%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN326+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 05:01:24 EDT 2022 % Result : Theorem 3.36s 1.52s % Output : Proof 9.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN326+1 : TPTP v8.1.0. Released v2.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.33 % Computer : n005.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 600 % 0.14/0.33 % DateTime : Tue Jul 12 08:49:07 EDT 2022 % 0.14/0.34 % CPUTime : % 0.52/0.58 ____ _ % 0.52/0.58 ___ / __ \_____(_)___ ________ __________ % 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.58 % 0.52/0.58 A Theorem Prover for First-Order Logic % 0.52/0.58 (ePrincess v.1.0) % 0.52/0.58 % 0.52/0.58 (c) Philipp Rümmer, 2009-2015 % 0.52/0.58 (c) Peter Backeman, 2014-2015 % 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.58 Bug reports to peter@backeman.se % 0.52/0.58 % 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.58 % 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.27/0.85 Prover 0: Preprocessing ... % 1.27/0.89 Prover 0: Warning: ignoring some quantifiers % 1.27/0.91 Prover 0: Constructing countermodel ... % 1.55/0.99 Prover 0: gave up % 1.55/1.00 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.55/1.01 Prover 1: Preprocessing ... % 1.88/1.07 Prover 1: Constructing countermodel ... % 1.88/1.08 Prover 1: gave up % 1.88/1.08 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.88/1.09 Prover 2: Preprocessing ... % 2.12/1.15 Prover 2: Warning: ignoring some quantifiers % 2.12/1.15 Prover 2: Constructing countermodel ... % 2.22/1.18 Prover 2: gave up % 2.22/1.18 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.22/1.18 Prover 3: Preprocessing ... % 2.22/1.19 Prover 3: Warning: ignoring some quantifiers % 2.22/1.19 Prover 3: Constructing countermodel ... % 2.22/1.20 Prover 3: gave up % 2.22/1.20 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 2.22/1.21 Prover 4: Preprocessing ... % 2.50/1.25 Prover 4: Warning: ignoring some quantifiers % 2.50/1.25 Prover 4: Constructing countermodel ... % 3.36/1.52 Prover 4: proved (318ms) % 3.36/1.52 % 3.36/1.52 No countermodel exists, formula is valid % 3.36/1.52 % SZS status Theorem for theBenchmark % 3.36/1.52 % 3.36/1.52 Generating proof ... Warning: ignoring some quantifiers % 8.72/2.85 found it (size 26) % 8.72/2.85 % 8.72/2.85 % SZS output start Proof for theBenchmark % 8.72/2.85 Assumed formulas after preprocessing and simplification: % 8.72/2.85 | (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] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_h(v5) = v9 & big_h(v0) = v2 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & big_f(v0, v0) = v3 & (v9 = 0 | (v8 = 0 & ~ (v1 = 0))) & (v3 = 0 | (v7 = 0 & v6 = 0 & ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (big_h(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_g(v0) = v3 & big_h(v5) = v9 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & big_f(v0, v0) = v2 & (v9 = 0 | (v8 = 0 & ~ (v3 = 0))) & (v2 = 0 | (v7 = 0 & v6 = 0 & ~ (v1 = 0))))) & ! [v0] : ! [v1] : ( ~ (big_f(v0, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_g(v0) = v3 & big_h(v5) = v9 & big_h(v0) = v2 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & (v9 = 0 | (v8 = 0 & ~ (v3 = 0))) & (v1 = 0 | (v7 = 0 & v6 = 0 & ~ (v2 = 0))))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_g(v0) = v3 & big_h(v5) = v9 & big_h(v0) = v1 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & big_f(v0, v0) = v2 & (v9 = 0 | (v8 = 0 & ~ (v3 = 0))) & (v2 = 0 | (v7 = 0 & v6 = 0 & ~ (v1 = 0)))) % 9.11/2.88 | Applying alpha-rule on (0) yields: % 9.11/2.88 | (1) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_g(v0) = v3 & big_h(v5) = v9 & big_h(v0) = v1 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & big_f(v0, v0) = v2 & (v9 = 0 | (v8 = 0 & ~ (v3 = 0))) & (v2 = 0 | (v7 = 0 & v6 = 0 & ~ (v1 = 0)))) % 9.11/2.88 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) % 9.11/2.88 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0)) % 9.11/2.88 | (4) ! [v0] : ! [v1] : ( ~ (big_f(v0, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_g(v0) = v3 & big_h(v5) = v9 & big_h(v0) = v2 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & (v9 = 0 | (v8 = 0 & ~ (v3 = 0))) & (v1 = 0 | (v7 = 0 & v6 = 0 & ~ (v2 = 0))))) % 9.11/2.88 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) % 9.11/2.89 | (6) ! [v0] : ! [v1] : ( ~ (big_h(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_g(v0) = v3 & big_h(v5) = v9 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & big_f(v0, v0) = v2 & (v9 = 0 | (v8 = 0 & ~ (v3 = 0))) & (v2 = 0 | (v7 = 0 & v6 = 0 & ~ (v1 = 0))))) % 9.23/2.89 | (7) ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & big_g(v4) = v7 & big_h(v5) = v9 & big_h(v0) = v2 & big_f(v5, v5) = v10 & big_f(v5, v0) = v8 & big_f(v4, v5) = v6 & big_f(v0, v4) = 0 & big_f(v0, v0) = v3 & (v9 = 0 | (v8 = 0 & ~ (v1 = 0))) & (v3 = 0 | (v7 = 0 & v6 = 0 & ~ (v2 = 0))))) % 9.23/2.89 | % 9.23/2.89 | Instantiating (1) 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, all_1_8_8, all_1_9_9, all_1_10_10 yields: % 9.23/2.89 | (8) ~ (all_1_0_0 = 0) & big_g(all_1_6_6) = all_1_3_3 & big_g(all_1_10_10) = all_1_7_7 & big_h(all_1_5_5) = all_1_1_1 & big_h(all_1_10_10) = all_1_9_9 & big_f(all_1_5_5, all_1_5_5) = all_1_0_0 & big_f(all_1_5_5, all_1_10_10) = all_1_2_2 & big_f(all_1_6_6, all_1_5_5) = all_1_4_4 & big_f(all_1_10_10, all_1_6_6) = 0 & big_f(all_1_10_10, all_1_10_10) = all_1_8_8 & (all_1_1_1 = 0 | (all_1_2_2 = 0 & ~ (all_1_7_7 = 0))) & (all_1_8_8 = 0 | (all_1_3_3 = 0 & all_1_4_4 = 0 & ~ (all_1_9_9 = 0))) % 9.23/2.89 | % 9.23/2.89 | Applying alpha-rule on (8) yields: % 9.23/2.89 | (9) big_g(all_1_6_6) = all_1_3_3 % 9.23/2.89 | (10) ~ (all_1_0_0 = 0) % 9.23/2.89 | (11) big_h(all_1_5_5) = all_1_1_1 % 9.23/2.89 | (12) big_f(all_1_10_10, all_1_10_10) = all_1_8_8 % 9.23/2.89 | (13) big_h(all_1_10_10) = all_1_9_9 % 9.23/2.89 | (14) big_f(all_1_5_5, all_1_5_5) = all_1_0_0 % 9.23/2.89 | (15) big_f(all_1_5_5, all_1_10_10) = all_1_2_2 % 9.23/2.89 | (16) big_f(all_1_10_10, all_1_6_6) = 0 % 9.23/2.89 | (17) big_f(all_1_6_6, all_1_5_5) = all_1_4_4 % 9.23/2.89 | (18) big_g(all_1_10_10) = all_1_7_7 % 