%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN349+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 05:01:40 EDT 2022 % Result : Theorem 5.25s 2.06s % Output : Proof 7.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN349+1 : TPTP v8.1.0. Released v2.0.0. % 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n025.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 20:16:02 EDT 2022 % 0.13/0.33 % CPUTime : % 0.55/0.61 ____ _ % 0.55/0.61 ___ / __ \_____(_)___ ________ __________ % 0.55/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.61 % 0.55/0.61 A Theorem Prover for First-Order Logic % 0.55/0.61 (ePrincess v.1.0) % 0.55/0.61 % 0.55/0.61 (c) Philipp Rümmer, 2009-2015 % 0.55/0.61 (c) Peter Backeman, 2014-2015 % 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.61 Bug reports to peter@backeman.se % 0.55/0.61 % 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.61 % 0.55/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.24/0.92 Prover 0: Preprocessing ... % 1.37/0.98 Prover 0: Warning: ignoring some quantifiers % 1.37/0.99 Prover 0: Constructing countermodel ... % 1.70/1.10 Prover 0: gave up % 1.70/1.10 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.70/1.11 Prover 1: Preprocessing ... % 1.70/1.15 Prover 1: Warning: ignoring some quantifiers % 1.70/1.16 Prover 1: Constructing countermodel ... % 2.16/1.25 Prover 1: gave up % 2.16/1.25 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.16/1.26 Prover 2: Preprocessing ... % 2.16/1.29 Prover 2: Warning: ignoring some quantifiers % 2.16/1.29 Prover 2: Constructing countermodel ... % 2.56/1.34 Prover 2: gave up % 2.56/1.34 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.56/1.35 Prover 3: Preprocessing ... % 2.56/1.36 Prover 3: Warning: ignoring some quantifiers % 2.56/1.36 Prover 3: Constructing countermodel ... % 2.56/1.38 Prover 3: gave up % 2.56/1.38 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 2.56/1.38 Prover 4: Preprocessing ... % 2.89/1.40 Prover 4: Warning: ignoring some quantifiers % 2.89/1.41 Prover 4: Constructing countermodel ... % 2.89/1.45 Prover 4: gave up % 2.89/1.45 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.89/1.45 Prover 5: Preprocessing ... % 2.89/1.46 Prover 5: Warning: ignoring some quantifiers % 2.89/1.46 Prover 5: Constructing countermodel ... % 3.26/1.50 Prover 5: gave up % 3.26/1.51 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.26/1.51 Prover 6: Preprocessing ... % 3.26/1.53 Prover 6: Warning: ignoring some quantifiers % 3.26/1.53 Prover 6: Constructing countermodel ... % 3.26/1.56 Prover 6: gave up % 3.26/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 3.26/1.56 Prover 7: Preprocessing ... % 3.26/1.57 Prover 7: Proving ... % 5.25/2.06 Prover 7: proved (505ms) % 5.25/2.06 % 5.25/2.06 % SZS status Theorem for theBenchmark % 5.25/2.06 % 5.25/2.06 Generating proof ... found it (size 72) % 7.97/2.90 % 7.97/2.90 % SZS output start Proof for theBenchmark % 7.97/2.90 Assumed formulas after preprocessing and simplification: % 7.97/2.90 | (0) ! [v0] : ? [v1] : ! [v2] : ? [v3] : (( ~ big_f(v3, v1) | (( ~ big_f(v2, v3) | (( ~ big_f(v3, v2) | ~ big_f(v0, v3)) & (big_f(v3, v2) | big_f(v0, v3)))) & (big_f(v2, v3) | (( ~ big_f(v3, v2) | big_f(v0, v3)) & ( ~ big_f(v0, v3) | big_f(v3, v2)))))) & ( ~ big_f(v1, v3) | big_f(v0, v3)) & ( ~ big_f(v0, v3) | big_f(v1, v3)) & (big_f(v3, v1) | (( ~ big_f(v2, v3) | (( ~ big_f(v3, v2) | big_f(v0, v3)) & ( ~ big_f(v0, v3) | big_f(v3, v2)))) & (big_f(v2, v3) | (( ~ big_f(v3, v2) | ~ big_f(v0, v3)) & (big_f(v3, v2) | big_f(v0, v3))))))) % 7.97/2.90 | Instantiating formula (0) with ex_0_0_0 yields: % 7.97/2.90 | (1) ? [v0] : ! [v1] : ? [v2] : (( ~ big_f(v2, v0) | (( ~ big_f(v1, v2) | (( ~ big_f(v2, v1) | ~ big_f(ex_0_0_0, v2)) & (big_f(v2, v1) | big_f(ex_0_0_0, v2)))) & (big_f(v1, v2) | (( ~ big_f(v2, v1) | big_f(ex_0_0_0, v2)) & ( ~ big_f(ex_0_0_0, v2) | big_f(v2, v1)))))) & ( ~ big_f(v0, v2) | big_f(ex_0_0_0, v2)) & ( ~ big_f(ex_0_0_0, v2) | big_f(v0, v2)) & (big_f(v2, v0) | (( ~ big_f(v1, v2) | (( ~ big_f(v2, v1) | big_f(ex_0_0_0, v2)) & ( ~ big_f(ex_0_0_0, v2) | big_f(v2, v1)))) & (big_f(v1, v2) | (( ~ big_f(v2, v1) | ~ big_f(ex_0_0_0, v2)) & (big_f(v2, v1) | big_f(ex_0_0_0, v2))))))) % 7.97/2.91 | % 7.97/2.91 | Instantiating (1) with all_1_0_1 yields: % 7.97/2.91 | (2) ! [v0] : ? [v1] : (( ~ big_f(v1, all_1_0_1) | (( ~ big_f(v0, v1) | (( ~ big_f(v1, v0) | ~ big_f(ex_0_0_0, v1)) & (big_f(v1, v0) | big_f(ex_0_0_0, v1)))) & (big_f(v0, v1) | (( ~ big_f(v1, v0) | big_f(ex_0_0_0, v1)) & ( ~ big_f(ex_0_0_0, v1) | big_f(v1, v0)))))) & ( ~ big_f(all_1_0_1, v1) | big_f(ex_0_0_0, v1)) & ( ~ big_f(ex_0_0_0, v1) | big_f(all_1_0_1, v1)) & (big_f(v1, all_1_0_1) | (( ~ big_f(v0, v1) | (( ~ big_f(v1, v0) | big_f(ex_0_0_0, v1)) & ( ~ big_f(ex_0_0_0, v1) | big_f(v1, v0)))) & (big_f(v0, v1) | (( ~ big_f(v1, v0) | ~ big_f(ex_0_0_0, v1)) & (big_f(v1, v0) | big_f(ex_0_0_0, v1))))))) % 7.97/2.91 | % 7.97/2.91 | Introducing new symbol ex_6_0_4 defined by: % 7.97/2.91 | (3) ex_6_0_4 = all_1_0_1 % 7.97/2.91 | % 7.97/2.91 | Instantiating formula (2) with ex_6_0_4 yields: % 7.97/2.91 | (4) ? [v0] : (( ~ big_f(v0, all_1_0_1) | (( ~ big_f(ex_6_0_4, v0) | (( ~ big_f(v0, ex_6_0_4) | ~ big_f(ex_0_0_0, v0)) & (big_f(v0, ex_6_0_4) | big_f(ex_0_0_0, v0)))) & (big_f(ex_6_0_4, v0) | (( ~ big_f(v0, ex_6_0_4) | big_f(ex_0_0_0, v0)) & ( ~ big_f(ex_0_0_0, v0) | big_f(v0, ex_6_0_4)))))) & ( ~ big_f(all_1_0_1, v0) | big_f(ex_0_0_0, v0)) & ( ~ big_f(ex_0_0_0, v0) | big_f(all_1_0_1, v0)) & (big_f(v0, all_1_0_1) | (( ~ big_f(ex_6_0_4, v0) | (( ~ big_f(v0, ex_6_0_4) | big_f(ex_0_0_0, v0)) & ( ~ big_f(ex_0_0_0, v0) | big_f(v0, ex_6_0_4)))) & (big_f(ex_6_0_4, v0) | (( ~ big_f(v0, ex_6_0_4) | ~ big_f(ex_0_0_0, v0)) & (big_f(v0, ex_6_0_4) | big_f(ex_0_0_0, v0))))))) % 7.97/2.91 | % 7.97/2.91 | Instantiating (4) with all_7_0_5 yields: % 7.97/2.91 | (5) ( ~ big_f(all_7_0_5, all_1_0_1) | (( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))))) & ( ~ big_f(all_1_0_1, all_7_0_5) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_1_0_1, all_7_0_5)) & (big_f(all_7_0_5, all_1_0_1) | (( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))))) % 7.97/2.91 | % 7.97/2.91 | Applying alpha-rule on (5) yields: % 7.97/2.91 | (6) ~ big_f(all_7_0_5, all_1_0_1) | (( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4))))) % 7.97/2.92 | (7) ~ big_f(all_1_0_1, all_7_0_5) | big_f(ex_0_0_0, all_7_0_5) % 7.97/2.92 | (8) ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_1_0_1, all_7_0_5) % 7.97/2.92 | (9) big_f(all_7_0_5, all_1_0_1) | (( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5))))) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (8), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (10) ~ big_f(ex_0_0_0, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (7), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (11) ~ big_f(all_1_0_1, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (6), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (12) ~ big_f(all_7_0_5, all_1_0_1) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (9), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (13) big_f(all_7_0_5, all_1_0_1) % 7.97/2.92 | % 7.97/2.92 | Using (13) and (12) yields: % 7.97/2.92 | (14) $false % 7.97/2.92 | % 7.97/2.92 |-The branch is then unsatisfiable % 7.97/2.92 |-Branch two: % 7.97/2.92 | (15) ( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))) % 7.97/2.92 | % 7.97/2.92 | Applying alpha-rule on (15) yields: % 7.97/2.92 | (16) ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4))) % 7.97/2.92 | (17) big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5))) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (17), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (18) big_f(ex_6_0_4, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 | From (3) and (18) follows: % 7.97/2.92 | (19) big_f(all_1_0_1, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 | Using (19) and (11) yields: % 7.97/2.92 | (14) $false % 7.97/2.92 | % 7.97/2.92 |-The branch is then unsatisfiable % 7.97/2.92 |-Branch two: % 7.97/2.92 | (21) ( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) % 7.97/2.92 | % 7.97/2.92 | Applying alpha-rule on (21) yields: % 7.97/2.92 | (22) ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5) % 7.97/2.92 | (23) big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (23), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (24) big_f(all_7_0_5, ex_6_0_4) % 7.97/2.92 | % 7.97/2.92 | From (3) and (24) follows: % 7.97/2.92 | (13) big_f(all_7_0_5, all_1_0_1) % 7.97/2.92 | % 7.97/2.92 | Using (13) and (12) yields: % 7.97/2.92 | (14) $false % 7.97/2.92 | % 7.97/2.92 |-The branch is then unsatisfiable % 7.97/2.92 |-Branch two: % 7.97/2.92 | (27) big_f(ex_0_0_0, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 | Using (27) and (10) yields: % 7.97/2.92 | (14) $false % 7.97/2.92 | % 7.97/2.92 |-The branch is then unsatisfiable % 7.97/2.92 |-Branch two: % 7.97/2.92 | (13) big_f(all_7_0_5, all_1_0_1) % 7.97/2.92 | (30) ( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))) % 7.97/2.92 | % 7.97/2.92 | Applying alpha-rule on (30) yields: % 7.97/2.92 | (31) ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5))) % 7.97/2.92 | (32) big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4))) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (31), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (33) ~ big_f(ex_6_0_4, all_7_0_5) % 7.97/2.92 | % 7.97/2.92 +-Applying beta-rule and splitting (32), into two cases. % 7.97/2.92 |-Branch one: % 7.97/2.92 | (18) big_f(ex_6_0_4, all_7_0_5) % 7.97/2.92 | % 7.97/2.93 | Using (18) and (33) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (36) ( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)) % 7.97/2.93 | % 7.97/2.93 | Applying alpha-rule on (36) yields: % 7.97/2.93 | (37) ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5) % 7.97/2.93 | (38) ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (37), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (39) ~ big_f(all_7_0_5, ex_6_0_4) % 7.97/2.93 | % 7.97/2.93 | From (3) and (39) follows: % 7.97/2.93 | (12) ~ big_f(all_7_0_5, all_1_0_1) % 7.97/2.93 | % 7.97/2.93 | Using (13) and (12) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (27) big_f(ex_0_0_0, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 | Using (27) and (10) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (18) big_f(ex_6_0_4, all_7_0_5) % 7.97/2.93 | (21) ( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) % 7.97/2.93 | % 7.97/2.93 | From (3) and (18) follows: % 7.97/2.93 | (19) big_f(all_1_0_1, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 | Using (19) and (11) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (27) big_f(ex_0_0_0, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 | Using (27) and (10) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (27) big_f(ex_0_0_0, all_7_0_5) % 7.97/2.93 | (19) big_f(all_1_0_1, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (6), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (12) ~ big_f(all_7_0_5, all_1_0_1) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (9), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (13) big_f(all_7_0_5, all_1_0_1) % 7.97/2.93 | % 7.97/2.93 | Using (13) and (12) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (15) ( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))) % 