%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET957+1 : TPTP v8.1.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 00:23:26 EDT 2022 % Result : Theorem 18.57s 5.43s % Output : Proof 53.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET957+1 : TPTP v8.1.0. Bugfixed v4.0.0. % 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n007.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 Jul 10 07:33:16 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.57 ____ _ % 0.53/0.57 ___ / __ \_____(_)___ ________ __________ % 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.57 % 0.53/0.57 A Theorem Prover for First-Order Logic % 0.53/0.57 (ePrincess v.1.0) % 0.53/0.57 % 0.53/0.57 (c) Philipp Rümmer, 2009-2015 % 0.53/0.57 (c) Peter Backeman, 2014-2015 % 0.53/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.57 Bug reports to peter@backeman.se % 0.53/0.57 % 0.53/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.57 % 0.53/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.29/0.89 Prover 0: Preprocessing ... % 1.60/1.03 Prover 0: Warning: ignoring some quantifiers % 1.60/1.05 Prover 0: Constructing countermodel ... % 3.07/1.45 Prover 0: gave up % 3.07/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.17/1.47 Prover 1: Preprocessing ... % 3.17/1.53 Prover 1: Warning: ignoring some quantifiers % 3.41/1.53 Prover 1: Constructing countermodel ... % 3.41/1.56 Prover 1: gave up % 3.41/1.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.57/1.57 Prover 2: Preprocessing ... % 3.57/1.63 Prover 2: Warning: ignoring some quantifiers % 3.57/1.63 Prover 2: Constructing countermodel ... % 3.90/1.67 Prover 2: gave up % 3.90/1.68 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.04/1.69 Prover 3: Preprocessing ... % 4.04/1.71 Prover 3: Warning: ignoring some quantifiers % 4.04/1.71 Prover 3: Constructing countermodel ... % 4.04/1.73 Prover 3: gave up % 4.04/1.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 4.34/1.74 Prover 4: Preprocessing ... % 4.43/1.80 Prover 4: Warning: ignoring some quantifiers % 4.43/1.81 Prover 4: Constructing countermodel ... % 9.32/2.96 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 9.32/2.97 Prover 5: Preprocessing ... % 9.64/3.01 Prover 5: Warning: ignoring some quantifiers % 9.64/3.01 Prover 5: Constructing countermodel ... % 9.64/3.05 Prover 5: gave up % 9.64/3.05 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 9.64/3.06 Prover 6: Preprocessing ... % 9.96/3.10 Prover 6: Warning: ignoring some quantifiers % 9.96/3.10 Prover 6: Constructing countermodel ... % 9.96/3.12 Prover 6: gave up % 9.96/3.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 9.96/3.13 Prover 7: Preprocessing ... % 9.96/3.14 Prover 7: Proving ... % 18.57/5.43 Prover 7: proved (2306ms) % 18.57/5.43 Prover 4: stopped % 18.57/5.43 % 18.57/5.43 % SZS status Theorem for theBenchmark % 18.57/5.43 % 18.57/5.43 Generating proof ... found it (size 52) % 53.12/28.43 % 53.12/28.43 % SZS output start Proof for theBenchmark % 53.12/28.43 Assumed formulas after preprocessing and simplification: % 53.12/28.43 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ subset(v0, v4) | ~ in(v3, v0) | ? [v5] : ? [v6] : (ordered_pair(v5, v6) = v3 & in(v6, v2) & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v3 = v0) & cartesian_product2(v4, v5) = v7 & cartesian_product2(v1, v2) = v6 & subset(v3, v7) & subset(v0, v6) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ in(v10, v3) | in(v10, v0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ in(v10, v0) | in(v10, v3))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 53.27/28.45 | Applying alpha-rule on (0) yields: % 53.27/28.45 | (1) ? [v0] : ~ empty(v0) % 53.27/28.45 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 53.27/28.45 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 53.27/28.45 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v3 = v0) & cartesian_product2(v4, v5) = v7 & cartesian_product2(v1, v2) = v6 & subset(v3, v7) & subset(v0, v6) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ in(v10, v3) | in(v10, v0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ in(v10, v0) | in(v10, v3))) % 53.27/28.45 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ subset(v0, v4) | ~ in(v3, v0) | ? [v5] : ? [v6] : (ordered_pair(v5, v6) = v3 & in(v6, v2) & in(v5, v1))) % 53.27/28.45 | (6) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 53.27/28.45 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 53.27/28.45 | (8) ! [v0] : subset(v0, v0) % 53.27/28.45 | (9) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 53.27/28.45 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 53.27/28.45 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 53.27/28.45 | (12) ? [v0] : empty(v0) % 53.27/28.45 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 53.27/28.46 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 53.27/28.46 | % 53.27/28.46 | Instantiating (4) with all_3_0_1, all_3_1_2, all_3_2_3, all_3_3_4, all_3_4_5, all_3_5_6, all_3_6_7, all_3_7_8 yields: % 53.27/28.46 | (15) ~ (all_3_4_5 = all_3_7_8) & cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1 & cartesian_product2(all_3_6_7, all_3_5_6) = all_3_1_2 & subset(all_3_4_5, all_3_0_1) & subset(all_3_7_8, all_3_1_2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_4_5) | in(v2, all_3_7_8)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_7_8) | in(v2, all_3_4_5)) % 53.27/28.46 | % 53.27/28.46 | Applying alpha-rule on (15) yields: % 53.27/28.46 | (16) cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1 % 53.27/28.46 | (17) cartesian_product2(all_3_6_7, all_3_5_6) = all_3_1_2 % 53.27/28.46 | (18) subset(all_3_7_8, all_3_1_2) % 53.27/28.46 | (19) subset(all_3_4_5, all_3_0_1) % 53.27/28.46 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_7_8) | in(v2, all_3_4_5)) % 53.27/28.46 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_4_5) | in(v2, all_3_7_8)) % 53.27/28.46 | (22) ~ (all_3_4_5 = all_3_7_8) % 53.27/28.46 | % 53.27/28.46 | Introducing new symbol ex_14_1_11 defined by: % 53.27/28.46 | (23) ex_14_1_11 = all_3_7_8 % 53.27/28.46 | % 53.27/28.46 | Introducing new symbol ex_14_0_10 defined by: % 53.27/28.46 | (24) ex_14_0_10 = all_3_4_5 % 53.27/28.46 | % 53.27/28.46 | Instantiating formula (6) with ex_14_0_10, ex_14_1_11 yields: % 53.27/28.46 | (25) ex_14_0_10 = ex_14_1_11 | ? [v0] : (( ~ in(v0, ex_14_0_10) | ~ in(v0, ex_14_1_11)) & (in(v0, ex_14_0_10) | in(v0, ex_14_1_11))) % 53.27/28.46 | % 53.27/28.46 +-Applying beta-rule and splitting (25), into two cases. % 53.27/28.46 |-Branch one: % 53.27/28.46 | (26) ex_14_0_10 = ex_14_1_11 % 53.27/28.46 | % 53.27/28.46 | Combining equations (26,24) yields a new equation: % 53.27/28.46 | (27) ex_14_1_11 = all_3_4_5 % 53.27/28.46 | % 53.27/28.46 | Simplifying 27 yields: % 53.27/28.46 | (28) ex_14_1_11 = all_3_4_5 % 53.27/28.46 | % 53.27/28.46 | Combining equations (28,23) yields a new equation: % 53.27/28.46 | (29) all_3_4_5 = all_3_7_8 % 53.27/28.46 | % 53.27/28.46 | Simplifying 29 yields: % 53.27/28.46 | (30) all_3_4_5 = all_3_7_8 % 53.27/28.46 | % 53.27/28.46 | Equations (30) can reduce 22 to: % 53.27/28.46 | (31) $false % 53.27/28.46 | % 53.27/28.46 |-The branch is then unsatisfiable % 53.27/28.46 |-Branch two: % 53.27/28.46 | (32) ? [v0] : (( ~ in(v0, ex_14_0_10) | ~ in(v0, ex_14_1_11)) & (in(v0, ex_14_0_10) | in(v0, ex_14_1_11))) % 