%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:22:32 PM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 06:20:49 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.52 % Refutation found
% 0.15/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.52 fof(f1,conjecture,(
% 0.15/0.52 (! [A,B,C,D] :~ ( r2_hidden(A,k2_xboole_0(C,D))& r2_hidden(B,k2_xboole_0(C,D))& ~ ( r2_hidden(A,k4_xboole_0(C,D))& r2_hidden(B,k4_xboole_0(C,D)) )& ~ ( r2_hidden(A,D)& r2_hidden(B,D) )& ~ ( r2_hidden(A,k4_xboole_0(C,D))& r2_hidden(B,D) )& ~ ( r2_hidden(A,D)& r2_hidden(B,k4_xboole_0(C,D)) ) ) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f2,negated_conjecture,(
% 0.15/0.52 ~((! [A,B,C,D] :~ ( r2_hidden(A,k2_xboole_0(C,D))& r2_hidden(B,k2_xboole_0(C,D))& ~ ( r2_hidden(A,k4_xboole_0(C,D))& r2_hidden(B,k4_xboole_0(C,D)) )& ~ ( r2_hidden(A,D)& r2_hidden(B,D) )& ~ ( r2_hidden(A,k4_xboole_0(C,D))& r2_hidden(B,D) )& ~ ( r2_hidden(A,D)& r2_hidden(B,k4_xboole_0(C,D)) ) ) ))),
% 0.15/0.52 inference(negated_conjecture,[status(cth)],[f1])).
% 0.15/0.52 fof(f4,axiom,(
% 0.15/0.52 (! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f5,axiom,(
% 0.15/0.52 (! [A,B,C] :( C = k2_xboole_0(A,B)<=> (! [D] :( r2_hidden(D,C)<=> ( r2_hidden(D,A)| r2_hidden(D,B) ) ) )) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f20,axiom,(
% 0.15/0.52 (! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f26,plain,(
% 0.15/0.52 (?[A,B,C,D]: (((((r2_hidden(A,k2_xboole_0(C,D))&r2_hidden(B,k2_xboole_0(C,D)))&(~r2_hidden(A,k4_xboole_0(C,D))|~r2_hidden(B,k4_xboole_0(C,D))))&(~r2_hidden(A,D)|~r2_hidden(B,D)))&(~r2_hidden(A,k4_xboole_0(C,D))|~r2_hidden(B,D)))&(~r2_hidden(A,D)|~r2_hidden(B,k4_xboole_0(C,D)))))),
% 0.15/0.52 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/0.52 fof(f27,plain,(
% 0.15/0.52 (((((r2_hidden(sK0_skl,k2_xboole_0(sK2_skl,sK3_skl))&r2_hidden(sK1_skl,k2_xboole_0(sK2_skl,sK3_skl)))&(~r2_hidden(sK0_skl,k4_xboole_0(sK2_skl,sK3_skl))|~r2_hidden(sK1_skl,k4_xboole_0(sK2_skl,sK3_skl))))&(~r2_hidden(sK0_skl,sK3_skl)|~r2_hidden(sK1_skl,sK3_skl)))&(~r2_hidden(sK0_skl,k4_xboole_0(sK2_skl,sK3_skl))|~r2_hidden(sK1_skl,sK3_skl)))&(~r2_hidden(sK0_skl,sK3_skl)|~r2_hidden(sK1_skl,k4_xboole_0(sK2_skl,sK3_skl))))),
% 0.15/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f26])).
