%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : COM007+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 : Fri Jul 15 01:07:45 EDT 2022 % Result : Theorem 19.18s 6.48s % Output : Proof 21.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : COM007+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n021.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Thu Jun 16 19:47:45 EDT 2022 % 0.14/0.35 % CPUTime : % 0.63/0.65 ____ _ % 0.63/0.65 ___ / __ \_____(_)___ ________ __________ % 0.63/0.65 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.65 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.65 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.65 % 0.63/0.65 A Theorem Prover for First-Order Logic % 0.63/0.65 (ePrincess v.1.0) % 0.63/0.65 % 0.63/0.65 (c) Philipp Rümmer, 2009-2015 % 0.63/0.65 (c) Peter Backeman, 2014-2015 % 0.63/0.65 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.65 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.65 Bug reports to peter@backeman.se % 0.63/0.65 % 0.63/0.65 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.65 % 0.63/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/1.00 Prover 0: Preprocessing ... % 1.60/1.07 Prover 0: Warning: ignoring some quantifiers % 1.70/1.09 Prover 0: Constructing countermodel ... % 17.00/6.00 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.18/6.04 Prover 1: Preprocessing ... % 17.47/6.15 Prover 1: Constructing countermodel ... % 17.85/6.19 Prover 1: gave up % 17.85/6.19 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 18.05/6.21 Prover 2: Preprocessing ... % 18.29/6.25 Prover 2: Warning: ignoring some quantifiers % 18.29/6.26 Prover 2: Constructing countermodel ... % 19.18/6.48 Prover 2: proved (284ms) % 19.18/6.48 Prover 0: stopped % 19.18/6.48 % 19.18/6.48 No countermodel exists, formula is valid % 19.18/6.48 % SZS status Theorem for theBenchmark % 19.18/6.48 % 19.18/6.48 Generating proof ... Warning: ignoring some quantifiers % 20.79/6.84 found it (size 70) % 20.79/6.84 % 20.79/6.84 % SZS output start Proof for theBenchmark % 20.79/6.84 Assumed formulas after preprocessing and simplification: % 20.79/6.84 | (0) reflexive_rewrite(a, c) = 0 & reflexive_rewrite(a, b) = 0 & ~ goal & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & reflexive_rewrite(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reflexive_rewrite(v1, v2) = 0) | ~ (reflexive_rewrite(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & equalish(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rewrite(v3, v2) = v1) | ~ (rewrite(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equalish(v3, v2) = v1) | ~ (equalish(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (reflexive_rewrite(v3, v2) = v1) | ~ (reflexive_rewrite(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rewrite(v0, v1) = v2) | ? [v3] : ((v3 = 0 & equalish(v0, v1) = 0) | ( ~ (v3 = 0) & reflexive_rewrite(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equalish(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & equalish(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equalish(v0, v1) = v2) | ? [v3] : ((v3 = 0 & rewrite(v0, v1) = 0) | ( ~ (v3 = 0) & reflexive_rewrite(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (reflexive_rewrite(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rewrite(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (reflexive_rewrite(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & equalish(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (rewrite(v0, v2) = 0) | ~ (rewrite(v0, v1) = 0) | ? [v3] : (rewrite(v2, v3) = 0 & rewrite(v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v1, v2) = 0) | reflexive_rewrite(v0, v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equalish(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (rewrite(v0, v1) = 