%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed 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 : Thu Jul 21 05:03:42 EDT 2022 % Result : Theorem 2.32s 1.27s % Output : Proof 3.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jul 12 07:39:12 EDT 2022 % 0.13/0.34 % CPUTime : % 0.50/0.58 ____ _ % 0.50/0.58 ___ / __ \_____(_)___ ________ __________ % 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic % 0.50/0.58 (ePrincess v.1.0) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2015 % 0.50/0.58 (c) Peter Backeman, 2014-2015 % 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.58 Bug reports to peter@backeman.se % 0.50/0.58 % 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.22/0.90 Prover 0: Preprocessing ... % 1.52/1.01 Prover 0: Warning: ignoring some quantifiers % 1.52/1.03 Prover 0: Constructing countermodel ... % 1.93/1.15 Prover 0: gave up % 1.93/1.15 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.09/1.17 Prover 1: Preprocessing ... % 2.09/1.21 Prover 1: Constructing countermodel ... % 2.32/1.27 Prover 1: proved (115ms) % 2.32/1.27 % 2.32/1.27 No countermodel exists, formula is valid % 2.32/1.27 % SZS status Theorem for theBenchmark % 2.32/1.27 % 2.32/1.27 Generating proof ... found it (size 49) % 2.98/1.49 % 2.98/1.49 % SZS output start Proof for theBenchmark % 2.98/1.49 Assumed formulas after preprocessing and simplification: % 2.98/1.49 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (g(v5) = v4) | ~ (g(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (f(v5) = v4) | ~ (f(v5) = v3)) & ((v2 = v0 & g(v1) = v0 & f(v0) = v1 & ! [v3] : ! [v4] : (v3 = v0 | ~ (f(v3) = v4) | ? [v5] : ( ~ (v5 = v3) & g(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (g(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & ~ (v5 = v3) & g(v5) = v6 & f(v6) = v5) | ( ~ (v5 = v3) & f(v4) = v5)))) | (v2 = v0 & g(v0) = v1 & f(v1) = v0 & ! [v3] : ! [v4] : (v3 = v0 | ~ (g(v3) = v4) | ? [v5] : ( ~ (v5 = v3) & f(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (f(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & ~ (v5 = v3) & g(v6) = v5 & f(v5) = v6) | ( ~ (v5 = v3) & g(v4) = v5)))))) % 2.98/1.52 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 2.98/1.52 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ((all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2)))) | (all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2))))) % 2.98/1.53 | % 2.98/1.53 | Applying alpha-rule on (1) yields: % 2.98/1.53 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) % 2.98/1.53 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) % 2.98/1.53 | (4) (all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2)))) | (all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2)))) % 2.98/1.53 | % 2.98/1.53 +-Applying beta-rule and splitting (4), into two cases. % 2.98/1.53 |-Branch one: % 2.98/1.53 | (5) all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2))) % 2.98/1.53 | % 2.98/1.53 | Applying alpha-rule on (5) yields: % 2.98/1.53 | (6) f(all_0_2_2) = all_0_1_1 % 2.98/1.53 | (7) ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2))) % 2.98/1.54 | (8) g(all_0_1_1) = all_0_2_2 % 2.98/1.54 | (9) all_0_0_0 = all_0_2_2 % 2.98/1.54 | (10) ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) % 2.98/1.54 | % 2.98/1.54 | Instantiating formula (7) with all_0_2_2, all_0_1_1 and discharging atoms g(all_0_1_1) = all_0_2_2, yields: % 2.98/1.54 | (11) ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & ~ (v0 = all_0_1_1) & g(v0) = v1 & f(v1) = v0) | ( ~ (v0 = all_0_1_1) & f(all_0_2_2) = v0)) % 3.24/1.54 | % 3.24/1.54 | Instantiating (11) with all_12_0_3, all_12_1_4, all_12_2_5 yields: % 3.24/1.54 | (12) (all_12_0_3 = all_12_2_5 & ~ (all_12_2_5 = all_0_1_1) & g(all_12_2_5) = all_12_1_4 & f(all_12_1_4) = all_12_2_5) | ( ~ (all_12_2_5 = all_0_1_1) & f(all_0_2_2) = all_12_2_5) % 3.24/1.54 | % 3.24/1.54 +-Applying beta-rule and splitting (12), into two cases. % 3.24/1.54 |-Branch one: % 3.24/1.54 | (13) all_12_0_3 = all_12_2_5 & ~ (all_12_2_5 = all_0_1_1) & g(all_12_2_5) = all_12_1_4 & f(all_12_1_4) = all_12_2_5 % 3.24/1.54 | % 3.24/1.54 | Applying alpha-rule on (13) yields: % 3.24/1.54 | (14) all_12_0_3 = all_12_2_5 % 3.24/1.54 | (15) ~ (all_12_2_5 = all_0_1_1) % 3.24/1.54 | (16) g(all_12_2_5) = all_12_1_4 % 3.24/1.54 | (17) f(all_12_1_4) = all_12_2_5 % 3.24/1.54 | % 3.24/1.54 | Instantiating formula (3) with all_0_2_2, all_12_2_5, all_0_1_1 and discharging atoms f(all_0_2_2) = all_0_1_1, yields: % 3.24/1.54 | (18) all_12_2_5 = all_0_1_1 | ~ (f(all_0_2_2) = all_12_2_5) % 3.24/1.54 | % 3.24/1.54 | Instantiating formula (10) with all_12_2_5, all_12_1_4 and discharging atoms f(all_12_1_4) = all_12_2_5, yields: % 3.24/1.54 | (19) all_12_1_4 = all_0_2_2 | ? [v0] : ( ~ (v0 = all_12_1_4) & g(all_12_2_5) = v0) % 3.24/1.54 | % 3.24/1.54 +-Applying beta-rule and splitting (18), into two cases. % 3.24/1.54 |-Branch one: % 3.24/1.54 | (20) ~ (f(all_0_2_2) = all_12_2_5) % 3.24/1.54 | % 3.24/1.54 +-Applying beta-rule and splitting (19), into two cases. % 3.24/1.54 |-Branch one: % 3.24/1.54 | (21) all_12_1_4 = all_0_2_2 % 3.24/1.54 | % 3.24/1.54 | From (21) and (17) follows: % 3.24/1.54 | (22) f(all_0_2_2) = all_12_2_5 % 3.24/1.54 | % 3.24/1.54 | Using (22) and (20) yields: % 3.24/1.54 | (23) $false % 3.24/1.54 | % 3.24/1.54 |-The branch is then unsatisfiable % 3.24/1.54 |-Branch two: % 3.24/1.54 | (24) ~ (all_12_1_4 = all_0_2_2) % 3.24/1.54 | (25) ? [v0] : ( ~ (v0 = all_12_1_4) & g(all_12_2_5) = v0) % 3.24/1.54 | % 3.24/1.54 | Instantiating (25) with all_27_0_9 yields: % 3.24/1.54 | (26) ~ (all_27_0_9 = all_12_1_4) & g(all_12_2_5) = all_27_0_9 % 3.24/1.54 | % 3.24/1.54 | Applying alpha-rule on (26) yields: % 3.24/1.54 | (27) ~ (all_27_0_9 = all_12_1_4) % 