%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN954+1 : TPTP v8.1.0. Released v3.1.0. % 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 : Thu Jul 21 05:06:04 EDT 2022 % Result : Theorem 2.53s 1.35s % Output : Proof 3.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYN954+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n021.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 17:13:08 EDT 2022 % 0.13/0.35 % CPUTime : % 0.56/0.60 ____ _ % 0.56/0.60 ___ / __ \_____(_)___ ________ __________ % 0.56/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.60 % 0.56/0.60 A Theorem Prover for First-Order Logic % 0.56/0.61 (ePrincess v.1.0) % 0.56/0.61 % 0.56/0.61 (c) Philipp Rümmer, 2009-2015 % 0.56/0.61 (c) Peter Backeman, 2014-2015 % 0.56/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.61 Bug reports to peter@backeman.se % 0.56/0.61 % 0.56/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.61 % 0.56/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.25/0.91 Prover 0: Preprocessing ... % 1.39/0.96 Prover 0: Warning: ignoring some quantifiers % 1.39/0.97 Prover 0: Constructing countermodel ... % 1.51/1.07 Prover 0: gave up % 1.51/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.72/1.09 Prover 1: Preprocessing ... % 2.04/1.17 Prover 1: Constructing countermodel ... % 2.11/1.21 Prover 1: gave up % 2.11/1.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.11/1.22 Prover 2: Preprocessing ... % 2.23/1.27 Prover 2: Warning: ignoring some quantifiers % 2.23/1.27 Prover 2: Constructing countermodel ... % 2.53/1.34 Prover 2: proved (130ms) % 2.53/1.35 % 2.53/1.35 No countermodel exists, formula is valid % 2.53/1.35 % SZS status Theorem for theBenchmark % 2.53/1.35 % 2.53/1.35 Generating proof ... Warning: ignoring some quantifiers % 3.08/1.59 found it (size 50) % 3.08/1.59 % 3.08/1.59 % SZS output start Proof for theBenchmark % 3.08/1.59 Assumed formulas after preprocessing and simplification: % 3.08/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (p(v1) = v3 & p(v0) = v2 & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (p(v6) = v5) | ~ (p(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (q(v6) = v5) | ~ (q(v6) = v4)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (p(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (q(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | v5 = 0 | ~ (p(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | ~ (q(v4) = v5) | p(v4) = 0) & ! [v4] : ! [v5] : ( ~ (v2 = 0) | v5 = 0 | ~ (q(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v2 = 0) | ~ (p(v4) = v5) | q(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (p(v4) = v5) | q(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (p(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & q(v4) = v6)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (q(v4) = v5) | p(v4) = 0) & ! [v4] : ( ~ (q(v4) = 0) | p(v4) = 0) & ? [v4] : ? [v5] : p(v4) = v5 & ? [v4] : ? [v5] : q(v4) = v5) % 3.08/1.62 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 3.08/1.62 | (1) p(all_0_2_2) = all_0_0_0 & p(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (p(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (q(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (p(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (q(v0) = v1) | p(v0) = 0) & ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | v1 = 0 | ~ (q(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | ~ (p(v0) = v1) | q(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | q(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & q(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1) | p(v0) = 0) & ! [v0] : ( ~ (q(v0) = 0) | p(v0) = 0) & ? [v0] : ? [v1] : p(v0) = v1 & ? [v0] : ? [v1] : q(v0) = v1 % 3.08/1.63 | % 3.08/1.63 | Applying alpha-rule on (1) yields: % 3.08/1.63 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 3.08/1.63 | (3) ? [v0] : ? [v1] : q(v0) = v1 % 3.08/1.63 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1) | p(v0) = 