0) | reflexive_rewrite(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equalish(v0, v1) = 0) | equalish(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (equalish(v0, v1) = 0) | reflexive_rewrite(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (reflexive_rewrite(v0, v1) = 0) | ? [v2] : ((v2 = 0 & rewrite(v0, v1) = 0) | (v2 = 0 & equalish(v0, v1) = 0))) & ! [v0] : ( ~ (reflexive_rewrite(c, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & reflexive_rewrite(b, v0) = v1)) & ! [v0] : ( ~ (reflexive_rewrite(b, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & reflexive_rewrite(c, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : rewrite(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equalish(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : reflexive_rewrite(v1, v0) = v2 % 21.02/6.88 | Applying alpha-rule on (0) yields: % 21.02/6.88 | (1) reflexive_rewrite(a, c) = 0 % 21.02/6.88 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reflexive_rewrite(v1, v2) = 0) | ~ (reflexive_rewrite(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & equalish(v0, v1) = v4)) % 21.02/6.88 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (reflexive_rewrite(v3, v2) = v1) | ~ (reflexive_rewrite(v3, v2) = v0)) % 21.02/6.88 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & reflexive_rewrite(v1, v2) = v4)) % 21.02/6.88 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equalish(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & equalish(v0, v1) = v3)) % 21.02/6.88 | (6) ! [v0] : ! [v1] : ( ~ (reflexive_rewrite(v0, v1) = 0) | ? [v2] : ((v2 = 0 & rewrite(v0, v1) = 0) | (v2 = 0 & equalish(v0, v1) = 0))) % 21.02/6.88 | (7) ! [v0] : ! [v1] : ( ~ (rewrite(v0, v1) = 0) | reflexive_rewrite(v0, v1) = 0) % 21.02/6.88 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (equalish(v0, v0) = v1)) % 21.02/6.88 | (9) ? [v0] : ? [v1] : ? [v2] : rewrite(v1, v0) = v2 % 21.02/6.88 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rewrite(v3, v2) = v1) | ~ (rewrite(v3, v2) = v0)) % 21.02/6.88 | (11) ~ goal % 21.02/6.88 | (12) ! [v0] : ( ~ (reflexive_rewrite(b, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & reflexive_rewrite(c, v0) = v1)) % 21.02/6.88 | (13) ! [v0] : ( ~ (reflexive_rewrite(c, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & reflexive_rewrite(b, v0) = v1)) % 21.02/6.88 | (14) ! [v0] : ! [v1] : ( ~ (equalish(v0, v1) = 0) | reflexive_rewrite(v0, v1) = 0) % 21.02/6.88 | (15) reflexive_rewrite(a, b) = 0 % 21.02/6.88 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (rewrite(v0, v2) = 0) | ~ (rewrite(v0, v1) = 0) | ? [v3] : (rewrite(v2, v3) = 0 & rewrite(v1, v3) = 0)) % 21.02/6.88 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equalish(v0, v1) = v2) | ? [v3] : ((v3 = 0 & rewrite(v0, v1) = 0) | ( ~ (v3 = 0) & reflexive_rewrite(v0, v1) = v3))) % 21.02/6.88 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equalish(v3, v2) = v1) | ~ (equalish(v3, v2) = v0)) % 21.02/6.88 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rewrite(v0, v1) = v2) | ? [v3] : ((v3 = 0 & equalish(v0, v1) = 0) | ( ~ (v3 = 0) & reflexive_rewrite(v0, v1) = v3))) % 21.02/6.88 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v1, v2) = 0) | reflexive_rewrite(v0, v2) = 0) % 21.02/6.88 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (reflexive_rewrite(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rewrite(v0, v1) = v3)) % 21.02/6.88 | (22) ! [v0] : ! [v1] : ( ~ (equalish(v0, v1) = 0) | equalish(v1, v0) = 0) % 21.02/6.88 | (23) ? [v0] : ? [v1] : ? [v2] : reflexive_rewrite(v1, v0) = v2 % 21.02/6.88 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (reflexive_rewrite(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & equalish(v0, v1) = v3)) % 