% 0.15/0.52 fof(f28,plain,(
% 0.15/0.52 r2_hidden(sK0_skl,k2_xboole_0(sK2_skl,sK3_skl))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.52 fof(f29,plain,(
% 0.15/0.52 r2_hidden(sK1_skl,k2_xboole_0(sK2_skl,sK3_skl))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.52 fof(f30,plain,(
% 0.15/0.52 ~r2_hidden(sK0_skl,k4_xboole_0(sK2_skl,sK3_skl))|~r2_hidden(sK1_skl,k4_xboole_0(sK2_skl,sK3_skl))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.52 fof(f31,plain,(
% 0.15/0.52 ~r2_hidden(sK0_skl,sK3_skl)|~r2_hidden(sK1_skl,sK3_skl)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.52 fof(f32,plain,(
% 0.15/0.52 ~r2_hidden(sK0_skl,k4_xboole_0(sK2_skl,sK3_skl))|~r2_hidden(sK1_skl,sK3_skl)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.52 fof(f33,plain,(
% 0.15/0.52 ~r2_hidden(sK0_skl,sK3_skl)|~r2_hidden(sK1_skl,k4_xboole_0(sK2_skl,sK3_skl))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.52 fof(f36,plain,(
% 0.15/0.52 ![X0,X1]: (k2_xboole_0(X0,X1)=k2_xboole_0(X1,X0))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f4])).
% 0.15/0.52 fof(f37,plain,(
% 0.15/0.52 ![A,B,C]: ((~C=k2_xboole_0(A,B)|(![D]: ((~r2_hidden(D,C)|(r2_hidden(D,A)|r2_hidden(D,B)))&(r2_hidden(D,C)|(~r2_hidden(D,A)&~r2_hidden(D,B))))))&(C=k2_xboole_0(A,B)|(?[D]: ((~r2_hidden(D,C)|(~r2_hidden(D,A)&~r2_hidden(D,B)))&(r2_hidden(D,C)|(r2_hidden(D,A)|r2_hidden(D,B)))))))),
% 0.15/0.52 inference(NNF_transformation,[status(thm)],[f5])).
% 0.15/0.52 fof(f38,plain,(
% 0.15/0.52 (![A,B,C]: (~C=k2_xboole_0(A,B)|((![D]: (~r2_hidden(D,C)|(r2_hidden(D,A)|r2_hidden(D,B))))&(![D]: (r2_hidden(D,C)|(~r2_hidden(D,A)&~r2_hidden(D,B)))))))&(![A,B,C]: (C=k2_xboole_0(A,B)|(?[D]: ((~r2_hidden(D,C)|(~r2_hidden(D,A)&~r2_hidden(D,B)))&(r2_hidden(D,C)|(r2_hidden(D,A)|r2_hidden(D,B)))))))),
% 0.15/0.52 inference(miniscoping,[status(thm)],[f37])).
% 0.15/0.52 fof(f39,plain,(
% 0.15/0.52 (![A,B,C]: (~C=k2_xboole_0(A,B)|((![D]: (~r2_hidden(D,C)|(r2_hidden(D,A)|r2_hidden(D,B))))&(![D]: (r2_hidden(D,C)|(~r2_hidden(D,A)&~r2_hidden(D,B)))))))&(![A,B,C]: (C=k2_xboole_0(A,B)|((~r2_hidden(sK4_skl(C,B,A),C)|(~r2_hidden(sK4_skl(C,B,A),A)&~r2_hidden(sK4_skl(C,B,A),B)))&(r2_hidden(sK4_skl(C,B,A),C)|(r2_hidden(sK4_skl(C,B,A),A)|r2_hidden(sK4_skl(C,B,A),B))))))),
% 0.15/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f38])).
% 0.15/0.53 fof(f40,plain,(
% 0.15/0.53 ![X0,X1,X2,X3]: (~X0=k2_xboole_0(X1,X2)|~r2_hidden(X3,X0)|r2_hidden(X3,X1)|r2_hidden(X3,X2))),
% 0.15/0.53 inference(cnf_transformation,[status(thm)],[f39])).
% 0.15/0.53 fof(f66,plain,(
% 0.15/0.53 ![X0,X1]: (k2_xboole_0(X0,k4_xboole_0(X1,X0))=k2_xboole_0(X0,X1))),
% 0.15/0.53 inference(cnf_transformation,[status(thm)],[f20])).
