%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN331+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 05:01:27 EDT 2022 % Result : Theorem 3.53s 1.57s % Output : Proof 10.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN331+1 : TPTP v8.1.0. Released v2.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 20:04:44 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.59 ____ _ % 0.48/0.59 ___ / __ \_____(_)___ ________ __________ % 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic % 0.48/0.59 (ePrincess v.1.0) % 0.48/0.59 % 0.48/0.59 (c) Philipp Rümmer, 2009-2015 % 0.48/0.59 (c) Peter Backeman, 2014-2015 % 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.59 Bug reports to peter@backeman.se % 0.48/0.59 % 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.59 % 0.48/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.20/0.90 Prover 0: Preprocessing ... % 1.39/0.94 Prover 0: Warning: ignoring some quantifiers % 1.39/0.95 Prover 0: Constructing countermodel ... % 1.50/1.04 Prover 0: gave up % 1.50/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.71/1.06 Prover 1: Preprocessing ... % 1.96/1.12 Prover 1: Constructing countermodel ... % 1.96/1.12 Prover 1: gave up % 1.96/1.13 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.96/1.14 Prover 2: Preprocessing ... % 2.12/1.18 Prover 2: Warning: ignoring some quantifiers % 2.12/1.18 Prover 2: Constructing countermodel ... % 2.12/1.20 Prover 2: gave up % 2.12/1.20 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.12/1.21 Prover 3: Preprocessing ... % 2.12/1.22 Prover 3: Warning: ignoring some quantifiers % 2.12/1.22 Prover 3: Constructing countermodel ... % 2.43/1.24 Prover 3: gave up % 2.43/1.24 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 2.43/1.24 Prover 4: Preprocessing ... % 2.58/1.28 Prover 4: Warning: ignoring some quantifiers % 2.58/1.29 Prover 4: Constructing countermodel ... % 3.53/1.57 Prover 4: proved (330ms) % 3.53/1.57 % 3.53/1.57 No countermodel exists, formula is valid % 3.53/1.57 % SZS status Theorem for theBenchmark % 3.53/1.57 % 3.53/1.57 Generating proof ... Warning: ignoring some quantifiers % 10.40/3.19 found it (size 25) % 10.40/3.19 % 10.40/3.19 % SZS output start Proof for theBenchmark % 10.40/3.19 Assumed formulas after preprocessing and simplification: % 10.40/3.19 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v0, v4) = 0 & big_f(v0, v1) = v3 & ( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0) & (v5 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & big_f(v0, v1) = v2 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0)) % 10.54/3.22 | Applying alpha-rule on (0) yields: % 10.54/3.22 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) % 10.54/3.22 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v0, v4) = 0 & big_f(v0, v1) = v3 & ( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0) & (v5 = 0 | v2 = 0))) % 10.54/3.22 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0))) % 10.54/3.22 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & big_f(v0, v1) = v2 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0)) % 10.54/3.22 | % 10.54/3.22 | 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, all_1_7_7 yields: % 10.54/3.22 | (5) ~ (all_1_0_0 = 0) & ~ (all_1_1_1 = 0) & big_f(all_1_3_3, all_1_3_3) = all_1_2_2 & big_f(all_1_3_3, all_1_6_6) = all_1_0_0 & big_f(all_1_3_3, all_1_7_7) = all_1_1_1 & big_f(all_1_6_6, all_1_3_3) = 0 & big_f(all_1_6_6, all_1_7_7) = all_1_4_4 & big_f(all_1_7_7, all_1_3_3) = 0 & big_f(all_1_7_7, all_1_6_6) = all_1_5_5 & ( ~ (all_1_2_2 = 0) | all_1_5_5 = 0) & ( ~ (all_1_5_5 = 0) | all_1_2_2 = 0) & (all_1_2_2 = 0 | all_1_4_4 = 0) % 10.54/3.23 | % 10.54/3.23 | Applying alpha-rule on (5) yields: % 10.54/3.23 | (6) big_f(all_1_3_3, all_1_3_3) = all_1_2_2 % 10.54/3.23 | (7) big_f(all_1_3_3, all_1_6_6) = all_1_0_0 % 10.54/3.23 | (8) ~ (all_1_5_5 = 0) | all_1_2_2 = 0 % 10.54/3.23 | (9) ~ (all_1_1_1 = 0) % 10.54/3.23 | (10) big_f(all_1_6_6, all_1_3_3) = 0 % 10.54/3.23 | (11) ~ (all_1_0_0 = 0) % 10.54/3.23 | (12) big_f(all_1_7_7, all_1_3_3) = 0 % 10.54/3.23 | (13) big_f(all_1_6_6, all_1_7_7) = all_1_4_4 % 10.54/3.23 | (14) all_1_2_2 = 0 | all_1_4_4 = 0 % 10.54/3.23 | (15) ~ (all_1_2_2 = 0) | all_1_5_5 = 0 % 10.54/3.23 | (16) big_f(all_1_3_3, all_1_7_7) = all_1_1_1 % 10.54/3.23 | (17) big_f(all_1_7_7, all_1_6_6) = all_1_5_5 % 10.54/3.23 | % 10.54/3.23 | Instantiating formula (3) with all_1_0_0, all_1_6_6, all_1_3_3 and discharging atoms big_f(all_1_3_3, all_1_6_6) = all_1_0_0, yields: % 10.54/3.23 | (18) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & big_f(v1, v1) = v2 & big_f(v1, all_1_3_3) = v3 & big_f(v1, all_1_6_6) = v4 & big_f(all_1_3_3, v1) = 0 & big_f(all_1_6_6, v1) = 0 & big_f(all_1_6_6, all_1_3_3) = v0 & ( ~ (v2 = 0) | all_1_0_0 = 0) & ( ~ (all_1_0_0 = 0) | v2 = 0) & (v2 = 0 | v0 = 0)) % 10.54/3.23 | % 10.54/3.23 | Instantiating (18) with all_14_0_22, all_14_1_23, all_14_2_24, all_14_3_25, all_14_4_26 yields: % 10.54/3.23 | (19) ~ (all_14_0_22 = 0) & ~ (all_14_1_23 = 0) & big_f(all_14_3_25, all_14_3_25) = all_14_2_24 & big_f(all_14_3_25, all_1_3_3) = all_14_1_23 & big_f(all_14_3_25, all_1_6_6) = all_14_0_22 & big_f(all_1_3_3, all_14_3_25) = 0 & big_f(all_1_6_6, all_14_3_25) = 0 & big_f(all_1_6_6, all_1_3_3) = all_14_4_26 & ( ~ (all_14_2_24 = 0) | all_1_0_0 = 0) & ( ~ (all_1_0_0 = 0) | all_14_2_24 = 0) & (all_14_2_24 = 0 | all_14_4_26 = 0) % 10.54/3.23 | % 10.54/3.23 | Applying alpha-rule on (19) yields: % 10.54/3.23 | (20) big_f(all_14_3_25, all_14_3_25) = all_14_2_24 % 10.54/3.23 | (21) ~ (all_14_2_24 = 0) | all_1_0_0 = 0 % 10.54/3.23 | (22) ~ (all_14_1_23 = 0) % 10.54/3.23 | (23) big_f(all_1_6_6, all_1_3_3) = all_14_4_26 % 10.54/3.23 | (24) big_f(all_14_3_25, all_1_6_6) = all_14_0_22 % 10.54/3.23 | (25) big_f(all_14_3_25, all_1_3_3) = all_14_1_23 % 10.54/3.23 | (26) big_f(all_1_6_6, all_14_3_25) = 0 % 10.54/3.23 | (27) all_14_2_24 = 0 | all_14_4_26 = 0 % 10.54/3.23 | (28) ~ (all_14_0_22 = 0) % 10.54/3.23 | (29) ~ (all_1_0_0 = 0) | all_14_2_24 = 0 % 10.54/3.23 | (30) big_f(all_1_3_3, all_14_3_25) = 0 % 10.54/3.23 | % 10.54/3.23 +-Applying beta-rule and splitting (21), into two cases. % 10.54/3.23 |-Branch one: % 10.54/3.23 | (31) ~ (all_14_2_24 = 0) % 10.54/3.23 | % 10.54/3.23 +-Applying beta-rule and splitting (27), into two cases. % 10.54/3.23 |-Branch one: % 10.54/3.23 | (32) all_14_2_24 = 0 % 10.54/3.23 | % 10.54/3.23 | Equations (32) can reduce 31 to: % 10.54/3.23 | (33) $false % 10.54/3.23 | % 10.54/3.23 |-The branch is then unsatisfiable % 10.54/3.23 |-Branch two: % 10.54/3.23 | (31) ~ (all_14_2_24 = 0) % 10.54/3.23 | (35) all_14_4_26 = 0 % 10.54/3.23 | % 10.54/3.23 | Instantiating formula (2) with all_14_2_24, all_14_3_25, all_14_3_25 