%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 : Mon Jul 18 16:25:08 EDT 2022 % Result : Theorem 53.02s 33.25s % Output : Proof 75.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 2 10:45:21 EDT 2022 % 0.13/0.34 % CPUTime : % 0.56/0.59 ____ _ % 0.56/0.59 ___ / __ \_____(_)___ ________ __________ % 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.59 % 0.56/0.59 A Theorem Prover for First-Order Logic % 0.56/0.59 (ePrincess v.1.0) % 0.56/0.59 % 0.56/0.59 (c) Philipp Rümmer, 2009-2015 % 0.56/0.59 (c) Peter Backeman, 2014-2015 % 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.59 Bug reports to peter@backeman.se % 0.56/0.59 % 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.59 % 0.56/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.77/0.94 Prover 0: Preprocessing ... % 2.10/1.09 Prover 0: Warning: ignoring some quantifiers % 2.10/1.10 Prover 0: Constructing countermodel ... % 3.24/1.39 Prover 0: gave up % 3.24/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.24/1.42 Prover 1: Preprocessing ... % 3.56/1.50 Prover 1: Warning: ignoring some quantifiers % 3.56/1.50 Prover 1: Constructing countermodel ... % 4.13/1.69 Prover 1: gave up % 4.13/1.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.44/1.71 Prover 2: Preprocessing ... % 4.44/1.76 Prover 2: Warning: ignoring some quantifiers % 4.44/1.76 Prover 2: Constructing countermodel ... % 4.93/1.86 Prover 2: gave up % 4.93/1.87 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.93/1.89 Prover 3: Preprocessing ... % 4.93/1.90 Prover 3: Warning: ignoring some quantifiers % 4.93/1.90 Prover 3: Constructing countermodel ... % 5.70/1.99 Prover 3: gave up % 5.70/1.99 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 5.70/2.01 Prover 4: Preprocessing ... % 5.70/2.05 Prover 4: Warning: ignoring some quantifiers % 5.70/2.05 Prover 4: Constructing countermodel ... % 6.33/2.21 Prover 4: gave up % 6.33/2.21 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 6.82/2.23 Prover 5: Preprocessing ... % 6.82/2.26 Prover 5: Warning: ignoring some quantifiers % 6.82/2.26 Prover 5: Constructing countermodel ... % 7.19/2.32 Prover 5: gave up % 7.19/2.32 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 7.19/2.33 Prover 6: Preprocessing ... % 7.19/2.36 Prover 6: Warning: ignoring some quantifiers % 7.19/2.36 Prover 6: Constructing countermodel ... % 7.59/2.43 Prover 6: gave up % 7.59/2.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 7.59/2.45 Prover 7: Preprocessing ... % 7.59/2.46 Prover 7: Proving ... % 28.05/13.02 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 28.10/13.05 Prover 8: Preprocessing ... % 28.10/13.08 Prover 8: Proving ... % 50.41/31.49 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal % 50.41/31.52 Prover 9: Preprocessing ... % 50.62/31.55 Prover 9: Proving ... % 53.02/33.24 Prover 9: proved (1750ms) % 53.02/33.25 Prover 8: stopped % 53.02/33.25 Prover 7: stopped % 53.02/33.25 % 53.02/33.25 % SZS status Theorem for theBenchmark % 53.02/33.25 % 53.02/33.25 Generating