%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS138+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 : Sun Jul 17 02:56:40 EDT 2022 % Result : Theorem 3.02s 1.40s % Output : Proof 4.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : KRS138+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n026.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 7 10:50:01 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.58 ____ _ % 0.48/0.58 ___ / __ \_____(_)___ ________ __________ % 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.58 % 0.48/0.58 A Theorem Prover for First-Order Logic % 0.48/0.58 (ePrincess v.1.0) % 0.48/0.58 % 0.48/0.58 (c) Philipp Rümmer, 2009-2015 % 0.48/0.58 (c) Peter Backeman, 2014-2015 % 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.58 Bug reports to peter@backeman.se % 0.48/0.58 % 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.58 % 0.48/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.42/0.91 Prover 0: Preprocessing ... % 1.72/1.02 Prover 0: Warning: ignoring some quantifiers % 1.72/1.03 Prover 0: Constructing countermodel ... % 2.01/1.13 Prover 0: gave up % 2.01/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.22/1.16 Prover 1: Preprocessing ... % 2.61/1.27 Prover 1: Constructing countermodel ... % 3.02/1.40 Prover 1: proved (271ms) % 3.02/1.40 % 3.02/1.40 No countermodel exists, formula is valid % 3.02/1.40 % SZS status Theorem for theBenchmark % 3.02/1.40 % 3.02/1.41 Generating proof ... found it (size 102) % 4.23/1.72 % 4.23/1.72 % SZS output start Proof for theBenchmark % 4.23/1.72 Assumed formulas after preprocessing and simplification: % 4.23/1.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (requalityOnA(ia, ia) = 0 & requalityOnA(ib, ib) = 0 & cowlThing(ic) = 0 & cowlThing(ia) = 0 & cowlThing(ib) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (requalityOnA(v7, v6) = v5) | ~ (requalityOnA(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (requalityOnA(v6, v4) = 0) | ~ (requalityOnA(v5, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (requalityOnA(v5, v4) = v6) | ~ (requalityOnA(v5, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (requalityOnA(v4, v5) = v6) | ~ (requalityOnA(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (xsd_string(v6) = v5) | ~ (xsd_string(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (xsd_integer(v6) = v5) | ~ (xsd_integer(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlThing(v6) = v5) | ~ (cowlThing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlNothing(v6) = v5) | ~ (cowlNothing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cA(v6) = v5) | ~ (cA(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | ~ (xsd_string(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | xsd_integer(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_integer(v4) = v5) | ~ (xsd_integer(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5) | ~ (cowlThing(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlNothing(v4) = v5) | ~ (cowlNothing(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cA(v4) = v5) | ~ (cA(v4) = 