%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN347+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 : Thu Jul 21 05:01:38 EDT 2022 % Result : Theorem 7.14s 2.79s % Output : Proof 12.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN347+1 : TPTP v8.1.0. Released v2.0.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n011.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 : Mon Jul 11 20:45:57 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.24/0.88 Prover 0: Preprocessing ... % 1.31/0.92 Prover 0: Warning: ignoring some quantifiers % 1.39/0.94 Prover 0: Constructing countermodel ... % 1.54/1.04 Prover 0: gave up % 1.54/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.54/1.06 Prover 1: Preprocessing ... % 1.85/1.10 Prover 1: Warning: ignoring some quantifiers % 1.85/1.10 Prover 1: Constructing countermodel ... % 2.17/1.22 Prover 1: gave up % 2.17/1.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.17/1.22 Prover 2: Preprocessing ... % 2.26/1.25 Prover 2: Warning: ignoring some quantifiers % 2.26/1.25 Prover 2: Constructing countermodel ... % 2.26/1.31 Prover 2: gave up % 2.26/1.31 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.26/1.32 Prover 3: Preprocessing ... % 2.61/1.32 Prover 3: Warning: ignoring some quantifiers % 2.61/1.32 Prover 3: Constructing countermodel ... % 2.61/1.34 Prover 3: gave up % 2.61/1.34 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 2.61/1.35 Prover 4: Preprocessing ... % 2.61/1.37 Prover 4: Warning: ignoring some quantifiers % 2.61/1.37 Prover 4: Constructing countermodel ... % 2.90/1.42 Prover 4: gave up % 2.90/1.42 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.90/1.43 Prover 5: Preprocessing ... % 2.90/1.44 Prover 5: Warning: ignoring some quantifiers % 2.90/1.44 Prover 5: Constructing countermodel ... % 3.16/1.49 Prover 5: gave up % 3.16/1.49 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.16/1.49 Prover 6: Preprocessing ... % 3.16/1.50 Prover 6: Warning: ignoring some quantifiers % 3.16/1.51 Prover 6: Constructing countermodel ... % 3.30/1.54 Prover 6: gave up % 3.30/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 3.30/1.54 Prover 7: Preprocessing ... % 3.30/1.55 Prover 7: Proving ... % 7.14/2.79 Prover 7: proved (1250ms) % 7.14/2.79 % 7.14/2.79 % SZS status Theorem for theBenchmark % 7.14/2.79 % 7.14/2.79 Generating proof ... found it (size 60) % 12.55/4.48 % 12.55/4.48 % SZS output start Proof for theBenchmark % 12.55/4.48 Assumed formulas after preprocessing and simplification: % 12.55/4.48 | (0) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ? [v4] : (( ~ big_f(v1, v4) | ~ big_f(v0, v4)) & ( ~ big_f(v0, v1) | (( ~ big_f(v3, v4) | ~ big_f(v2, v4)) & (big_f(v3, v4) | big_f(v2, v4)))) & (big_f(v1, v4) | big_f(v0, v4)) & (big_f(v0, v1) | (( ~ big_f(v3, v4) | big_f(v2, v4)) & ( ~ big_f(v2, v4) | big_f(v3, v4))))) % 12.55/4.48 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 12.55/4.48 | (1) ! [v0] : ! [v1] : ? [v2] : (( ~ big_f(all_0_0_0, v2) | ~ big_f(all_0_1_1, v2)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(v1, v2) | ~ big_f(v0, v2)) & (big_f(v1, v2) | big_f(v0, v2)))) & (big_f(all_0_0_0, v2) | big_f(all_0_1_1, v2)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(v1, v2) | big_f(v0, v2)) & ( ~ big_f(v0, v2) | big_f(v1, v2))))) % 12.55/4.48 | % 12.55/4.48 | Instantiating formula (1) with ex_2_0_2, ex_2_1_3 yields: % 12.55/4.48 | (2) ? [v0] : (( ~ big_f(all_0_0_0, v0) | ~ big_f(all_0_1_1, v0)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, v0) | ~ big_f(ex_2_1_3, v0)) & (big_f(ex_2_0_2, v0) | big_f(ex_2_1_3, v0)))) & (big_f(all_0_0_0, v0) | big_f(all_0_1_1, v0)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, v0) | big_f(ex_2_1_3, v0)) & ( ~ big_f(ex_2_1_3, v0) | big_f(ex_2_0_2, v0))))) % 12.55/4.49 | % 12.55/4.49 | Instantiating (2) with all_3_0_4 yields: % 12.55/4.49 | (3) ( ~ big_f(all_0_0_0, all_3_0_4) | ~ big_f(all_0_1_1, all_3_0_4)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | ~ big_f(ex_2_1_3, all_3_0_4)) & (big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)))) & (big_f(all_0_0_0, all_3_0_4) | big_f(all_0_1_1, all_3_0_4)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)) & ( ~ big_f(ex_2_1_3, all_3_0_4) | big_f(ex_2_0_2, all_3_0_4)))) % 12.55/4.49 | % 12.55/4.49 | Applying alpha-rule on (3) yields: % 12.55/4.49 | (4) ~ big_f(all_0_0_0, all_3_0_4) | ~ big_f(all_0_1_1, all_3_0_4) % 12.55/4.49 | (5) ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | ~ big_f(ex_2_1_3, all_3_0_4)) & (big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4))) % 12.55/4.49 | (6) big_f(all_0_0_0, all_3_0_4) | big_f(all_0_1_1, all_3_0_4) % 12.55/4.49 | (7) big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)) & ( ~ big_f(ex_2_1_3, all_3_0_4) | big_f(ex_2_0_2, all_3_0_4))) % 12.55/4.49 | % 12.55/4.49 +-Applying beta-rule and splitting (7), into two cases. % 12.55/4.49 |-Branch one: % 12.55/4.49 | (8) big_f(all_0_1_1, all_0_0_0) % 12.55/4.49 | % 12.55/4.49 | Introducing new symbol ex_35_1_6 defined by: % 12.55/4.49 | (9) ex_35_1_6 = arbitrary_constant % 12.55/4.49 | % 12.55/4.49 | Introducing new symbol ex_35_0_5 defined by: % 12.55/4.49 | (10) ex_35_0_5 = arbitrary_constant % 12.55/4.49 | % 12.55/4.49 | Instantiating formula (1) with ex_35_0_5, ex_35_1_6 yields: % 12.55/4.49 | (11) ? [v0] : (( ~ big_f(all_0_0_0, v0) | ~ big_f(all_0_1_1, v0)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, v0) | ~ big_f(ex_35_1_6, v0)) & (big_f(ex_35_0_5, v0) | big_f(ex_35_1_6, v0)))) & (big_f(all_0_0_0, v0) | big_f(all_0_1_1, v0)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, v0) | big_f(ex_35_1_6, v0)) & ( ~ big_f(ex_35_1_6, v0) | big_f(ex_35_0_5, v0))))) % 12.55/4.49 | % 12.55/4.49 | Instantiating (11) with all_36_0_7 yields: % 12.55/4.49 | (12) ( ~ big_f(all_0_0_0, all_36_0_7) | ~ big_f(all_0_1_1, all_36_0_7)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)) & (big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)))) & (big_f(all_0_0_0, all_36_0_7) | big_f(all_0_1_1, all_36_0_7)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)) & ( ~ big_f(ex_35_1_6, all_36_0_7) | big_f(ex_35_0_5, all_36_0_7)))) % 12.55/4.49 | % 12.55/4.49 | Applying alpha-rule on (12) yields: % 12.55/4.49 | (13) ~ big_f(all_0_0_0, all_36_0_7) | ~ big_f(all_0_1_1, all_36_0_7) % 12.55/4.49 | (14) ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)) & (big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7))) % 12.55/4.49 | (15) big_f(all_0_0_0, all_36_0_7) | big_f(all_0_1_1, all_36_0_7) % 12.55/4.49 | (16) big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)) & ( ~ big_f(ex_35_1_6, all_36_0_7) | big_f(ex_35_0_5, all_36_0_7))) % 12.55/4.49 | % 12.55/4.49 +-Applying beta-rule and splitting (14), into two cases. % 12.55/4.49 |-Branch one: % 12.55/4.49 | (17) ~ big_f(all_0_1_1, all_0_0_0) % 12.55/4.49 | % 12.55/4.49 | Using (8) and (17) yields: % 12.55/4.49 | (18) $false % 12.55/4.49 | % 12.55/4.49 |-The branch is then unsatisfiable % 12.55/4.49 |-Branch two: % 12.55/4.49 | (19) ( ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)) & (big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)) % 12.55/4.49 | % 12.55/4.49 | Applying alpha-rule on (19) yields: % 12.55/4.49 | (20) ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7) % 12.55/4.49 | (21) big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 +-Applying beta-rule and splitting (21), into two cases. % 12.55/4.49 |-Branch one: % 12.55/4.49 | (22) big_f(ex_35_0_5, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 +-Applying beta-rule and splitting (20), into two cases. % 12.55/4.49 |-Branch one: % 12.55/4.49 | (23) ~ big_f(ex_35_0_5, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 | Using (22) and (23) yields: % 12.55/4.49 | (18) $false % 12.55/4.49 | % 12.55/4.49 |-The branch is then unsatisfiable % 12.55/4.49 |-Branch two: % 12.55/4.49 | (25) ~ big_f(ex_35_1_6, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 | From (10) and (22) follows: % 12.55/4.49 | (26) big_f(arbitrary_constant, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 | From (9) and (25) follows: % 12.55/4.49 | (27) ~ big_f(arbitrary_constant, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 | Using (26) and (27) yields: % 12.55/4.49 | (18) $false % 12.55/4.49 | % 12.55/4.49 |-The branch is then unsatisfiable % 12.55/4.49 |-Branch two: % 12.55/4.49 | (23) ~ big_f(ex_35_0_5, all_36_0_7) % 12.55/4.49 | (30) big_f(ex_35_1_6, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 | From (9) and (30) follows: % 12.55/4.49 | (26) big_f(arbitrary_constant, all_36_0_7) % 12.55/4.49 | % 12.55/4.49 | From (10) and (23) follows: % 12.55/4.49 | (27) ~ big_f(arbitrary_constant, all_36_0_7) % 12.55/4.50 | % 12.55/4.50 | Using (26) and (27) yields: % 12.55/4.50 | (18) $false % 12.55/4.50 | % 12.55/4.50 |-The branch is then unsatisfiable % 12.55/4.50 |-Branch two: % 12.55/4.50 | (17) ~ big_f(all_0_1_1, all_0_0_0) % 12.55/4.50 | (35) ( ~ big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)) & ( ~ big_f(ex_2_1_3, all_3_0_4) | big_f(ex_2_0_2, all_3_0_4)) % 12.55/4.50 | % 12.55/4.50 | Introducing new symbol ex_35_1_12 defined by: % 12.55/4.50 | (36) ex_35_1_12 = all_0_0_0 % 12.55/4.50 | % 12.55/4.50 | Introducing new symbol ex_35_0_11 defined by: % 12.55/4.50 | (37) ex_35_0_11 = all_0_1_1 % 12.55/4.50 | % 12.55/4.50 | Instantiating formula (1) with ex_35_0_11, ex_35_1_12 yields: % 12.55/4.50 | (38) ? [v0] : (( ~ big_f(all_0_0_0, v0) | ~ big_f(all_0_1_1, v0)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, v0) | ~ big_f(ex_35_1_12, v0)) & (big_f(ex_35_0_11, v0) | big_f(ex_35_1_12, v0)))) & (big_f(all_0_0_0, v0) | big_f(all_0_1_1, v0)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, v0) | big_f(ex_35_1_12, v0)) & ( ~ big_f(ex_35_1_12, v0) | big_f(ex_35_0_11, v0))))) % 12.55/4.50 | % 12.55/4.50 | Instantiating (38) with all_36_0_13 yields: % 12.55/4.50 | (39) ( ~ big_f(all_0_0_0, all_36_0_13) | ~ big_f(all_0_1_1, all_36_0_13)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | ~ big_f(ex_35_1_12, all_36_0_13)) & (big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)))) & (big_f(all_0_0_0, all_36_0_13) | big_f(all_0_1_1, all_36_0_13)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13)))) % 12.55/4.50 | % 12.55/4.50 | Applying alpha-rule on (39) yields: % 12.55/4.50 | (40) ~ big_f(all_0_0_0, all_36_0_13) | ~ big_f(all_0_1_1, all_36_0_13) % 12.55/4.50 | (41) ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | ~ big_f(ex_35_1_12, all_36_0_13)) & (big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13))) % 