%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEV515+1 : TPTP v8.1.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 16:56:43 EDT 2022 % Result : Theorem 8.74s 2.87s % Output : Proof 12.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEV515+1 : TPTP v8.1.0. Released v7.0.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n006.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 : Tue Jun 28 12:10:38 EDT 2022 % 0.19/0.33 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.58 % 0.58/0.58 A Theorem Prover for First-Order Logic % 0.58/0.58 (ePrincess v.1.0) % 0.58/0.58 % 0.58/0.58 (c) Philipp Rümmer, 2009-2015 % 0.58/0.58 (c) Peter Backeman, 2014-2015 % 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.58 Bug reports to peter@backeman.se % 0.58/0.58 % 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.58 % 0.58/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.48/0.91 Prover 0: Preprocessing ... % 1.74/1.03 Prover 0: Warning: ignoring some quantifiers % 1.74/1.05 Prover 0: Constructing countermodel ... % 1.91/1.16 Prover 0: gave up % 1.91/1.16 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.28/1.18 Prover 1: Preprocessing ... % 2.48/1.27 Prover 1: Constructing countermodel ... % 2.48/1.28 Prover 1: gave up % 2.48/1.28 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.48/1.30 Prover 2: Preprocessing ... % 3.15/1.42 Prover 2: Warning: ignoring some quantifiers % 3.15/1.43 Prover 2: Constructing countermodel ... % 3.15/1.46 Prover 2: gave up % 3.15/1.46 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.57/1.48 Prover 3: Preprocessing ... % 3.57/1.49 Prover 3: Warning: ignoring some quantifiers % 3.57/1.49 Prover 3: Constructing countermodel ... % 3.72/1.52 Prover 3: gave up % 3.72/1.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 3.82/1.53 Prover 4: Preprocessing ... % 3.82/1.60 Prover 4: Warning: ignoring some quantifiers % 3.82/1.61 Prover 4: Constructing countermodel ... % 5.07/1.81 Prover 4: gave up % 5.14/1.81 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.17/1.82 Prover 5: Preprocessing ... % 5.17/1.86 Prover 5: Warning: ignoring some quantifiers % 5.17/1.86 Prover 5: Constructing countermodel ... % 5.17/1.87 Prover 5: gave up % 5.17/1.87 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.17/1.88 Prover 6: Preprocessing ... % 5.59/1.93 Prover 6: Warning: ignoring some quantifiers % 5.59/1.93 Prover 6: Constructing countermodel ... % 5.59/1.95 Prover 6: gave up % 5.59/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 5.59/1.96 Prover 7: Preprocessing ... % 5.59/1.97 Prover 7: Proving ... % 8.74/2.87 Prover 7: proved (922ms) % 8.74/2.87 % 8.74/2.87 % SZS status Theorem for theBenchmark % 8.74/2.87 % 8.74/2.87 Generating proof ... found it (size 146) % 11.98/3.88 % 11.98/3.88 % SZS output start Proof for theBenchmark % 11.98/3.88 Assumed formulas after preprocessing and simplification: % 11.98/3.88 | (0) ! [v0] : ! [v1] : ( ~ g_false(v0, v1) | ~ g_true(v0, v1) | g_both(v0, v1)) & ! [v0] : ! [v1] : ( ~ g_false(v0, v1) | g_true(v0, v1) | g_false_only(v0, v1)) & ! [v0] : ! [v1] : ( ~ g_true(v0, v1) | g_false(v0, v1) | g_true_only(v0, v1)) & ! [v0] : ! [v1] : ( ~ g_false_only(v0, v1) | (g_false(v0, v1) & ~ g_true(v0, v1))) & ! [v0] : ! [v1] : ( ~ g_both(v0, v1) | (g_false(v0, v1) & g_true(v0, v1))) & ! [v0] : ! [v1] : ( ~ g_true_only(v0, v1) | (g_true(v0, v1) & ~ g_false(v0, v1))) & ! [v0] : ! [v1] : (g_false_only(v0, v1) | g_both(v0, v1) | g_true_only(v0, v1)) & ? [v0] : ( ! [v1] : ( ~ g_false_only(v1, v0) | ( ~ g_false_only(v1, v1) & ~ g_both(v1, v1))) & ! [v1] : ( ~ g_both(v1, v0) | ( ~ g_false_only(v1, v1) & ~ g_true_only(v1, v1))) & ! [v1] : ( ~ g_true_only(v1, v0) | ( ~ g_both(v1, v1) & ~ g_true_only(v1, v1)))) & ( ? [v0] : ! [v1] : ((g_false_only(v1, v1) & g_true_only(v1, v0)) | (g_false_only(v1, v0) & g_true_only(v1, v1))) | ! [v0] : ( ? [v1] : ((g_false_only(v1, v0) & (g_false_only(v1, v1) | g_both(v1, v1))) | (g_both(v1, v0) & (g_false_only(v1, v1) | g_true_only(v1, v1))) | (g_true_only(v1, v0) & (g_both(v1, v1) | g_true_only(v1, v1)))) | ! [v1] : ( ~ g_both(v1, v1) | ~ g_both(v1, v0)))) % 11.98/3.88 | Applying alpha-rule on (0) yields: % 11.98/3.88 | (1) ! [v0] : ! [v1] : ( ~ g_both(v0, v1) | (g_false(v0, v1) & g_true(v0, v1))) % 11.98/3.88 | (2) ! [v0] : ! [v1] : ( ~ g_false(v0, v1) | g_true(v0, v1) | g_false_only(v0, v1)) % 11.98/3.88 | (3) ! [v0] : ! [v1] : ( ~ g_true(v0, v1) | g_false(v0, v1) | g_true_only(v0, v1)) % 11.98/3.88 | (4) ! [v0] : ! [v1] : (g_false_only(v0, v1) | g_both(v0, v1) | g_true_only(v0, v1)) % 11.98/3.88 | (5) ! [v0] : ! [v1] : ( ~ g_true_only(v0, v1) | (g_true(v0, v1) & ~ g_false(v0, v1))) % 11.98/3.88 | (6) ? [v0] : ! [v1] : ((g_false_only(v1, v1) & g_true_only(v1, v0)) | (g_false_only(v1, v0) & g_true_only(v1, v1))) | ! [v0] : ( ? [v1] : ((g_false_only(v1, v0) & (g_false_only(v1, v1) | g_both(v1, v1))) | (g_both(v1, v0) & (g_false_only(v1, v1) | g_true_only(v1, v1))) | (g_true_only(v1, v0) & (g_both(v1, v1) | g_true_only(v1, v1)))) | ! [v1] : ( ~ g_both(v1, v1) | ~ g_both(v1, v0))) % 11.98/3.88 | (7) ! [v0] : ! [v1] : ( ~ g_false(v0, v1) | ~ g_true(v0, v1) | g_both(v0, v1)) % 11.98/3.88 | (8) ? [v0] : ( ! [v1] : ( ~ g_false_only(v1, v0) | ( ~ g_false_only(v1, v1) & ~ g_both(v1, v1))) & ! [v1] : ( ~ g_both(v1, v0) | ( ~ g_false_only(v1, v1) & ~ g_true_only(v1, v1))) & ! [v1] : ( ~ g_true_only(v1, v0) | ( ~ g_both(v1, v1) & ~ g_true_only(v1, v1)))) % 11.98/3.88 | (9) ! [v0] : ! [v1] : ( ~ g_false_only(v0, v1) | (g_false(v0, v1) & ~ g_true(v0, v1))) % 11.98/3.88 | % 11.98/3.88 | Instantiating (8) with all_1_0_0 yields: % 11.98/3.88 | (10) ! [v0] : ( ~ g_false_only(v0, all_1_0_0) | ( ~ g_false_only(v0, v0) & ~ g_both(v0, v0))) & ! [v0] : ( ~ g_both(v0, all_1_0_0) | ( ~ g_false_only(v0, v0) & ~ g_true_only(v0, v0))) & ! [v0] : ( ~ g_true_only(v0, all_1_0_0) | ( ~ g_both(v0, v0) & ~ g_true_only(v0, v0))) % 11.98/3.88 | % 11.98/3.88 | Applying alpha-rule on (10) yields: % 11.98/3.88 | (11) ! [v0] : ( ~ g_false_only(v0, all_1_0_0) | ( ~ g_false_only(v0, v0) & ~ g_both(v0, v0))) % 11.98/3.89 | (12) ! [v0] : ( ~ g_both(v0, all_1_0_0) | ( ~ g_false_only(v0, v0) & ~ g_true_only(v0, v0))) % 11.98/3.89 | (13) ! [v0] : ( ~ g_true_only(v0, all_1_0_0) | ( ~ g_both(v0, v0) & ~ g_true_only(v0, v0))) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (6), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (14) ? [v0] : ! [v1] : ((g_false_only(v1, v1) & g_true_only(v1, v0)) | (g_false_only(v1, v0) & g_true_only(v1, v1))) % 11.98/3.89 | % 11.98/3.89 | Instantiating (14) with all_6_0_1 yields: % 11.98/3.89 | (15) ! [v0] : ((g_false_only(v0, v0) & g_true_only(v0, all_6_0_1)) | (g_false_only(v0, all_6_0_1) & g_true_only(v0, v0))) % 11.98/3.89 | % 11.98/3.89 | Introducing