53.27/28.46 | % 53.27/28.46 | Instantiating (32) with all_17_0_12 yields: % 53.27/28.46 | (33) ( ~ in(all_17_0_12, ex_14_0_10) | ~ in(all_17_0_12, ex_14_1_11)) & (in(all_17_0_12, ex_14_0_10) | in(all_17_0_12, ex_14_1_11)) % 53.27/28.46 | % 53.27/28.46 | Applying alpha-rule on (33) yields: % 53.27/28.46 | (34) ~ in(all_17_0_12, ex_14_0_10) | ~ in(all_17_0_12, ex_14_1_11) % 53.27/28.46 | (35) in(all_17_0_12, ex_14_0_10) | in(all_17_0_12, ex_14_1_11) % 53.27/28.46 | % 53.27/28.46 +-Applying beta-rule and splitting (34), into two cases. % 53.27/28.46 |-Branch one: % 53.27/28.46 | (36) ~ in(all_17_0_12, ex_14_0_10) % 53.27/28.46 | % 53.27/28.46 +-Applying beta-rule and splitting (35), into two cases. % 53.27/28.46 |-Branch one: % 53.27/28.46 | (37) in(all_17_0_12, ex_14_0_10) % 53.27/28.46 | % 53.27/28.46 | Using (37) and (36) yields: % 53.27/28.46 | (38) $false % 53.27/28.46 | % 53.27/28.46 |-The branch is then unsatisfiable % 53.27/28.46 |-Branch two: % 53.27/28.46 | (39) in(all_17_0_12, ex_14_1_11) % 53.27/28.46 | % 53.27/28.46 | Instantiating formula (5) with all_3_0_1, all_17_0_12, all_3_2_3, all_3_3_4, all_3_4_5 and discharging atoms cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1, subset(all_3_4_5, all_3_0_1), yields: % 53.27/28.46 | (40) ~ in(all_17_0_12, all_3_4_5) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_2_3) & in(v0, all_3_3_4)) % 53.27/28.46 | % 53.27/28.46 | Instantiating formula (5) with all_3_1_2, all_17_0_12, all_3_5_6, all_3_6_7, all_3_7_8 and discharging atoms cartesian_product2(all_3_6_7, all_3_5_6) = all_3_1_2, subset(all_3_7_8, all_3_1_2), yields: % 53.27/28.46 | (41) ~ in(all_17_0_12, all_3_7_8) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_5_6) & in(v0, all_3_6_7)) % 53.27/28.46 | % 53.27/28.46 +-Applying beta-rule and splitting (41), into two cases. % 53.27/28.46 |-Branch one: % 53.27/28.46 | (42) ~ in(all_17_0_12, all_3_7_8) % 53.27/28.46 | % 53.27/28.46 | From (23) and (39) follows: % 53.27/28.46 | (43) in(all_17_0_12, all_3_7_8) % 53.27/28.46 | % 53.27/28.46 | Using (43) and (42) yields: % 53.27/28.46 | (38) $false % 53.27/28.46 | % 53.27/28.46 |-The branch is then unsatisfiable % 53.27/28.46 |-Branch two: % 53.27/28.46 | (43) in(all_17_0_12, all_3_7_8) % 53.27/28.46 | (46) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_5_6) & in(v0, all_3_6_7)) % 53.27/28.46 | % 53.27/28.46 | Instantiating (46) with all_35_0_30, all_35_1_31 yields: % 53.27/28.46 | (47) ordered_pair(all_35_1_31, all_35_0_30) = all_17_0_12 & in(all_35_0_30, all_3_5_6) & in(all_35_1_31, all_3_6_7) % 53.27/28.46 | % 53.27/28.46 | Applying alpha-rule on (47) yields: % 53.27/28.46 | (48) ordered_pair(all_35_1_31, all_35_0_30) = all_17_0_12 % 53.27/28.46 | (49) in(all_35_0_30, all_3_5_6) % 53.27/28.46 | (50) in(all_35_1_31, all_3_6_7) % 53.27/28.46 | % 53.27/28.46 | Instantiating formula (20) with all_17_0_12, all_35_0_30, all_35_1_31 and discharging atoms ordered_pair(all_35_1_31, all_35_0_30) = all_17_0_12, yields: % 53.27/28.46 | (51) ~ in(all_17_0_12, all_3_7_8) | in(all_17_0_12, all_3_4_5) % 53.27/28.46 | % 53.27/28.46 +-Applying beta-rule and splitting (40), into two cases. % 53.27/28.46 |-Branch one: % 53.27/28.46 | (52) ~ in(all_17_0_12, all_3_4_5) % 53.27/28.47 | % 53.27/28.47 +-Applying beta-rule and splitting (51), into two cases. % 53.27/28.47 |-Branch one: % 53.27/28.47 | (42) ~ in(all_17_0_12, all_3_7_8) % 53.27/28.47 | % 53.27/28.47 | Using (43) and (42) yields: % 53.27/28.47 | (38) $false % 53.27/28.47 | % 53.27/28.47 |-The branch is then unsatisfiable % 53.27/28.47 |-Branch two: % 53.27/28.47 | (55) in(all_17_0_12, all_3_4_5) % 53.27/28.47 | % 53.27/28.47 | Using (55) and (52) yields: % 53.27/28.47 | (38) $false % 53.27/28.47 | % 53.27/28.47 |-The branch is then unsatisfiable % 53.27/28.47 |-Branch two: % 53.27/28.47 | (55) in(all_17_0_12, all_3_4_5) % 53.27/28.47 | (58) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_2_3) & in(v0, all_3_3_4)) % 53.27/28.47 | % 53.27/28.47 | From (24) and (36) follows: % 53.27/28.47 | (52) ~ in(all_17_0_12, all_3_4_5) % 53.27/28.47 | % 53.27/28.47 | Using (55) and (52) yields: % 53.27/28.47 | (38) $false % 53.27/28.47 | % 53.27/28.47 |-The branch is then unsatisfiable % 53.27/28.47 |-Branch two: % 53.27/28.47 | (37) in(all_17_0_12, ex_14_0_10) % 53.27/28.47 | (62) ~ in(all_17_0_12, ex_14_1_11) % 53.27/28.47 | % 53.27/28.47 | Instantiating formula (5) with all_3_0_1, all_17_0_12, all_3_2_3, all_3_3_4, all_3_4_5 and discharging atoms cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1, subset(all_3_4_5, all_3_0_1), yields: % 53.27/28.47 | (40) ~ in(all_17_0_12, all_3_4_5) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_2_3) & in(v0, all_3_3_4)) % 53.27/28.47 | % 53.27/28.47 | Instantiating formula (5) with all_3_1_2, all_17_0_12, all_3_5_6, all_3_6_7, all_3_7_8 and discharging atoms cartesian_product2(all_3_6_7, all_3_5_6) = all_3_1_2, subset(all_3_7_8, all_3_1_2), yields: % 53.27/28.47 | (41) ~ in(all_17_0_12, all_3_7_8) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_5_6) & in(v0, all_3_6_7)) % 53.27/28.47 | % 53.27/28.47 +-Applying beta-rule and splitting (41), into two cases. % 53.27/28.47 |-Branch one: % 53.27/28.47 | (42) ~ in(all_17_0_12, all_3_7_8) % 53.27/28.47 | % 53.27/28.47 +-Applying beta-rule and splitting (40), into two cases. % 53.27/28.47 |-Branch one: % 53.27/28.47 | (52) ~ in(all_17_0_12, all_3_4_5) % 53.27/28.47 | % 53.27/28.47 | From (24) and (37) follows: % 53.27/28.47 | (55) in(all_17_0_12, all_3_4_5) % 53.27/28.47 | % 53.27/28.47 | Using (55) and (52) yields: % 53.27/28.47 | (38) $false % 53.27/28.47 | % 53.27/28.47 |-The branch is then unsatisfiable % 53.27/28.47 |-Branch two: % 53.27/28.47 | (55) in(all_17_0_12, all_3_4_5) % 53.27/28.47 | (58) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_2_3) & in(v0, all_3_3_4)) % 53.27/28.47 | % 53.27/28.47 | Instantiating (58) with all_42_0_32, all_42_1_33 yields: % 53.27/28.47 | (71) ordered_pair(all_42_1_33, all_42_0_32) = all_17_0_12 & in(all_42_0_32, all_3_2_3) & in(all_42_1_33, all_3_3_4) % 53.27/28.47 | % 53.27/28.47 | Applying alpha-rule on (71) yields: % 53.27/28.47 | (72) ordered_pair(all_42_1_33, all_42_0_32) = all_17_0_12 % 53.27/28.47 | (73) in(all_42_0_32, all_3_2_3) % 53.27/28.47 | (74) in(all_42_1_33, all_3_3_4) % 53.27/28.47 | % 53.27/28.47 | Instantiating formula (21) with all_17_0_12, all_42_0_32, all_42_1_33 and discharging atoms ordered_pair(all_42_1_33, all_42_0_32) = all_17_0_12, ~ in(all_17_0_12, all_3_7_8), yields: % 53.27/28.47 | (52) ~ in(all_17_0_12, all_3_4_5) % 53.27/28.47 | % 53.27/28.47 | Using (55) and (52) yields: % 53.27/28.47 | (38) $false % 53.27/28.47 | % 53.27/28.47 |-The branch is then unsatisfiable % 53.27/28.47 |-Branch two: % 53.27/28.47 | (43) in(all_17_0_12, all_3_7_8) % 53.27/28.47 | (46) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_17_0_12 & in(v1, all_3_5_6) & in(v0, all_3_6_7)) % 53.27/28.47 | % 53.27/28.47 | From (23) and (62) follows: % 53.27/28.47 | (42) ~ in(all_17_0_12, all_3_7_8) % 53.27/28.47 | % 53.27/28.47 | Using (43) and (42) yields: % 53.27/28.47 | (38) $false % 53.27/28.47 | % 53.27/28.47 |-The branch is then unsatisfiable % 53.27/28.47 % SZS output end Proof for theBenchmark % 53.27/28.47 % 53.27/28.47 27889ms %------------------------------------------------------------------------------