%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN325+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 05:01:23 EDT 2022 % Result : Theorem 2.39s 1.28s % Output : Proof 3.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN325+1 : TPTP v8.1.0. Released v2.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n008.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 : Mon Jul 11 18:20:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.58 ____ _ % 0.20/0.58 ___ / __ \_____(_)___ ________ __________ % 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic % 0.20/0.58 (ePrincess v.1.0) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2015 % 0.20/0.58 (c) Peter Backeman, 2014-2015 % 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.58 Bug reports to peter@backeman.se % 0.20/0.58 % 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.58 % 0.20/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.22/0.87 Prover 0: Preprocessing ... % 1.28/0.90 Prover 0: Warning: ignoring some quantifiers % 1.28/0.91 Prover 0: Constructing countermodel ... % 1.37/0.99 Prover 0: gave up % 1.37/1.00 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.56/1.01 Prover 1: Preprocessing ... % 1.56/1.06 Prover 1: Constructing countermodel ... % 1.80/1.07 Prover 1: gave up % 1.80/1.07 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.80/1.08 Prover 2: Preprocessing ... % 1.80/1.11 Prover 2: Warning: ignoring some quantifiers % 1.80/1.11 Prover 2: Constructing countermodel ... % 1.80/1.13 Prover 2: gave up % 1.80/1.14 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.80/1.14 Prover 3: Preprocessing ... % 1.80/1.15 Prover 3: Warning: ignoring some quantifiers % 1.80/1.15 Prover 3: Constructing countermodel ... % 1.80/1.16 Prover 3: gave up % 1.80/1.16 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 1.80/1.17 Prover 4: Preprocessing ... % 2.23/1.20 Prover 4: Warning: ignoring some quantifiers % 2.23/1.20 Prover 4: Constructing countermodel ... % 2.39/1.28 Prover 4: proved (120ms) % 2.39/1.28 % 2.39/1.28 No countermodel exists, formula is valid % 2.39/1.28 % SZS status Theorem for theBenchmark % 2.39/1.28 % 2.39/1.28 Generating proof ... Warning: ignoring some quantifiers % 3.44/1.57 found it (size 23) % 3.44/1.57 % 3.44/1.57 % SZS output start Proof for theBenchmark % 3.44/1.58 Assumed formulas after preprocessing and simplification: % 3.44/1.58 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (big_f(v0, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & big_f(v3, v3) = v4 & big_f(v0, v3) = v5 & big_g(v3) = v6 & big_g(v0) = v2 & ((v5 = 0 & v2 = 0) | (v1 = 0 & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & big_f(v3, v3) = v4 & big_f(v0, v3) = v5 & big_f(v0, v0) = v2 & big_g(v3) = v6 & ((v5 = 0 & v1 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & big_f(v3, v3) = v4 & big_f(v0, v3) = v5 & big_f(v0, v0) = v1 & big_g(v3) = v6 & big_g(v0) = v2 & ((v5 = 0 & v2 = 0) | (v1 = 0 & ~ (v4 = 0)))) % 3.44/1.61 | Applying alpha-rule on (0) yields: % 3.44/1.61 | (1) ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & big_f(v3, v3) = v4 & big_f(v0, v3) = v5 & big_f(v0, v0) = v2 & big_g(v3) = v6 & ((v5 = 0 & v1 = 0) | (v2 = 0 & ~ (v4 = 0))))) % 3.44/1.61 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) % 3.44/1.61 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) % 3.44/1.61 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & big_f(v3, v3) = v4 & big_f(v0, v3) = v5 & big_f(v0, v0) = v1 & big_g(v3) = v6 & big_g(v0) = v2 & ((v5 = 0 & v2 = 0) | (v1 = 0 & ~ (v4 = 0)))) % 3.44/1.61 | (5) ! [v0] : ! [v1] : ( ~ (big_f(v0, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & big_f(v3, v3) = v4 & big_f(v0, v3) = v5 & big_g(v3) = v6 & big_g(v0) = v2 & ((v5 = 0 & v2 = 0) | (v1 = 0 & ~ (v4 = 0))))) % 3.44/1.61 | % 3.44/1.61 | Instantiating (4) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5, all_1_6_6 yields: % 3.44/1.61 | (6) ~ (all_1_0_0 = 0) & big_f(all_1_3_3, all_1_3_3) = all_1_2_2 & big_f(all_1_6_6, all_1_3_3) = all_1_1_1 & big_f(all_1_6_6, all_1_6_6) = all_1_5_5 & big_g(all_1_3_3) = all_1_0_0 & big_g(all_1_6_6) = all_1_4_4 & ((all_1_1_1 = 0 & all_1_4_4 = 0) | (all_1_5_5 = 0 & ~ (all_1_2_2 = 0))) % 3.44/1.61 | % 3.44/1.61 | Applying alpha-rule on (6) yields: % 3.44/1.61 | (7) ~ (all_1_0_0 = 0) % 3.44/1.61 | (8) big_f(all_1_6_6, all_1_6_6) = all_1_5_5 % 3.44/1.61 | (9) big_g(all_1_3_3) = all_1_0_0 % 3.44/1.61 | (10) (all_1_1_1 = 0 & all_1_4_4 = 0) | (all_1_5_5 = 0 & ~ (all_1_2_2 = 0)) % 3.44/1.61 | (11) big_g(all_1_6_6) = all_1_4_4 % 3.44/1.61 | (12) big_f(all_1_6_6, all_1_3_3) = all_1_1_1 % 3.44/1.61 | (13) big_f(all_1_3_3, all_1_3_3) = all_1_2_2 % 3.44/1.61 | % 3.44/1.61 | Instantiating formula (1) with all_1_0_0, all_1_3_3 and discharging atoms big_g(all_1_3_3) = all_1_0_0, yields: % 3.44/1.61 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_f(v1, v1) = v2 & big_f(all_1_3_3, v1) = v3 & big_f(all_1_3_3, all_1_3_3) = v0 & big_g(v1) = v4 & ((v3 = 0 & all_1_0_0 = 0) | (v0 = 0 & ~ (v2 = 0)))) % 3.44/1.62 | % 3.44/1.62 | Instantiating (14) with all_10_0_12, all_10_1_13, all_10_2_14, all_10_3_15, all_10_4_16 yields: % 3.44/1.62 | (15) ~ (all_10_0_12 = 0) & big_f(all_10_3_15, all_10_3_15) = all_10_2_14 & big_f(all_1_3_3, all_10_3_15) = all_10_1_13 & big_f(all_1_3_3, all_1_3_3) = all_10_4_16 & big_g(all_10_3_15) = all_10_0_12 & ((all_10_1_13 = 0 & all_1_0_0 = 0) | (all_10_4_16 = 0 & ~ (all_10_2_14 = 0))) % 3.44/1.62 | % 3.44/1.62 | Applying alpha-rule on (15) yields: % 3.44/1.62 | (16) ~ (all_10_0_12 = 0) % 3.44/1.62 | (17) big_f(all_1_3_3, all_1_3_3) = all_10_4_16 % 3.44/1.62 | (18) big_f(all_1_3_3, all_10_3_15) = all_10_1_13 % 3.44/1.62 | (19) (all_10_1_13 = 0 & all_1_0_0 = 0) | (all_10_4_16 = 0 & ~ (all_10_2_14 = 0)) % 3.44/1.62 | (20) big_f(all_10_3_15, all_10_3_15) = all_10_2_14 % 3.44/1.62 | (21) big_g(all_10_3_15) = all_10_0_12 % 3.44/1.62 | % 3.44/1.62 +-Applying beta-rule and splitting (19), into two cases. % 3.44/1.62 |-Branch one: % 3.44/1.62 | (22) all_10_1_13 = 0 & all_1_0_0 = 0 % 3.44/1.62 | % 3.44/1.62 | Applying alpha-rule