new symbol ex_8_1_3 defined by: % 11.98/3.89 | (16) ex_8_1_3 = all_1_0_0 % 11.98/3.89 | % 11.98/3.89 | Introducing new symbol ex_8_0_2 defined by: % 11.98/3.89 | (17) ex_8_0_2 = all_1_0_0 % 11.98/3.89 | % 11.98/3.89 | Instantiating formula (4) with ex_8_0_2, ex_8_1_3 yields: % 11.98/3.89 | (18) g_false_only(ex_8_1_3, ex_8_0_2) | g_both(ex_8_1_3, ex_8_0_2) | g_true_only(ex_8_1_3, ex_8_0_2) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (18), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (19) g_false_only(ex_8_1_3, ex_8_0_2) % 11.98/3.89 | % 11.98/3.89 | Instantiating formula (11) with ex_8_1_3 yields: % 11.98/3.89 | (20) ~ g_false_only(ex_8_1_3, all_1_0_0) | ( ~ g_false_only(ex_8_1_3, ex_8_1_3) & ~ g_both(ex_8_1_3, ex_8_1_3)) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (20), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (21) ~ g_false_only(ex_8_1_3, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16)(17) and (19) follows: % 11.98/3.89 | (22) g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16) and (21) follows: % 11.98/3.89 | (23) ~ g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | Using (22) and (23) yields: % 11.98/3.89 | (24) $false % 11.98/3.89 | % 11.98/3.89 |-The branch is then unsatisfiable % 11.98/3.89 |-Branch two: % 11.98/3.89 | (25) ~ g_false_only(ex_8_1_3, ex_8_1_3) & ~ g_both(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | % 11.98/3.89 | Applying alpha-rule on (25) yields: % 11.98/3.89 | (26) ~ g_false_only(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | (27) ~ g_both(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | % 11.98/3.89 | From (16)(17) and (19) follows: % 11.98/3.89 | (22) g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16)(16) and (26) follows: % 11.98/3.89 | (23) ~ g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | Using (22) and (23) yields: % 11.98/3.89 | (24) $false % 11.98/3.89 | % 11.98/3.89 |-The branch is then unsatisfiable % 11.98/3.89 |-Branch two: % 11.98/3.89 | (31) g_both(ex_8_1_3, ex_8_0_2) | g_true_only(ex_8_1_3, ex_8_0_2) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (31), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (32) g_both(ex_8_1_3, ex_8_0_2) % 11.98/3.89 | % 11.98/3.89 | Instantiating formula (12) with ex_8_1_3 yields: % 11.98/3.89 | (33) ~ g_both(ex_8_1_3, all_1_0_0) | ( ~ g_false_only(ex_8_1_3, ex_8_1_3) & ~ g_true_only(ex_8_1_3, ex_8_1_3)) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (33), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (34) ~ g_both(ex_8_1_3, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16)(17) and (32) follows: % 11.98/3.89 | (35) g_both(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16) and (34) follows: % 11.98/3.89 | (36) ~ g_both(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | Using (35) and (36) yields: % 11.98/3.89 | (24) $false % 11.98/3.89 | % 11.98/3.89 |-The branch is then unsatisfiable % 11.98/3.89 |-Branch two: % 11.98/3.89 | (38) ~ g_false_only(ex_8_1_3, ex_8_1_3) & ~ g_true_only(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | % 11.98/3.89 | Applying alpha-rule on (38) yields: % 11.98/3.89 | (26) ~ g_false_only(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | (40) ~ g_true_only(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | % 11.98/3.89 | Introducing new symbol ex_31_0_4 defined by: % 11.98/3.89 | (41) ex_31_0_4 = all_1_0_0 % 11.98/3.89 | % 11.98/3.89 | Instantiating formula (15) with ex_31_0_4 yields: % 11.98/3.89 | (42) (g_false_only(ex_31_0_4, ex_31_0_4) & g_true_only(ex_31_0_4, all_6_0_1)) | (g_false_only(ex_31_0_4, all_6_0_1) & g_true_only(ex_31_0_4, ex_31_0_4)) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (42), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (43) g_false_only(ex_31_0_4, ex_31_0_4) & g_true_only(ex_31_0_4, all_6_0_1) % 11.98/3.89 | % 11.98/3.89 | Applying alpha-rule on (43) yields: % 11.98/3.89 | (44) g_false_only(ex_31_0_4, ex_31_0_4) % 11.98/3.89 | (45) g_true_only(ex_31_0_4, all_6_0_1) % 11.98/3.89 | % 11.98/3.89 | From (41)(41) and (44) follows: % 11.98/3.89 | (22) g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16)(16) and (26) follows: % 11.98/3.89 | (23) ~ g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | Using (22) and (23) yields: % 11.98/3.89 | (24) $false % 11.98/3.89 | % 11.98/3.89 |-The branch is then unsatisfiable % 11.98/3.89 |-Branch two: % 11.98/3.89 | (49) g_false_only(ex_31_0_4, all_6_0_1) & g_true_only(ex_31_0_4, ex_31_0_4) % 11.98/3.89 | % 11.98/3.89 | Applying alpha-rule on (49) yields: % 11.98/3.89 | (50) g_false_only(ex_31_0_4, all_6_0_1) % 11.98/3.89 | (51) g_true_only(ex_31_0_4, ex_31_0_4) % 11.98/3.89 | % 11.98/3.89 | From (41)(41) and (51) follows: % 11.98/3.89 | (52) g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16)(16) and (40) follows: % 11.98/3.89 | (53) ~ g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | Using (52) and (53) yields: % 11.98/3.89 | (24) $false % 11.98/3.89 | % 11.98/3.89 |-The branch is then unsatisfiable % 11.98/3.89 |-Branch two: % 11.98/3.89 | (55) g_true_only(ex_8_1_3, ex_8_0_2) % 11.98/3.89 | % 11.98/3.89 | Instantiating formula (13) with ex_8_1_3 yields: % 11.98/3.89 | (56) ~ g_true_only(ex_8_1_3, all_1_0_0) | ( ~ g_both(ex_8_1_3, ex_8_1_3) & ~ g_true_only(ex_8_1_3, ex_8_1_3)) % 11.98/3.89 | % 11.98/3.89 +-Applying beta-rule and splitting (56), into two cases. % 11.98/3.89 |-Branch one: % 11.98/3.89 | (57) ~ g_true_only(ex_8_1_3, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16)(17) and (55) follows: % 11.98/3.89 | (52) g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | From (16) and (57) follows: % 11.98/3.89 | (53) ~ g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.89 | % 11.98/3.89 | Using (52) and (53) yields: % 11.98/3.89 | (24) $false % 11.98/3.89 | % 11.98/3.89 |-The branch is then unsatisfiable % 11.98/3.89 |-Branch two: % 11.98/3.89 | (61) ~ g_both(ex_8_1_3, ex_8_1_3) & ~ g_true_only(ex_8_1_3, ex_8_1_3) % 11.98/3.89 | % 11.98/3.89 | Applying alpha-rule on (61) yields: % 11.98/3.90 | (27) ~ g_both(ex_8_1_3, ex_8_1_3) % 11.98/3.90 | (40) ~ g_true_only(ex_8_1_3, ex_8_1_3) % 11.98/3.90 | % 11.98/3.90 | From (16)(17) and (55) follows: % 11.98/3.90 | (52) g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | From (16)(16) and (40) follows: % 11.98/3.90 | (53) ~ g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | Using (52) and (53) yields: % 11.98/3.90 | (24) $false % 11.98/3.90 | % 11.98/3.90 |-The branch is then unsatisfiable % 11.98/3.90 |-Branch two: % 11.98/3.90 | (67) ! [v0] : ( ? [v1] : ((g_false_only(v1, v0) & (g_false_only(v1, v1) | g_both(v1, v1))) | (g_both(v1, v0) & (g_false_only(v1, v1) | g_true_only(v1, v1))) | (g_true_only(v1, v0) & (g_both(v1, v1) | g_true_only(v1, v1)))) | ! [v1] : ( ~ g_both(v1, v1) | ~ g_both(v1, v0))) % 11.98/3.90 | % 11.98/3.90 | Introducing new symbol ex_7_1_6 defined by: % 11.98/3.90 | (68) ex_7_1_6 = all_1_0_0 % 11.98/3.90 | % 11.98/3.90 | Introducing new symbol ex_7_0_5 defined by: % 11.98/3.90 | (69) ex_7_0_5 = all_1_0_0 % 11.98/3.90 | % 11.98/3.90 | Instantiating formula (4) with ex_7_0_5, ex_7_1_6 yields: % 11.98/3.90 | (70) g_false_only(ex_7_1_6, ex_7_0_5) | g_both(ex_7_1_6, ex_7_0_5) | g_true_only(ex_7_1_6, ex_7_0_5) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (70), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (71) g_false_only(ex_7_1_6, ex_7_0_5) % 11.98/3.90 | % 11.98/3.90 | Instantiating formula (11) with ex_7_1_6 yields: % 11.98/3.90 | (72) ~ g_false_only(ex_7_1_6, all_1_0_0) | ( ~ g_false_only(ex_7_1_6, ex_7_1_6) & ~ g_both(ex_7_1_6, ex_7_1_6)) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (72), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (73) ~ g_false_only(ex_7_1_6, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | From (68)(69) and (71) follows: % 11.98/3.90 | (22) g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | From (68) and (73) follows: % 11.98/3.90 | (23) ~ g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | Using (22) and (23) yields: % 11.98/3.90 | (24) $false % 11.98/3.90 | % 11.98/3.90 |-The branch is then unsatisfiable % 11.98/3.90 |-Branch two: % 11.98/3.90 | (77) ~ g_false_only(ex_7_1_6, ex_7_1_6) & ~ g_both(ex_7_1_6, ex_7_1_6) % 11.98/3.90 | % 11.98/3.90 | Applying alpha-rule on (77) yields: % 11.98/3.90 | (78) ~ g_false_only(ex_7_1_6, ex_7_1_6) % 11.98/3.90 | (79) ~ g_both(ex_7_1_6, ex_7_1_6) % 11.98/3.90 | % 11.98/3.90 | From (68)(69) and (71) follows: % 11.98/3.90 | (22) g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | From (68)(68) and (78) follows: % 11.98/3.90 | (23) ~ g_false_only(all_1_0_0, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | Using (22) and (23) yields: % 11.98/3.90 | (24) $false % 11.98/3.90 | % 11.98/3.90 |-The branch is then unsatisfiable % 11.98/3.90 |-Branch two: % 11.98/3.90 | (83) g_both(ex_7_1_6, ex_7_0_5) | g_true_only(ex_7_1_6, ex_7_0_5) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (83), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (84) g_both(ex_7_1_6, ex_7_0_5) % 11.98/3.90 | % 11.98/3.90 | Introducing new symbol ex_30_0_7 defined by: % 11.98/3.90 | (85) ex_30_0_7 = all_1_0_0 % 11.98/3.90 | % 11.98/3.90 | Instantiating formula (67) with ex_30_0_7 yields: % 11.98/3.90 | (86) ? [v0] : ((g_false_only(v0, ex_30_0_7) & (g_false_only(v0, v0) | g_both(v0, v0))) | (g_both(v0, ex_30_0_7) & (g_false_only(v0, v0) | g_true_only(v0, v0))) | (g_true_only(v0, ex_30_0_7) & (g_both(v0, v0) | g_true_only(v0, v0)))) | ! [v0] : ( ~ g_both(v0, v0) | ~ g_both(v0, ex_30_0_7)) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (86), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (87) ? [v0] : ((g_false_only(v0, ex_30_0_7) & (g_false_only(v0, v0) | g_both(v0, v0))) | (g_both(v0, ex_30_0_7) & (g_false_only(v0, v0) | g_true_only(v0, v0))) | (g_true_only(v0, ex_30_0_7) & (g_both(v0, v0) | g_true_only(v0, v0)))) % 11.98/3.90 | % 11.98/3.90 | Instantiating (87) with all_32_0_8 yields: % 11.98/3.90 | (88) (g_false_only(all_32_0_8, ex_30_0_7) & (g_false_only(all_32_0_8, all_32_0_8) | g_both(all_32_0_8, all_32_0_8))) | (g_both(all_32_0_8, ex_30_0_7) & (g_false_only(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8))) | (g_true_only(all_32_0_8, ex_30_0_7) & (g_both(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8))) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (88), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (89) (g_false_only(all_32_0_8, ex_30_0_7) & (g_false_only(all_32_0_8, all_32_0_8) | g_both(all_32_0_8, all_32_0_8))) | (g_both(all_32_0_8, ex_30_0_7) & (g_false_only(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8))) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (89), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (90) g_false_only(all_32_0_8, ex_30_0_7) & (g_false_only(all_32_0_8, all_32_0_8) | g_both(all_32_0_8, all_32_0_8)) % 11.98/3.90 | % 11.98/3.90 | Applying alpha-rule on (90) yields: % 11.98/3.90 | (91) g_false_only(all_32_0_8, ex_30_0_7) % 11.98/3.90 | (92) g_false_only(all_32_0_8, all_32_0_8) | g_both(all_32_0_8, all_32_0_8) % 11.98/3.90 | % 11.98/3.90 | Instantiating formula (11) with all_32_0_8 yields: % 11.98/3.90 | (93) ~ g_false_only(all_32_0_8, all_1_0_0) | ( ~ g_false_only(all_32_0_8, all_32_0_8) & ~ g_both(all_32_0_8, all_32_0_8)) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (92), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (94) g_false_only(all_32_0_8, all_32_0_8) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (93), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (95) ~ g_false_only(all_32_0_8, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | From (85) and (91) follows: % 11.98/3.90 | (96) g_false_only(all_32_0_8, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | Using (96) and (95) yields: % 11.98/3.90 | (24) $false % 11.98/3.90 | % 11.98/3.90 |-The branch is then unsatisfiable % 11.98/3.90 |-Branch two: % 11.98/3.90 | (98) ~ g_false_only(all_32_0_8, all_32_0_8) & ~ g_both(all_32_0_8, all_32_0_8) % 11.98/3.90 | % 11.98/3.90 | Applying alpha-rule on (98) yields: % 11.98/3.90 | (99) ~ g_false_only(all_32_0_8, all_32_0_8) % 11.98/3.90 | (100) ~ g_both(all_32_0_8, all_32_0_8) % 11.98/3.90 | % 11.98/3.90 | Using (94) and (99) yields: % 11.98/3.90 | (24) $false % 11.98/3.90 | % 11.98/3.90 |-The branch is then unsatisfiable % 11.98/3.90 |-Branch two: % 11.98/3.90 | (102) g_both(all_32_0_8, all_32_0_8) % 11.98/3.90 | % 11.98/3.90 +-Applying beta-rule and splitting (93), into two cases. % 11.98/3.90 |-Branch one: % 11.98/3.90 | (95) ~ g_false_only(all_32_0_8, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | From (85) and (91) follows: % 11.98/3.90 | (96) g_false_only(all_32_0_8, all_1_0_0) % 11.98/3.90 | % 11.98/3.90 | Using (96) and (95) yields: % 11.98/3.90 | (24) $false % 11.98/3.90 | % 11.98/3.90 |-The branch is then unsatisfiable % 11.98/3.90 |-Branch two: % 11.98/3.90 | (98) ~ g_false_only(all_32_0_8, all_32_0_8) & ~ g_both(all_32_0_8, all_32_0_8) % 11.98/3.90 | % 11.98/3.90 | Applying alpha-rule on (98) yields: % 11.98/3.91 | (99) ~ g_false_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | (100) ~ g_both(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Using (102) and (100) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (110) g_both(all_32_0_8, ex_30_0_7) & (g_false_only(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8)) % 11.98/3.91 | % 11.98/3.91 | Applying alpha-rule on (110) yields: % 11.98/3.91 | (111) g_both(all_32_0_8, ex_30_0_7) % 11.98/3.91 | (112) g_false_only(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Instantiating formula (12) with all_32_0_8 yields: % 11.98/3.91 | (113) ~ g_both(all_32_0_8, all_1_0_0) | ( ~ g_false_only(all_32_0_8, all_32_0_8) & ~ g_true_only(all_32_0_8, all_32_0_8)) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (112), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (94) g_false_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (113), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (115) ~ g_both(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | From (85) and (111) follows: % 11.98/3.91 | (116) g_both(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | Using (116) and (115) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (118) ~ g_false_only(all_32_0_8, all_32_0_8) & ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Applying alpha-rule on (118) yields: % 11.98/3.91 | (99) ~ g_false_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | (120) ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Using (94) and (99) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (122) g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (113), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (115) ~ g_both(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | From (85) and (111) follows: % 11.98/3.91 | (116) g_both(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | Using (116) and (115) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (118) ~ g_false_only(all_32_0_8, all_32_0_8) & ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Applying alpha-rule on (118) yields: % 11.98/3.91 | (99) ~ g_false_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | (120) ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Using (122) and (120) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (130) g_true_only(all_32_0_8, ex_30_0_7) & (g_both(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8)) % 11.98/3.91 | % 11.98/3.91 | Applying alpha-rule on (130) yields: % 11.98/3.91 | (131) g_true_only(all_32_0_8, ex_30_0_7) % 11.98/3.91 | (132) g_both(all_32_0_8, all_32_0_8) | g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Instantiating formula (13) with all_32_0_8 yields: % 11.98/3.91 | (133) ~ g_true_only(all_32_0_8, all_1_0_0) | ( ~ g_both(all_32_0_8, all_32_0_8) & ~ g_true_only(all_32_0_8, all_32_0_8)) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (132), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (102) g_both(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (133), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (135) ~ g_true_only(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | From (85) and (131) follows: % 11.98/3.91 | (136) g_true_only(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | Using (136) and (135) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (138) ~ g_both(all_32_0_8, all_32_0_8) & ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Applying alpha-rule on (138) yields: % 11.98/3.91 | (100) ~ g_both(all_32_0_8, all_32_0_8) % 11.98/3.91 | (120) ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Using (102) and (100) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (122) g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (133), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (135) ~ g_true_only(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | From (85) and (131) follows: % 11.98/3.91 | (136) g_true_only(all_32_0_8, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | Using (136) and (135) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (138) ~ g_both(all_32_0_8, all_32_0_8) & ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Applying alpha-rule on (138) yields: % 11.98/3.91 | (100) ~ g_both(all_32_0_8, all_32_0_8) % 11.98/3.91 | (120) ~ g_true_only(all_32_0_8, all_32_0_8) % 11.98/3.91 | % 11.98/3.91 | Using (122) and (120) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (150) ! [v0] : ( ~ g_both(v0, v0) | ~ g_both(v0, ex_30_0_7)) % 11.98/3.91 | % 11.98/3.91 | Instantiating formula (150) with ex_7_1_6 yields: % 11.98/3.91 | (151) ~ g_both(ex_7_1_6, ex_30_0_7) | ~ g_both(ex_7_1_6, ex_7_1_6) % 11.98/3.91 | % 11.98/3.91 +-Applying beta-rule and splitting (151), into two cases. % 11.98/3.91 |-Branch one: % 11.98/3.91 | (152) ~ g_both(ex_7_1_6, ex_30_0_7) % 11.98/3.91 | % 11.98/3.91 | From (68)(69) and (84) follows: % 11.98/3.91 | (35) g_both(all_1_0_0, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | From (68)(85) and (152) follows: % 11.98/3.91 | (36) ~ g_both(all_1_0_0, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | Using (35) and (36) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (79) ~ g_both(ex_7_1_6, ex_7_1_6) % 11.98/3.91 | % 11.98/3.91 | From (68)(69) and (84) follows: % 11.98/3.91 | (35) g_both(all_1_0_0, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | From (68)(68) and (79) follows: % 11.98/3.91 | (36) ~ g_both(all_1_0_0, all_1_0_0) % 11.98/3.91 | % 11.98/3.91 | Using (35) and (36) yields: % 11.98/3.91 | (24) $false % 11.98/3.91 | % 11.98/3.91 |-The branch is then unsatisfiable % 11.98/3.91 |-Branch two: % 11.98/3.91 | (160) g_true_only(ex_7_1_6, ex_7_0_5) % 11.98/3.92 | % 11.98/3.92 | Instantiating formula (13) with ex_7_1_6 yields: % 11.98/3.92 | (161) ~ g_true_only(ex_7_1_6, all_1_0_0) | ( ~ g_both(ex_7_1_6, ex_7_1_6) & ~ g_true_only(ex_7_1_6, ex_7_1_6)) % 11.98/3.92 | % 11.98/3.92 +-Applying beta-rule and splitting (161), into two cases. % 11.98/3.92 |-Branch one: % 11.98/3.92 | (162) ~ g_true_only(ex_7_1_6, all_1_0_0) % 11.98/3.92 | % 11.98/3.92 | From (68)(69) and (160) follows: % 11.98/3.92 | (52) g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.92 | % 11.98/3.92 | From (68) and (162) follows: % 11.98/3.92 | (53) ~ g_true_only(all_1_0_0, all_1_0_0) % 11.98/3.92 | % 11.98/3.92 | Using (52) and (53) yields: % 11.98/3.92 | (24) $false % 11.98/3.92 | % 11.98/3.92 |-The branch is then unsatisfiable % 11.98/3.92 |-Branch two: % 11.98/3.92 | (166) ~ g_both(ex_7_1_6, ex_7_1_6) & ~ g_true_only(ex_7_1_6, ex_7_1_6) % 11.98/3.92 | % 11.98/3.92 | Applying alpha-rule on (166) yields: % 11.98/3.92 | (79) ~ g_both(ex_7_1_6, ex_7_1_6) % 11.98/3.92 | (168) ~ g_true_only(ex_7_1_6, ex_7_1_6) % 11.98/3.92 | % 11.98/3.92 | From (68)(69) and (160) follows: % 12.39/3.92 | (52) g_true_only(all_1_0_0, all_1_0_0) % 12.39/3.92 | % 12.39/3.92 | From (68)(68) and (168) follows: % 12.39/3.92 | (53) ~ g_true_only(all_1_0_0, all_1_0_0) % 12.39/3.92 | % 12.39/3.92 | Using (52) and (53) yields: % 12.39/3.92 | (24) $false % 12.39/3.92 | % 12.39/3.92 |-The branch is then unsatisfiable % 12.39/3.92 % SZS output end Proof for theBenchmark % 12.39/3.92 % 12.39/3.92 3325ms %------------------------------------------------------------------------------