%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN943+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 05:06:00 EDT 2022 % Result : Theorem 2.68s 1.33s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN943+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n004.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 : Mon Jul 11 11:41:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.57 ____ _ % 0.54/0.57 ___ / __ \_____(_)___ ________ __________ % 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.57 % 0.54/0.57 A Theorem Prover for First-Order Logic % 0.54/0.57 (ePrincess v.1.0) % 0.54/0.57 % 0.54/0.57 (c) Philipp Rümmer, 2009-2015 % 0.54/0.57 (c) Peter Backeman, 2014-2015 % 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.57 Bug reports to peter@backeman.se % 0.54/0.57 % 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.57 % 0.54/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.24/0.86 Prover 0: Preprocessing ... % 1.42/0.94 Prover 0: Warning: ignoring some quantifiers % 1.46/0.95 Prover 0: Constructing countermodel ... % 1.62/1.06 Prover 0: gave up % 1.62/1.06 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.62/1.08 Prover 1: Preprocessing ... % 1.88/1.15 Prover 1: Constructing countermodel ... % 2.17/1.17 Prover 1: gave up % 2.17/1.17 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.17/1.18 Prover 2: Preprocessing ... % 2.46/1.26 Prover 2: Warning: ignoring some quantifiers % 2.46/1.27 Prover 2: Constructing countermodel ... % 2.68/1.33 Prover 2: proved (156ms) % 2.68/1.33 % 2.68/1.33 No countermodel exists, formula is valid % 2.68/1.33 % SZS status Theorem for theBenchmark % 2.68/1.33 % 2.68/1.33 Generating proof ... Warning: ignoring some quantifiers % 3.57/1.55 found it (size 30) % 3.57/1.55 % 3.57/1.55 % SZS output start Proof for theBenchmark % 3.57/1.55 Assumed formulas after preprocessing and simplification: % 3.57/1.55 | (0) ? [v0] : (p(v0) = 0 & e(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (s(v4, v3) = v2) | ~ (s(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (c(v2) = v3) | ~ (f(v1) = v2) | ? [v4] : ((v4 = 0 & g(v1) = 0) | ( ~ (v4 = 0) & e(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (f(v1) = v2) | ~ (s(v1, v2) = v3) | ? [v4] : ((v4 = 0 & g(v1) = 0) | ( ~ (v4 = 0) & e(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (p(v3) = v2) | ~ (p(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (c(v3) = v2) | ~ (c(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (g(v3) = v2) | ~ (g(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (e(v3) = v2) | ~ (e(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (f(v3) = v2) | ~ (f(v3) = v1)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (p(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & s(v0, v1) = v3)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (g(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & c(v3) = 0 & f(v1) = v3) | ( ~ (v3 = 0) & e(v1) = v3))) & ! [v1] : ! [v2] : (v2 = 0 | ~ (g(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & f(v1) = v3 & s(v1, v3) = 0) | ( ~ (v3 = 0) & e(v1) = v3))) & ! [v1] : ( ~ (p(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & c(v1) = v2)) & ! [v1] : ( ~ (p(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & g(v1) = v2)) & ! [v1] : ( ~ (c(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & p(v1) = v2)) & ! [v1] : ( ~ (g(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & p(v1) = v2)) & ! [v1] : ( ~ (e(v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & c(v2) = 0 & f(v1) = v2) | (v2 = 0 & g(v1) = 0))) & ! [v1] : ( ~ (e(v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & f(v1) = v2 & s(v1, v2) = 0) | (v2 = 0 & g(v1) = 0))) & ! [v1] : ( ~ (s(v0, v1) = 0) | p(v1) = 0) & ? [v1] : ? [v2] : ? [v3] : s(v2, v1) = v3 & ? [v1] : ? [v2] : p(v1) = v2 & ? [v1] : ? [v2] : c(v1) = v2 & ? [v1] : ? [v2] : g(v1) = v2 & ? [v1] : ? [v2] : e(v1) = v2 & ? [v1] : ? [v2] : f(v1) = v2) % 3.57/1.59 | Instantiating (0) with all_0_0_0 yields: % 3.57/1.59 | (1) p(all_0_0_0) = 0 & e(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (c(v1) = v2) | ~ (f(v0) = v1) | ? [v3] : ((v3 = 0 & g(v0) = 0) | ( ~ (v3 = 0) & e(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (f(v0) = v1) | ~ (s(v0, v1) = v2) | ? [v3] : ((v3 = 0 & g(v0) = 0) | ( ~ (v3 = 0) & e(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (e(v2) = v1) | ~ (e(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & s(all_0_0_0, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (g(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & c(v2) = 0 & f(v0) = v2) | ( ~ (v2 = 0) & e(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (g(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & f(v0) = v2 & s(v0, v2) = 0) | ( ~ (v2 = 0) & e(v0) = v2))) & ! [v0] : ( ~ (p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & c(v0) = v1)) & ! [v0] : ( ~ (p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & g(v0) = v1)) & ! [v0] : ( ~ (c(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & p(v0) = v1)) & ! [v0] : ( ~ (g(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & p(v0) = v1)) & ! [v0] : ( ~ (e(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & c(v1) = 0 & f(v0) = v1) | (v1 = 0 & g(v0) = 0))) & ! [v0] : ( ~ (e(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & f(v0) = v1 & s(v0, v1) = 0) | (v1 = 0 & g(v0) = 0))) & ! [v0] : ( ~ (s(all_0_0_0, v0) = 0) | p(v0) = 0) & ? [v0] : ? [v1] : ? [v2] : s(v1, v0) = v2 & ? [v0] : ? [v1] : p(v0) = v1 & ? [v0] : ? [v1] : c(v0) = v1 & ? [v0] : ? [v1] : g(v0) = v1 & ? [v0] : ? [v1] : e(v0) = v1 & ? [v0] : ? [v1] : f(v0) = v1 % 3.57/1.60 | % 3.57/1.60 | Applying alpha-rule on (1) yields: % 3.57/1.60 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (g(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & c(v2) = 0 & f(v0) = v2) | ( ~ (v2 = 0) & e(v0) = v2))) % 3.57/1.60 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) % 3.57/1.60 | (4) ! [v0] : ( ~ (s(all_0_0_0, v0) = 0) | p(v0) = 0) % 3.57/1.60 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) % 3.57/1.60 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (f(v0) = v1) | ~ (s(v0, v1) = v2) | ? [v3] : ((v3 = 0 & g(v0) = 0) | ( ~ (v3 = 0) & e(v0) = v3))) % 3.57/1.60 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 3.57/1.60 | (8) p(all_0_0_0) = 0 % 3.57/1.60 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & s(all_0_0_0, v0) = v2)) % 