%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 03:18:52 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:43:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.41 fof(f1,conjecture,(
% 0.09/0.41 ( (! [X] :( ( big_p(a)& ( big_p(X)=> (? [Y] :( big_p(Y)& big_r(X,Y) ) )) )=> (? [Z,W] :( big_p(Z)& big_r(X,W)& big_r(W,Z) ) )))<=> (! [X1] :( ( ~ big_p(a)| big_p(X1)| (? [Z1,W1] :( big_p(Z1)& big_r(X1,W1)& big_r(W1,Z1) ) ))& ( ~ big_p(a)| ~ (? [Y1] :( big_p(Y1)& big_r(X1,Y1) ))| (? [Z2,W2] :( big_p(Z2)& big_r(X1,W2)& big_r(W2,Z2) ) )) ) )) ),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f2,negated_conjecture,(
% 0.09/0.41 ~(( (! [X] :( ( big_p(a)& ( big_p(X)=> (? [Y] :( big_p(Y)& big_r(X,Y) ) )) )=> (? [Z,W] :( big_p(Z)& big_r(X,W)& big_r(W,Z) ) )))<=> (! [X1] :( ( ~ big_p(a)| big_p(X1)| (? [Z1,W1] :( big_p(Z1)& big_r(X1,W1)& big_r(W1,Z1) ) ))& ( ~ big_p(a)| ~ (? [Y1] :( big_p(Y1)& big_r(X1,Y1) ))| (? [Z2,W2] :( big_p(Z2)& big_r(X1,W2)& big_r(W2,Z2) ) )) ) )) )),
% 0.09/0.41 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.41 fof(f3,plain,(
% 0.09/0.41 ((![X]: ((~big_p(a)|(big_p(X)&(![Y]: (~big_p(Y)|~big_r(X,Y)))))|(?[Z,W]: ((big_p(Z)&big_r(X,W))&big_r(W,Z)))))<~>(![X1]: (((~big_p(a)|big_p(X1))|(?[Z1,W1]: ((big_p(Z1)&big_r(X1,W1))&big_r(W1,Z1))))&((~big_p(a)|(![Y1]: (~big_p(Y1)|~big_r(X1,Y1))))|(?[Z2,W2]: ((big_p(Z2)&big_r(X1,W2))&big_r(W2,Z2)))))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.09/0.41 fof(f4,definition,(
% 0.09/0.41 ![X]: (sP0_prd(X)<=>((~big_p(a)|(big_p(X)&(![Y]: (~big_p(Y)|~big_r(X,Y)))))|(?[Z,W]: ((big_p(Z)&big_r(X,W))&big_r(W,Z)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.41 fof(f5,definition,(
% 0.09/0.41 ![X1]: (sP1_prd(X1)<=>((~big_p(a)|big_p(X1))|(?[Z1,W1]: ((big_p(Z1)&big_r(X1,W1))&big_r(W1,Z1)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.09/0.41 fof(f6,plain,(
% 0.09/0.41 (![X]: sP0_prd(X))<~>(![X1]: (sP1_prd(X1)&((~big_p(a)|(![Y1]: (~big_p(Y1)|~big_r(X1,Y1))))|(?[Z2,W2]: ((big_p(Z2)&big_r(X1,W2))&big_r(W2,Z2))))))),
% 0.09/0.41 inference(formula_renaming,[status(thm)],[f3,f5,f4])).
% 0.09/0.41 fof(f7,plain,(
% 0.09/0.41 ((![X]: sP0_prd(X))|(![X1]: (sP1_prd(X1)&((~big_p(a)|(![Y1]: (~big_p(Y1)|~big_r(X1,Y1))))|(?[Z2,W2]: ((big_p(Z2)&big_r(X1,W2))&big_r(W2,Z2)))))))&((?[X]: ~sP0_prd(X))|(?[X1]: (~sP1_prd(X1)|((big_p(a)&(?[Y1]: (big_p(Y1)&big_r(X1,Y1))))&(![Z2,W2]: ((~big_p(Z2)|~big_r(X1,W2))|~big_r(W2,Z2)))))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f6])).
% 0.09/0.41 fof(f8,plain,(
% 0.09/0.41 ((![X]: sP0_prd(X))|((![X1]: sP1_prd(X1))&(![X1]: ((~big_p(a)|(![Y1]: (~big_p(Y1)|~big_r(X1,Y1))))|(?[Z2,W2]: ((big_p(Z2)&big_r(X1,W2))&big_r(W2,Z2)))))))&((?[X]: ~sP0_prd(X))|((?[X1]: ~sP1_prd(X1))|(?[X1]: ((big_p(a)&(?[Y1]: (big_p(Y1)&big_r(X1,Y1))))&(![Z2,W2]: ((~big_p(Z2)|~big_r(X1,W2))|~big_r(W2,Z2)))))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f7])).