9.23/2.89 | (19) all_1_1_1 = 0 | (all_1_2_2 = 0 & ~ (all_1_7_7 = 0)) % 9.23/2.89 | (20) all_1_8_8 = 0 | (all_1_3_3 = 0 & all_1_4_4 = 0 & ~ (all_1_9_9 = 0)) % 9.23/2.89 | % 9.23/2.89 | Instantiating formula (4) with all_1_0_0, all_1_5_5 and discharging atoms big_f(all_1_5_5, all_1_5_5) = all_1_0_0, yields: % 9.23/2.89 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & big_g(v2) = v5 & big_g(all_1_5_5) = v1 & big_h(v3) = v7 & big_h(all_1_5_5) = v0 & big_f(v3, v3) = v8 & big_f(v3, all_1_5_5) = v6 & big_f(v2, v3) = v4 & big_f(all_1_5_5, v2) = 0 & (v7 = 0 | (v6 = 0 & ~ (v1 = 0))) & (all_1_0_0 = 0 | (v5 = 0 & v4 = 0 & ~ (v0 = 0)))) % 9.23/2.90 | % 9.23/2.90 | Instantiating (21) with all_10_0_20, all_10_1_21, all_10_2_22, all_10_3_23, all_10_4_24, all_10_5_25, all_10_6_26, all_10_7_27, all_10_8_28 yields: % 9.23/2.90 | (22) ~ (all_10_0_20 = 0) & big_g(all_10_6_26) = all_10_3_23 & big_g(all_1_5_5) = all_10_7_27 & big_h(all_10_5_25) = all_10_1_21 & big_h(all_1_5_5) = all_10_8_28 & big_f(all_10_5_25, all_10_5_25) = all_10_0_20 & big_f(all_10_5_25, all_1_5_5) = all_10_2_22 & big_f(all_10_6_26, all_10_5_25) = all_10_4_24 & big_f(all_1_5_5, all_10_6_26) = 0 & (all_10_1_21 = 0 | (all_10_2_22 = 0 & ~ (all_10_7_27 = 0))) & (all_1_0_0 = 0 | (all_10_3_23 = 0 & all_10_4_24 = 0 & ~ (all_10_8_28 = 0))) % 9.23/2.90 | % 9.23/2.90 | Applying alpha-rule on (22) yields: % 9.23/2.90 | (23) big_f(all_10_5_25, all_1_5_5) = all_10_2_22 % 9.23/2.90 | (24) ~ (all_10_0_20 = 0) % 9.23/2.90 | (25) all_10_1_21 = 0 | (all_10_2_22 = 0 & ~ (all_10_7_27 = 0)) % 9.23/2.90 | (26) all_1_0_0 = 0 | (all_10_3_23 = 0 & all_10_4_24 = 0 & ~ (all_10_8_28 = 0)) % 9.23/2.90 | (27) big_f(all_1_5_5, all_10_6_26) = 0 % 9.23/2.90 | (28) big_h(all_1_5_5) = all_10_8_28 % 9.23/2.90 | (29) big_h(all_10_5_25) = all_10_1_21 % 9.23/2.90 | (30) big_g(all_10_6_26) = all_10_3_23 % 9.23/2.90 | (31) big_g(all_1_5_5) = all_10_7_27 % 9.23/2.90 | (32) big_f(all_10_5_25, all_10_5_25) = all_10_0_20 % 9.23/2.90 | (33) big_f(all_10_6_26, all_10_5_25) = all_10_4_24 % 9.23/2.90 | % 9.23/2.90 +-Applying beta-rule and splitting (26), into two cases. % 9.23/2.90 |-Branch one: % 9.23/2.90 | (34) all_1_0_0 = 0 % 9.23/2.90 | % 9.23/2.90 | Equations (34) can reduce 10 to: % 9.23/2.90 | (35) $false % 9.23/2.90 | % 9.23/2.90 |-The branch is then unsatisfiable % 9.23/2.90 |-Branch two: % 9.23/2.90 | (10) ~ (all_1_0_0 = 0) % 9.23/2.90 | (37) all_10_3_23 = 0 & all_10_4_24 = 0 & ~ (all_10_8_28 = 0) % 9.23/2.90 | % 9.23/2.90 | Applying alpha-rule on (37) yields: % 9.23/2.90 | (38) all_10_3_23 = 0 % 9.23/2.90 | (39) all_10_4_24 = 0 % 9.23/2.90 | (40) ~ (all_10_8_28 = 0) % 9.23/2.90 | % 9.23/2.90 | From (38) and (30) follows: % 9.23/2.90 | (41) big_g(all_10_6_26) = 0 % 9.23/2.90 | % 9.23/2.90 | Instantiating formula (7) with 0, all_10_6_26 and discharging atoms big_g(all_10_6_26) = 0, yields: % 9.23/2.90 | (42) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & big_g(v2) = v5 & big_h(v3) = 0 & big_h(all_10_6_26) = v0 & big_f(v3, v3) = v7 & big_f(v3, all_10_6_26) = v6 & big_f(v2, v3) = v4 & big_f(all_10_6_26, v2) = 0 & big_f(all_10_6_26, all_10_6_26) = v1 & (v1 = 0 | (v5 = 0 & v4 = 0 & ~ (v0 = 0)))) % 9.23/2.90 | % 9.23/2.90 | Instantiating (42) with all_59_0_146, all_59_1_147, all_59_2_148, all_59_3_149, all_59_4_150, all_59_5_151, all_59_6_152, all_59_7_153 yields: % 9.23/2.90 | (43) ~ (all_59_0_146 = 0) & big_g(all_59_5_151) = all_59_2_148 & big_h(all_59_4_150) = 0 & big_h(all_10_6_26) = all_59_7_153 & big_f(all_59_4_150, all_59_4_150) = all_59_0_146 & big_f(all_59_4_150, all_10_6_26) = all_59_1_147 & big_f(all_59_5_151, all_59_4_150) = all_59_3_149 & big_f(all_10_6_26, all_59_5_151) = 0 & big_f(all_10_6_26, all_10_6_26) = all_59_6_152 & (all_59_6_152 = 0 | (all_59_2_148 = 0 & all_59_3_149 = 0 & ~ (all_59_7_153 = 0))) % 9.23/2.90 | % 9.23/2.90 | Applying alpha-rule on (43) yields: % 9.23/2.90 | (44) big_f(all_10_6_26, all_10_6_26) = all_59_6_152 % 9.23/2.90 | (45) big_f(all_59_4_150, all_59_4_150) = all_59_0_146 % 9.23/2.90 | (46) big_h(all_10_6_26) = all_59_7_153 % 9.23/2.90 | (47) big_f(all_10_6_26, all_59_5_151) = 0 % 9.23/2.90 | (48) all_59_6_152 = 0 | (all_59_2_148 = 0 & all_59_3_149 = 0 & ~ (all_59_7_153 = 0)) % 9.23/2.90 | (49) big_f(all_59_5_151, all_59_4_150) = all_59_3_149 % 9.23/2.90 | (50) big_h(all_59_4_150) = 0 % 9.23/2.90 | (51) ~ (all_59_0_146 = 0) % 9.23/2.90 | (52) big_g(all_59_5_151) = all_59_2_148 % 9.23/2.90 | (53) big_f(all_59_4_150, all_10_6_26) = all_59_1_147 % 9.23/2.90 | % 9.23/2.90 | Instantiating formula (6) with 0, all_59_4_150 and discharging atoms big_h(all_59_4_150) = 0, yields: % 9.23/2.91 | (54) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & big_g(v1) = v4 & big_g(all_59_4_150) = v0 & big_h(v2) = v6 & big_f(v2, v2) = v7 & big_f(v2, all_59_4_150) = v5 & big_f(v1, v2) = v3 & big_f(all_59_4_150, v1) = 0 & big_f(all_59_4_150, all_59_4_150) = 0 & (v6 = 0 | (v5 = 0 & ~ (v0 = 0)))) % 9.23/2.91 | % 9.23/2.91 | Instantiating formula (4) with all_59_0_146, all_59_4_150 and discharging atoms big_f(all_59_4_150, all_59_4_150) = all_59_0_146, yields: % 9.23/2.91 | (55) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & big_g(v2) = v5 & big_g(all_59_4_150) = v1 & big_h(v3) = v7 & big_h(all_59_4_150) = v0 & big_f(v3, v3) = v8 & big_f(v3, all_59_4_150) = v6 & big_f(v2, v3) = v4 & big_f(all_59_4_150, v2) = 0 & (v7 = 0 | (v6 = 0 & ~ (v1 = 0))) & (all_59_0_146 = 0 | (v5 = 0 & v4 = 0 & ~ (v0 = 0)))) % 9.23/2.91 | % 9.23/2.91 | Instantiating (54) with all_282_0_736, all_282_1_737, all_282_2_738, all_282_3_739, all_282_4_740, all_282_5_741, all_282_6_742, all_282_7_743 yields: % 9.23/2.91 | (56) ~ (all_282_0_736 = 0) & big_g(all_282_6_742) = all_282_3_739 & big_g(all_59_4_150) = all_282_7_743 & big_h(all_282_5_741) = all_282_1_737 & big_f(all_282_5_741, all_282_5_741) = all_282_0_736 & big_f(all_282_5_741, all_59_4_150) = all_282_2_738 & big_f(all_282_6_742, all_282_5_741) = all_282_4_740 & big_f(all_59_4_150, all_282_6_742) = 0 & big_f(all_59_4_150, all_59_4_150) = 0 & (all_282_1_737 = 0 | (all_282_2_738 = 0 & ~ (all_282_7_743 = 0))) % 9.23/2.91 | % 9.23/2.91 | Applying alpha-rule on (56) yields: % 9.23/2.91 | (57) big_f(all_59_4_150, all_59_4_150) = 