0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : drodi -timeout(180) /export/starexec/sandbox2/benchmark/theBenchmark.p 0.09/0.35 % Computer : n010.cluster.edu 0.09/0.35 % Model : x86_64 x86_64 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.35 % Memory : 8046.5625MB 0.09/0.35 % OS : Linux 6.8.0-71-generic 0.09/0.35 % CPULimit : 1440 0.09/0.35 % WCLimit : 180 0.09/0.35 % DateTime : Mon Jul 27 09:51:34 UTC 2026 0.09/0.36 % CPUTime : 0.09/0.37 % Drodi V4.1.1 1390.10/176.12 % Refutation found 1390.10/176.12 % SZS status Theorem for theBenchmark: Theorem is valid 1390.10/176.12 % SZS output start CNFRefutation for theBenchmark 1390.10/176.12 fof(f1,axiom,( 1390.10/176.12 (! [X,Y] :( is_a_theorem(Y)<= ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) ) ) )), 1390.10/176.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')). 1390.10/176.12 fof(f2,conjecture,( 1390.10/176.12 is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))) ), 1390.10/176.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')). 1390.10/176.12 fof(f3,negated_conjecture,( 1390.10/176.12 ~(is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))) )), 1390.10/176.12 inference(negated_conjecture,[status(cth)],[f2])). 1390.10/176.12 fof(f4,axiom,( 1390.10/176.12 (! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O] : is_a_theorem(implies(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(G,H),implies(implies(H,I),implies(G,I))),implies(implies(implies(n(J),J),J),K)),K),implies(implies(L,implies(n(L),M)),N)),N),O)),O)) )), 1390.10/176.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')). 1390.10/176.12 fof(f5,plain,( 1390.10/176.12 ![X,Y]: (is_a_theorem(Y)|(~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))), 1390.10/176.12 inference(pre_NNF_transformation,[status(thm)],[f1])). 1390.10/176.12 fof(f6,plain,( 1390.10/176.12 ![Y]: (is_a_theorem(Y)|(![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))))), 1390.10/176.12 inference(miniscoping,[status(thm)],[f5])). 1390.10/176.12 fof(f7,plain,( 1390.10/176.12 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~is_a_theorem(X0))), 1390.10/176.12 inference(cnf_transformation,[status(thm)],[f6])). 1390.10/176.12 fof(f8,plain,( 1390.10/176.12 ~is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u)))), 1390.10/176.12 inference(cnf_transformation,[status(thm)],[f3])). 1390.10/176.12 fof(f9,plain,( 1390.10/176.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14]: (is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14)))), 1390.10/176.12 inference(cnf_transformation,[status(thm)],[f4])). 1390.10/176.12 fof(f10,plain,( 1390.10/176.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14]: (is_a_theorem(X0)|~is_a_theorem(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X0))))), 1390.10/176.12 inference(resolution,[status(thm)],[f9,f7])). 1390.10/176.12 fof(f11,plain,( 1390.10/176.12 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))), 1390.10/176.12 inference(resolution,[status(thm)],[f10,f9])). 1390.10/176.12 fof(f12,plain,( 1390.10/176.12 ![X0,X1,X2,X3,X4,X5]: (is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5)))), 1390.10/176.12 inference(resolution,[status(thm)],[f11,f10])). 1390.10/176.12 fof(f13,plain,( 1390.10/176.12 ![X0,X1]: (is_a_theorem(implies(X0,X1))|~is_a_theorem(X1))), 1390.10/176.12 inference(resolution,[status(thm)],[f11,f7])). 1390.10/176.12 fof(f15,plain,( 1390.10/176.12 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))))), 1390.10/176.12 inference(resolution,[status(thm)],[f13,f11])). 1390.10/176.12 fof(f16,plain,( 1390.10/176.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (is_a_theorem(implies(X0,implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8))))), 1390.10/176.12 inference(resolution,[status(thm)],[f15,f10])). 1390.10/176.12 fof(f17,plain,( 1390.10/176.12 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,implies(X2,X1))))), 1390.10/176.12 inference(resolution,[status(thm)],[f15,f7])). 1390.10/176.12 fof(f19,definition,( 1390.10/176.12 ![X0]: (sQ0_spl <=> (~is_a_theorem(X0)))), 1390.10/176.12 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])). 1390.10/176.12 fof(f20,plain,( 1390.10/176.12 ![X0]: (~is_a_theorem(X0)|~sQ0_spl)), 1390.10/176.12 inference(component_clause,[status(thm)],[f19])). 1390.10/176.12 fof(f22,definition,( 1390.10/176.12 ![X1,X2]: (sQ1_spl <=> (is_a_theorem(implies(X1,implies(X2,X1)))))), 1390.10/176.12 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])). 1390.10/176.13 fof(f23,plain,( 1390.10/176.13 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~sQ1_spl)), 1390.10/176.13 inference(component_clause,[status(thm)],[f22])). 1390.10/176.13 fof(f25,plain,( 1390.10/176.13 sQ0_spl|sQ1_spl), 1390.10/176.13 inference(split_clause,[status(thm)],[f17,f19,f22])). 1390.10/176.13 fof(f27,plain,( 1390.10/176.13 ![X0,X1,X2,X3,X4,X5]: (~is_a_theorem(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)))|is_a_theorem(X5))), 1390.10/176.13 inference(resolution,[status(thm)],[f12,f7])). 