21.02/6.88 | (25) ? [v0] : ? [v1] : ? [v2] : equalish(v1, v0) = v2 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (6) with c, a and discharging atoms reflexive_rewrite(a, c) = 0, yields: % 21.02/6.89 | (26) ? [v0] : ((v0 = 0 & rewrite(a, c) = 0) | (v0 = 0 & equalish(a, c) = 0)) % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (6) with b, a and discharging atoms reflexive_rewrite(a, b) = 0, yields: % 21.02/6.89 | (27) ? [v0] : ((v0 = 0 & rewrite(a, b) = 0) | (v0 = 0 & equalish(a, b) = 0)) % 21.02/6.89 | % 21.02/6.89 | Instantiating (27) with all_13_0_9 yields: % 21.02/6.89 | (28) (all_13_0_9 = 0 & rewrite(a, b) = 0) | (all_13_0_9 = 0 & equalish(a, b) = 0) % 21.02/6.89 | % 21.02/6.89 | Instantiating (26) with all_14_0_10 yields: % 21.02/6.89 | (29) (all_14_0_10 = 0 & rewrite(a, c) = 0) | (all_14_0_10 = 0 & equalish(a, c) = 0) % 21.02/6.89 | % 21.02/6.89 +-Applying beta-rule and splitting (28), into two cases. % 21.02/6.89 |-Branch one: % 21.02/6.89 | (30) all_13_0_9 = 0 & rewrite(a, b) = 0 % 21.02/6.89 | % 21.02/6.89 | Applying alpha-rule on (30) yields: % 21.02/6.89 | (31) all_13_0_9 = 0 % 21.02/6.89 | (32) rewrite(a, b) = 0 % 21.02/6.89 | % 21.02/6.89 +-Applying beta-rule and splitting (29), into two cases. % 21.02/6.89 |-Branch one: % 21.02/6.89 | (33) all_14_0_10 = 0 & rewrite(a, c) = 0 % 21.02/6.89 | % 21.02/6.89 | Applying alpha-rule on (33) yields: % 21.02/6.89 | (34) all_14_0_10 = 0 % 21.02/6.89 | (35) rewrite(a, c) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (16) with c, b, a and discharging atoms rewrite(a, c) = 0, rewrite(a, b) = 0, yields: % 21.02/6.89 | (36) ? [v0] : (rewrite(c, v0) = 0 & rewrite(b, v0) = 0) % 21.02/6.89 | % 21.02/6.89 | Instantiating (36) with all_138_0_30 yields: % 21.02/6.89 | (37) rewrite(c, all_138_0_30) = 0 & rewrite(b, all_138_0_30) = 0 % 21.02/6.89 | % 21.02/6.89 | Applying alpha-rule on (37) yields: % 21.02/6.89 | (38) rewrite(c, all_138_0_30) = 0 % 21.02/6.89 | (39) rewrite(b, all_138_0_30) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (7) with all_138_0_30, c and discharging atoms rewrite(c, all_138_0_30) = 0, yields: % 21.02/6.89 | (40) reflexive_rewrite(c, all_138_0_30) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (7) with all_138_0_30, b and discharging atoms rewrite(b, all_138_0_30) = 0, yields: % 21.02/6.89 | (41) reflexive_rewrite(b, all_138_0_30) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (13) with all_138_0_30 and discharging atoms reflexive_rewrite(c, all_138_0_30) = 0, yields: % 21.02/6.89 | (42) ? [v0] : ( ~ (v0 = 0) & reflexive_rewrite(b, all_138_0_30) = v0) % 21.02/6.89 | % 21.02/6.89 | Instantiating (42) with all_168_0_39 yields: % 21.02/6.89 | (43) ~ (all_168_0_39 = 0) & reflexive_rewrite(b, all_138_0_30) = all_168_0_39 % 21.02/6.89 | % 21.02/6.89 | Applying alpha-rule on (43) yields: % 21.02/6.89 | (44) ~ (all_168_0_39 = 0) % 21.02/6.89 | (45) reflexive_rewrite(b, all_138_0_30) = all_168_0_39 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (3) with b, all_138_0_30, all_168_0_39, 0 and discharging atoms reflexive_rewrite(b, all_138_0_30) = all_168_0_39, reflexive_rewrite(b, all_138_0_30) = 0, yields: % 21.02/6.89 | (46) all_168_0_39 = 0 % 21.02/6.89 | % 21.02/6.89 | Equations (46) can reduce 44 to: % 21.02/6.89 | (47) $false % 21.02/6.89 | % 21.02/6.89 |-The branch is then unsatisfiable % 21.02/6.89 |-Branch two: % 21.02/6.89 | (48) all_14_0_10 = 0 & equalish(a, c) = 0 % 21.02/6.89 | % 21.02/6.89 | Applying alpha-rule on (48) yields: % 21.02/6.89 | (34) all_14_0_10 = 0 % 21.02/6.89 | (50) equalish(a, c) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (22) with c, a and discharging atoms equalish(a, c) = 0, yields: % 21.02/6.89 | (51) equalish(c, a) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (20) with b, a, c and discharging atoms equalish(c, a) = 0, reflexive_rewrite(a, b) = 0, yields: % 21.02/6.89 | (52) reflexive_rewrite(c, b) = 0 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (13) with b and discharging atoms reflexive_rewrite(c, b) = 0, yields: % 21.02/6.89 | (53) ? [v0] : ( ~ (v0 = 0) & reflexive_rewrite(b, b) = v0) % 21.02/6.89 | % 21.02/6.89 | Instantiating (53) with all_160_0_52 yields: % 21.02/6.89 | (54) ~ (all_160_0_52 = 0) & reflexive_rewrite(b, b) = all_160_0_52 % 21.02/6.89 | % 21.02/6.89 | Applying alpha-rule on (54) yields: % 21.02/6.89 | (55) ~ (all_160_0_52 = 0) % 21.02/6.89 | (56) reflexive_rewrite(b, b) = all_160_0_52 % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (2) with all_160_0_52, b, a, b and discharging atoms reflexive_rewrite(b, b) = all_160_0_52, reflexive_rewrite(a, b) = 0, yields: % 21.02/6.89 | (57) all_160_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & equalish(b, a) = v0) % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (21) with all_160_0_52, b, b and discharging atoms reflexive_rewrite(b, b) = all_160_0_52, yields: % 21.02/6.89 | (58) all_160_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & rewrite(b, b) = v0) % 21.02/6.89 | % 21.02/6.89 | Instantiating formula (24) with all_160_0_52, b, b and discharging atoms reflexive_rewrite(b, b) = all_160_0_52, yields: % 21.02/6.89 | (59) all_160_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & equalish(b, b) = v0) % 21.02/6.89 | % 21.02/6.90 +-Applying beta-rule and splitting (57), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (60) all_160_0_52 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (60) can reduce 55 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (55) ~ (all_160_0_52 = 0) % 21.02/6.90 | (63) ? [v0] : ( ~ (v0 = 0) & equalish(b, a) = v0) % 21.02/6.90 | % 21.02/6.90 +-Applying beta-rule and splitting (58), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (60) all_160_0_52 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (60) can reduce 55 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (55) ~ (all_160_0_52 = 0) % 21.02/6.90 | (67) ? [v0] : ( ~ (v0 = 0) & rewrite(b, b) = v0) % 21.02/6.90 | % 21.02/6.90 +-Applying beta-rule and splitting (59), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (60) all_160_0_52 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (60) can reduce 55 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (55) ~ (all_160_0_52 = 0) % 21.02/6.90 | (71) ? [v0] : ( ~ (v0 = 0) & equalish(b, b) = v0) % 21.02/6.90 | % 21.02/6.90 | Instantiating (71) with all_239_0_72 yields: % 21.02/6.90 | (72) ~ (all_239_0_72 = 0) & equalish(b, b) = all_239_0_72 % 21.02/6.90 | % 21.02/6.90 | Applying alpha-rule on (72) yields: % 21.02/6.90 | (73) ~ (all_239_0_72 = 0) % 21.02/6.90 | (74) equalish(b, b) = all_239_0_72 % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (8) with all_239_0_72, b and discharging atoms equalish(b, b) = all_239_0_72, yields: % 21.02/6.90 | (75) all_239_0_72 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (75) can reduce 73 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (77) all_13_0_9 = 0 & equalish(a, b) = 0 % 21.02/6.90 | % 21.02/6.90 | Applying alpha-rule on (77) yields: % 21.02/6.90 | (31) all_13_0_9 = 0 % 21.02/6.90 | (79) equalish(a, b) = 0 % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (22) with b, a and discharging atoms equalish(a, b) = 0, yields: % 21.02/6.90 | (80) equalish(b, a) = 0 % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (20) with c, a, b and discharging atoms equalish(b, a) = 0, reflexive_rewrite(a, c) = 0, yields: % 21.02/6.90 | (81) reflexive_rewrite(b, c) = 0 % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (12) with c and discharging atoms reflexive_rewrite(b, c) = 0, yields: % 21.02/6.90 | (82) ? [v0] : ( ~ (v0 = 0) & reflexive_rewrite(c, c) = v0) % 21.02/6.90 | % 21.02/6.90 | Instantiating (82) with all_38_0_76 yields: % 21.02/6.90 | (83) ~ (all_38_0_76 = 0) & reflexive_rewrite(c, c) = all_38_0_76 % 21.02/6.90 | % 21.02/6.90 | Applying alpha-rule on (83) yields: % 21.02/6.90 | (84) ~ (all_38_0_76 = 0) % 21.02/6.90 | (85) reflexive_rewrite(c, c) = all_38_0_76 % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (2) with all_38_0_76, c, b, c and discharging atoms reflexive_rewrite(c, c) = all_38_0_76, reflexive_rewrite(b, c) = 0, yields: % 21.02/6.90 | (86) all_38_0_76 = 0 | ? [v0] : ( ~ (v0 = 0) & equalish(c, b) = v0) % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (2) with all_38_0_76, c, a, c and discharging atoms reflexive_rewrite(c, c) = all_38_0_76, reflexive_rewrite(a, c) = 0, yields: % 21.02/6.90 | (87) all_38_0_76 = 0 | ? [v0] : ( ~ (v0 = 0) & equalish(c, a) = v0) % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (21) with all_38_0_76, c, c and discharging atoms reflexive_rewrite(c, c) = all_38_0_76, yields: % 21.02/6.90 | (88) all_38_0_76 = 0 | ? [v0] : ( ~ (v0 = 0) & rewrite(c, c) = v0) % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (24) with all_38_0_76, c, c and discharging atoms reflexive_rewrite(c, c) = all_38_0_76, yields: % 21.02/6.90 | (89) all_38_0_76 = 0 | ? [v0] : ( ~ (v0 = 0) & equalish(c, c) = v0) % 21.02/6.90 | % 21.02/6.90 +-Applying beta-rule and splitting (88), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (90) all_38_0_76 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (90) can reduce 84 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (84) ~ (all_38_0_76 = 0) % 21.02/6.90 | (93) ? [v0] : ( ~ (v0 = 0) & rewrite(c, c) = v0) % 21.02/6.90 | % 21.02/6.90 +-Applying beta-rule and splitting (86), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (90) all_38_0_76 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (90) can reduce 84 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (84) ~ (all_38_0_76 = 0) % 21.02/6.90 | (97) ? [v0] : ( ~ (v0 = 0) & equalish(c, b) = v0) % 21.02/6.90 | % 21.02/6.90 +-Applying beta-rule and splitting (87), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (90) all_38_0_76 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (90) can reduce 84 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (84) ~ (all_38_0_76 = 0) % 21.02/6.90 | (101) ? [v0] : ( ~ (v0 = 0) & equalish(c, a) = v0) % 21.02/6.90 | % 21.02/6.90 +-Applying beta-rule and splitting (89), into two cases. % 21.02/6.90 |-Branch one: % 21.02/6.90 | (90) all_38_0_76 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (90) can reduce 84 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 |-Branch two: % 21.02/6.90 | (84) ~ (all_38_0_76 = 0) % 21.02/6.90 | (105) ? [v0] : ( ~ (v0 = 0) & equalish(c, c) = v0) % 21.02/6.90 | % 21.02/6.90 | Instantiating (105) with all_80_0_85 yields: % 21.02/6.90 | (106) ~ (all_80_0_85 = 0) & equalish(c, c) = all_80_0_85 % 21.02/6.90 | % 21.02/6.90 | Applying alpha-rule on (106) yields: % 21.02/6.90 | (107) ~ (all_80_0_85 = 0) % 21.02/6.90 | (108) equalish(c, c) = all_80_0_85 % 21.02/6.90 | % 21.02/6.90 | Instantiating formula (8) with all_80_0_85, c and discharging atoms equalish(c, c) = all_80_0_85, yields: % 21.02/6.90 | (109) all_80_0_85 = 0 % 21.02/6.90 | % 21.02/6.90 | Equations (109) can reduce 107 to: % 21.02/6.90 | (47) $false % 21.02/6.90 | % 21.02/6.90 |-The branch is then unsatisfiable % 21.02/6.90 % SZS output end Proof for theBenchmark % 21.02/6.91 % 21.02/6.91 6235ms %------------------------------------------------------------------------------