7_2_5) % 37.78/11.89 | (29) set_difference(all_7_2_5, all_7_3_6) = all_7_1_4 % 37.78/11.89 | (30) set_union2(all_7_3_6, all_7_1_4) = all_7_0_3 % 37.78/11.89 | (31) subset(all_7_3_6, all_7_2_5) % 37.78/11.89 | % 37.78/11.89 | Instantiating formula (7) with all_7_1_4, all_7_3_6, all_7_2_5 and discharging atoms set_difference(all_7_2_5, all_7_3_6) = all_7_1_4, yields: % 37.78/11.89 | (32) ! [v0] : ( ~ in(v0, all_7_1_4) | (in(v0, all_7_2_5) & ~ in(v0, all_7_3_6))) & ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_1_4) | in(v0, all_7_3_6)) % 37.78/11.89 | % 37.78/11.89 | Applying alpha-rule on (32) yields: % 37.78/11.89 | (33) ! [v0] : ( ~ in(v0, all_7_1_4) | (in(v0, all_7_2_5) & ~ in(v0, all_7_3_6))) % 37.78/11.89 | (34) ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_1_4) | in(v0, all_7_3_6)) % 37.78/11.89 | % 37.78/11.89 | Instantiating formula (9) with all_7_0_3, all_7_1_4, all_7_3_6 and discharging atoms set_union2(all_7_3_6, all_7_1_4) = all_7_0_3, yields: % 37.78/11.89 | (35) set_union2(all_7_1_4, all_7_3_6) = all_7_0_3 % 37.78/11.89 | % 37.78/11.89 | Instantiating formula (25) with all_7_2_5, all_7_3_6 and discharging atoms subset(all_7_3_6, all_7_2_5), yields: % 37.78/11.89 | (36) ! [v0] : ( ~ in(v0, all_7_3_6) | in(v0, all_7_2_5)) % 37.78/11.89 | % 37.78/11.89 | Instantiating formula (14) with all_7_0_3, all_7_3_6, all_7_1_4 and discharging atoms set_union2(all_7_1_4, all_7_3_6) = all_7_0_3, yields: % 37.78/11.89 | (37) ! [v0] : (v0 = all_7_0_3 | ? [v1] : (( ~ in(v1, v0) | ( ~ in(v1, all_7_1_4) & ~ in(v1, all_7_3_6))) & (in(v1, v0) | in(v1, all_7_1_4) | in(v1, all_7_3_6)))) % 37.78/11.89 | % 37.78/11.89 | Introducing new symbol ex_73_0_14 defined by: % 37.78/11.89 | (38) ex_73_0_14 = all_7_2_5 % 37.78/11.89 | % 37.78/11.89 | Instantiating formula (37) with ex_73_0_14 yields: % 37.78/11.89 | (39) ex_73_0_14 = all_7_0_3 | ? [v0] : (( ~ in(v0, ex_73_0_14) | ( ~ in(v0, all_7_1_4) & ~ in(v0, all_7_3_6))) & (in(v0, ex_73_0_14) | in(v0, all_7_1_4) | in(v0, all_7_3_6))) % 37.78/11.89 | % 37.78/11.89 +-Applying beta-rule and splitting (39), into two cases. % 37.78/11.89 |-Branch one: % 37.78/11.89 | (40) ex_73_0_14 = all_7_0_3 % 37.78/11.89 | % 37.78/11.89 | Combining equations (38,40) yields a new equation: % 37.78/11.89 | (41) all_7_0_3 = all_7_2_5 % 37.78/11.89 | % 37.78/11.89 | Equations (41) can reduce 28 to: % 37.78/11.89 | (42) $false % 37.78/11.89 | % 37.78/11.90 |-The branch is then unsatisfiable % 37.78/11.90 |-Branch two: % 37.78/11.90 | (43) ? [v0] : (( ~ in(v0, ex_73_0_14) | ( ~ in(v0, all_7_1_4) & ~ in(v0, all_7_3_6))) & (in(v0, ex_73_0_14) | in(v0, all_7_1_4) | in(v0, all_7_3_6))) % 37.78/11.90 | % 37.78/11.90 | Instantiating (43) with all_76_0_15 yields: % 37.78/11.90 | (44) ( ~ in(all_76_0_15, ex_73_0_14) | ( ~ in(all_76_0_15, all_7_1_4) & ~ in(all_76_0_15, all_7_3_6))) & (in(all_76_0_15, ex_73_0_14) | in(all_76_0_15, all_7_1_4) | in(all_76_0_15, all_7_3_6)) % 37.78/11.90 | % 37.78/11.90 | Applying alpha-rule on (44) yields: % 37.78/11.90 | (45) ~ in(all_76_0_15, ex_73_0_14) | ( ~ in(all_76_0_15, all_7_1_4) & ~ in(all_76_0_15, all_7_3_6)) % 37.78/11.90 | (46) in(all_76_0_15, ex_73_0_14) | in(all_76_0_15, all_7_1_4) | in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 +-Applying beta-rule and splitting (46), into two cases. % 37.78/11.90 |-Branch one: % 37.78/11.90 | (47) in(all_76_0_15, ex_73_0_14) % 37.78/11.90 | % 37.78/11.90 +-Applying beta-rule and splitting (45), into two cases. % 37.78/11.90 |-Branch one: % 37.78/11.90 | (48) ~ in(all_76_0_15, ex_73_0_14) % 37.78/11.90 | % 37.78/11.90 | Using (47) and (48) yields: % 37.78/11.90 | (49) $false % 37.78/11.90 | % 37.78/11.90 |-The branch is then unsatisfiable % 37.78/11.90 |-Branch two: % 37.78/11.90 | (50) ~ in(all_76_0_15, all_7_1_4) & ~ in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 | Applying alpha-rule on (50) yields: % 37.78/11.90 | (51) ~ in(all_76_0_15, all_7_1_4) % 37.78/11.90 | (52) ~ in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 | Instantiating formula (34) with all_76_0_15 and discharging atoms ~ in(all_76_0_15, all_7_1_4), ~ in(all_76_0_15, all_7_3_6), yields: % 37.78/11.90 | (53) ~ in(all_76_0_15, all_7_2_5) % 37.78/11.90 | % 37.78/11.90 | From (38) and (47) follows: % 37.78/11.90 | (54) in(all_76_0_15, all_7_2_5) % 37.78/11.90 | % 37.78/11.90 | Using (54) and (53) yields: % 37.78/11.90 | (49) $false % 37.78/11.90 | % 37.78/11.90 |-The branch is then unsatisfiable % 37.78/11.90 |-Branch two: % 37.78/11.90 | (48) ~ in(all_76_0_15, ex_73_0_14) % 37.78/11.90 | (57) in(all_76_0_15, all_7_1_4) | in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 +-Applying beta-rule and splitting (57), into two cases. % 37.78/11.90 |-Branch one: % 37.78/11.90 | (58) in(all_76_0_15, all_7_1_4) % 37.78/11.90 | % 37.78/11.90 | Instantiating formula (33) with all_76_0_15 and discharging atoms in(all_76_0_15, all_7_1_4), yields: % 37.78/11.90 | (59) in(all_76_0_15, all_7_2_5) & ~ in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 | Applying alpha-rule on (59) yields: % 37.78/11.90 | (54) in(all_76_0_15, all_7_2_5) % 37.78/11.90 | (52) ~ in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 | From (38) and (48) follows: % 37.78/11.90 | (53) ~ in(all_76_0_15, all_7_2_5) % 37.78/11.90 | % 37.78/11.90 | Using (54) and (53) yields: % 37.78/11.90 | (49) $false % 37.78/11.90 | % 37.78/11.90 |-The branch is then unsatisfiable % 37.78/11.90 |-Branch two: % 37.78/11.90 | (64) in(all_76_0_15, all_7_3_6) % 37.78/11.90 | % 37.78/11.90 | Instantiating formula (36) with all_76_0_15 and discharging atoms in(all_76_0_15, all_7_3_6), yields: % 37.78/11.90 | (54) in(all_76_0_15, all_7_2_5) % 37.78/11.90 | % 37.78/11.90 | From (38) and (48) follows: % 37.78/11.90 | (53) ~ in(all_76_0_15, all_7_2_5) % 37.78/11.90 | % 37.78/11.90 | Using (54) and (53) yields: % 37.78/11.90 | (49) $false % 37.78/11.90 | % 37.78/11.90 |-The branch is then unsatisfiable % 37.78/11.90 % SZS output end Proof for theBenchmark % 37.78/11.90 % 37.78/11.90 11306ms %------------------------------------------------------------------------------