3.24/1.54 | (28) g(all_12_2_5) = all_27_0_9 % 3.24/1.54 | % 3.24/1.54 | Instantiating formula (2) with all_12_2_5, all_27_0_9, all_12_1_4 and discharging atoms g(all_12_2_5) = all_27_0_9, g(all_12_2_5) = all_12_1_4, yields: % 3.24/1.54 | (29) all_27_0_9 = all_12_1_4 % 3.24/1.54 | % 3.24/1.54 | Equations (29) can reduce 27 to: % 3.24/1.54 | (30) $false % 3.24/1.55 | % 3.24/1.55 |-The branch is then unsatisfiable % 3.24/1.55 |-Branch two: % 3.24/1.55 | (22) f(all_0_2_2) = all_12_2_5 % 3.24/1.55 | (32) all_12_2_5 = all_0_1_1 % 3.24/1.55 | % 3.24/1.55 | Equations (32) can reduce 15 to: % 3.24/1.55 | (30) $false % 3.24/1.55 | % 3.24/1.55 |-The branch is then unsatisfiable % 3.24/1.55 |-Branch two: % 3.24/1.55 | (34) ~ (all_12_2_5 = all_0_1_1) & f(all_0_2_2) = all_12_2_5 % 3.24/1.55 | % 3.24/1.55 | Applying alpha-rule on (34) yields: % 3.24/1.55 | (15) ~ (all_12_2_5 = all_0_1_1) % 3.24/1.55 | (22) f(all_0_2_2) = all_12_2_5 % 3.24/1.55 | % 3.24/1.55 | Instantiating formula (3) with all_0_2_2, all_12_2_5, all_0_1_1 and discharging atoms f(all_0_2_2) = all_12_2_5, f(all_0_2_2) = all_0_1_1, yields: % 3.24/1.55 | (32) all_12_2_5 = all_0_1_1 % 3.24/1.55 | % 3.24/1.55 | Equations (32) can reduce 15 to: % 3.24/1.55 | (30) $false % 3.24/1.55 | % 3.24/1.55 |-The branch is then unsatisfiable % 3.24/1.55 |-Branch two: % 3.24/1.55 | (39) all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2))) % 3.24/1.55 | % 3.24/1.55 | Applying alpha-rule on (39) yields: % 3.24/1.55 | (40) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2))) % 3.24/1.55 | (9) all_0_0_0 = all_0_2_2 % 3.24/1.55 | (42) g(all_0_2_2) = all_0_1_1 % 3.24/1.55 | (43) ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) % 3.24/1.55 | (44) f(all_0_1_1) = all_0_2_2 % 3.24/1.55 | % 3.24/1.55 | Instantiating formula (40) with all_0_2_2, all_0_1_1 and discharging atoms f(all_0_1_1) = all_0_2_2, yields: % 3.24/1.55 | (45) ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & ~ (v0 = all_0_1_1) & g(v1) = v0 & f(v0) = v1) | ( ~ (v0 = all_0_1_1) & g(all_0_2_2) = v0)) % 3.24/1.55 | % 3.24/1.55 | Instantiating (45) with all_12_0_10, all_12_1_11, all_12_2_12 yields: % 3.24/1.55 | (46) (all_12_0_10 = all_12_2_12 & ~ (all_12_2_12 = all_0_1_1) & g(all_12_1_11) = all_12_2_12 & f(all_12_2_12) = all_12_1_11) | ( ~ (all_12_2_12 = all_0_1_1) & g(all_0_2_2) = all_12_2_12) % 3.24/1.55 | % 3.24/1.55 +-Applying beta-rule and splitting (46), into two cases. % 3.24/1.55 |-Branch one: % 3.24/1.55 | (47) all_12_0_10 = all_12_2_12 & ~ (all_12_2_12 = all_0_1_1) & g(all_12_1_11) = all_12_2_12 & f(all_12_2_12) = all_12_1_11 % 3.24/1.55 | % 3.24/1.55 | Applying alpha-rule on (47) yields: % 3.24/1.55 | (48) all_12_0_10 = all_12_2_12 % 3.24/1.55 | (49) ~ (all_12_2_12 = all_0_1_1) % 3.24/1.55 | (50) g(all_12_1_11) = all_12_2_12 % 3.24/1.55 | (51) f(all_12_2_12) = all_12_1_11 % 3.24/1.55 | % 3.24/1.55 | Instantiating formula (2) with all_0_2_2, all_12_2_12, all_0_1_1 and discharging atoms g(all_0_2_2) = all_0_1_1, yields: % 3.24/1.55 | (52) all_12_2_12 = all_0_1_1 | ~ (g(all_0_2_2) = all_12_2_12) % 3.24/1.55 | % 3.24/1.55 | Instantiating formula (43) with all_12_2_12, all_12_1_11 and discharging atoms g(all_12_1_11) = all_12_2_12, yields: % 3.24/1.55 | (53) all_12_1_11 = all_0_2_2 | ? [v0] : ( ~ (v0 = all_12_1_11) & f(all_12_2_12) = v0) % 3.24/1.55 | % 3.24/1.55 +-Applying beta-rule and splitting (52), into two cases. % 3.24/1.55 |-Branch one: % 3.24/1.55 | (54) ~ (g(all_0_2_2) = all_12_2_12) % 3.24/1.55 | % 3.24/1.55 +-Applying beta-rule and splitting (53), into two cases. % 3.24/1.55 |-Branch one: % 3.24/1.55 | (55) all_12_1_11 = all_0_2_2 % 3.24/1.55 | % 3.24/1.55 | From (55) and (50) follows: % 3.24/1.55 | (56) g(all_0_2_2) = all_12_2_12 % 3.24/1.56 | % 3.24/1.56 | Using (56) and (54) yields: % 3.24/1.56 | (23) $false % 3.24/1.56 | % 3.24/1.56 |-The branch is then unsatisfiable % 3.24/1.56 |-Branch two: % 3.24/1.56 | (58) ~ (all_12_1_11 = all_0_2_2) % 3.24/1.56 | (59) ? [v0] : ( ~ (v0 = all_12_1_11) & f(all_12_2_12) = v0) % 3.24/1.56 | % 3.24/1.56 | Instantiating (59) with all_27_0_16 yields: % 3.24/1.56 | (60) ~ (all_27_0_16 = all_12_1_11) & f(all_12_2_12) = all_27_0_16 % 3.24/1.56 | % 3.24/1.56 | Applying alpha-rule on (60) yields: % 3.24/1.56 | (61) ~ (all_27_0_16 = all_12_1_11) % 3.24/1.56 | (62) f(all_12_2_12) = all_27_0_16 % 3.24/1.56 | % 3.24/1.56 | Instantiating formula (3) with all_12_2_12, all_27_0_16, all_12_1_11 and discharging atoms f(all_12_2_12) = all_27_0_16, f(all_12_2_12) = all_12_1_11, yields: % 3.24/1.56 | (63) all_27_0_16 = all_12_1_11 % 3.24/1.56 | % 3.24/1.56 | Equations (63) can reduce 61 to: % 3.24/1.56 | (30) $false % 3.24/1.56 | % 3.24/1.56 |-The branch is then unsatisfiable % 3.24/1.56 |-Branch two: % 3.24/1.56 | (56) g(all_0_2_2) = all_12_2_12 % 3.24/1.56 | (66) all_12_2_12 = all_0_1_1 % 3.24/1.56 | % 3.24/1.56 | Equations (66) can reduce 49 to: % 3.24/1.56 | (30) $false % 3.24/1.56 | % 3.24/1.56 |-The branch is then unsatisfiable % 3.24/1.56 |-Branch two: % 3.24/1.56 | (68) ~ (all_12_2_12 = all_0_1_1) & g(all_0_2_2) = all_12_2_12 % 3.24/1.56 | % 3.24/1.56 | Applying alpha-rule on (68) yields: % 3.24/1.56 | (49) ~ (all_12_2_12 = all_0_1_1) % 3.24/1.56 | (56) g(all_0_2_2) = all_12_2_12 % 3.24/1.56 | % 3.24/1.56 | Instantiating formula (2) with all_0_2_2, all_12_2_12, all_0_1_1 and discharging atoms g(all_0_2_2) = all_12_2_12, g(all_0_2_2) = all_0_1_1, yields: % 3.24/1.56 | (66) all_12_2_12 = all_0_1_1 % 3.24/1.56 | % 3.24/1.56 | Equations (66) can reduce 49 to: % 3.24/1.56 | (30) $false % 3.24/1.56 | % 3.24/1.56 |-The branch is then unsatisfiable % 3.24/1.56 % SZS output end Proof for theBenchmark % 3.24/1.56 % 3.24/1.56 966ms %------------------------------------------------------------------------------