proof ... found it (size 57) % 75.30/52.16 % 75.30/52.16 % SZS output start Proof for theBenchmark % 75.30/52.16 Assumed formulas after preprocessing and simplification: % 75.30/52.16 | (0) ? [v0] : (r1(v0) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ r2(v2, v3) | ~ r2(v1, v3)) & ! [v1] : ! [v2] : ( ~ r2(v1, v2) | ~ r1(v2)) & ! [v1] : (v1 = v0 | ~ r1(v1)) & ! [v1] : ! [v2] : ? [v3] : (r4(v1, v2, v3) & ! [v4] : (v4 = v3 | ~ r4(v1, v2, v4))) & ! [v1] : ! [v2] : ? [v3] : (r3(v1, v2, v3) & ! [v4] : (v4 = v3 | ~ r3(v1, v2, v4))) & ! [v1] : ? [v2] : (r3(v1, v2, v1) & r1(v2)) & ! [v1] : ? [v2] : (r2(v1, v2) & ! [v3] : (v3 = v2 | ~ r2(v1, v3))) & ! [v1] : ? [v2] : ? [v3] : ((v3 = v1 & r2(v2, v1)) | (v2 = v1 & r1(v1))) & ! [v1] : ? [v2] : ? [v3] : (r4(v1, v3, v2) & r1(v3) & r1(v2)) & ! [v1] : ! [v2] : ? [v3] : ? [v4] : ? [v5] : (r4(v1, v5, v3) & r4(v1, v2, v4) & r3(v4, v1, v3) & r2(v2, v5)) & ! [v1] : ! [v2] : ? [v3] : ? [v4] : ? [v5] : (r3(v1, v5, v3) & r3(v1, v2, v4) & r2(v4, v3) & r2(v2, v5)) & ! [v1] : ? [v2] : ? [v3] : ? [v4] : ((v2 = v1 & r2(v4, v3) & r2(v3, v1) & r1(v4)) | (v2 = v1 & r1(v1)))) % 75.30/52.17 | Instantiating (0) with all_0_0_0 yields: % 75.30/52.17 | (1) r1(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ r2(v1, v2) | ~ r2(v0, v2)) & ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1)) & ! [v0] : (v0 = all_0_0_0 | ~ r1(v0)) & ! [v0] : ! [v1] : ? [v2] : (r4(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r4(v0, v1, v3))) & ! [v0] : ! [v1] : ? [v2] : (r3(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r3(v0, v1, v3))) & ! [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1)) & ! [v0] : ? [v1] : (r2(v0, v1) & ! [v2] : (v2 = v1 | ~ r2(v0, v2))) & ! [v0] : ? [v1] : ? [v2] : ((v2 = v0 & r2(v1, v0)) | (v1 = v0 & r1(v0))) & ! [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) & r1(v2) & r1(v1)) & ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v4)) & ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v4)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : ((v1 = v0 & r2(v3, v2) & r2(v2, v0) & r1(v3)) | (v1 = v0 & r1(v0))) % 75.30/52.17 | % 75.30/52.17 | Applying alpha-rule on (1) yields: % 75.30/52.17 | (2) ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v4)) % 75.30/52.17 | (3) ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v4)) % 75.30/52.17 | (4) ! [v0] : ? [v1] : (r2(v0, v1) & ! [v2] : (v2 = v1 | ~ r2(v0, v2))) % 75.30/52.17 | (5) ! [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) & r1(v2) & r1(v1)) % 75.30/52.17 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ r2(v1, v2) | ~ r2(v0, v2)) % 75.30/52.17 | (7) r1(all_0_0_0) % 75.30/52.17 | (8) ! [v0] : ! [v1] : ? [v2] : (r3(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r3(v0, v1, v3))) % 75.30/52.17 | (9) ! [v0] : ? [v1] : ? [v2] : ((v2 = v0 & r2(v1, v0)) | (v1 = v0 & r1(v0))) % 75.30/52.17 | (10) ! [v0] : ? [v1] : ? [v2] : ? [v3] : ((v1 = v0 & r2(v3, v2) & r2(v2, v0) & r1(v3)) | (v1 = v0 & r1(v0))) % 75.30/52.17 | (11) ! [v0] : ! [v1] : ? [v2] : (r4(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r4(v0, v1, v3))) % 75.30/52.17 | (12) ! [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1)) % 75.30/52.17 | (13) ! [v0] : (v0 = all_0_0_0 | ~ r1(v0)) % 75.30/52.17 | (14) ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1)) % 75.30/52.17 | % 75.30/52.17 | Introducing new symbol ex_19_0_4 defined by: % 75.30/52.17 | (15) ex_19_0_4 = all_0_0_0 % 75.30/52.17 | % 75.30/52.17 | Instantiating formula (9) with ex_19_0_4 yields: % 75.30/52.17 | (16) ? [v0] : ? [v1] : ((v1 = ex_19_0_4 & r2(v0, ex_19_0_4)) | (v0 = ex_19_0_4 & r1(ex_19_0_4))) % 75.30/52.17 | % 75.30/52.17 | Instantiating (16) with all_20_0_5, all_20_1_6 yields: % 75.30/52.17 | (17) (all_20_0_5 = ex_19_0_4 & r2(all_20_1_6, ex_19_0_4)) | (all_20_1_6 = ex_19_0_4 & r1(ex_19_0_4)) % 75.30/52.17 | % 75.30/52.17 +-Applying beta-rule and splitting (17), into two cases. % 75.30/52.17 |-Branch one: % 75.30/52.17 | (18) all_20_0_5 = ex_19_0_4 & r2(all_20_1_6, ex_19_0_4) % 75.30/52.17 | % 75.30/52.17 | Applying alpha-rule on (18) yields: % 75.30/52.17 | (19) all_20_0_5 = ex_19_0_4 % 75.30/52.17 | (20) r2(all_20_1_6, ex_19_0_4) % 75.30/52.17 | % 75.30/52.17 | Instantiating formula (14) with all_0_0_0, all_20_1_6 and discharging atoms r1(all_0_0_0), yields: % 75.30/52.17 | (21) ~ r2(all_20_1_6, all_0_0_0) % 75.30/52.17 | % 75.30/52.18 | From (15) and (20) follows: % 75.30/52.18 | (22) r2(all_20_1_6, all_0_0_0) % 75.30/52.18 | % 75.30/52.18 | Using (22) and (21) yields: % 75.30/52.18 | (23) $false % 75.30/52.18 | % 75.30/52.18 |-The branch is then unsatisfiable % 75.30/52.18 |-Branch two: % 75.30/52.18 | (24) all_20_1_6 = ex_19_0_4 & r1(ex_19_0_4) % 75.30/52.18 | % 75.30/52.18 | Applying alpha-rule on (24) yields: % 75.30/52.18 | (25) all_20_1_6 = ex_19_0_4 % 75.30/52.18 | (26) r1(ex_19_0_4) % 75.30/52.18 | % 75.30/52.18 | Combining equations (15,25) yields a new equation: % 75.30/52.18 | (27) all_20_1_6 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | Introducing new symbol ex_43_0_10 defined by: % 75.30/52.18 | (28) ex_43_0_10 = all_20_1_6 % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (4) with ex_43_0_10 yields: % 75.30/52.18 | (29) ? [v0] : (r2(ex_43_0_10, v0) & ! [v1] : (v1 = v0 | ~ r2(ex_43_0_10, v1))) % 75.30/52.18 | % 75.30/52.18 | Instantiating (29) with all_44_0_11 yields: % 75.30/52.18 | (30) r2(ex_43_0_10, all_44_0_11) & ! [v0] : (v0 = all_44_0_11 | ~ r2(ex_43_0_10, v0)) % 75.30/52.18 | % 75.30/52.18 | Applying alpha-rule on (30) yields: % 75.30/52.18 | (31) r2(ex_43_0_10, all_44_0_11) % 75.30/52.18 | (32) ! [v0] : (v0 = all_44_0_11 | ~ r2(ex_43_0_10, v0)) % 75.30/52.18 | % 75.30/52.18 | Introducing new symbol ex_73_0_14 defined by: % 75.30/52.18 | (33) ex_73_0_14 = all_20_1_6 % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (3) with ex_73_0_14, ex_73_1_15 yields: % 75.30/52.18 | (34) ? [v0] : ? [v1] : ? [v2] : (r4(ex_73_1_15, v2, v0) & r4(ex_73_1_15, ex_73_0_14, v1) & r3(v1, ex_73_1_15, v0) & r2(ex_73_0_14, v2)) % 