%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n025.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 05:27:36 EDT 2022 % Result : Theorem 0.19s 0.49s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 21:23:16 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.49 % 0.19/0.49 SPASS V 3.9 % 0.19/0.49 SPASS beiseite: Proof found. % 0.19/0.49 % SZS status Theorem % 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.19/0.49 SPASS derived 610 clauses, backtracked 19 clauses, performed 3 splits and kept 324 clauses. % 0.19/0.49 SPASS allocated 85536 KBytes. % 0.19/0.49 SPASS spent 0:00:00.14 on the problem. % 0.19/0.49 0:00:00.03 for the input. % 0.19/0.49 0:00:00.03 for the FLOTTER CNF translation. % 0.19/0.49 0:00:00.01 for inferences. % 0.19/0.49 0:00:00.00 for the backtracking. % 0.19/0.49 0:00:00.04 for the reduction. % 0.19/0.49 % 0.19/0.49 % 0.19/0.49 Here is a proof with depth 10, length 50 : % 0.19/0.49 % SZS output start Refutation % 0.19/0.49 1[0:Inp] || -> equal(union(u,v),union(v,u))*. % 0.19/0.49 2[0:Inp] || intersect(u,v)*+ -> intersect(v,u)*. % 0.19/0.49 3[0:Inp] || member(u,v) -> member(u,union(v,w))*. % 0.19/0.49 4[0:Inp] || member(u,v) -> member(u,union(w,v))*. % 0.19/0.49 5[0:Inp] || intersect(u,v) -> member(skf2(v,u),u)*. % 0.19/0.49 6[0:Inp] || intersect(u,v)*+ -> member(skf2(v,w),v)*. % 0.19/0.49 7[0:Inp] || intersect(skc3,skc4) intersect(skc3,union(skc4,skc5))* -> . % 0.19/0.49 8[0:Inp] || intersect(skc3,skc5) intersect(skc3,union(skc4,skc5))* -> . % 0.19/0.49 9[0:Inp] || -> intersect(skc3,skc5) intersect(skc3,skc4) intersect(skc3,union(skc4,skc5))*. % 0.19/0.49 10[0:Inp] || member(u,v)*+ member(u,w)* -> intersect(w,v)*. % 0.19/0.49 13[0:Inp] || member(u,union(v,w))* -> member(u,v) member(u,w). % 0.19/0.49 16[1:Spt:8.1] || intersect(skc3,union(skc4,skc5))* -> . % 0.19/0.49 17[1:MRR:9.2,16.0] || -> intersect(skc3,skc5)* intersect(skc3,skc4). % 0.19/0.49 24[1:Res:17.0,6.0] || -> intersect(skc3,skc4) member(skf2(skc5,u),skc5)*. % 0.19/0.49 26[2:Spt:24.0] || -> intersect(skc3,skc4)*. % 0.19/0.49 28[2:Res:26.0,2.0] || -> intersect(skc4,skc3)*. % 0.19/0.49 29[2:Res:28.0,6.0] || -> member(skf2(skc3,u),skc3)*. % 0.19/0.49 37[2:Res:29.0,10.0] || member(skf2(skc3,u),v)* -> intersect(v,skc3). % 0.19/0.49 39[0:Res:3.1,10.0] || member(u,v)*+ member(u,w)* -> intersect(w,union(v,x))*. % 0.19/0.49 49[2:Res:4.1,37.0] || member(skf2(skc3,u),v)*+ -> intersect(union(w,v),skc3)*. % 0.19/0.49 59[0:Res:5.1,13.0] || intersect(union(u,v),w)+ -> member(skf2(w,union(u,v)),u)* member(skf2(w,union(u,v)),v)*. % 0.19/0.49 118[2:Res:5.1,49.0] || intersect(u,skc3) -> intersect(union(v,u),skc3)*. % 0.19/0.49 208[2:SpR:1.0,118.1] || intersect(u,skc3) -> intersect(union(u,v),skc3)*. % 0.19/0.49 241[2:Res:208.1,2.0] || intersect(u,skc3) -> intersect(skc3,union(u,v))*. % 0.19/0.49 250[2:Res:241.1,16.0] || intersect(skc4,skc3)* -> . % 0.19/0.49 254[2:MRR:250.0,28.0] || -> . % 0.19/0.49 255[2:Spt:254.0,24.0,26.0] || intersect(skc3,skc4)* -> . % 0.19/0.49 256[2:Spt:254.0,24.1] || -> member(skf2(skc5,u),skc5)*. % 0.19/0.49 257[2:MRR:17.1,255.0] || -> intersect(skc3,skc5)*. % 0.19/0.49 261[2:Res:256.0,39.0] || member(skf2(skc5,u),v)*+ -> intersect(v,union(skc5,w))*. % 0.19/0.49 294[2:Res:5.1,261.0] || intersect(u,skc5) -> intersect(u,union(skc5,v))*. % 0.19/0.49 342[2:SpR:1.0,294.1] || intersect(u,skc5) -> intersect(u,union(v,skc5))*. % 0.19/0.49 372[2:Res:342.1,16.0] || intersect(skc3,skc5)* -> . % 0.19/0.49 377[2:MRR:372.0,257.0] || -> . % 0.19/0.49 378[1:Spt:377.0,8.1,16.0] || -> intersect(skc3,union(skc4,skc5))*. % 0.19/0.49 379[1:Spt:377.0,8.0] || intersect(skc3,skc5)* -> . % 0.19/0.49 380[1:MRR:7.1,378.0] || intersect(skc3,skc4)* -> . % 0.19/0.49 383[1:Res:378.0,2.0] || -> intersect(union(skc4,skc5),skc3)*. % 0.19/0.49 385[1:Res:383.0,6.0] || -> member(skf2(skc3,u),skc3)*. % 0.19/0.49 387[1:Res:383.0,59.0] || -> member(skf2(skc3,union(skc4,skc5)),skc4) member(skf2(skc3,union(skc4,skc5)),skc5)*. % 0.19/0.49 394[1:Res:385.0,10.0] || member(skf2(skc3,u),v)* -> intersect(v,skc3). % 0.19/0.49 639[1:Res:387.1,394.0] || -> member(skf2(skc3,union(skc4,skc5)),skc4)* intersect(skc5,skc3). % 0.19/0.49 649[2:Spt:639.0] || -> member(skf2(skc3,union(skc4,skc5)),skc4)*. % 0.19/0.49 654[2:Res:649.0,394.0] || -> intersect(skc4,skc3)*. % 0.19/0.49 661[2:Res:654.0,2.0] || -> intersect(skc3,skc4)*. % 0.19/0.49 662[2:MRR:661.0,380.0] || -> . % 0.19/0.49 663[2:Spt:662.0,639.0,649.0] || member(skf2(skc3,union(skc4,skc5)),skc4)* -> . % 0.19/0.49 664[2:Spt:662.0,639.1] || -> intersect(skc5,skc3)*. % 0.19/0.49 675[2:Res:664.0,2.0] || -> intersect(skc3,skc5)*. % 0.19/0.49 676[2:MRR:675.0,379.0] || -> . % 0.19/0.49 % SZS output end Refutation % 0.19/0.49 Formulae used in the proof : commutativity_of_union symmetry_of_intersect union_defn intersect_defn prove_intersect_with_union % 0.19/0.49 %------------------------------------------------------------------------------