0 % 9.23/2.91 | (58) big_g(all_59_4_150) = all_282_7_743 % 9.23/2.91 | (59) big_f(all_282_5_741, all_59_4_150) = all_282_2_738 % 9.23/2.91 | (60) big_h(all_282_5_741) = all_282_1_737 % 9.23/2.91 | (61) big_f(all_59_4_150, all_282_6_742) = 0 % 9.23/2.91 | (62) big_f(all_282_5_741, all_282_5_741) = all_282_0_736 % 9.23/2.91 | (63) all_282_1_737 = 0 | (all_282_2_738 = 0 & ~ (all_282_7_743 = 0)) % 9.23/2.91 | (64) big_g(all_282_6_742) = all_282_3_739 % 9.23/2.91 | (65) big_f(all_282_6_742, all_282_5_741) = all_282_4_740 % 9.23/2.91 | (66) ~ (all_282_0_736 = 0) % 9.23/2.91 | % 9.23/2.91 | Instantiating (55) with all_308_0_852, all_308_1_853, all_308_2_854, all_308_3_855, all_308_4_856, all_308_5_857, all_308_6_858, all_308_7_859, all_308_8_860 yields: % 9.23/2.91 | (67) ~ (all_308_0_852 = 0) & big_g(all_308_6_858) = all_308_3_855 & big_g(all_59_4_150) = all_308_7_859 & big_h(all_308_5_857) = all_308_1_853 & big_h(all_59_4_150) = all_308_8_860 & big_f(all_308_5_857, all_308_5_857) = all_308_0_852 & big_f(all_308_5_857, all_59_4_150) = all_308_2_854 & big_f(all_308_6_858, all_308_5_857) = all_308_4_856 & big_f(all_59_4_150, all_308_6_858) = 0 & (all_308_1_853 = 0 | (all_308_2_854 = 0 & ~ (all_308_7_859 = 0))) & (all_59_0_146 = 0 | (all_308_3_855 = 0 & all_308_4_856 = 0 & ~ (all_308_8_860 = 0))) % 9.23/2.91 | % 9.23/2.91 | Applying alpha-rule on (67) yields: % 9.23/2.91 | (68) big_f(all_59_4_150, all_308_6_858) = 0 % 9.23/2.91 | (69) big_g(all_308_6_858) = all_308_3_855 % 9.23/2.91 | (70) all_308_1_853 = 0 | (all_308_2_854 = 0 & ~ (all_308_7_859 = 0)) % 9.23/2.91 | (71) ~ (all_308_0_852 = 0) % 9.23/2.91 | (72) big_h(all_308_5_857) = all_308_1_853 % 9.23/2.91 | (73) big_h(all_59_4_150) = all_308_8_860 % 9.23/2.91 | (74) all_59_0_146 = 0 | (all_308_3_855 = 0 & all_308_4_856 = 0 & ~ (all_308_8_860 = 0)) % 9.23/2.91 | (75) big_f(all_308_6_858, all_308_5_857) = all_308_4_856 % 9.23/2.91 | (76) big_f(all_308_5_857, all_59_4_150) = all_308_2_854 % 9.23/2.91 | (77) big_g(all_59_4_150) = all_308_7_859 % 9.23/2.91 | (78) big_f(all_308_5_857, all_308_5_857) = all_308_0_852 % 9.23/2.91 | % 9.23/2.91 +-Applying beta-rule and splitting (74), into two cases. % 9.23/2.91 |-Branch one: % 9.23/2.91 | (79) all_59_0_146 = 0 % 9.23/2.91 | % 9.23/2.91 | Equations (79) can reduce 51 to: % 9.23/2.91 | (35) $false % 9.23/2.91 | % 9.23/2.91 |-The branch is then unsatisfiable % 9.23/2.91 |-Branch two: % 9.23/2.91 | (51) ~ (all_59_0_146 = 0) % 9.23/2.91 | (82) all_308_3_855 = 0 & all_308_4_856 = 0 & ~ (all_308_8_860 = 0) % 9.23/2.91 | % 9.23/2.91 | Instantiating formula (5) with all_59_4_150, all_59_4_150, 0, all_59_0_146 and discharging atoms big_f(all_59_4_150, all_59_4_150) = all_59_0_146, big_f(all_59_4_150, all_59_4_150) = 0, yields: % 9.23/2.91 | (79) all_59_0_146 = 0 % 9.23/2.91 | % 9.23/2.91 | Equations (79) can reduce 51 to: % 9.23/2.91 | (35) $false % 9.23/2.91 | % 9.23/2.91 |-The branch is then unsatisfiable % 9.23/2.91 % SZS output end Proof for theBenchmark % 9.23/2.91 % 9.23/2.91 2320ms %------------------------------------------------------------------------------