% 0.09/0.41 fof(f9,plain,(
% 0.09/0.41 ((![X]: sP0_prd(X))|((![X1]: sP1_prd(X1))&(![X1]: ((~big_p(a)|(![Y1]: (~big_p(Y1)|~big_r(X1,Y1))))|((big_p(sK0_skl(X1))&big_r(X1,sK1_skl(X1)))&big_r(sK1_skl(X1),sK0_skl(X1)))))))&(~sP0_prd(sK2_skl)|(~sP1_prd(sK3_skl)|((big_p(a)&(big_p(sK5_skl)&big_r(sK4_skl,sK5_skl)))&(![Z2,W2]: ((~big_p(Z2)|~big_r(sK4_skl,W2))|~big_r(W2,Z2))))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(Z2,sK0_skl(X1)),skolemize(W2,sK1_skl(X1)),skolemize(X,sK2_skl),skolemize(X1,sK3_skl),skolemize(X1,sK4_skl),skolemize(Y1,sK5_skl)],[f8])).
% 0.09/0.41 fof(f10,plain,(
% 0.09/0.41 ![X0,X1]: (sP0_prd(X0)|sP1_prd(X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f11,plain,(
% 0.09/0.41 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(a)|~big_p(X1)|~big_r(X2,X1)|big_p(sK0_skl(X2)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f12,plain,(
% 0.09/0.41 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(a)|~big_p(X1)|~big_r(X2,X1)|big_r(X2,sK1_skl(X2)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f13,plain,(
% 0.09/0.41 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(a)|~big_p(X1)|~big_r(X2,X1)|big_r(sK1_skl(X2),sK0_skl(X2)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f14,plain,(
% 0.09/0.41 ~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|big_p(a)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f15,plain,(
% 0.09/0.41 ~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|big_p(sK5_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f16,plain,(
% 0.09/0.41 ~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|big_r(sK4_skl,sK5_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f17,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|~big_p(X0)|~big_r(sK4_skl,X1)|~big_r(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.41 fof(f18,definition,(
% 0.09/0.41 ![X]: (sP2_prd(X)<=>(big_p(X)&(![Y]: (~big_p(Y)|~big_r(X,Y)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 0.09/0.41 fof(f19,plain,(
% 0.09/0.41 ![X]: (sP0_prd(X)<=>((~big_p(a)|sP2_prd(X))|(?[Z,W]: ((big_p(Z)&big_r(X,W))&big_r(W,Z)))))),
% 0.09/0.41 inference(formula_renaming,[status(thm)],[f4,f18])).
% 0.09/0.41 fof(f20,plain,(
% 0.09/0.41 ![X]: ((~sP0_prd(X)|((~big_p(a)|sP2_prd(X))|(?[Z,W]: ((big_p(Z)&big_r(X,W))&big_r(W,Z)))))&(sP0_prd(X)|((big_p(a)&~sP2_prd(X))&(![Z,W]: ((~big_p(Z)|~big_r(X,W))|~big_r(W,Z))))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f19])).
% 0.09/0.41 fof(f21,plain,(
% 0.09/0.41 (![X]: (~sP0_prd(X)|((~big_p(a)|sP2_prd(X))|(?[Z,W]: ((big_p(Z)&big_r(X,W))&big_r(W,Z))))))&(![X]: (sP0_prd(X)|((big_p(a)&~sP2_prd(X))&(![Z,W]: ((~big_p(Z)|~big_r(X,W))|~big_r(W,Z))))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f20])).
% 0.09/0.41 fof(f22,plain,(
% 0.09/0.41 (![X]: (~sP0_prd(X)|((~big_p(a)|sP2_prd(X))|((big_p(sK6_skl(X))&big_r(X,sK7_skl(X)))&big_r(sK7_skl(X),sK6_skl(X))))))&(![X]: (sP0_prd(X)|((big_p(a)&~sP2_prd(X))&(![Z,W]: ((~big_p(Z)|~big_r(X,W))|~big_r(W,Z))))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(Z,sK6_skl(X)),skolemize(W,sK7_skl(X))],[f21])).
% 0.09/0.41 fof(f23,plain,(
% 0.09/0.41 ![X0]: (~sP0_prd(X0)|~big_p(a)|sP2_prd(X0)|big_p(sK6_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f24,plain,(
% 0.09/0.41 ![X0]: (~sP0_prd(X0)|~big_p(a)|sP2_prd(X0)|big_r(X0,sK7_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f25,plain,(
% 0.09/0.41 ![X0]: (~sP0_prd(X0)|~big_p(a)|sP2_prd(X0)|big_r(sK7_skl(X0),sK6_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f26,plain,(
% 0.09/0.41 ![X0]: (sP0_prd(X0)|big_p(a))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f27,plain,(
% 0.09/0.41 ![X0]: (sP0_prd(X0)|~sP2_prd(X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f28,plain,(
% 0.09/0.41 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(X1)|~big_r(X0,X2)|~big_r(X2,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f29,plain,(
% 0.09/0.41 ![X1]: ((~sP1_prd(X1)|((~big_p(a)|big_p(X1))|(?[Z1,W1]: ((big_p(Z1)&big_r(X1,W1))&big_r(W1,Z1)))))&(sP1_prd(X1)|((big_p(a)&~big_p(X1))&(![Z1,W1]: ((~big_p(Z1)|~big_r(X1,W1))|~big_r(W1,Z1))))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f5])).