3.57/1.60 | (10) ! [v0] : ( ~ (e(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & c(v1) = 0 & f(v0) = v1) | (v1 = 0 & g(v0) = 0))) % 3.57/1.60 | (11) ? [v0] : ? [v1] : e(v0) = v1 % 3.57/1.60 | (12) ? [v0] : ? [v1] : f(v0) = v1 % 3.57/1.60 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (g(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & f(v0) = v2 & s(v0, v2) = 0) | ( ~ (v2 = 0) & e(v0) = v2))) % 3.57/1.60 | (14) ! [v0] : ( ~ (c(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & p(v0) = v1)) % 3.57/1.61 | (15) ! [v0] : ( ~ (p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & c(v0) = v1)) % 3.57/1.61 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (c(v1) = v2) | ~ (f(v0) = v1) | ? [v3] : ((v3 = 0 & g(v0) = 0) | ( ~ (v3 = 0) & e(v0) = v3))) % 3.57/1.61 | (17) ? [v0] : ? [v1] : ? [v2] : s(v1, v0) = v2 % 3.57/1.61 | (18) ! [v0] : ( ~ (g(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & p(v0) = v1)) % 3.57/1.61 | (19) ! [v0] : ( ~ (p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & g(v0) = v1)) % 3.57/1.61 | (20) ! [v0] : ( ~ (e(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & f(v0) = v1 & s(v0, v1) = 0) | (v1 = 0 & g(v0) = 0))) % 3.57/1.61 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) % 3.57/1.61 | (22) ? [v0] : ? [v1] : p(v0) = v1 % 3.57/1.61 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (e(v2) = v1) | ~ (e(v2) = v0)) % 3.57/1.61 | (24) ? [v0] : ? [v1] : g(v0) = v1 % 3.57/1.61 | (25) ? [v0] : ? [v1] : c(v0) = v1 % 3.57/1.61 | (26) e(all_0_0_0) = 0 % 3.57/1.61 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 3.57/1.61 | % 3.57/1.61 | Instantiating formula (19) with all_0_0_0 and discharging atoms p(all_0_0_0) = 0, yields: % 3.57/1.61 | (28) ? [v0] : ( ~ (v0 = 0) & g(all_0_0_0) = v0) % 3.57/1.61 | % 3.57/1.61 | Instantiating formula (10) with all_0_0_0 and discharging atoms e(all_0_0_0) = 0, yields: % 3.57/1.61 | (29) ? [v0] : ? [v1] : ((v1 = 0 & c(v0) = 0 & f(all_0_0_0) = v0) | (v0 = 0 & g(all_0_0_0) = 0)) % 3.57/1.61 | % 3.57/1.61 | Instantiating formula (20) with all_0_0_0 and discharging atoms e(all_0_0_0) = 0, yields: % 3.57/1.61 | (30) ? [v0] : ? [v1] : ((v1 = 0 & f(all_0_0_0) = v0 & s(all_0_0_0, v0) = 0) | (v0 = 0 & g(all_0_0_0) = 0)) % 3.57/1.61 | % 3.57/1.61 | Instantiating (30) with all_20_0_14, all_20_1_15 yields: % 3.57/1.61 | (31) (all_20_0_14 = 0 & f(all_0_0_0) = all_20_1_15 & s(all_0_0_0, all_20_1_15) = 0) | (all_20_1_15 = 0 & g(all_0_0_0) = 0) % 3.57/1.61 | % 3.57/1.61 | Instantiating (28) with all_21_0_16 yields: % 3.57/1.61 | (32) ~ (all_21_0_16 = 0) & g(all_0_0_0) = all_21_0_16 % 3.57/1.61 | % 3.57/1.61 | Applying alpha-rule on (32) yields: % 3.57/1.61 | (33) ~ (all_21_0_16 = 0) % 3.57/1.61 | (34) g(all_0_0_0) = all_21_0_16 % 3.57/1.61 | % 3.57/1.61 | Instantiating (29) with all_25_0_18, all_25_1_19 yields: % 3.57/1.61 | (35) (all_25_0_18 = 0 & c(all_25_1_19) = 0 & f(all_0_0_0) = all_25_1_19) | (all_25_1_19 = 0 & g(all_0_0_0) = 0) % 3.57/1.61 | % 3.57/1.61 +-Applying beta-rule and splitting (31), into two cases. % 3.57/1.61 |-Branch one: % 3.57/1.61 | (36) all_20_0_14 = 0 & f(all_0_0_0) = all_20_1_15 & s(all_0_0_0, all_20_1_15) = 