0) % 3.08/1.63 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | q(v0) = 0) % 3.08/1.63 | (6) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (q(v0) = v1)) % 3.08/1.63 | (7) p(all_0_2_2) = all_0_0_0 % 3.43/1.63 | (8) ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | ~ (p(v0) = v1) | q(v0) = 0) % 3.43/1.63 | (9) ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | v1 = 0 | ~ (q(v0) = v1)) % 3.43/1.63 | (10) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (p(v0) = v1)) % 3.43/1.63 | (11) p(all_0_3_3) = all_0_1_1 % 3.43/1.63 | (12) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (q(v0) = v1) | p(v0) = 0) % 3.43/1.63 | (13) ? [v0] : ? [v1] : p(v0) = v1 % 3.43/1.63 | (14) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (p(v0) = v1)) % 3.43/1.63 | (15) ! [v0] : ( ~ (q(v0) = 0) | p(v0) = 0) % 3.43/1.63 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & q(v0) = v2)) % 3.43/1.63 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) % 3.43/1.63 | % 3.43/1.63 | Instantiating (3) with all_3_0_4, all_3_1_5 yields: % 3.43/1.63 | (18) q(all_3_1_5) = all_3_0_4 % 3.43/1.63 | % 3.43/1.63 | Instantiating formula (10) with 0, all_0_3_3 yields: % 3.43/1.63 | (19) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (p(all_0_3_3) = 0) % 3.43/1.63 | % 3.43/1.63 | Instantiating formula (9) with all_3_0_4, all_3_1_5 and discharging atoms q(all_3_1_5) = all_3_0_4, yields: % 3.43/1.63 | (20) ~ (all_0_1_1 = 0) | all_3_0_4 = 0 % 3.43/1.64 | % 3.43/1.64 | Instantiating formula (8) with all_0_0_0, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_0_0, yields: % 3.43/1.64 | (21) ~ (all_0_1_1 = 0) | q(all_0_2_2) = 0 % 3.43/1.64 | % 3.43/1.64 | Instantiating formula (16) with all_0_0_0, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_0_0, yields: % 3.43/1.64 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & q(all_0_2_2) = v0) % 3.43/1.64 | % 3.43/1.64 | Instantiating formula (8) with 0, all_0_3_3 yields: % 3.43/1.64 | (23) ~ (all_0_1_1 = 0) | ~ (p(all_0_3_3) = 0) | q(all_0_3_3) = 0 % 3.43/1.64 | % 3.43/1.64 | Instantiating formula (5) with all_0_1_1, all_0_3_3 and discharging atoms p(all_0_3_3) = all_0_1_1, yields: % 3.43/1.64 | (24) all_0_1_1 = 0 | q(all_0_3_3) = 0 % 3.43/1.64 | % 3.43/1.64 | Instantiating formula (16) with all_0_1_1, all_0_3_3 and discharging atoms p(all_0_3_3) = all_0_1_1, yields: % 3.43/1.64 | (25) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & q(all_0_3_3) = v0) % 3.43/1.64 | % 3.43/1.64 +-Applying beta-rule and splitting (24), into two cases. % 3.43/1.64 |-Branch one: % 3.43/1.64 | (26) q(all_0_3_3) = 0 % 3.43/1.64 | % 3.43/1.64 +-Applying beta-rule and splitting (25), into two cases. % 3.43/1.64 |-Branch one: % 3.43/1.64 | (27) all_0_1_1 = 0 % 3.43/1.64 | % 3.43/1.64 | From (27) and (11) follows: % 3.43/1.64 | (28) p(all_0_3_3) = 0 % 3.43/1.64 | % 3.43/1.64 +-Applying beta-rule and splitting (19), into two cases. % 3.43/1.64 |-Branch one: % 3.43/1.64 | (29) ~ (p(all_0_3_3) = 0) % 3.43/1.64 | % 3.43/1.64 | Using (28) and (29) yields: % 3.43/1.64 | (30) $false % 3.43/1.64 | % 3.43/1.64 |-The branch is then unsatisfiable % 3.43/1.64 |-Branch two: % 3.43/1.64 | (28) p(all_0_3_3) = 0 % 3.43/1.64 | (32) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) % 3.43/1.64 | % 3.43/1.64 +-Applying beta-rule and splitting (32), into two cases. % 3.43/1.64 |-Branch one: % 3.43/1.64 | (33) ~ (all_0_0_0 = 0) % 3.43/1.64 | % 3.43/1.64 +-Applying beta-rule and splitting (21), into two cases. % 3.43/1.64 |-Branch one: % 3.43/1.64 | (34) q(all_0_2_2) = 0 % 3.43/1.64 | % 3.43/1.64 +-Applying beta-rule and splitting (22), into two cases. % 3.43/1.64 |-Branch one: % 3.43/1.64 | (35) all_0_0_0 = 0 % 3.43/1.64 | % 3.43/1.64 | Equations (35) can reduce 33 to: % 3.43/1.64 | (36) $false % 3.43/1.64 | % 3.43/1.64 |-The branch is then unsatisfiable % 3.43/1.64 |-Branch two: % 3.43/1.64 | (33) ~ (all_0_0_0 = 0) % 3.43/1.64 | (38) ? [v0] : ( ~ (v0 = 0) & q(all_0_2_2) = v0) % 