% 0.09/0.41 fof(f30,plain,(
% 0.09/0.41 (![X1]: (~sP1_prd(X1)|((~big_p(a)|big_p(X1))|(?[Z1,W1]: ((big_p(Z1)&big_r(X1,W1))&big_r(W1,Z1))))))&(![X1]: (sP1_prd(X1)|((big_p(a)&~big_p(X1))&(![Z1,W1]: ((~big_p(Z1)|~big_r(X1,W1))|~big_r(W1,Z1))))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f29])).
% 0.09/0.41 fof(f31,plain,(
% 0.09/0.41 (![X1]: (~sP1_prd(X1)|((~big_p(a)|big_p(X1))|((big_p(sK8_skl(X1))&big_r(X1,sK9_skl(X1)))&big_r(sK9_skl(X1),sK8_skl(X1))))))&(![X1]: (sP1_prd(X1)|((big_p(a)&~big_p(X1))&(![Z1,W1]: ((~big_p(Z1)|~big_r(X1,W1))|~big_r(W1,Z1))))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(Z1,sK8_skl(X1)),skolemize(W1,sK9_skl(X1))],[f30])).
% 0.09/0.41 fof(f32,plain,(
% 0.09/0.41 ![X0]: (~sP1_prd(X0)|~big_p(a)|big_p(X0)|big_p(sK8_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f33,plain,(
% 0.09/0.41 ![X0]: (~sP1_prd(X0)|~big_p(a)|big_p(X0)|big_r(X0,sK9_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f34,plain,(
% 0.09/0.41 ![X0]: (~sP1_prd(X0)|~big_p(a)|big_p(X0)|big_r(sK9_skl(X0),sK8_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f35,plain,(
% 0.09/0.41 ![X0]: (sP1_prd(X0)|big_p(a))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f36,plain,(
% 0.09/0.41 ![X0]: (sP1_prd(X0)|~big_p(X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f37,plain,(
% 0.09/0.41 ![X0,X1,X2]: (sP1_prd(X0)|~big_p(X1)|~big_r(X0,X2)|~big_r(X2,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f38,plain,(
% 0.09/0.41 ![X]: ((~sP2_prd(X)|(big_p(X)&(![Y]: (~big_p(Y)|~big_r(X,Y)))))&(sP2_prd(X)|(~big_p(X)|(?[Y]: (big_p(Y)&big_r(X,Y))))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f18])).
% 0.09/0.41 fof(f39,plain,(
% 0.09/0.41 (![X]: (~sP2_prd(X)|(big_p(X)&(![Y]: (~big_p(Y)|~big_r(X,Y))))))&(![X]: (sP2_prd(X)|(~big_p(X)|(?[Y]: (big_p(Y)&big_r(X,Y))))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f38])).
% 0.09/0.41 fof(f40,plain,(
% 0.09/0.41 (![X]: (~sP2_prd(X)|(big_p(X)&(![Y]: (~big_p(Y)|~big_r(X,Y))))))&(![X]: (sP2_prd(X)|(~big_p(X)|(big_p(sK10_skl(X))&big_r(X,sK10_skl(X))))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(Y,sK10_skl(X))],[f39])).
% 0.09/0.41 fof(f41,plain,(
% 0.09/0.41 ![X0]: (~sP2_prd(X0)|big_p(X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.41 fof(f42,plain,(
% 0.09/0.41 ![X0,X1]: (~sP2_prd(X0)|~big_p(X1)|~big_r(X0,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.41 fof(f43,plain,(
% 0.09/0.41 ![X0]: (sP2_prd(X0)|~big_p(X0)|big_p(sK10_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.41 fof(f44,plain,(
% 0.09/0.41 ![X0]: (sP2_prd(X0)|~big_p(X0)|big_r(X0,sK10_skl(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.41 fof(f45,definition,(
% 0.09/0.41 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f46,plain,(
% 0.09/0.41 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f45])).
% 0.09/0.41 fof(f48,definition,(
% 0.09/0.41 ![X1]: (sQ1_spl <=> (sP1_prd(X1)))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f49,plain,(
% 0.09/0.41 ![X0]: (sP1_prd(X0)|~sQ1_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f48])).
% 0.09/0.41 fof(f51,plain,(
% 0.09/0.41 sQ0_spl|sQ1_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f10,f45,f48])).
% 0.09/0.41 fof(f52,definition,(
% 0.09/0.41 sQ2_spl <=> (big_p(a))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f55,definition,(
% 0.09/0.41 ![X1,X2]: (sQ3_spl <=> (~big_p(X1)|~big_r(X2,X1)|big_p(sK0_skl(X2))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f56,plain,(
% 0.09/0.41 ![X0,X1]: (~big_p(X0)|~big_r(X1,X0)|big_p(sK0_skl(X1))|~sQ3_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f55])).