0)) & ! [v4] : ! [v5] : ( ~ (requalityOnA(v4, v5) = 0) | cA(v5) = 0) & ! [v4] : (v4 = ia | v4 = ib | ~ (cA(v4) = 0)) & ! [v4] : (v4 = 0 | ~ (cA(ia) = v4)) & ! [v4] : (v4 = 0 | ~ (cA(ib) = v4)) & ! [v4] : ( ~ (xsd_string(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_integer(v4) = v5)) & ! [v4] : ~ (cowlNothing(v4) = 0) & ((v2 = 0 & ~ (v3 = 0) & requalityOnA(v1, v0) = v3 & requalityOnA(v0, v1) = 0) | (v2 = 0 & ~ (v0 = ic) & ~ (v0 = ia) & ~ (v0 = ib) & requalityOnA(v0, v1) = 0) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & ( ~ (v1 = 0) | v2 = 0)))) % 4.51/1.75 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 4.51/1.75 | (1) requalityOnA(ia, ia) = 0 & requalityOnA(ib, ib) = 0 & cowlThing(ic) = 0 & cowlThing(ia) = 0 & cowlThing(ib) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (requalityOnA(v3, v2) = v1) | ~ (requalityOnA(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (requalityOnA(v2, v0) = 0) | ~ (requalityOnA(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (requalityOnA(v1, v0) = v2) | ~ (requalityOnA(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (requalityOnA(v0, v1) = v2) | ~ (requalityOnA(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (requalityOnA(v0, v1) = 0) | cA(v1) = 0) & ! [v0] : (v0 = ia | v0 = ib | ~ (cA(v0) = 0)) & ! [v0] : (v0 = 0 | ~ (cA(ia) = v0)) & ! [v0] : (v0 = 0 | ~ (cA(ib) = v0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ((all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & requalityOnA(all_0_2_2, all_0_3_3) = all_0_0_0 & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_3_3 = ic) & ~ (all_0_3_3 = ia) & ~ (all_0_3_3 = ib) & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) | (cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0))) % 4.57/1.76 | % 4.57/1.76 | Applying alpha-rule on (1) yields: % 4.57/1.76 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 4.57/1.76 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 4.57/1.76 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) % 4.57/1.76 | (5) ! [v0] : (v0 = 0 | ~ (cA(ia) = v0)) % 4.57/1.76 | (6) cowlThing(ib) = 0 % 4.57/1.76 | (7) requalityOnA(ib, ib) = 0 % 4.57/1.76 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) % 4.57/1.76 | (9) requalityOnA(ia, ia) = 0 % 4.57/1.76 | (10) cowlThing(ia) = 0 % 4.57/1.76 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 4.57/1.76 | (12) ! [v0] : (v0 = 0 | ~ (cA(ib) = v0)) % 4.57/1.76 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 4.57/1.77 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (requalityOnA(v3, v2) = v1) | ~ (requalityOnA(v3, v2) = v0)) % 4.57/1.77 | (15) ! [v0] : ~ (cowlNothing(v0) = 0) % 4.57/1.77 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 4.57/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 4.57/1.77 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (requalityOnA(v0, v1) = v2) | ~ (requalityOnA(v0, v1) = 0)) % 4.57/1.77 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 4.57/1.77 | (20) ! [v0] : ! [v1] : ( ~ (requalityOnA(v0, v1) = 0) | cA(v1) = 0) % 4.57/1.77 | (21) cowlThing(ic) = 0 % 4.57/1.77 