%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN321+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 05:01:20 EDT 2022 % Result : Theorem 2.69s 1.34s % Output : Proof 3.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYN321+1 : TPTP v8.1.0. Released v2.0.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n026.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 : Tue Jul 12 02:43:57 EDT 2022 % 0.13/0.33 % CPUTime : % 0.59/0.57 ____ _ % 0.59/0.57 ___ / __ \_____(_)___ ________ __________ % 0.59/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.57 % 0.59/0.57 A Theorem Prover for First-Order Logic % 0.59/0.57 (ePrincess v.1.0) % 0.59/0.57 % 0.59/0.57 (c) Philipp Rümmer, 2009-2015 % 0.59/0.57 (c) Peter Backeman, 2014-2015 % 0.59/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.57 Bug reports to peter@backeman.se % 0.59/0.57 % 0.59/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.57 % 0.59/0.57 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 % 1.24/0.83 Prover 0: Preprocessing ... % 1.32/0.88 Prover 0: Warning: ignoring some quantifiers % 1.32/0.90 Prover 0: Constructing countermodel ... % 1.56/1.01 Prover 0: gave up % 1.56/1.01 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.81/1.04 Prover 1: Preprocessing ... % 1.95/1.09 Prover 1: Constructing countermodel ... % 1.95/1.10 Prover 1: gave up % 1.95/1.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.95/1.11 Prover 2: Preprocessing ... % 1.95/1.15 Prover 2: Warning: ignoring some quantifiers % 2.17/1.15 Prover 2: Constructing countermodel ... % 2.17/1.17 Prover 2: gave up % 2.17/1.18 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.17/1.18 Prover 3: Preprocessing ... % 2.28/1.19 Prover 3: Warning: ignoring some quantifiers % 2.28/1.19 Prover 3: Constructing countermodel ... % 2.28/1.22 Prover 3: gave up % 2.28/1.22 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 2.28/1.23 Prover 4: Preprocessing ... % 2.49/1.26 Prover 4: Warning: ignoring some quantifiers % 2.49/1.26 Prover 4: Constructing countermodel ... % 2.69/1.34 Prover 4: proved (118ms) % 2.69/1.34 % 2.69/1.34 No countermodel exists, formula is valid % 2.69/1.34 % SZS status Theorem for theBenchmark % 2.69/1.34 % 2.69/1.34 Generating proof ... Warning: ignoring some quantifiers % 3.07/1.48 found it (size 19) % 3.07/1.48 % 3.07/1.48 % SZS output start Proof for theBenchmark % 3.07/1.48 Assumed formulas after preprocessing and simplification: % 3.07/1.48 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v2 = 0 | ~ (big_g(v0, v3) = v4) | ~ (big_f(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (big_g(v0, v1) = v2) | ~ (big_f(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_g(v3, v2) = v1) | ~ (big_g(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & big_g(v1, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (big_f(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & big_g(v0, v2) = v3)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & big_g(v0, v2) = 0) | (v3 = 0 & big_f(v0, v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & big_g(v0, v1) = 0) | ( ~ (v3 = 0) & big_f(v0, v2) = v3)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v3 = 0) & big_g(v0, v2) = v3) | ( ~ (v2 = 0) & big_f(v0, v1) = v2)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (big_g(v1, v1) = v2 & big_f(v1, v0) = v3 & ( ~ (v2 = 0) | v3 = 0)) % 3.16/1.51 | Applying alpha-rule on (0) yields: % 3.16/1.51 | (1) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & big_g(v1, v1) = v3)) % 3.16/1.52 | (2) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v3 = 0) & big_g(v0, v2) = v3) | ( ~ (v2 = 0) & big_f(v0, v1) = v2)) % 3.16/1.52 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (big_g(v0, v1) = v2) | ~ (big_f(v0, v3) = 0)) % 3.16/1.52 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_g(v3, v2) = v1) | ~ (big_g(v3, v2) = v0)) % 3.16/1.52 | (5) ! [v0] : ! [v1] : ( ~ (big_f(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & big_g(v0, v2) = v3)) % 3.16/1.52 | (6) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & big_g(v0, v1) = 0) | ( ~ (v3 = 0) & big_f(v0, v2) = v3)) % 3.16/1.52 | (7) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & big_g(v0, v2) = 0) | (v3 = 0 & big_f(v0, v1) = 0)) % 3.16/1.52 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) % 3.16/1.52 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v2 = 0 | ~ (big_g(v0, v3) = v4) | ~ (big_f(v0, v1) = v2)) % 3.16/1.52 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (big_g(v1, v1) = v2 & big_f(v1, v0) = v3 & ( ~ (v2 = 0) | v3 = 0)) % 3.16/1.52 | % 3.16/1.52 | Instantiating (10) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3 yields: % 3.16/1.52 | (11) big_g(all_1_2_2, all_1_2_2) = all_1_1_1 & big_f(all_1_2_2, all_1_3_3) = all_1_0_0 & ( ~ (all_1_1_1 = 0) | all_1_0_0 = 0) % 3.16/1.52 | % 3.16/1.52 | Applying alpha-rule on (11) yields: % 3.16/1.52 | (12) big_g(all_1_2_2, all_1_2_2) = all_1_1_1 % 3.16/1.52 | (13) big_f(all_1_2_2, all_1_3_3) = all_1_0_0 % 3.16/1.52 | (14) ~ (all_1_1_1 = 0) | all_1_0_0 = 0 % 3.16/1.52 | % 3.16/1.52 | Instantiating formula (9) with all_1_1_1, all_1_2_2, all_1_0_0, all_1_3_3, all_1_2_2 and discharging atoms big_g(all_1_2_2, all_1_2_2) = all_1_1_1, big_f(all_1_2_2, all_1_3_3) = all_1_0_0, yields: % 3.16/1.52 | (15) all_1_0_0 = 0 | all_1_1_1 = 0 % 3.16/1.52 | % 3.16/1.52 +-Applying beta-rule and splitting (14), into two cases. % 3.16/1.52 |-Branch one: % 3.16/1.52 | (16) ~ (all_1_1_1 = 0) % 3.16/1.52 | % 3.16/1.52 +-Applying beta-rule and splitting (15), into two cases. % 3.16/1.52 |-Branch one: % 3.16/1.52 | (17) all_1_0_0 = 0 % 3.16/1.52 | % 3.16/1.53 | From (17) and (13) follows: % 3.16/1.53 | (18) big_f(all_1_2_2, all_1_3_3) = 0 % 3.16/1.53 | % 3.16/1.53 | Instantiating formula (3) with all_1_3_3, all_1_1_1, all_1_2_2, all_1_2_2 and discharging atoms big_g(all_1_2_2, all_1_2_2) = all_1_1_1, big_f(all_1_2_2, all_1_3_3) = 0, yields: % 3.16/1.53 | (19) all_1_1_1 = 0 % 3.16/1.53 | % 3.16/1.53 | Equations (19) can reduce 16 to: % 3.16/1.53 | (20) $false % 3.16/1.53 | % 3.16/1.53 |-The branch is then unsatisfiable % 3.16/1.53 |-Branch two: % 3.16/1.53 | (21) ~ (all_1_0_0 = 0) % 3.16/1.53 | (19) all_1_1_1 = 0 % 3.16/1.53 | % 3.16/1.53 | Equations (19) can reduce 16 to: % 3.16/1.53 | (20) $false % 3.16/1.53 | % 3.16/1.53 |-The branch is then unsatisfiable % 3.16/1.53 |-Branch two: % 3.16/1.53 | (19) all_1_1_1 = 0 % 3.16/1.53 | (17) all_1_0_0 = 0 % 3.16/1.53 | % 3.16/1.53 | From (17) and (13) follows: % 3.16/1.53 | (18) big_f(all_1_2_2, all_1_3_3) = 0 % 3.16/1.53 | % 3.16/1.53 | Instantiating formula (5) with all_1_3_3, all_1_2_2 and discharging atoms big_f(all_1_2_2, all_1_3_3) = 0, yields: % 3.16/1.53 | (27) ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_g(all_1_2_2, v0) = v1) % 3.16/1.53 | % 3.16/1.53 | Instantiating (27) with all_39_0_16, all_39_1_17 yields: % 3.16/1.53 | (28) ~ (all_39_0_16 = 0) & big_g(all_1_2_2, all_39_1_17) = all_39_0_16 % 3.16/1.53 | % 3.16/1.53 | Applying alpha-rule on (28) yields: % 3.16/1.53 | (29) ~ (all_39_0_16 = 0) % 3.16/1.53 | (30) big_g(all_1_2_2, all_39_1_17) = all_39_0_16 % 3.16/1.53 | % 3.16/1.53 | Instantiating formula (3) with all_1_3_3, all_39_0_16, all_39_1_17, all_1_2_2 and discharging atoms big_g(all_1_2_2, all_39_1_17) = all_39_0_16, big_f(all_1_2_2, all_1_3_3) = 0, yields: % 3.16/1.53 | (31) all_39_0_16 = 0 % 3.16/1.53 | % 3.16/1.53 | Equations (31) can reduce 29 to: % 3.16/1.53 | (20) $false % 3.16/1.53 | % 3.16/1.53 |-The branch is then unsatisfiable % 3.16/1.53 % SZS output end Proof for theBenchmark % 3.16/1.53 % 3.16/1.53 951ms %------------------------------------------------------------------------------