%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n006.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 : Tue Jul 19 05:29:37 EDT 2022 % Result : Theorem 0.20s 0.46s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n006.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 02:59:20 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.46 % 0.20/0.46 SPASS V 3.9 % 0.20/0.46 SPASS beiseite: Proof found. % 0.20/0.46 % SZS status Theorem % 0.20/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.46 SPASS derived 86 clauses, backtracked 7 clauses, performed 2 splits and kept 67 clauses. % 0.20/0.46 SPASS allocated 85216 KBytes. % 0.20/0.46 SPASS spent 0:00:00.10 on the problem. % 0.20/0.46 0:00:00.04 for the input. % 0.20/0.46 0:00:00.03 for the FLOTTER CNF translation. % 0.20/0.46 0:00:00.00 for inferences. % 0.20/0.46 0:00:00.00 for the backtracking. % 0.20/0.46 0:00:00.01 for the reduction. % 0.20/0.46 % 0.20/0.46 % 0.20/0.46 Here is a proof with depth 3, length 34 : % 0.20/0.46 % SZS output start Refutation % 0.20/0.46 7[0:Inp] || in(ordered_pair(u,v),cartesian_product2(w,x))* -> in(u,w). % 0.20/0.46 8[0:Inp] || in(ordered_pair(u,v),cartesian_product2(w,x))* -> in(v,x). % 0.20/0.46 9[0:Inp] || -> equal(skc8,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc9)))*. % 0.20/0.46 10[0:Inp] || -> equal(skc9,skc7) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc9)))*. % 0.20/0.46 12[0:Inp] || in(u,v)* equal(v,singleton(w))*+ -> equal(u,w)*. % 0.20/0.46 13[0:Inp] || equal(u,v)* equal(w,singleton(v))*+ -> in(u,w)*. % 0.20/0.46 15[0:Inp] || in(u,v) in(w,x) -> in(ordered_pair(u,w),cartesian_product2(v,x))*. % 0.20/0.46 16[0:Inp] || equal(skc9,skc7) equal(skc8,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc9)))* -> . % 0.20/0.46 18[1:Spt:10.0] || -> equal(skc9,skc7)**. % 0.20/0.46 19[1:Rew:18.0,16.0] || equal(skc7,skc7) equal(skc8,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc9)))* -> . % 0.20/0.46 20[1:Rew:18.0,9.1] || -> equal(skc8,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc7)))*. % 0.20/0.46 21[1:Obv:19.0] || equal(skc8,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc9)))* -> . % 0.20/0.46 22[1:Rew:18.0,21.1] || equal(skc8,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc7)))* -> . % 0.20/0.46 42[2:Spt:20.0] || -> equal(skc8,skc6)**. % 0.20/0.46 43[2:Rew:42.0,22.0] || equal(skc6,skc6) in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc7)))* -> . % 0.20/0.46 44[2:Obv:43.0] || in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc7)))* -> . % 0.20/0.46 45[2:Rew:42.0,44.0] || in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc6),singleton(skc7)))* -> . % 0.20/0.46 47[0:EqR:13.1] || equal(u,v) -> in(u,singleton(v))*. % 0.20/0.46 50[0:EqR:12.1] || in(u,singleton(v))* -> equal(u,v). % 0.20/0.46 102[2:Res:15.2,45.0] || in(skc6,singleton(skc6)) in(skc7,singleton(skc7))* -> . % 0.20/0.46 103[2:Res:47.1,102.1] || equal(skc7,skc7) in(skc6,singleton(skc6))* -> . % 0.20/0.46 104[2:Obv:103.0] || in(skc6,singleton(skc6))* -> . % 0.20/0.46 105[2:Res:47.1,104.0] || equal(skc6,skc6)* -> . % 0.20/0.46 106[2:Obv:105.0] || -> . % 0.20/0.46 107[2:Spt:106.0,20.0,42.0] || equal(skc8,skc6)** -> . % 0.20/0.46 108[2:Spt:106.0,20.1] || -> in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc7)))*. % 0.20/0.46 110[2:Res:108.0,7.0] || -> in(skc6,singleton(skc8))*. % 0.20/0.46 113[2:Res:110.0,50.0] || -> equal(skc8,skc6)**. % 0.20/0.46 114[2:MRR:113.0,107.0] || -> . % 0.20/0.46 115[1:Spt:114.0,10.0,18.0] || equal(skc9,skc7)** -> . % 0.20/0.46 116[1:Spt:114.0,10.1] || -> in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),singleton(skc9)))*. % 0.20/0.46 119[1:Res:116.0,8.0] || -> in(skc7,singleton(skc9))*. % 0.20/0.46 128[1:Res:119.0,50.0] || -> equal(skc9,skc7)**. % 0.20/0.46 129[1:MRR:128.0,115.0] || -> . % 0.20/0.46 % SZS output end Refutation % 0.20/0.46 Formulae used in the proof : l55_zfmisc_1 t34_zfmisc_1 d1_tarski antisymmetry_r2_hidden % 0.20/0.46 %------------------------------------------------------------------------------