% 0.09/0.41 fof(f58,plain,(
% 0.09/0.41 sQ0_spl|~sQ2_spl|sQ3_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f11,f45,f52,f55])).
% 0.09/0.41 fof(f59,definition,(
% 0.09/0.41 ![X1,X2]: (sQ4_spl <=> (~big_p(X1)|~big_r(X2,X1)|big_r(X2,sK1_skl(X2))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f60,plain,(
% 0.09/0.41 ![X0,X1]: (~big_p(X0)|~big_r(X1,X0)|big_r(X1,sK1_skl(X1))|~sQ4_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f59])).
% 0.09/0.41 fof(f62,plain,(
% 0.09/0.41 sQ0_spl|~sQ2_spl|sQ4_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f12,f45,f52,f59])).
% 0.09/0.41 fof(f63,definition,(
% 0.09/0.41 ![X1,X2]: (sQ5_spl <=> (~big_p(X1)|~big_r(X2,X1)|big_r(sK1_skl(X2),sK0_skl(X2))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f64,plain,(
% 0.09/0.41 ![X0,X1]: (~big_p(X0)|~big_r(X1,X0)|big_r(sK1_skl(X1),sK0_skl(X1))|~sQ5_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f63])).
% 0.09/0.41 fof(f66,plain,(
% 0.09/0.41 sQ0_spl|~sQ2_spl|sQ5_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f13,f45,f52,f63])).
% 0.09/0.41 fof(f67,definition,(
% 0.09/0.41 sQ6_spl <=> (sP0_prd(sK2_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f69,plain,(
% 0.09/0.41 ~sP0_prd(sK2_skl)|sQ6_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f67])).
% 0.09/0.41 fof(f70,definition,(
% 0.09/0.41 sQ7_spl <=> (sP1_prd(sK3_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f72,plain,(
% 0.09/0.41 ~sP1_prd(sK3_skl)|sQ7_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f70])).
% 0.09/0.41 fof(f73,plain,(
% 0.09/0.41 ~sQ6_spl|~sQ7_spl|sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f14,f67,f70,f52])).
% 0.09/0.41 fof(f74,definition,(
% 0.09/0.41 sQ8_spl <=> (big_p(sK5_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f75,plain,(
% 0.09/0.41 big_p(sK5_skl)|~sQ8_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f74])).
% 0.09/0.41 fof(f77,plain,(
% 0.09/0.41 ~sQ6_spl|~sQ7_spl|sQ8_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f15,f67,f70,f74])).
% 0.09/0.41 fof(f78,definition,(
% 0.09/0.41 sQ9_spl <=> (big_r(sK4_skl,sK5_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f79,plain,(
% 0.09/0.41 big_r(sK4_skl,sK5_skl)|~sQ9_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f78])).
% 0.09/0.41 fof(f81,plain,(
% 0.09/0.41 ~sQ6_spl|~sQ7_spl|sQ9_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f16,f67,f70,f78])).
% 0.09/0.41 fof(f82,definition,(
% 0.09/0.41 ![X0,X1]: (sQ10_spl <=> (~big_p(X0)|~big_r(sK4_skl,X1)|~big_r(X1,X0)))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f83,plain,(
% 0.09/0.41 ![X0,X1]: (~big_p(X0)|~big_r(sK4_skl,X1)|~big_r(X1,X0)|~sQ10_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f82])).
% 0.09/0.41 fof(f85,plain,(
% 0.09/0.41 ~sQ6_spl|~sQ7_spl|sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f17,f67,f70,f82])).
% 0.09/0.41 fof(f86,definition,(
% 0.09/0.41 ![X0]: (sQ11_spl <=> (~sP0_prd(X0)|sP2_prd(X0)|big_p(sK6_skl(X0))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f87,plain,(
% 0.09/0.41 ![X0]: (~sP0_prd(X0)|sP2_prd(X0)|big_p(sK6_skl(X0))|~sQ11_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f86])).
% 0.09/0.41 fof(f89,plain,(
% 0.09/0.41 sQ11_spl|~sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f23,f86,f52])).
% 0.09/0.41 fof(f90,definition,(
% 0.09/0.41 ![X0]: (sQ12_spl <=> (~sP0_prd(X0)|sP2_prd(X0)|big_r(X0,sK7_skl(X0))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f91,plain,(
% 0.09/0.41 ![X0]: (~sP0_prd(X0)|sP2_prd(X0)|big_r(X0,sK7_skl(X0))|~sQ12_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f90])).
% 0.09/0.41 fof(f93,plain,(
% 0.09/0.41 sQ12_spl|~sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f24,f90,f52])).
% 0.09/0.41 fof(f94,definition,(
% 0.09/0.41 ![X0]: (sQ13_spl <=> (~sP0_prd(X0)|sP2_prd(X0)|big_r(sK7_skl(X0),sK6_skl(X0))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f95,plain,(
% 0.09/0.41 ![X0]: (~sP0_prd(X0)|sP2_prd(X0)|big_r(sK7_skl(X0),sK6_skl(X0))|~sQ13_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f94])).