and discharging atoms big_f(all_14_3_25, all_14_3_25) = all_14_2_24, yields: % 10.54/3.23 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & big_f(v1, v1) = v2 & big_f(v1, all_14_3_25) = v4 & big_f(v1, all_14_3_25) = v3 & big_f(all_14_3_25, v1) = 0 & big_f(all_14_3_25, all_14_3_25) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0) & (v2 = 0 | all_14_2_24 = 0)) % 10.54/3.23 | % 10.54/3.23 | Instantiating (36) with all_315_0_625, all_315_1_626, all_315_2_627, all_315_3_628, all_315_4_629 yields: % 10.54/3.23 | (37) ~ (all_315_0_625 = 0) & ~ (all_315_1_626 = 0) & big_f(all_315_3_628, all_315_3_628) = all_315_2_627 & big_f(all_315_3_628, all_14_3_25) = all_315_0_625 & big_f(all_315_3_628, all_14_3_25) = all_315_1_626 & big_f(all_14_3_25, all_315_3_628) = 0 & big_f(all_14_3_25, all_14_3_25) = all_315_4_629 & ( ~ (all_315_2_627 = 0) | all_315_4_629 = 0) & ( ~ (all_315_4_629 = 0) | all_315_2_627 = 0) & (all_315_2_627 = 0 | all_14_2_24 = 0) % 10.54/3.23 | % 10.54/3.23 | Applying alpha-rule on (37) yields: % 10.54/3.23 | (38) big_f(all_315_3_628, all_14_3_25) = all_315_1_626 % 10.54/3.23 | (39) ~ (all_315_1_626 = 0) % 10.54/3.23 | (40) ~ (all_315_0_625 = 0) % 10.54/3.23 | (41) big_f(all_14_3_25, all_14_3_25) = all_315_4_629 % 10.54/3.23 | (42) big_f(all_315_3_628, all_315_3_628) = all_315_2_627 % 10.54/3.23 | (43) ~ (all_315_4_629 = 0) | all_315_2_627 = 0 % 10.54/3.23 | (44) ~ (all_315_2_627 = 0) | all_315_4_629 = 0 % 10.54/3.23 | (45) big_f(all_315_3_628, all_14_3_25) = all_315_0_625 % 10.54/3.23 | (46) big_f(all_14_3_25, all_315_3_628) = 0 % 10.54/3.23 | (47) all_315_2_627 = 0 | all_14_2_24 = 0 % 10.54/3.23 | % 10.54/3.23 +-Applying beta-rule and splitting (47), into two cases. % 10.54/3.23 |-Branch one: % 10.54/3.23 | (48) all_315_2_627 = 0 % 10.54/3.23 | % 10.54/3.24 +-Applying beta-rule and splitting (44), into two cases. % 10.54/3.24 |-Branch one: % 10.54/3.24 | (49) ~ (all_315_2_627 = 0) % 10.54/3.24 | % 10.54/3.24 | Equations (48) can reduce 49 to: % 10.54/3.24 | (33) $false % 10.54/3.24 | % 10.54/3.24 |-The branch is then unsatisfiable % 10.54/3.24 |-Branch two: % 10.54/3.24 | (48) all_315_2_627 = 0 % 10.54/3.24 | (52) all_315_4_629 = 0 % 10.54/3.24 | % 10.54/3.24 | From (52) and (41) follows: % 10.54/3.24 | (53) big_f(all_14_3_25, all_14_3_25) = 0 % 10.54/3.24 | % 10.54/3.24 | Instantiating formula (1) with all_14_3_25, all_14_3_25, 0, all_14_2_24 and discharging atoms big_f(all_14_3_25, all_14_3_25) = all_14_2_24, big_f(all_14_3_25, all_14_3_25) = 0, yields: % 10.54/3.24 | (32) all_14_2_24 = 0 % 10.54/3.24 | % 10.54/3.24 | Equations (32) can reduce 31 to: % 10.54/3.24 | (33) $false % 10.54/3.24 | % 10.54/3.24 |-The branch is then unsatisfiable % 10.54/3.24 |-Branch two: % 10.54/3.24 | (49) ~ (all_315_2_627 = 0) % 10.54/3.24 | (32) all_14_2_24 = 0 % 10.54/3.24 | % 10.54/3.24 | Equations (32) can reduce 31 to: % 10.54/3.24 | (33) $false % 10.54/3.24 | % 10.54/3.24 |-The branch is then unsatisfiable % 10.54/3.24 |-Branch two: % 10.54/3.24 | (32) all_14_2_24 = 0 % 10.54/3.24 | (60) all_1_0_0 = 0 % 10.54/3.24 | % 10.54/3.24 | Equations (60) can reduce 11 to: % 10.54/3.24 | (33) $false % 10.54/3.24 | % 10.54/3.24 |-The branch is then unsatisfiable % 10.54/3.24 % SZS output end Proof for theBenchmark % 10.54/3.24 % 10.54/3.24 2636ms %------------------------------------------------------------------------------