75.30/52.18 | % 75.30/52.18 | Instantiating (34) with all_74_0_16, all_74_1_17, all_74_2_18 yields: % 75.30/52.18 | (35) r4(ex_73_1_15, all_74_0_16, all_74_2_18) & r4(ex_73_1_15, ex_73_0_14, all_74_1_17) & r3(all_74_1_17, ex_73_1_15, all_74_2_18) & r2(ex_73_0_14, all_74_0_16) % 75.30/52.18 | % 75.30/52.18 | Applying alpha-rule on (35) yields: % 75.30/52.18 | (36) r4(ex_73_1_15, all_74_0_16, all_74_2_18) % 75.30/52.18 | (37) r4(ex_73_1_15, ex_73_0_14, all_74_1_17) % 75.30/52.18 | (38) r3(all_74_1_17, ex_73_1_15, all_74_2_18) % 75.30/52.18 | (39) r2(ex_73_0_14, all_74_0_16) % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (32) with all_74_0_16 yields: % 75.30/52.18 | (40) all_74_0_16 = all_44_0_11 | ~ r2(ex_43_0_10, all_74_0_16) % 75.30/52.18 | % 75.30/52.18 +-Applying beta-rule and splitting (40), into two cases. % 75.30/52.18 |-Branch one: % 75.30/52.18 | (41) ~ r2(ex_43_0_10, all_74_0_16) % 75.30/52.18 | % 75.30/52.18 | Combining equations (27,28) yields a new equation: % 75.30/52.18 | (42) ex_43_0_10 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | Combining equations (27,33) yields a new equation: % 75.30/52.18 | (43) ex_73_0_14 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | From (43) and (39) follows: % 75.30/52.18 | (44) r2(all_0_0_0, all_74_0_16) % 75.30/52.18 | % 75.30/52.18 | From (42) and (41) follows: % 75.30/52.18 | (45) ~ r2(all_0_0_0, all_74_0_16) % 75.30/52.18 | % 75.30/52.18 | Using (44) and (45) yields: % 75.30/52.18 | (23) $false % 75.30/52.18 | % 75.30/52.18 |-The branch is then unsatisfiable % 75.30/52.18 |-Branch two: % 75.30/52.18 | (47) all_74_0_16 = all_44_0_11 % 75.30/52.18 | % 75.30/52.18 | Introducing new symbol ex_107_0_19 defined by: % 75.30/52.18 | (48) ex_107_0_19 = all_74_0_16 % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (10) with ex_107_0_19 yields: % 75.30/52.18 | (49) ? [v0] : ? [v1] : ? [v2] : ((v0 = ex_107_0_19 & r2(v2, v1) & r2(v1, ex_107_0_19) & r1(v2)) | (v0 = ex_107_0_19 & r1(ex_107_0_19))) % 75.30/52.18 | % 75.30/52.18 | Instantiating (49) with all_108_0_20, all_108_1_21, all_108_2_22 yields: % 75.30/52.18 | (50) (all_108_2_22 = ex_107_0_19 & r2(all_108_0_20, all_108_1_21) & r2(all_108_1_21, ex_107_0_19) & r1(all_108_0_20)) | (all_108_2_22 = ex_107_0_19 & r1(ex_107_0_19)) % 75.30/52.18 | % 75.30/52.18 +-Applying beta-rule and splitting (50), into two cases. % 75.30/52.18 |-Branch one: % 75.30/52.18 | (51) all_108_2_22 = ex_107_0_19 & r2(all_108_0_20, all_108_1_21) & r2(all_108_1_21, ex_107_0_19) & r1(all_108_0_20) % 75.30/52.18 | % 75.30/52.18 | Applying alpha-rule on (51) yields: % 75.30/52.18 | (52) all_108_2_22 = ex_107_0_19 % 75.30/52.18 | (53) r2(all_108_0_20, all_108_1_21) % 75.30/52.18 | (54) r2(all_108_1_21, ex_107_0_19) % 75.30/52.18 | (55) r1(all_108_0_20) % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (6) with all_44_0_11, all_108_1_21, ex_43_0_10 and discharging atoms r2(ex_43_0_10, all_44_0_11), yields: % 75.30/52.18 | (56) all_108_1_21 = ex_43_0_10 | ~ r2(all_108_1_21, all_44_0_11) % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (13) with all_108_0_20 and discharging atoms r1(all_108_0_20), yields: % 75.30/52.18 | (57) all_108_0_20 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | From (57) and (53) follows: % 75.30/52.18 | (58) r2(all_0_0_0, all_108_1_21) % 75.30/52.18 | % 75.30/52.18 +-Applying beta-rule and splitting (56), into two cases. % 75.30/52.18 |-Branch one: % 75.30/52.18 | (59) ~ r2(all_108_1_21, all_44_0_11) % 75.30/52.18 | % 75.30/52.18 | Combining equations (47,48) yields a new equation: % 75.30/52.18 | (60) ex_107_0_19 = all_44_0_11 % 75.30/52.18 | % 75.30/52.18 | From (60) and (54) follows: % 75.30/52.18 | (61) r2(all_108_1_21, all_44_0_11) % 75.30/52.18 | % 75.30/52.18 | Using (61) and (59) yields: % 75.30/52.18 | (23) $false % 75.30/52.18 | % 75.30/52.18 |-The branch is then unsatisfiable % 75.30/52.18 |-Branch two: % 75.30/52.18 | (63) all_108_1_21 = ex_43_0_10 % 75.30/52.18 | % 75.30/52.18 | From (63) and (58) follows: % 75.30/52.18 | (64) r2(all_0_0_0, ex_43_0_10) % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (14) with all_0_0_0, all_0_0_0 and discharging atoms r1(all_0_0_0), yields: % 75.30/52.18 | (65) ~ r2(all_0_0_0, all_0_0_0) % 75.30/52.18 | % 75.30/52.18 | Combining equations (27,28) yields a new equation: % 75.30/52.18 | (42) ex_43_0_10 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | From (42) and (64) follows: % 75.30/52.18 | (67) r2(all_0_0_0, all_0_0_0) % 75.30/52.18 | % 75.30/52.18 | Using (67) and (65) yields: % 75.30/52.18 | (23) $false % 75.30/52.18 | % 75.30/52.18 |-The branch is then unsatisfiable % 75.30/52.18 |-Branch two: % 75.30/52.18 | (69) all_108_2_22 = ex_107_0_19 & r1(ex_107_0_19) % 75.30/52.18 | % 75.30/52.18 | Applying alpha-rule on (69) yields: % 75.30/52.18 | (52) all_108_2_22 = ex_107_0_19 % 75.30/52.18 | (71) r1(ex_107_0_19) % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (14) with all_44_0_11, ex_43_0_10 and discharging atoms r2(ex_43_0_10, all_44_0_11), yields: % 75.30/52.18 | (72) ~ r1(all_44_0_11) % 75.30/52.18 | % 75.30/52.18 | Instantiating formula (13) with ex_107_0_19 and discharging atoms r1(ex_107_0_19), yields: % 75.30/52.18 | (73) ex_107_0_19 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | Combining equations (48,73) yields a new equation: % 75.30/52.18 | (74) all_74_0_16 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | Simplifying 74 yields: % 75.30/52.18 | (75) all_74_0_16 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | Combining equations (75,47) yields a new equation: % 75.30/52.18 | (76) all_44_0_11 = all_0_0_0 % 75.30/52.18 | % 75.30/52.18 | From (76) and (72) follows: % 75.30/52.19 | (77) ~ r1(all_0_0_0) % 75.30/52.19 | % 75.30/52.19 | Using (7) and (77) yields: % 75.30/52.19 | (23) $false % 75.30/52.19 | % 75.30/52.19 |-The branch is then unsatisfiable % 75.30/52.19 % SZS output end Proof for theBenchmark % 75.30/52.19 % 75.30/52.19 51584ms %------------------------------------------------------------------------------