% 0.09/0.41 fof(f97,plain,(
% 0.09/0.41 sQ13_spl|~sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f25,f94,f52])).
% 0.09/0.41 fof(f98,plain,(
% 0.09/0.41 sQ0_spl|sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f26,f45,f52])).
% 0.09/0.42 fof(f99,definition,(
% 0.09/0.42 ![X0]: (sQ14_spl <=> (~sP1_prd(X0)|big_p(X0)|big_p(sK8_skl(X0))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f100,plain,(
% 0.09/0.42 ![X0]: (~sP1_prd(X0)|big_p(X0)|big_p(sK8_skl(X0))|~sQ14_spl)),
% 0.09/0.42 inference(component_clause,[status(thm)],[f99])).
% 0.09/0.42 fof(f102,plain,(
% 0.09/0.42 sQ14_spl|~sQ2_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f32,f99,f52])).
% 0.09/0.42 fof(f103,definition,(
% 0.09/0.42 ![X0]: (sQ15_spl <=> (~sP1_prd(X0)|big_p(X0)|big_r(X0,sK9_skl(X0))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f104,plain,(
% 0.09/0.42 ![X0]: (~sP1_prd(X0)|big_p(X0)|big_r(X0,sK9_skl(X0))|~sQ15_spl)),
% 0.09/0.42 inference(component_clause,[status(thm)],[f103])).
% 0.09/0.42 fof(f106,plain,(
% 0.09/0.42 sQ15_spl|~sQ2_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f33,f103,f52])).
% 0.09/0.42 fof(f107,definition,(
% 0.09/0.42 ![X0]: (sQ16_spl <=> (~sP1_prd(X0)|big_p(X0)|big_r(sK9_skl(X0),sK8_skl(X0))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f108,plain,(
% 0.09/0.42 ![X0]: (~sP1_prd(X0)|big_p(X0)|big_r(sK9_skl(X0),sK8_skl(X0))|~sQ16_spl)),
% 0.09/0.42 inference(component_clause,[status(thm)],[f107])).
% 0.09/0.42 fof(f110,plain,(
% 0.09/0.42 sQ16_spl|~sQ2_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f34,f107,f52])).
% 0.09/0.42 fof(f111,plain,(
% 0.09/0.42 sQ1_spl|sQ2_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f35,f48,f52])).
% 0.09/0.42 fof(f112,plain,(
% 0.09/0.42 ![X0]: (sP2_prd(X0)|big_p(sK6_skl(X0))|~sQ0_spl|~sQ11_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f87,f46])).
% 0.09/0.42 fof(f113,plain,(
% 0.09/0.42 ![X0]: (sP2_prd(X0)|big_r(X0,sK7_skl(X0))|~sQ0_spl|~sQ12_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f91,f46])).
% 0.09/0.42 fof(f114,plain,(
% 0.09/0.42 ![X0]: (sP2_prd(X0)|big_r(sK7_skl(X0),sK6_skl(X0))|~sQ0_spl|~sQ13_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f95,f46])).
% 0.09/0.42 fof(f115,plain,(
% 0.09/0.42 ~big_p(sK3_skl)|sQ7_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f36,f72])).
% 0.09/0.42 fof(f119,plain,(
% 0.09/0.42 ![X0,X1]: (sP2_prd(X0)|sP1_prd(X1)|~big_p(sK6_skl(X0))|~big_r(X1,sK7_skl(X0))|~sQ0_spl|~sQ13_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f114,f37])).
% 0.09/0.42 fof(f120,plain,(
% 0.09/0.42 ![X0,X1]: (sP2_prd(X0)|sP1_prd(X1)|~big_r(X1,sK7_skl(X0))|~sQ11_spl|~sQ0_spl|~sQ13_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f119,f112])).
% 0.09/0.42 fof(f122,plain,(
% 0.09/0.42 ![X0]: (sP2_prd(X0)|sP1_prd(X0)|sP2_prd(X0)|~sQ11_spl|~sQ13_spl|~sQ0_spl|~sQ12_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f120,f113])).
% 0.09/0.42 fof(f123,plain,(
% 0.09/0.42 ![X0]: (sP2_prd(X0)|sP1_prd(X0)|~sQ11_spl|~sQ13_spl|~sQ0_spl|~sQ12_spl)),
% 0.09/0.42 inference(duplicate_literals_removal,[status(thm)],[f122])).
% 0.09/0.42 fof(f124,plain,(
% 0.09/0.42 sP2_prd(sK3_skl)|~sQ11_spl|~sQ13_spl|~sQ0_spl|~sQ12_spl|sQ7_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f123,f72])).
% 0.09/0.42 fof(f128,plain,(
% 0.09/0.42 big_p(sK3_skl)|~sQ11_spl|~sQ13_spl|~sQ0_spl|~sQ12_spl|sQ7_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f124,f41])).
% 0.09/0.42 fof(f129,plain,(
% 0.09/0.42 $false|~sQ11_spl|~sQ13_spl|~sQ0_spl|~sQ12_spl|sQ7_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f128,f115])).
