%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n009.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 05:30:14 EDT 2022 % Result : Theorem 0.19s 0.45s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n009.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 06:21:07 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.45 % 0.19/0.45 SPASS V 3.9 % 0.19/0.45 SPASS beiseite: Proof found. % 0.19/0.45 % SZS status Theorem % 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.45 SPASS derived 61 clauses, backtracked 12 clauses, performed 2 splits and kept 53 clauses. % 0.19/0.45 SPASS allocated 85118 KBytes. % 0.19/0.45 SPASS spent 0:00:00.09 on the problem. % 0.19/0.45 0:00:00.04 for the input. % 0.19/0.45 0:00:00.02 for the FLOTTER CNF translation. % 0.19/0.45 0:00:00.00 for inferences. % 0.19/0.45 0:00:00.00 for the backtracking. % 0.19/0.45 0:00:00.00 for the reduction. % 0.19/0.45 % 0.19/0.45 % 0.19/0.45 Here is a proof with depth 6, length 35 : % 0.19/0.45 % SZS output start Refutation % 0.19/0.45 1[0:Inp] || -> empty(empty_set)*. % 0.19/0.45 3[0:Inp] || empty(skc7)* -> . % 0.19/0.45 6[0:Inp] || -> subset(empty_set,u)*. % 0.19/0.45 7[0:Inp] || subset(skc8,skc9)* -> . % 0.19/0.45 8[0:Inp] || equal(u,empty_set) -> equal(cartesian_product2(u,v),empty_set)**. % 0.19/0.45 9[0:Inp] || equal(u,empty_set) -> equal(cartesian_product2(v,u),empty_set)**. % 0.19/0.45 10[0:Inp] || equal(cartesian_product2(u,v),empty_set)** -> equal(u,empty_set) equal(v,empty_set). % 0.19/0.45 11[0:Inp] || -> subset(cartesian_product2(skc8,skc7),cartesian_product2(skc9,skc11))* subset(cartesian_product2(skc7,skc8),cartesian_product2(skc10,skc9)). % 0.19/0.45 12[0:Inp] || subset(cartesian_product2(u,v),cartesian_product2(w,x))* -> subset(u,w) equal(cartesian_product2(u,v),empty_set). % 0.19/0.45 13[0:Inp] || subset(cartesian_product2(u,v),cartesian_product2(w,x))* -> subset(v,x) equal(cartesian_product2(u,v),empty_set). % 0.19/0.45 14[0:Res:13.1,7.0] || subset(cartesian_product2(u,skc8),cartesian_product2(v,skc9))* -> equal(cartesian_product2(u,skc8),empty_set). % 0.19/0.45 15[0:Res:12.1,7.0] || subset(cartesian_product2(skc8,u),cartesian_product2(skc9,v))* -> equal(cartesian_product2(skc8,u),empty_set). % 0.19/0.45 39[0:Res:11.0,15.0] || -> subset(cartesian_product2(skc7,skc8),cartesian_product2(skc10,skc9))* equal(cartesian_product2(skc8,skc7),empty_set). % 0.19/0.45 47[0:Res:39.0,14.0] || -> equal(cartesian_product2(skc8,skc7),empty_set)** equal(cartesian_product2(skc7,skc8),empty_set). % 0.19/0.45 51[1:Spt:47.0] || -> equal(cartesian_product2(skc8,skc7),empty_set)**. % 0.19/0.45 58[1:SpL:51.0,10.0] || equal(empty_set,empty_set) -> equal(skc8,empty_set)** equal(skc7,empty_set). % 0.19/0.45 59[1:Obv:58.0] || -> equal(skc8,empty_set)** equal(skc7,empty_set). % 0.19/0.45 60[2:Spt:59.0] || -> equal(skc8,empty_set)**. % 0.19/0.45 61[2:Rew:60.0,7.0] || subset(empty_set,skc9)* -> . % 0.19/0.45 67[2:MRR:61.0,6.0] || -> . % 0.19/0.45 72[2:Spt:67.0,59.0,60.0] || equal(skc8,empty_set)** -> . % 0.19/0.45 73[2:Spt:67.0,59.1] || -> equal(skc7,empty_set)**. % 0.19/0.45 74[2:Rew:73.0,3.0] || empty(empty_set)* -> . % 0.19/0.45 75[2:MRR:74.0,1.0] || -> . % 0.19/0.45 77[1:Spt:75.0,47.0,51.0] || equal(cartesian_product2(skc8,skc7),empty_set)** -> . % 0.19/0.45 78[1:Spt:75.0,47.1] || -> equal(cartesian_product2(skc7,skc8),empty_set)**. % 0.19/0.45 83[1:SpL:78.0,10.0] || equal(empty_set,empty_set) -> equal(skc7,empty_set) equal(skc8,empty_set)**. % 0.19/0.45 84[1:Obv:83.0] || -> equal(skc7,empty_set) equal(skc8,empty_set)**. % 0.19/0.45 85[1:SpL:9.1,77.0] || equal(skc7,empty_set)** equal(empty_set,empty_set) -> . % 0.19/0.45 86[1:SpL:8.1,77.0] || equal(skc8,empty_set)** equal(empty_set,empty_set) -> . % 0.19/0.45 87[1:Obv:85.1] || equal(skc7,empty_set)** -> . % 0.19/0.45 88[1:MRR:84.0,87.0] || -> equal(skc8,empty_set)**. % 0.19/0.45 97[1:Obv:86.1] || equal(skc8,empty_set)** -> . % 0.19/0.45 98[1:Rew:88.0,97.0] || equal(empty_set,empty_set)* -> . % 0.19/0.45 99[1:Obv:98.0] || -> . % 0.19/0.45 % SZS output end Refutation % 0.19/0.45 Formulae used in the proof : fc1_xboole_0 t139_zfmisc_1 t2_xboole_1 t113_zfmisc_1 t138_zfmisc_1 % 0.19/0.45 %------------------------------------------------------------------------------