%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET580+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n029.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 05:27:05 EDT 2022 % Result : Theorem 0.20s 0.45s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET580+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n029.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 : Sun Jul 10 02:17:31 EDT 2022 % 0.13/0.35 % CPUTime : % 0.20/0.45 % 0.20/0.45 SPASS V 3.9 % 0.20/0.45 SPASS beiseite: Proof found. % 0.20/0.45 % SZS status Theorem % 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.20/0.45 SPASS derived 82 clauses, backtracked 11 clauses, performed 3 splits and kept 67 clauses. % 0.20/0.45 SPASS allocated 85225 KBytes. % 0.20/0.45 SPASS spent 0:00:00.09 on the problem. % 0.20/0.45 0:00:00.03 for the input. % 0.20/0.45 0:00:00.03 for the FLOTTER CNF translation. % 0.20/0.45 0:00:00.00 for inferences. % 0.20/0.45 0:00:00.00 for the backtracking. % 0.20/0.45 0:00:00.01 for the reduction. % 0.20/0.45 % 0.20/0.45 % 0.20/0.45 Here is a proof with depth 5, length 44 : % 0.20/0.45 % SZS output start Refutation % 0.20/0.45 3[0:Inp] || member(u,v) -> member(u,union(v,w))*. % 0.20/0.45 4[0:Inp] || member(u,v) -> member(u,union(w,v))*. % 0.20/0.45 5[0:Inp] || member(u,difference(v,w))* -> member(u,v). % 0.20/0.45 6[0:Inp] || member(u,v) member(u,difference(w,v))* -> . % 0.20/0.45 7[0:Inp] || -> member(skc3,skc5) member(skc3,skc4) member(skc3,symmetric_difference(skc4,skc5))*. % 0.20/0.45 8[0:Inp] || -> equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v))**. % 0.20/0.45 11[0:Inp] || member(u,union(v,w))* -> member(u,v) member(u,w). % 0.20/0.45 12[0:Inp] || member(u,v) -> member(u,w) member(u,difference(v,w))*. % 0.20/0.45 13[0:Inp] || member(skc3,skc5) member(skc3,skc4) -> member(skc3,symmetric_difference(skc4,skc5))*. % 0.20/0.45 14[0:Inp] || member(skc3,skc4) member(skc3,symmetric_difference(skc4,skc5))* -> member(skc3,skc5). % 0.20/0.45 15[0:Inp] || member(skc3,skc5) member(skc3,symmetric_difference(skc4,skc5))* -> member(skc3,skc4). % 0.20/0.45 18[1:Spt:7.0] || -> member(skc3,skc5)*. % 0.20/0.45 19[1:MRR:15.0,18.0] || member(skc3,symmetric_difference(skc4,skc5))* -> member(skc3,skc4). % 0.20/0.45 20[1:MRR:13.0,18.0] || member(skc3,skc4) -> member(skc3,symmetric_difference(skc4,skc5))*. % 0.20/0.45 29[2:Spt:19.0] || member(skc3,symmetric_difference(skc4,skc5))* -> . % 0.20/0.45 30[2:MRR:20.1,29.0] || member(skc3,skc4)* -> . % 0.20/0.45 36[0:SpR:8.0,3.1] || member(u,difference(v,w)) -> member(u,symmetric_difference(v,w))*. % 0.20/0.45 38[0:SpR:8.0,4.1] || member(u,difference(v,w)) -> member(u,symmetric_difference(w,v))*. % 0.20/0.45 48[2:Res:38.1,29.0] || member(skc3,difference(skc5,skc4))* -> . % 0.20/0.45 50[2:Res:12.2,48.0] || member(skc3,skc5)* -> member(skc3,skc4). % 0.20/0.45 53[2:MRR:50.0,50.1,18.0,30.0] || -> . % 0.20/0.45 54[2:Spt:53.0,19.0,29.0] || -> member(skc3,symmetric_difference(skc4,skc5))*. % 0.20/0.45 55[2:Spt:53.0,19.1] || -> member(skc3,skc4)*. % 0.20/0.45 58[0:SpL:8.0,11.0] || member(u,symmetric_difference(v,w))* -> member(u,difference(v,w)) member(u,difference(w,v)). % 0.20/0.45 76[2:Res:54.0,58.0] || -> member(skc3,difference(skc4,skc5)) member(skc3,difference(skc5,skc4))*. % 0.20/0.45 82[2:Res:76.1,6.1] || member(skc3,skc4) -> member(skc3,difference(skc4,skc5))*. % 0.20/0.45 83[2:MRR:82.0,55.0] || -> member(skc3,difference(skc4,skc5))*. % 0.20/0.45 85[2:Res:83.0,6.1] || member(skc3,skc5)* -> . % 0.20/0.45 86[2:MRR:85.0,18.0] || -> . % 0.20/0.45 87[1:Spt:86.0,7.0,18.0] || member(skc3,skc5)* -> . % 0.20/0.45 88[1:Spt:86.0,7.1,7.2] || -> member(skc3,skc4) member(skc3,symmetric_difference(skc4,skc5))*. % 0.20/0.45 89[1:MRR:14.2,87.0] || member(skc3,skc4) member(skc3,symmetric_difference(skc4,skc5))* -> . % 0.20/0.45 90[2:Spt:88.0] || -> member(skc3,skc4)*. % 0.20/0.45 91[2:MRR:89.0,90.0] || member(skc3,symmetric_difference(skc4,skc5))* -> . % 0.20/0.45 92[2:Res:36.1,91.0] || member(skc3,difference(skc4,skc5))* -> . % 0.20/0.45 104[2:Res:12.2,92.0] || member(skc3,skc4) -> member(skc3,skc5)*. % 0.20/0.45 105[2:MRR:104.0,104.1,90.0,87.0] || -> . % 0.20/0.45 106[2:Spt:105.0,88.0,90.0] || member(skc3,skc4)* -> . % 0.20/0.45 107[2:Spt:105.0,88.1] || -> member(skc3,symmetric_difference(skc4,skc5))*. % 0.20/0.45 108[2:Res:107.0,58.0] || -> member(skc3,difference(skc4,skc5)) member(skc3,difference(skc5,skc4))*. % 0.20/0.45 109[2:Res:108.1,5.0] || -> member(skc3,difference(skc4,skc5))* member(skc3,skc5). % 0.20/0.45 111[2:MRR:109.1,87.0] || -> member(skc3,difference(skc4,skc5))*. % 0.20/0.45 112[2:Res:111.0,5.0] || -> member(skc3,skc4)*. % 0.20/0.45 114[2:MRR:112.0,106.0] || -> . % 0.20/0.45 % SZS output end Refutation % 0.20/0.45 Formulae used in the proof : union_defn difference_defn prove_th23 symmetric_difference_defn % 0.20/0.45 %------------------------------------------------------------------------------