% 0.09/0.42 fof(f130,plain,(
% 0.09/0.42 ~sQ11_spl|~sQ13_spl|~sQ0_spl|~sQ12_spl|sQ7_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f129])).
% 0.09/0.42 fof(f131,plain,(
% 0.09/0.42 $false|~sQ0_spl|sQ6_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f69,f46])).
% 0.09/0.42 fof(f132,plain,(
% 0.09/0.42 ~sQ0_spl|sQ6_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f131])).
% 0.09/0.42 fof(f133,plain,(
% 0.09/0.42 ![X0]: (big_p(X0)|big_p(sK8_skl(X0))|~sQ1_spl|~sQ14_spl)),
% 0.09/0.42 inference(backward_subsumption_resolution,[status(thm)],[f100,f49])).
% 0.09/0.42 fof(f134,plain,(
% 0.09/0.42 ![X0]: (big_p(X0)|big_r(sK9_skl(X0),sK8_skl(X0))|~sQ1_spl|~sQ16_spl)),
% 0.09/0.42 inference(backward_subsumption_resolution,[status(thm)],[f108,f49])).
% 0.09/0.42 fof(f136,plain,(
% 0.09/0.42 ![X0]: (~big_p(X0)|~big_r(sK10_skl(sK4_skl),X0)|sP2_prd(sK4_skl)|~big_p(sK4_skl)|~sQ10_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f83,f44])).
% 0.09/0.42 fof(f137,definition,(
% 0.09/0.42 ![X0]: (sQ17_spl <=> (~big_p(X0)|~big_r(sK10_skl(sK4_skl),X0)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f138,plain,(
% 0.09/0.42 ![X0]: (~big_p(X0)|~big_r(sK10_skl(sK4_skl),X0)|~sQ17_spl)),
% 0.09/0.42 inference(component_clause,[status(thm)],[f137])).
% 0.09/0.42 fof(f140,definition,(
% 0.09/0.42 sQ18_spl <=> (sP2_prd(sK4_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f141,plain,(
% 0.09/0.42 sP2_prd(sK4_skl)|~sQ18_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f140])).
% 0.09/0.42 fof(f143,definition,(
% 0.09/0.42 sQ19_spl <=> (big_p(sK4_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f146,plain,(
% 0.09/0.42 sQ17_spl|sQ18_spl|~sQ19_spl|~sQ10_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f136,f137,f140,f143,f82])).
% 0.09/0.42 fof(f150,plain,(
% 0.09/0.42 ![X0]: (~big_p(X0)|~big_r(sK5_skl,X0)|~sQ9_spl|~sQ10_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f79,f83])).
% 0.09/0.42 fof(f157,plain,(
% 0.09/0.42 ![X0]: (~big_p(X0)|~big_r(sK4_skl,X0)|~sQ18_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f141,f42])).
% 0.09/0.42 fof(f159,plain,(
% 0.09/0.42 ![X0]: (sP2_prd(sK4_skl)|~big_p(X0)|~big_r(sK7_skl(sK4_skl),X0)|~sQ0_spl|~sQ12_spl|~sQ10_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f113,f83])).
% 0.09/0.42 fof(f160,definition,(
% 0.09/0.42 ![X0]: (sQ21_spl <=> (~big_p(X0)|~big_r(sK7_skl(sK4_skl),X0)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f161,plain,(
% 0.09/0.42 ![X0]: (~big_p(X0)|~big_r(sK7_skl(sK4_skl),X0)|~sQ21_spl)),
% 0.09/0.42 inference(component_clause,[status(thm)],[f160])).
% 0.09/0.42 fof(f163,plain,(
% 0.09/0.42 sQ18_spl|sQ21_spl|~sQ0_spl|~sQ12_spl|~sQ10_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f159,f140,f160,f45,f90,f82])).
% 0.09/0.42 fof(f165,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK5_skl))|sP2_prd(sK5_skl)|~big_p(sK5_skl)|~sQ9_spl|~sQ10_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f150,f44])).
% 0.09/0.42 fof(f169,definition,(
% 0.09/0.42 sQ23_spl <=> (sP2_prd(sK5_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f170,plain,(
% 0.09/0.42 sP2_prd(sK5_skl)|~sQ23_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f169])).
% 0.09/0.42 fof(f173,definition,(
% 0.09/0.42 sQ24_spl <=> (big_p(sK10_skl(sK5_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f175,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK5_skl))|sQ24_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f173])).
% 0.09/0.42 fof(f176,plain,(
% 0.09/0.42 ~sQ24_spl|sQ23_spl|~sQ8_spl|~sQ9_spl|~sQ10_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f165,f173,f169,f74,f78,f82])).
% 0.09/0.42 fof(f178,plain,(
% 0.09/0.42 big_p(sK5_skl)|~sQ23_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f170,f41])).
% 0.09/0.42 fof(f180,plain,(
% 0.09/0.42 ![X0]: (sP1_prd(X0)|~big_p(sK5_skl)|~big_r(X0,sK4_skl)|~sQ9_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f37,f79])).