% 0.15/0.53 fof(f77,definition,(
% 0.15/0.53 sQ0_spl <=> (r2_hidden(sK0_skl,k4_xboole_0(sK2_skl,sK3_skl)))),
% 0.15/0.53 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.53 fof(f80,definition,(
% 0.15/0.53 sQ1_spl <=> (r2_hidden(sK1_skl,k4_xboole_0(sK2_skl,sK3_skl)))),
% 0.15/0.53 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.53 fof(f83,plain,(
% 0.15/0.53 ~sQ0_spl|~sQ1_spl),
% 0.15/0.53 inference(split_clause,[status(thm)],[f30,f77,f80])).
% 0.15/0.53 fof(f84,definition,(
% 0.15/0.53 sQ2_spl <=> (r2_hidden(sK0_skl,sK3_skl))),
% 0.15/0.53 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.53 fof(f87,definition,(
% 0.15/0.53 sQ3_spl <=> (r2_hidden(sK1_skl,sK3_skl))),
% 0.15/0.53 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/0.53 fof(f90,plain,(
% 0.15/0.53 ~sQ2_spl|~sQ3_spl),
% 0.15/0.53 inference(split_clause,[status(thm)],[f31,f84,f87])).
% 0.15/0.53 fof(f91,plain,(
% 0.15/0.53 ~sQ0_spl|~sQ3_spl),
% 0.15/0.53 inference(split_clause,[status(thm)],[f32,f77,f87])).
% 0.15/0.53 fof(f92,plain,(
% 0.15/0.53 ~sQ2_spl|~sQ1_spl),
% 0.15/0.53 inference(split_clause,[status(thm)],[f33,f84,f80])).
% 0.15/0.53 fof(f93,plain,(
% 0.15/0.53 ![X0,X1,X2]: (~r2_hidden(X0,k2_xboole_0(X1,X2))|r2_hidden(X0,X1)|r2_hidden(X0,X2))),
% 0.15/0.53 inference(destructive_equality_resolution,[status(thm)],[f40])).
% 0.15/0.53 fof(f175,plain,(
% 0.15/0.53 ![X0,X1,X2]: (~r2_hidden(X0,k2_xboole_0(X1,X2))|r2_hidden(X0,X1)|r2_hidden(X0,k4_xboole_0(X2,X1)))),
% 0.15/0.53 inference(paramodulation,[status(thm)],[f66,f93])).
% 0.15/0.53 fof(f207,plain,(
% 0.15/0.53 ![X0,X1,X2]: (~r2_hidden(X0,k2_xboole_0(X1,X2))|r2_hidden(X0,X2)|r2_hidden(X0,k4_xboole_0(X1,X2)))),
% 0.15/0.53 inference(paramodulation,[status(thm)],[f36,f175])).
% 0.15/0.53 fof(f329,plain,(
% 0.15/0.53 r2_hidden(sK1_skl,sK3_skl)|r2_hidden(sK1_skl,k4_xboole_0(sK2_skl,sK3_skl))),
% 0.15/0.53 inference(resolution,[status(thm)],[f207,f29])).
% 0.15/0.53 fof(f332,plain,(
% 0.15/0.53 r2_hidden(sK0_skl,sK3_skl)|r2_hidden(sK0_skl,k4_xboole_0(sK2_skl,sK3_skl))),
% 0.15/0.53 inference(resolution,[status(thm)],[f207,f28])).
% 0.15/0.53 fof(f356,plain,(
% 0.15/0.53 sQ3_spl|sQ1_spl),
% 0.15/0.53 inference(split_clause,[status(thm)],[f329,f87,f80])).
% 0.15/0.53 fof(f357,plain,(
% 0.15/0.53 sQ2_spl|sQ0_spl),
% 0.15/0.53 inference(split_clause,[status(thm)],[f332,f84,f77])).
% 0.15/0.53 fof(f358,plain,(
% 0.15/0.53 $false),
% 0.15/0.53 inference(sat_refutation,[status(thm)],[f83,f90,f91,f92,f356,f357])).
% 0.15/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.55 % Elapsed time: 0.110246 seconds
% 0.15/0.55 % CPU time: 0.555394 seconds
% 0.15/0.55 % Total memory used: 108.014 MB
% 0.15/0.55 % Net memory used: 107.341 MB
%------------------------------------------------------------------------------