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 4.57/1.77 | (23) ! [v0] : (v0 = ia | v0 = ib | ~ (cA(v0) = 0)) % 4.57/1.77 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (requalityOnA(v1, v0) = v2) | ~ (requalityOnA(v1, v0) = 0)) % 4.57/1.77 | (25) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & requalityOnA(all_0_2_2, all_0_3_3) = all_0_0_0 & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_3_3 = ic) & ~ (all_0_3_3 = ia) & ~ (all_0_3_3 = ib) & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) | (cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)) % 4.57/1.77 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 4.57/1.77 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 4.57/1.77 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (requalityOnA(v2, v0) = 0) | ~ (requalityOnA(v1, v0) = 0)) % 4.57/1.77 | (29) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 4.57/1.77 | % 4.57/1.77 +-Applying beta-rule and splitting (25), into two cases. % 4.57/1.77 |-Branch one: % 4.57/1.77 | (30) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & requalityOnA(all_0_2_2, all_0_3_3) = all_0_0_0 & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_3_3 = ic) & ~ (all_0_3_3 = ia) & ~ (all_0_3_3 = ib) & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) % 4.57/1.77 | % 4.57/1.77 +-Applying beta-rule and splitting (30), into two cases. % 4.57/1.77 |-Branch one: % 4.57/1.77 | (31) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & requalityOnA(all_0_2_2, all_0_3_3) = all_0_0_0 & requalityOnA(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_3_3 = ic) & ~ (all_0_3_3 = ia) & ~ (all_0_3_3 = ib) & requalityOnA(all_0_3_3, all_0_2_2) = 0) % 4.57/1.77 | % 4.57/1.77 +-Applying beta-rule and splitting (31), into two cases. % 4.57/1.77 |-Branch one: % 4.57/1.77 | (32) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & requalityOnA(all_0_2_2, all_0_3_3) = all_0_0_0 & requalityOnA(all_0_3_3, all_0_2_2) = 0 % 4.57/1.77 | % 4.57/1.77 | Applying alpha-rule on (32) yields: % 4.57/1.77 | (33) all_0_1_1 = 0 % 4.57/1.77 | (34) ~ (all_0_0_0 = 0) % 4.57/1.77 | (35) requalityOnA(all_0_2_2, all_0_3_3) = all_0_0_0 % 4.57/1.77 | (36) requalityOnA(all_0_3_3, all_0_2_2) = 0 % 4.57/1.77 | % 4.57/1.77 | Instantiating formula (28) with all_0_3_3, ia, ia and discharging atoms requalityOnA(ia, ia) = 0, yields: % 4.57/1.77 | (37) all_0_3_3 = ia | ~ (requalityOnA(all_0_3_3, ia) = 0) % 4.57/1.77 | % 4.57/1.77 | Instantiating formula (28) with all_0_3_3, ib, ib and discharging atoms requalityOnA(ib, ib) = 0, yields: % 4.57/1.77 | (38) all_0_3_3 = ib | ~ (requalityOnA(all_0_3_3, ib) = 0) % 4.57/1.77 | % 4.57/1.77 | Instantiating formula (20) with all_0_2_2, all_0_3_3 and discharging atoms requalityOnA(all_0_3_3, all_0_2_2) = 0, yields: % 4.57/1.77 | (39) cA(all_0_2_2) = 0 % 4.57/1.77 | % 4.57/1.78 | Instantiating formula (23) with all_0_2_2 and discharging atoms cA(all_0_2_2) = 0, yields: % 4.57/1.78 | (40) all_0_2_2 = ia | all_0_2_2 = ib % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (38), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (41) ~ (requalityOnA(all_0_3_3, ib) = 