% 0.09/0.42 fof(f183,definition,(
% 0.09/0.42 ![X0]: (sQ25_spl <=> (sP1_prd(X0)|~big_r(X0,sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f186,plain,(
% 0.09/0.42 sQ25_spl|~sQ8_spl|~sQ9_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f180,f183,f74,f78])).
% 0.09/0.42 fof(f187,plain,(
% 0.09/0.42 sP2_prd(sK5_skl)|~big_p(sK5_skl)|sQ24_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f175,f43])).
% 0.09/0.42 fof(f188,plain,(
% 0.09/0.42 sQ23_spl|~sQ8_spl|sQ24_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f187,f169,f74,f173])).
% 0.09/0.42 fof(f189,plain,(
% 0.09/0.42 ~big_p(sK5_skl)|~sQ18_spl|~sQ9_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f157,f79])).
% 0.09/0.42 fof(f192,plain,(
% 0.09/0.42 $false|~sQ8_spl|~sQ18_spl|~sQ9_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f189,f75])).
% 0.09/0.42 fof(f193,plain,(
% 0.09/0.42 ~sQ8_spl|~sQ18_spl|~sQ9_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f192])).
% 0.09/0.42 fof(f231,plain,(
% 0.09/0.42 ~big_p(sK6_skl(sK4_skl))|sP2_prd(sK4_skl)|~sQ21_spl|~sQ0_spl|~sQ13_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f161,f114])).
% 0.09/0.42 fof(f234,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK7_skl(sK4_skl)))|sP2_prd(sK7_skl(sK4_skl))|~big_p(sK7_skl(sK4_skl))|~sQ21_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f161,f44])).
% 0.09/0.42 fof(f235,definition,(
% 0.09/0.42 sQ32_spl <=> (big_p(sK6_skl(sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f237,plain,(
% 0.09/0.42 ~big_p(sK6_skl(sK4_skl))|sQ32_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f235])).
% 0.09/0.42 fof(f238,plain,(
% 0.09/0.42 ~sQ32_spl|sQ18_spl|~sQ21_spl|~sQ0_spl|~sQ13_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f231,f235,f140,f160,f45,f94])).
% 0.09/0.42 fof(f242,definition,(
% 0.09/0.42 sQ34_spl <=> (big_p(sK7_skl(sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f244,plain,(
% 0.09/0.42 ~big_p(sK7_skl(sK4_skl))|sQ34_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f242])).
% 0.09/0.42 fof(f249,definition,(
% 0.09/0.42 sQ36_spl <=> (sP2_prd(sK7_skl(sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f250,plain,(
% 0.09/0.42 sP2_prd(sK7_skl(sK4_skl))|~sQ36_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f249])).
% 0.09/0.42 fof(f253,definition,(
% 0.09/0.42 sQ37_spl <=> (big_p(sK10_skl(sK7_skl(sK4_skl))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f255,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK7_skl(sK4_skl)))|sQ37_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f253])).
% 0.09/0.42 fof(f256,plain,(
% 0.09/0.42 ~sQ37_spl|sQ36_spl|~sQ34_spl|~sQ21_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f234,f253,f249,f242,f160])).
% 0.09/0.42 fof(f258,plain,(
% 0.09/0.42 big_p(sK7_skl(sK4_skl))|~sQ36_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f250,f41])).
% 0.09/0.42 fof(f259,plain,(
% 0.09/0.42 sP2_prd(sK4_skl)|sQ32_spl|~sQ0_spl|~sQ11_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f237,f112])).
% 0.09/0.42 fof(f260,plain,(
% 0.09/0.42 sQ18_spl|sQ32_spl|~sQ0_spl|~sQ11_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f259,f140,f235,f45,f86])).
% 0.09/0.42 fof(f261,plain,(
% 0.09/0.42 $false|~sQ1_spl|sQ7_spl),
% 0.09/0.42 inference(backward_subsumption_resolution,[status(thm)],[f72,f49])).
% 0.09/0.42 fof(f262,plain,(
% 0.09/0.42 ~sQ1_spl|sQ7_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f261])).
% 0.09/0.42 fof(f263,plain,(
% 0.09/0.42 ![X0]: (big_p(X0)|big_r(X0,sK9_skl(X0))|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f104,f49])).
% 0.09/0.42 fof(f265,plain,(
% 0.09/0.42 sP2_prd(sK7_skl(sK4_skl))|~big_p(sK7_skl(sK4_skl))|sQ37_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f255,f43])).
% 0.09/0.42 fof(f266,plain,(
% 0.09/0.42 sQ36_spl|~sQ34_spl|sQ37_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f265,f249,f242,f253])).
% 0.09/0.42 fof(f277,definition,(
% 0.09/0.42 sQ40_spl <=> (big_p(sK10_skl(sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f279,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK4_skl))|sQ40_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f277])).
% 0.09/0.42 fof(f281,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_p(sK8_skl(X1))|~big_r(X0,sK9_skl(X1))|big_p(X1)|~sQ1_spl|~sQ16_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f28,f134])).