on (22) yields: % 3.44/1.62 | (23) all_10_1_13 = 0 % 3.44/1.62 | (24) all_1_0_0 = 0 % 3.44/1.62 | % 3.44/1.62 | Equations (24) can reduce 7 to: % 3.44/1.62 | (25) $false % 3.44/1.62 | % 3.44/1.62 |-The branch is then unsatisfiable % 3.44/1.62 |-Branch two: % 3.44/1.62 | (26) all_10_4_16 = 0 & ~ (all_10_2_14 = 0) % 3.44/1.62 | % 3.44/1.62 | Applying alpha-rule on (26) yields: % 3.44/1.62 | (27) all_10_4_16 = 0 % 3.44/1.62 | (28) ~ (all_10_2_14 = 0) % 3.44/1.62 | % 3.44/1.62 | Instantiating formula (1) with all_10_0_12, all_10_3_15 and discharging atoms big_g(all_10_3_15) = all_10_0_12, yields: % 3.44/1.62 | (29) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_f(v1, v1) = v2 & big_f(all_10_3_15, v1) = v3 & big_f(all_10_3_15, all_10_3_15) = v0 & big_g(v1) = v4 & ((v3 = 0 & all_10_0_12 = 0) | (v0 = 0 & ~ (v2 = 0)))) % 3.44/1.62 | % 3.44/1.62 | Instantiating (29) with all_45_0_47, all_45_1_48, all_45_2_49, all_45_3_50, all_45_4_51 yields: % 3.44/1.62 | (30) ~ (all_45_0_47 = 0) & big_f(all_45_3_50, all_45_3_50) = all_45_2_49 & big_f(all_10_3_15, all_45_3_50) = all_45_1_48 & big_f(all_10_3_15, all_10_3_15) = all_45_4_51 & big_g(all_45_3_50) = all_45_0_47 & ((all_45_1_48 = 0 & all_10_0_12 = 0) | (all_45_4_51 = 0 & ~ (all_45_2_49 = 0))) % 3.44/1.62 | % 3.44/1.62 | Applying alpha-rule on (30) yields: % 3.44/1.62 | (31) ~ (all_45_0_47 = 0) % 3.44/1.62 | (32) (all_45_1_48 = 0 & all_10_0_12 = 0) | (all_45_4_51 = 0 & ~ (all_45_2_49 = 0)) % 3.44/1.62 | (33) big_f(all_10_3_15, all_45_3_50) = all_45_1_48 % 3.44/1.62 | (34) big_f(all_10_3_15, all_10_3_15) = all_45_4_51 % 3.44/1.62 | (35) big_f(all_45_3_50, all_45_3_50) = all_45_2_49 % 3.44/1.62 | (36) big_g(all_45_3_50) = all_45_0_47 % 3.44/1.62 | % 3.44/1.62 +-Applying beta-rule and splitting (32), into two cases. % 3.44/1.62 |-Branch one: % 3.44/1.62 | (37) all_45_1_48 = 0 & all_10_0_12 = 0 % 3.44/1.62 | % 3.44/1.62 | Applying alpha-rule on (37) yields: % 3.44/1.62 | (38) all_45_1_48 = 0 % 3.44/1.62 | (39) all_10_0_12 = 0 % 3.44/1.62 | % 3.44/1.62 | Equations (39) can reduce 16 to: % 3.44/1.62 | (25) $false % 3.44/1.62 | % 3.44/1.62 |-The branch is then unsatisfiable % 3.44/1.62 |-Branch two: % 3.44/1.62 | (41) all_45_4_51 = 0 & ~ (all_45_2_49 = 0) % 3.44/1.62 | % 3.44/1.62 | Applying alpha-rule on (41) yields: % 3.44/1.62 | (42) all_45_4_51 = 0 % 3.44/1.62 | (43) ~ (all_45_2_49 = 0) % 3.44/1.62 | % 3.44/1.62 | From (42) and (34) follows: % 3.44/1.63 | (44) big_f(all_10_3_15, all_10_3_15) = 0 % 3.44/1.63 | % 3.44/1.63 | Instantiating formula (3) with all_10_3_15, all_10_3_15, 0, all_10_2_14 and discharging atoms big_f(all_10_3_15, all_10_3_15) = all_10_2_14, big_f(all_10_3_15, all_10_3_15) = 0, yields: % 3.44/1.63 | (45) all_10_2_14 = 0 % 3.44/1.63 | % 3.44/1.63 | Equations (45) can reduce 28 to: % 3.44/1.63 | (25) $false % 3.44/1.63 | % 3.44/1.63 |-The branch is then unsatisfiable % 3.44/1.63 % SZS output end Proof for theBenchmark % 3.44/1.63 % 3.44/1.63 1036ms %------------------------------------------------------------------------------