7.97/2.93 | % 7.97/2.93 | Applying alpha-rule on (15) yields: % 7.97/2.93 | (16) ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4))) % 7.97/2.93 | (17) big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5))) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (17), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (18) big_f(ex_6_0_4, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (16), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (33) ~ big_f(ex_6_0_4, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 | Using (18) and (33) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (36) ( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)) % 7.97/2.93 | % 7.97/2.93 | Applying alpha-rule on (36) yields: % 7.97/2.93 | (37) ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5) % 7.97/2.93 | (38) ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (38), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (10) ~ big_f(ex_0_0_0, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 | Using (27) and (10) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (24) big_f(all_7_0_5, ex_6_0_4) % 7.97/2.93 | % 7.97/2.93 | From (3) and (24) follows: % 7.97/2.93 | (13) big_f(all_7_0_5, all_1_0_1) % 7.97/2.93 | % 7.97/2.93 | Using (13) and (12) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (33) ~ big_f(ex_6_0_4, all_7_0_5) % 7.97/2.93 | (21) ( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) % 7.97/2.93 | % 7.97/2.93 | From (3) and (33) follows: % 7.97/2.93 | (11) ~ big_f(all_1_0_1, all_7_0_5) % 7.97/2.93 | % 7.97/2.93 | Using (19) and (11) yields: % 7.97/2.93 | (14) $false % 7.97/2.93 | % 7.97/2.93 |-The branch is then unsatisfiable % 7.97/2.93 |-Branch two: % 7.97/2.93 | (13) big_f(all_7_0_5, all_1_0_1) % 7.97/2.93 | (30) ( ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)))) & (big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4)))) % 7.97/2.93 | % 7.97/2.93 | Applying alpha-rule on (30) yields: % 7.97/2.93 | (31) ~ big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5))) % 7.97/2.93 | (32) big_f(ex_6_0_4, all_7_0_5) | (( ~ big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) & ( ~ big_f(ex_0_0_0, all_7_0_5) | big_f(all_7_0_5, ex_6_0_4))) % 7.97/2.93 | % 7.97/2.93 +-Applying beta-rule and splitting (31), into two cases. % 7.97/2.93 |-Branch one: % 7.97/2.93 | (33) ~ big_f(ex_6_0_4, all_7_0_5) % 7.97/2.93 | % 7.97/2.94 | From (3) and (33) follows: % 7.97/2.94 | (11) ~ big_f(all_1_0_1, all_7_0_5) % 7.97/2.94 | % 7.97/2.94 | Using (19) and (11) yields: % 7.97/2.94 | (14) $false % 7.97/2.94 | % 7.97/2.94 |-The branch is then unsatisfiable % 7.97/2.94 |-Branch two: % 7.97/2.94 | (21) ( ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5)) & (big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5)) % 7.97/2.94 | % 7.97/2.94 | Applying alpha-rule on (21) yields: % 7.97/2.94 | (22) ~ big_f(all_7_0_5, ex_6_0_4) | ~ big_f(ex_0_0_0, all_7_0_5) % 7.97/2.94 | (23) big_f(all_7_0_5, ex_6_0_4) | big_f(ex_0_0_0, all_7_0_5) % 7.97/2.94 | % 7.97/2.94 +-Applying beta-rule and splitting (22), into two cases. % 7.97/2.94 |-Branch one: % 7.97/2.94 | (39) ~ big_f(all_7_0_5, ex_6_0_4) % 7.97/2.94 | % 7.97/2.94 | From (3) and (39) follows: % 7.97/2.94 | (12) ~ big_f(all_7_0_5, all_1_0_1) % 7.97/2.94 | % 7.97/2.94 | Using (13) and (12) yields: % 7.97/2.94 | (14) $false % 7.97/2.94 | % 7.97/2.94 |-The branch is then unsatisfiable % 7.97/2.94 |-Branch two: % 7.97/2.94 | (10) ~ big_f(ex_0_0_0, all_7_0_5) % 7.97/2.94 | % 7.97/2.94 | Using (27) and (10) yields: % 7.97/2.94 | (14) $false % 7.97/2.94 | % 7.97/2.94 |-The branch is then unsatisfiable % 7.97/2.94 % SZS output end Proof for theBenchmark % 7.97/2.94 % 7.97/2.94 2308ms %------------------------------------------------------------------------------