12.55/4.50 | (42) big_f(all_0_0_0, all_36_0_13) | big_f(all_0_1_1, all_36_0_13) % 12.55/4.50 | (43) big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13))) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (42), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (44) big_f(all_0_0_0, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (40), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (45) ~ big_f(all_0_0_0, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | Using (44) and (45) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (47) ~ big_f(all_0_1_1, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (43), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (8) big_f(all_0_1_1, all_0_0_0) % 12.88/4.50 | % 12.88/4.50 | Using (8) and (17) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (50) ( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13)) % 12.88/4.50 | % 12.88/4.50 | Applying alpha-rule on (50) yields: % 12.88/4.50 | (51) ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13) % 12.88/4.50 | (52) ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (52), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (53) ~ big_f(ex_35_1_12, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | From (36) and (53) follows: % 12.88/4.50 | (45) ~ big_f(all_0_0_0, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | Using (44) and (45) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (56) big_f(ex_35_0_11, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | From (37) and (56) follows: % 12.88/4.50 | (57) big_f(all_0_1_1, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | Using (57) and (47) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (45) ~ big_f(all_0_0_0, all_36_0_13) % 12.88/4.50 | (57) big_f(all_0_1_1, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (43), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (8) big_f(all_0_1_1, all_0_0_0) % 12.88/4.50 | % 12.88/4.50 | Using (8) and (17) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (50) ( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13)) % 12.88/4.50 | % 12.88/4.50 | Applying alpha-rule on (50) yields: % 12.88/4.50 | (51) ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13) % 12.88/4.50 | (52) ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (52), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (53) ~ big_f(ex_35_1_12, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 +-Applying beta-rule and splitting (51), into two cases. % 12.88/4.50 |-Branch one: % 12.88/4.50 | (67) ~ big_f(ex_35_0_11, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | From (37) and (67) follows: % 12.88/4.50 | (47) ~ big_f(all_0_1_1, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | Using (57) and (47) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (70) big_f(ex_35_1_12, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | Using (70) and (53) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 |-Branch two: % 12.88/4.50 | (70) big_f(ex_35_1_12, all_36_0_13) % 12.88/4.50 | (56) big_f(ex_35_0_11, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | From (36) and (70) follows: % 12.88/4.50 | (44) big_f(all_0_0_0, all_36_0_13) % 12.88/4.50 | % 12.88/4.50 | Using (44) and (45) yields: % 12.88/4.50 | (18) $false % 12.88/4.50 | % 12.88/4.50 |-The branch is then unsatisfiable % 12.88/4.50 % SZS output end Proof for theBenchmark % 12.88/4.50 % 12.88/4.50 3919ms %------------------------------------------------------------------------------