1390.10/176.13 fof(f50,plain,( 1390.10/176.13 $false|~sQ0_spl), 1390.10/176.13 inference(backward_subsumption_resolution,[status(thm)],[f12,f20])). 1390.10/176.13 fof(f55,plain,( 1390.10/176.13 ~sQ0_spl), 1390.10/176.13 inference(contradiction_clause,[status(thm)],[f50])). 1390.10/176.13 fof(f82,plain,( 1390.10/176.13 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (is_a_theorem(X0)|~is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8),X0)))), 1390.10/176.13 inference(resolution,[status(thm)],[f10,f13])). 1390.10/176.13 fof(f146,plain,( 1390.10/176.13 ![X0,X1,X2,X3,X4,X5,X6,X7]: (is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7)))), 1390.10/176.13 inference(resolution,[status(thm)],[f16,f82])). 1390.10/176.13 fof(f202,plain,( 1390.10/176.13 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)))|is_a_theorem(X7))), 1390.10/176.13 inference(resolution,[status(thm)],[f146,f7])). 1390.10/176.13 fof(f210,plain,( 1390.10/176.13 ![X0,X1,X2,X3,X4]: (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f202,f23])). 1390.10/176.13 fof(f241,plain,( 1390.10/176.13 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2)))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f210,f27])). 1390.10/176.13 fof(f242,plain,( 1390.10/176.13 ![X0,X1,X2,X3,X4]: (is_a_theorem(X0)|~is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X0)))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f210,f7])). 1390.10/176.13 fof(f250,plain,( 1390.10/176.13 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f241,f202])). 1390.10/176.13 fof(f292,plain,( 1390.10/176.13 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f242,f241])). 1390.10/176.13 fof(f319,plain,( 1390.10/176.13 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))|~is_a_theorem(implies(X2,X0))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f250,f7])). 1390.10/176.13 fof(f328,plain,( 1390.10/176.13 ![X0,X1,X2]: (is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(implies(X2,X0),X1))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f292,f7])). 1390.10/176.13 fof(f405,plain,( 1390.10/176.13 ![X0,X1]: (is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f328,f210])). 1390.10/176.13 fof(f409,plain,( 1390.10/176.13 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1))))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f328,f250])). 1390.10/176.13 fof(f570,plain,( 1390.10/176.13 ~is_a_theorem(implies(implies(y,implies(x,z)),implies(x,implies(y,z))))|~sQ1_spl), 1390.10/176.13 inference(resolution,[status(thm)],[f319,f8])). 1390.10/176.13 fof(f580,plain,( 1390.10/176.13 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X2,X0))|is_a_theorem(implies(X2,X1))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f319,f7])). 1390.10/176.13 fof(f2454,plain,( 1390.10/176.13 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(implies(implies(n(X1),X1),X1),X2)))|is_a_theorem(implies(X0,X2))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f580,f405])). 1390.10/176.13 fof(f2472,plain,( 1390.10/176.13 ![X0,X1,X2,X3]: (~is_a_theorem(implies(X0,implies(X1,X2)))|is_a_theorem(implies(X0,implies(X3,X2)))|~is_a_theorem(implies(X3,X1))|~sQ1_spl)), 1390.10/176.13 inference(resolution,[status(thm)],[f580,f319])). 1390.10/176.13 fof(f14912,plain,( 1390.10/176.13 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))|~sQ1_spl)), 1390.10/176.21 inference(resolution,[status(thm)],[f2454,f250])). 1390.10/176.21 fof(f19155,plain,( 1390.10/176.21 ![X0,X1,X2,X3]: (is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(implies(implies(X0,X2),implies(X3,X2)),X1))|~sQ1_spl)), 1390.10/176.21 inference(resolution,[status(thm)],[f580,f409])). 1390.10/176.21 fof(f25486,plain,( 1390.10/176.21 ![X0]: (~is_a_theorem(implies(implies(y,implies(x,z)),implies(X0,implies(y,z))))|~is_a_theorem(implies(x,X0))|~sQ1_spl)), 1390.10/176.21 inference(resolution,[status(thm)],[f2472,f570])). 1390.10/176.21 fof(f31880,plain,( 1390.10/176.21 ~is_a_theorem(implies(x,implies(implies(x,z),z)))|~sQ1_spl), 1390.10/176.21 inference(resolution,[status(thm)],[f25486,f250])). 1390.10/176.21 fof(f69669,plain,( 1390.10/176.21 ![X0,X1]: (is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))|~sQ1_spl)), 1390.10/176.21 inference(resolution,[status(thm)],[f19155,f14912])). 1390.10/176.21 fof(f69832,plain,( 1390.10/176.21 $false|~sQ1_spl), 1390.10/176.21 inference(backward_subsumption_resolution,[status(thm)],[f31880,f69669])). 1390.10/176.21 fof(f69988,plain,( 1390.10/176.21 ~sQ1_spl), 1390.10/176.21 inference(contradiction_clause,[status(thm)],[f69832])). 1390.10/176.21 fof(f69989,plain,( 1390.10/176.21 $false), 1390.10/176.21 inference(sat_refutation,[status(thm)],[f25,f55,f69988])). 1390.10/176.21 % SZS output end CNFRefutation for theBenchmark.p 394.21/177.40 % Elapsed time: 176.824346 seconds 394.21/177.40 % CPU time: 1307.434258 seconds 394.21/177.40 % Total memory used: 2.088 GB 394.21/177.40 % Net memory used: 1.898 GB 394.21/177.41 EOF