0) % 4.57/1.78 | % 4.57/1.78 | Using (36) and (41) yields: % 4.57/1.78 | (42) ~ (all_0_2_2 = ib) % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (40), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (43) all_0_2_2 = ia % 4.57/1.78 | % 4.57/1.78 | From (43) and (35) follows: % 4.57/1.78 | (44) requalityOnA(ia, all_0_3_3) = all_0_0_0 % 4.57/1.78 | % 4.57/1.78 | From (43) and (36) follows: % 4.57/1.78 | (45) requalityOnA(all_0_3_3, ia) = 0 % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (37), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (46) ~ (requalityOnA(all_0_3_3, ia) = 0) % 4.57/1.78 | % 4.57/1.78 | Using (45) and (46) yields: % 4.57/1.78 | (47) $false % 4.57/1.78 | % 4.57/1.78 |-The branch is then unsatisfiable % 4.57/1.78 |-Branch two: % 4.57/1.78 | (45) requalityOnA(all_0_3_3, ia) = 0 % 4.57/1.78 | (49) all_0_3_3 = ia % 4.57/1.78 | % 4.57/1.78 | From (49) and (45) follows: % 4.57/1.78 | (9) requalityOnA(ia, ia) = 0 % 4.57/1.78 | % 4.57/1.78 | From (49) and (44) follows: % 4.57/1.78 | (51) requalityOnA(ia, ia) = all_0_0_0 % 4.57/1.78 | % 4.57/1.78 | Instantiating formula (24) with all_0_0_0, ia, ia and discharging atoms requalityOnA(ia, ia) = all_0_0_0, requalityOnA(ia, ia) = 0, yields: % 4.57/1.78 | (52) all_0_0_0 = 0 % 4.57/1.78 | % 4.57/1.78 | Equations (52) can reduce 34 to: % 4.57/1.78 | (53) $false % 4.57/1.78 | % 4.57/1.78 |-The branch is then unsatisfiable % 4.57/1.78 |-Branch two: % 4.57/1.78 | (54) ~ (all_0_2_2 = ia) % 4.57/1.78 | (55) all_0_2_2 = ib % 4.57/1.78 | % 4.57/1.78 | Equations (55) can reduce 42 to: % 4.57/1.78 | (53) $false % 4.57/1.78 | % 4.57/1.78 |-The branch is then unsatisfiable % 4.57/1.78 |-Branch two: % 4.57/1.78 | (57) requalityOnA(all_0_3_3, ib) = 0 % 4.57/1.78 | (58) all_0_3_3 = ib % 4.57/1.78 | % 4.57/1.78 | From (58) and (35) follows: % 4.57/1.78 | (59) requalityOnA(all_0_2_2, ib) = all_0_0_0 % 4.57/1.78 | % 4.57/1.78 | From (58) and (36) follows: % 4.57/1.78 | (60) requalityOnA(ib, all_0_2_2) = 0 % 4.57/1.78 | % 4.57/1.78 | From (58) and (57) follows: % 4.57/1.78 | (7) requalityOnA(ib, ib) = 0 % 4.57/1.78 | % 4.57/1.78 | Instantiating formula (24) with all_0_0_0, ib, ib and discharging atoms requalityOnA(ib, ib) = 0, yields: % 4.57/1.78 | (62) all_0_0_0 = 0 | ~ (requalityOnA(ib, ib) = all_0_0_0) % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (37), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (46) ~ (requalityOnA(all_0_3_3, ia) = 0) % 4.57/1.78 | % 4.57/1.78 | From (58) and (46) follows: % 4.57/1.78 | (64) ~ (requalityOnA(ib, ia) = 0) % 4.57/1.78 | % 4.57/1.78 | Using (60) and (64) yields: % 4.57/1.78 | (54) ~ (all_0_2_2 = ia) % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (40), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (43) all_0_2_2 = ia % 4.57/1.78 | % 4.57/1.78 | Equations (43) can reduce 54 to: % 4.57/1.78 | (53) $false % 4.57/1.78 | % 4.57/1.78 |-The branch is then unsatisfiable % 4.57/1.78 |-Branch two: % 4.57/1.78 | (54) ~ (all_0_2_2 = ia) % 4.57/1.78 | (55) all_0_2_2 = ib % 4.57/1.78 | % 4.57/1.78 | From (55) and (59) follows: % 4.57/1.78 | (70) requalityOnA(ib, ib) = all_0_0_0 % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (62), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (71) ~ (requalityOnA(ib, ib) = all_0_0_0) % 4.57/1.78 | % 4.57/1.78 | Using (70) and (71) yields: % 4.57/1.78 | (47) $false % 4.57/1.78 | % 4.57/1.78 |-The branch is then unsatisfiable % 4.57/1.78 |-Branch two: % 4.57/1.78 | (70) requalityOnA(ib, ib) = all_0_0_0 % 4.57/1.78 | (52) all_0_0_0 = 0 % 4.57/1.78 | % 4.57/1.78 | Equations (52) can reduce 34 to: % 4.57/1.78 | (53) $false % 4.57/1.78 | % 4.57/1.78 |-The branch is then unsatisfiable % 4.57/1.78 |-Branch two: % 4.57/1.78 | (45) requalityOnA(all_0_3_3, ia) = 0 % 4.57/1.78 | (49) all_0_3_3 = ia % 4.57/1.78 | % 4.57/1.78 | Combining equations (49,58) yields a new equation: % 4.57/1.78 | (78) ia = ib % 4.57/1.78 | % 4.57/1.78 | Simplifying 78 yields: % 4.57/1.78 | (79) ia = ib % 4.57/1.78 | % 4.57/1.78 +-Applying beta-rule and splitting (40), into two cases. % 4.57/1.78 |-Branch one: % 4.57/1.78 | (43) all_0_2_2 = ia % 4.57/1.79 | % 4.57/1.79 | Combining equations (79,43) yields a new equation: % 4.57/1.79 | (55) all_0_2_2 = ib % 4.57/1.79 | % 4.57/1.79 | From (55) and (59) follows: % 4.57/1.79 | (70) requalityOnA(ib, ib) = all_0_0_0 % 4.57/1.79 | % 4.57/1.79 +-Applying beta-rule and splitting (62), into two cases. % 4.57/1.79 |-Branch one: % 4.57/1.79 | (71) ~ (requalityOnA(ib, ib) = all_0_0_0) % 4.57/1.79 | % 4.57/1.79 | Using (70) and (71) yields: % 4.57/1.79 | (47) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (70) requalityOnA(ib, ib) = all_0_0_0 % 4.57/1.79 | (52) all_0_0_0 = 0 % 4.57/1.79 | % 4.57/1.79 | Equations (52) can reduce 34 to: % 4.57/1.79 | (53) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (54) ~ (all_0_2_2 = ia) % 4.57/1.79 | (55) all_0_2_2 = ib % 4.57/1.79 | % 4.57/1.79 | Equations (55,79) can reduce 54 to: % 4.57/1.79 | (53) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (91) all_0_1_1 = 0 & ~ (all_0_3_3 = ic) & ~ (all_0_3_3 = ia) & ~ (all_0_3_3 = ib) & requalityOnA(all_0_3_3, all_0_2_2) = 0 % 4.57/1.79 | % 4.57/1.79 | Applying alpha-rule on (91) yields: % 4.57/1.79 | (92) ~ (all_0_3_3 = ia) % 4.57/1.79 | (36) requalityOnA(all_0_3_3, all_0_2_2) = 0 % 4.57/1.79 | (94) ~ (all_0_3_3 = ib) % 4.57/1.79 | (95) ~ (all_0_3_3 = ic) % 4.57/1.79 | (33) all_0_1_1 = 0 % 4.57/1.79 | % 4.57/1.79 | Instantiating formula (28) with all_0_3_3, ia, ia and discharging atoms requalityOnA(ia, ia) = 0, yields: % 4.57/1.79 | (37) all_0_3_3 = ia | ~ (requalityOnA(all_0_3_3, ia) = 0) % 4.57/1.79 | % 4.57/1.79 | Instantiating formula (28) with all_0_3_3, ib, ib and discharging atoms requalityOnA(ib, ib) = 0, yields: % 4.57/1.79 | (38) all_0_3_3 = ib | ~ (requalityOnA(all_0_3_3, ib) = 0) % 4.57/1.79 | % 4.57/1.79 | Instantiating formula (20) with all_0_2_2, all_0_3_3 and discharging atoms requalityOnA(all_0_3_3, all_0_2_2) = 0, yields: % 4.57/1.79 | (39) cA(all_0_2_2) = 0 % 4.57/1.79 | % 4.57/1.79 +-Applying beta-rule and splitting (38), into two cases. % 4.57/1.79 |-Branch one: % 4.57/1.79 | (41) ~ (requalityOnA(all_0_3_3, ib) = 0) % 4.57/1.79 | % 