0 % 3.57/1.61 | % 3.57/1.61 | Applying alpha-rule on (36) yields: % 3.57/1.61 | (37) all_20_0_14 = 0 % 3.57/1.61 | (38) f(all_0_0_0) = all_20_1_15 % 3.57/1.62 | (39) s(all_0_0_0, all_20_1_15) = 0 % 3.57/1.62 | % 3.91/1.62 +-Applying beta-rule and splitting (35), into two cases. % 3.91/1.62 |-Branch one: % 3.91/1.62 | (40) all_25_0_18 = 0 & c(all_25_1_19) = 0 & f(all_0_0_0) = all_25_1_19 % 3.91/1.62 | % 3.91/1.62 | Applying alpha-rule on (40) yields: % 3.91/1.62 | (41) all_25_0_18 = 0 % 3.91/1.62 | (42) c(all_25_1_19) = 0 % 3.91/1.62 | (43) f(all_0_0_0) = all_25_1_19 % 3.91/1.62 | % 3.91/1.62 | Instantiating formula (5) with all_0_0_0, all_20_1_15, all_25_1_19 and discharging atoms f(all_0_0_0) = all_25_1_19, f(all_0_0_0) = all_20_1_15, yields: % 3.91/1.62 | (44) all_25_1_19 = all_20_1_15 % 3.91/1.62 | % 3.91/1.62 | From (44) and (42) follows: % 3.91/1.62 | (45) c(all_20_1_15) = 0 % 3.91/1.62 | % 3.91/1.62 | Instantiating formula (14) with all_20_1_15 and discharging atoms c(all_20_1_15) = 0, yields: % 3.91/1.62 | (46) ? [v0] : ( ~ (v0 = 0) & p(all_20_1_15) = v0) % 3.91/1.62 | % 3.91/1.62 | Instantiating formula (4) with all_20_1_15 and discharging atoms s(all_0_0_0, all_20_1_15) = 0, yields: % 3.91/1.62 | (47) p(all_20_1_15) = 0 % 3.91/1.62 | % 3.91/1.62 | Instantiating (46) with all_44_0_20 yields: % 3.91/1.62 | (48) ~ (all_44_0_20 = 0) & p(all_20_1_15) = all_44_0_20 % 3.91/1.62 | % 3.91/1.62 | Applying alpha-rule on (48) yields: % 3.91/1.62 | (49) ~ (all_44_0_20 = 0) % 3.91/1.62 | (50) p(all_20_1_15) = all_44_0_20 % 3.91/1.62 | % 3.91/1.62 | Instantiating formula (27) with all_20_1_15, 0, all_44_0_20 and discharging atoms p(all_20_1_15) = all_44_0_20, p(all_20_1_15) = 0, yields: % 3.91/1.62 | (51) all_44_0_20 = 0 % 3.91/1.62 | % 3.91/1.62 | Equations (51) can reduce 49 to: % 3.91/1.62 | (52) $false % 3.91/1.62 | % 3.91/1.62 |-The branch is then unsatisfiable % 3.91/1.62 |-Branch two: % 3.91/1.62 | (53) all_25_1_19 = 0 & g(all_0_0_0) = 0 % 3.91/1.62 | % 3.91/1.62 | Applying alpha-rule on (53) yields: % 3.91/1.62 | (54) all_25_1_19 = 0 % 3.91/1.62 | (55) g(all_0_0_0) = 0 % 3.91/1.62 | % 3.91/1.62 | Instantiating formula (21) with all_0_0_0, 0, all_21_0_16 and discharging atoms g(all_0_0_0) = all_21_0_16, g(all_0_0_0) = 0, yields: % 3.91/1.62 | (56) all_21_0_16 = 0 % 3.91/1.62 | % 3.91/1.62 | Equations (56) can reduce 33 to: % 3.91/1.62 | (52) $false % 3.91/1.62 | % 3.91/1.62 |-The branch is then unsatisfiable % 3.91/1.62 |-Branch two: % 3.91/1.62 | (58) all_20_1_15 = 0 & g(all_0_0_0) = 0 % 3.91/1.62 | % 3.91/1.62 | Applying alpha-rule on (58) yields: % 3.91/1.62 | (59) all_20_1_15 = 0 % 3.91/1.62 | (55) g(all_0_0_0) = 0 % 3.91/1.62 | % 3.91/1.62 | Instantiating formula (21) with all_0_0_0, 0, all_21_0_16 and discharging atoms g(all_0_0_0) = all_21_0_16, g(all_0_0_0) = 0, yields: % 3.91/1.62 | (56) all_21_0_16 = 0 % 3.91/1.62 | % 3.91/1.62 | Equations (56) can reduce 33 to: % 3.91/1.62 | (52) $false % 3.91/1.62 | % 3.91/1.62 |-The branch is then unsatisfiable % 3.91/1.62 % SZS output end Proof for theBenchmark % 3.91/1.62 % 3.91/1.62 1042ms %------------------------------------------------------------------------------