%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN061+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 04:59:33 EDT 2022 % Result : Theorem 2.40s 1.22s % Output : Proof 3.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : SYN061+1 : TPTP v8.1.0. Released v2.0.0. % 0.06/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.31 % Computer : n012.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 600 % 0.11/0.31 % DateTime : Mon Jul 11 19:10:57 EDT 2022 % 0.11/0.31 % CPUTime : % 0.16/0.51 ____ _ % 0.16/0.51 ___ / __ \_____(_)___ ________ __________ % 0.16/0.51 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.16/0.51 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.16/0.51 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.16/0.51 % 0.16/0.51 A Theorem Prover for First-Order Logic % 0.16/0.51 (ePrincess v.1.0) % 0.16/0.51 % 0.16/0.51 (c) Philipp Rümmer, 2009-2015 % 0.16/0.51 (c) Peter Backeman, 2014-2015 % 0.16/0.51 (contributions by Angelo Brillout, Peter Baumgartner) % 0.16/0.51 Free software under GNU Lesser General Public License (LGPL). % 0.16/0.51 Bug reports to peter@backeman.se % 0.16/0.51 % 0.16/0.51 For more information, visit http://user.uu.se/~petba168/breu/ % 0.16/0.51 % 0.16/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.54/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.22/0.84 Prover 0: Preprocessing ... % 1.26/0.89 Prover 0: Warning: ignoring some quantifiers % 1.26/0.91 Prover 0: Constructing countermodel ... % 1.62/1.00 Prover 0: gave up % 1.62/1.00 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.62/1.01 Prover 1: Preprocessing ... % 1.89/1.08 Prover 1: Constructing countermodel ... % 1.99/1.10 Prover 1: gave up % 1.99/1.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.99/1.11 Prover 2: Preprocessing ... % 2.25/1.17 Prover 2: Warning: ignoring some quantifiers % 2.25/1.17 Prover 2: Constructing countermodel ... % 2.40/1.22 Prover 2: proved (122ms) % 2.40/1.22 % 2.40/1.22 No countermodel exists, formula is valid % 2.40/1.22 % SZS status Theorem for theBenchmark % 2.40/1.23 % 2.40/1.23 Generating proof ... Warning: ignoring some quantifiers % 2.89/1.40 found it (size 15) % 2.89/1.40 % 2.89/1.40 % SZS output start Proof for theBenchmark % 2.89/1.40 Assumed formulas after preprocessing and simplification: % 2.89/1.40 | (0) ? [v0] : (big_i(v0) = 0 & big_f(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_j(v3) = v2) | ~ (big_j(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_i(v3) = v2) | ~ (big_i(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_g(v3) = v2) | ~ (big_g(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_f(v3) = v2) | ~ (big_f(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_h(v3) = v2) | ~ (big_h(v3) = v1)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (big_j(v1) = v2) | big_h(v1) = 0) & ! [v1] : ! [v2] : (v2 = 0 | ~ (big_h(v1) = v2) | big_j(v1) = 0) & ! [v1] : ! [v2] : ( ~ (big_g(v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ~ (v2 = 0) & big_h(v1) = v3) | ( ~ (v3 = 0) & big_f(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (big_h(v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ~ (v2 = 0) & big_g(v1) = v3) | ( ~ (v3 = 0) & big_f(v1) = v3))) & ! [v1] : ( ~ (big_j(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_i(v1) = v2)) & ! [v1] : ( ~ (big_i(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_j(v1) = v2)) & ! [v1] : ( ~ (big_f(v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & big_g(v1) = v2 & big_h(v1) = v3)) & ? [v1] : ? [v2] : big_j(v1) = v2 & ? [v1] : ? [v2] : big_i(v1) = v2 & ? [v1] : ? [v2] : big_g(v1) = v2 & ? [v1] : ? [v2] : big_f(v1) = v2 & ? [v1] : ? [v2] : big_h(v1) = v2) % 2.89/1.43 | Instantiating (0) with all_0_0_0 yields: % 2.89/1.43 | (1) big_i(all_0_0_0) = 0 & big_f(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(v0) = v1) | big_h(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_h(v0) = v1) | big_j(v0) = 0) & ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_h(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (big_h(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ( ~ (big_j(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_i(v0) = v1)) & ! [v0] : ( ~ (big_i(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_j(v0) = v1)) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = v2)) & ? [v0] : ? [v1] : big_j(v0) = v1 & ? [v0] : ? [v1] : big_i(v0) = v1 & ? [v0] : ? [v1] : big_g(v0) = v1 & ? [v0] : ? [v1] : big_f(v0) = v1 & ? [v0] : ? [v1] : big_h(v0) = v1 % 3.13/1.44 | % 3.13/1.44 | Applying alpha-rule on (1) yields: % 3.13/1.44 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) % 3.13/1.44 | (3) big_i(all_0_0_0) = 0 % 3.13/1.44 | (4) ? [v0] : ? [v1] : big_j(v0) = v1 % 3.13/1.44 | (5) ! [v0] : ( ~ (big_i(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_j(v0) = v1)) % 3.13/1.44 | (6) ! [v0] : ( ~ (big_j(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_i(v0) = v1)) % 3.13/1.44 | (7) ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = v2)) % 3.13/1.44 | (8) ? [v0] : ? [v1] : big_g(v0) = v1 % 3.13/1.44 | (9) ? [v0] : ? [v1] : big_h(v0) = v1 % 3.13/1.44 | (10) ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_h(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) % 3.13/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0)) % 3.13/1.44 | (12) ? [v0] : ? [v1] : big_f(v0) = v1 % 3.13/1.44 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0)) % 3.13/1.44 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_h(v0) = v1) | big_j(v0) = 0) % 3.13/1.44 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(v0) = v1) | big_h(v0) = 0) % 3.13/1.44 | (16) ! [v0] : ! [v1] : ( ~ (big_h(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) % 3.13/1.44 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) % 3.13/1.44 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) % 3.13/1.44 | (19) ? [v0] : ? [v1] : big_i(v0) = v1 % 3.13/1.44 | (20) big_f(all_0_0_0) = 0 % 3.13/1.44 | % 3.13/1.44 | Instantiating formula (5) with all_0_0_0 and discharging atoms big_i(all_0_0_0) = 0, yields: % 3.13/1.45 | (21) ? [v0] : ( ~ (v0 = 0) & big_j(all_0_0_0) = v0) % 3.13/1.45 | % 3.13/1.45 | Instantiating formula (7) with all_0_0_0 and discharging atoms big_f(all_0_0_0) = 0, yields: % 3.13/1.45 | (22) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & big_g(all_0_0_0) = v0 & big_h(all_0_0_0) = v1) % 3.13/1.45 | % 3.13/1.45 | Instantiating (22) with all_18_0_11, all_18_1_12 yields: % 3.13/1.45 | (23) ~ (all_18_0_11 = 0) & ~ (all_18_1_12 = 0) & big_g(all_0_0_0) = all_18_1_12 & big_h(all_0_0_0) = all_18_0_11 % 3.13/1.45 | % 3.13/1.45 | Applying alpha-rule on (23) yields: % 3.13/1.45 | (24) ~ (all_18_0_11 = 0) % 3.13/1.45 | (25) ~ (all_18_1_12 = 0) % 3.13/1.45 | (26) big_g(all_0_0_0) = all_18_1_12 % 3.13/1.45 | (27) big_h(all_0_0_0) = all_18_0_11 % 3.13/1.45 | % 3.13/1.45 | Instantiating (21) with all_20_0_13 yields: % 3.13/1.45 | (28) ~ (all_20_0_13 = 0) & big_j(all_0_0_0) = all_20_0_13 % 3.13/1.45 | % 3.13/1.45 | Applying alpha-rule on (28) yields: % 3.13/1.45 | (29) ~ (all_20_0_13 = 0) % 3.13/1.45 | (30) big_j(all_0_0_0) = all_20_0_13 % 3.13/1.45 | % 3.13/1.45 | Instantiating formula (15) with all_20_0_13, all_0_0_0 and discharging atoms big_j(all_0_0_0) = all_20_0_13, yields: % 3.13/1.45 | (31) all_20_0_13 = 0 | big_h(all_0_0_0) = 0 % 3.13/1.45 | % 3.13/1.45 +-Applying beta-rule and splitting (31), into two cases. % 3.13/1.45 |-Branch one: % 3.13/1.45 | (32) big_h(all_0_0_0) = 0 % 3.13/1.45 | % 3.13/1.45 | Instantiating formula (11) with all_0_0_0, 0, all_18_0_11 and discharging atoms big_h(all_0_0_0) = all_18_0_11, big_h(all_0_0_0) = 0, yields: % 3.13/1.45 | (33) all_18_0_11 = 0 % 3.13/1.45 | % 3.13/1.45 | Equations (33) can reduce 24 to: % 3.13/1.45 | (34) $false % 3.13/1.45 | % 3.13/1.45 |-The branch is then unsatisfiable % 3.13/1.45 |-Branch two: % 3.13/1.45 | (35) ~ (big_h(all_0_0_0) = 0) % 3.13/1.45 | (36) all_20_0_13 = 0 % 3.13/1.45 | % 3.13/1.45 | Equations (36) can reduce 29 to: % 3.13/1.45 | (34) $false % 3.13/1.45 | % 3.13/1.45 |-The branch is then unsatisfiable % 3.13/1.45 % SZS output end Proof for theBenchmark % 3.13/1.45 % 3.13/1.45 912ms %------------------------------------------------------------------------------