3.43/1.64 | % 3.43/1.64 | Instantiating (38) with all_45_0_8 yields: % 3.43/1.64 | (39) ~ (all_45_0_8 = 0) & q(all_0_2_2) = all_45_0_8 % 3.43/1.64 | % 3.43/1.64 | Applying alpha-rule on (39) yields: % 3.43/1.64 | (40) ~ (all_45_0_8 = 0) % 3.43/1.64 | (41) q(all_0_2_2) = all_45_0_8 % 3.43/1.64 | % 3.43/1.64 | Instantiating formula (17) with all_0_2_2, 0, all_45_0_8 and discharging atoms q(all_0_2_2) = all_45_0_8, q(all_0_2_2) = 0, yields: % 3.43/1.64 | (42) all_45_0_8 = 0 % 3.43/1.64 | % 3.43/1.64 | Equations (42) can reduce 40 to: % 3.43/1.64 | (36) $false % 3.43/1.64 | % 3.43/1.64 |-The branch is then unsatisfiable % 3.43/1.64 |-Branch two: % 3.43/1.64 | (44) ~ (q(all_0_2_2) = 0) % 3.43/1.64 | (45) ~ (all_0_1_1 = 0) % 3.43/1.64 | % 3.43/1.64 | Equations (27) can reduce 45 to: % 3.43/1.64 | (36) $false % 3.43/1.64 | % 3.43/1.64 |-The branch is then unsatisfiable % 3.43/1.64 |-Branch two: % 3.43/1.64 | (35) all_0_0_0 = 0 % 3.43/1.64 | (45) ~ (all_0_1_1 = 0) % 3.43/1.64 | % 3.43/1.64 | Equations (27) can reduce 45 to: % 3.43/1.64 | (36) $false % 3.43/1.64 | % 3.43/1.64 |-The branch is then unsatisfiable % 3.43/1.64 |-Branch two: % 3.43/1.64 | (45) ~ (all_0_1_1 = 0) % 3.43/1.65 | (51) ? [v0] : ( ~ (v0 = 0) & q(all_0_3_3) = v0) % 3.43/1.65 | % 3.43/1.65 | Instantiating (51) with all_25_0_9 yields: % 3.43/1.65 | (52) ~ (all_25_0_9 = 0) & q(all_0_3_3) = all_25_0_9 % 3.43/1.65 | % 3.43/1.65 | Applying alpha-rule on (52) yields: % 3.43/1.65 | (53) ~ (all_25_0_9 = 0) % 3.43/1.65 | (54) q(all_0_3_3) = all_25_0_9 % 3.43/1.65 | % 3.43/1.65 | Instantiating formula (17) with all_0_3_3, 0, all_25_0_9 and discharging atoms q(all_0_3_3) = all_25_0_9, q(all_0_3_3) = 0, yields: % 3.43/1.65 | (55) all_25_0_9 = 0 % 3.43/1.65 | % 3.43/1.65 | Equations (55) can reduce 53 to: % 3.43/1.65 | (36) $false % 3.43/1.65 | % 3.43/1.65 |-The branch is then unsatisfiable % 3.43/1.65 |-Branch two: % 3.43/1.65 | (57) ~ (q(all_0_3_3) = 0) % 3.43/1.65 | (27) all_0_1_1 = 0 % 3.43/1.65 | % 3.43/1.65 | From (27) and (11) follows: % 3.43/1.65 | (28) p(all_0_3_3) = 0 % 3.43/1.65 | % 3.43/1.65 +-Applying beta-rule and splitting (20), into two cases. % 3.43/1.65 |-Branch one: % 3.43/1.65 | (45) ~ (all_0_1_1 = 0) % 3.43/1.65 | % 3.43/1.65 | Equations (27) can reduce 45 to: % 3.43/1.65 | (36) $false % 3.43/1.65 | % 3.43/1.65 |-The branch is then unsatisfiable % 3.43/1.65 |-Branch two: % 3.43/1.65 | (27) all_0_1_1 = 0 % 3.43/1.65 | (63) all_3_0_4 = 0 % 3.43/1.65 | % 3.43/1.65 +-Applying beta-rule and splitting (19), into two cases. % 3.43/1.65 |-Branch one: % 3.43/1.65 | (29) ~ (p(all_0_3_3) = 0) % 3.43/1.65 | % 3.43/1.65 | Using (28) and (29) yields: % 3.43/1.65 | (30) $false % 3.43/1.65 | % 3.43/1.65 |-The branch is then unsatisfiable % 3.43/1.65 |-Branch two: % 3.43/1.65 | (28) p(all_0_3_3) = 0 % 3.43/1.65 | (32) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) % 3.43/1.65 | % 3.43/1.65 +-Applying beta-rule and splitting (23), into two cases. % 3.43/1.65 |-Branch one: % 3.43/1.65 | (29) ~ (p(all_0_3_3) = 0) % 3.43/1.65 | % 3.43/1.65 | Using (28) and (29) yields: % 3.43/1.65 | (30) $false % 3.43/1.65 | % 3.43/1.65 |-The branch is then unsatisfiable % 3.43/1.65 |-Branch two: % 3.43/1.65 | (28) p(all_0_3_3) = 0 % 3.43/1.65 | (71) ~ (all_0_1_1 = 0) | q(all_0_3_3) = 0 % 3.43/1.65 | % 3.43/1.65 +-Applying beta-rule and splitting (71), into two cases. % 3.43/1.65 |-Branch one: % 3.43/1.65 | (26) q(all_0_3_3) = 0 % 3.43/1.65 | % 3.43/1.65 | Using (26) and (57) yields: % 3.43/1.65 | (30) $false % 3.43/1.65 | % 3.43/1.65 |-The branch is then unsatisfiable % 3.43/1.65 |-Branch two: % 3.43/1.65 | (57) ~ (q(all_0_3_3) = 0) % 3.43/1.65 | (45) ~ (all_0_1_1 = 0) % 3.43/1.65 | % 3.43/1.65 | Equations (27) can reduce 45 to: % 3.43/1.65 | (36) $false % 3.43/1.65 | % 3.43/1.65 |-The branch is then unsatisfiable % 3.43/1.65 % SZS output end Proof for theBenchmark % 3.43/1.65 % 3.43/1.65 1035ms %------------------------------------------------------------------------------