4.57/1.79 +-Applying beta-rule and splitting (37), into two cases. % 4.57/1.79 |-Branch one: % 4.57/1.79 | (46) ~ (requalityOnA(all_0_3_3, ia) = 0) % 4.57/1.79 | % 4.57/1.79 | Instantiating formula (23) with all_0_2_2 and discharging atoms cA(all_0_2_2) = 0, yields: % 4.57/1.79 | (40) all_0_2_2 = ia | all_0_2_2 = ib % 4.57/1.79 | % 4.57/1.79 | Using (36) and (46) yields: % 4.57/1.79 | (54) ~ (all_0_2_2 = ia) % 4.57/1.79 | % 4.57/1.79 | Using (36) and (41) yields: % 4.57/1.79 | (42) ~ (all_0_2_2 = ib) % 4.57/1.79 | % 4.57/1.79 +-Applying beta-rule and splitting (40), into two cases. % 4.57/1.79 |-Branch one: % 4.57/1.79 | (43) all_0_2_2 = ia % 4.57/1.79 | % 4.57/1.79 | Equations (43) can reduce 54 to: % 4.57/1.79 | (53) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (54) ~ (all_0_2_2 = ia) % 4.57/1.79 | (55) all_0_2_2 = ib % 4.57/1.79 | % 4.57/1.79 | Equations (55) can reduce 42 to: % 4.57/1.79 | (53) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (45) requalityOnA(all_0_3_3, ia) = 0 % 4.57/1.79 | (49) all_0_3_3 = ia % 4.57/1.79 | % 4.57/1.79 | Equations (49) can reduce 92 to: % 4.57/1.79 | (53) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (57) requalityOnA(all_0_3_3, ib) = 0 % 4.57/1.79 | (58) all_0_3_3 = ib % 4.57/1.79 | % 4.57/1.79 | Equations (58) can reduce 94 to: % 4.57/1.79 | (53) $false % 4.57/1.79 | % 4.57/1.79 |-The branch is then unsatisfiable % 4.57/1.79 |-Branch two: % 4.57/1.79 | (116) xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0))) % 4.57/1.79 | % 4.57/1.79 | Applying alpha-rule on (116) yields: % 4.57/1.79 | (117) xsd_string(all_0_3_3) = all_0_2_2 % 4.57/1.79 | (118) xsd_integer(all_0_3_3) = all_0_1_1 % 4.57/1.79 | (119) (all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)) % 4.57/1.79 | % 4.57/1.79 | Instantiating formula (29) with all_0_3_3 yields: % 4.57/1.79 | (120) ~ (xsd_string(all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0) % 4.57/1.79 | % 4.57/1.79 | Instantiating formula (2) with all_0_2_2, all_0_3_3 and discharging atoms xsd_string(all_0_3_3) = all_0_2_2, yields: % 4.57/1.79 | (121) all_0_2_2 = 0 | xsd_integer(all_0_3_3) = 0 % 4.57/1.79 | % 4.57/1.79 +-Applying beta-rule and splitting (119), into two cases. % 4.57/1.79 |-Branch one: % 4.57/1.79 | (122) all_0_1_1 = 0 & all_0_2_2 = 0 % 4.57/1.79 | % 4.57/1.79 | Applying alpha-rule on (122) yields: % 4.57/1.79 | (33) all_0_1_1 = 0 % 4.57/1.79 | (124) all_0_2_2 = 0 % 4.57/1.79 | % 4.57/1.79 | From (124) and (117) follows: % 4.57/1.79 | (125) xsd_string(all_0_3_3) = 0 % 4.57/1.80 | % 4.57/1.80 | From (33) and (118) follows: % 4.57/1.80 | (126) xsd_integer(all_0_3_3) = 0 % 4.57/1.80 | % 4.57/1.80 +-Applying beta-rule and splitting (120), into two cases. % 4.57/1.80 |-Branch one: % 4.57/1.80 | (127) ~ (xsd_string(all_0_3_3) = 0) % 4.57/1.80 | % 4.57/1.80 | Using (125) and (127) yields: % 4.57/1.80 | (47) $false % 4.57/1.80 | % 4.57/1.80 |-The branch is then unsatisfiable % 4.57/1.80 |-Branch two: % 4.57/1.80 | (125) xsd_string(all_0_3_3) = 0 % 4.57/1.80 | (130) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0) % 4.57/1.80 | % 4.57/1.80 | Instantiating (130) with all_27_0_4 yields: % 4.57/1.80 | (131) ~ (all_27_0_4 = 0) & xsd_integer(all_0_3_3) = all_27_0_4 % 4.57/1.80 | % 4.57/1.80 | Applying alpha-rule on (131) yields: % 4.57/1.80 | (132) ~ (all_27_0_4 = 0) % 4.57/1.80 | (133) xsd_integer(all_0_3_3) = all_27_0_4 % 4.57/1.80 | % 4.57/1.80 | Instantiating formula (27) with all_0_3_3, 0, all_27_0_4 and discharging atoms xsd_integer(all_0_3_3) = all_27_0_4, xsd_integer(all_0_3_3) = 0, yields: % 4.57/1.80 | (134) all_27_0_4 = 0 % 4.57/1.80 | % 4.57/1.80 | Equations (134) can reduce 132 to: % 4.57/1.80 | (53) $false % 4.57/1.80 | % 4.57/1.80 |-The branch is then unsatisfiable % 4.57/1.80 |-Branch two: % 4.57/1.80 | (136) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) % 4.57/1.80 | % 4.57/1.80 | Applying alpha-rule on (136) yields: % 4.57/1.80 | (137) ~ (all_0_1_1 = 0) % 4.57/1.80 | (138) ~ (all_0_2_2 = 0) % 4.57/1.80 | % 4.57/1.80 +-Applying beta-rule and splitting (121), into two cases. % 4.57/1.80 |-Branch one: % 4.57/1.80 | (126) xsd_integer(all_0_3_3) = 0 % 4.57/1.80 | % 4.57/1.80 | Instantiating formula (27) with all_0_3_3, 0, all_0_1_1 and discharging atoms xsd_integer(all_0_3_3) = all_0_1_1, xsd_integer(all_0_3_3) = 0, yields: % 4.57/1.80 | (33) all_0_1_1 = 0 % 4.57/1.80 | % 4.57/1.80 | Equations (33) can reduce 137 to: % 4.57/1.80 | (53) $false % 4.57/1.80 | % 4.57/1.80 |-The branch is then unsatisfiable % 4.57/1.80 |-Branch two: % 4.57/1.80 | (142) ~ (xsd_integer(all_0_3_3) = 0) % 4.57/1.80 | (124) all_0_2_2 = 0 % 4.57/1.80 | % 4.57/1.80 | Equations (124) can reduce 138 to: % 4.57/1.80 | (53) $false % 4.57/1.80 | % 4.57/1.80 |-The branch is then unsatisfiable % 4.57/1.80 |-Branch two: % 4.57/1.80 | (145) cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0) % 4.57/1.80 | % 4.57/1.80 | Applying alpha-rule on (145) yields: % 4.57/1.80 | (146) cowlThing(all_0_3_3) = all_0_2_2 % 4.57/1.80 | (147) cowlNothing(all_0_3_3) = all_0_1_1 % 4.57/1.80 | (148) ~ (all_0_2_2 = 0) | all_0_1_1 = 0 % 4.57/1.80 | % 4.57/1.80 | Instantiating formula (11) with all_0_2_2, all_0_3_3 and discharging atoms cowlThing(all_0_3_3) = all_0_2_2, yields: % 4.57/1.80 | (124) all_0_2_2 = 0 % 4.57/1.80 | % 4.57/1.80 | Instantiating formula (15) with all_0_3_3 yields: % 4.57/1.80 | (150) ~ (cowlNothing(all_0_3_3) = 0) % 4.57/1.80 | % 4.57/1.80 +-Applying beta-rule and splitting (148), into two cases. % 4.57/1.80 |-Branch one: % 4.57/1.80 | (138) ~ (all_0_2_2 = 0) % 4.57/1.80 | % 4.57/1.80 | Equations (124) can reduce 138 to: % 4.57/1.80 | (53) $false % 4.57/1.80 | % 4.57/1.80 |-The branch is then unsatisfiable % 4.57/1.80 |-Branch two: % 4.57/1.80 | (124) all_0_2_2 = 0 % 4.57/1.80 | (33) all_0_1_1 = 0 % 4.57/1.80 | % 4.57/1.80 | From (33) and (147) follows: % 4.57/1.80 | (155) cowlNothing(all_0_3_3) = 0 % 4.57/1.80 | % 4.57/1.80 | Using (155) and (150) yields: % 4.57/1.80 | (47) $false % 4.57/1.80 | % 4.57/1.80 |-The branch is then unsatisfiable % 4.57/1.80 % SZS output end Proof for theBenchmark % 4.57/1.80 % 4.57/1.80 1210ms %------------------------------------------------------------------------------