% 0.09/0.42 fof(f282,plain,(
% 0.09/0.42 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(sK0_skl(X1))|~big_r(X0,sK1_skl(X1))|~big_p(X2)|~big_r(X1,X2)|~sQ5_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f28,f64])).
% 0.09/0.42 fof(f284,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_p(sK10_skl(X1))|~big_r(X0,X1)|sP2_prd(X1)|~big_p(X1))),
% 0.09/0.42 inference(resolution,[status(thm)],[f28,f44])).
% 0.09/0.42 fof(f285,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_r(X0,sK9_skl(X1))|big_p(X1)|~sQ14_spl|~sQ1_spl|~sQ16_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f281,f133])).
% 0.09/0.42 fof(f286,plain,(
% 0.09/0.42 ![X0,X1,X2]: (sP0_prd(X0)|~big_r(X0,sK1_skl(X1))|~big_p(X2)|~big_r(X1,X2)|~sQ3_spl|~sQ5_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f282,f56])).
% 0.09/0.42 fof(f287,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_r(X0,X1)|sP2_prd(X1)|~big_p(X1))),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f284,f43])).
% 0.09/0.42 fof(f298,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK10_skl(sK4_skl)))|sP2_prd(sK10_skl(sK4_skl))|~big_p(sK10_skl(sK4_skl))|~sQ17_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f138,f44])).
% 0.09/0.42 fof(f307,definition,(
% 0.09/0.42 sQ43_spl <=> (big_p(sK10_skl(sK10_skl(sK4_skl))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f309,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK10_skl(sK4_skl)))|sQ43_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f307])).
% 0.09/0.42 fof(f310,definition,(
% 0.09/0.42 sQ44_spl <=> (sP2_prd(sK10_skl(sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f311,plain,(
% 0.09/0.42 sP2_prd(sK10_skl(sK4_skl))|~sQ44_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f310])).
% 0.09/0.42 fof(f312,plain,(
% 0.09/0.42 ~sP2_prd(sK10_skl(sK4_skl))|sQ44_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f310])).
% 0.09/0.42 fof(f313,plain,(
% 0.09/0.42 ~sQ43_spl|sQ44_spl|~sQ40_spl|~sQ17_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f298,f307,f310,f277,f137])).
% 0.09/0.42 fof(f315,plain,(
% 0.09/0.42 big_p(sK10_skl(sK4_skl))|~sQ44_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f311,f41])).
% 0.09/0.42 fof(f316,plain,(
% 0.09/0.42 sP2_prd(sK10_skl(sK4_skl))|~big_p(sK10_skl(sK4_skl))|sQ43_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f309,f43])).
% 0.09/0.42 fof(f317,plain,(
% 0.09/0.42 sQ44_spl|~sQ40_spl|sQ43_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f316,f310,f277,f307])).
% 0.09/0.42 fof(f332,plain,(
% 0.09/0.42 sQ8_spl|~sQ23_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f178,f74,f169])).
% 0.09/0.42 fof(f333,plain,(
% 0.09/0.42 $false|~sQ44_spl|sQ40_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f279,f315])).
% 0.09/0.42 fof(f334,plain,(
% 0.09/0.42 ~sQ44_spl|sQ40_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f333])).
% 0.09/0.42 fof(f335,plain,(
% 0.09/0.42 $false|~sQ36_spl|sQ34_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f244,f258])).
% 0.09/0.42 fof(f336,plain,(
% 0.09/0.42 ~sQ36_spl|sQ34_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f335])).
% 0.09/0.42 fof(f343,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|big_p(X0)|big_p(X0)|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f285,f263])).
% 0.09/0.42 fof(f344,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|big_p(X0)|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(duplicate_literals_removal,[status(thm)],[f343])).
% 0.09/0.42 fof(f348,plain,(
% 0.09/0.42 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(X1)|~big_r(X0,X1)|~big_p(X2)|~big_r(X0,X2)|~sQ3_spl|~sQ5_spl|~sQ4_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f286,f60])).
% 0.09/0.42 fof(f349,plain,(
% 0.09/0.42 sP2_prd(sK4_skl)|~big_p(sK4_skl)|sQ40_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f279,f43])).
% 0.09/0.42 fof(f350,plain,(
% 0.09/0.42 sQ18_spl|~sQ19_spl|sQ40_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f349,f140,f143,f277])).
% 0.09/0.42 fof(f352,plain,(
% 0.09/0.42 ![X0]: (big_p(X0)|sP2_prd(X0)|big_r(X0,sK7_skl(X0))|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ12_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f344,f91])).
% 0.09/0.42 fof(f353,plain,(
% 0.09/0.42 ![X0]: (big_p(X0)|big_r(X0,sK7_skl(X0))|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ12_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f352,f41])).
% 0.09/0.42 fof(f359,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP2_prd(sK10_skl(X0))|~big_p(sK10_skl(X0))|sP2_prd(X0)|~big_p(X0))),
% 0.09/0.42 inference(resolution,[status(thm)],[f287,f44])).
% 0.09/0.42 fof(f363,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP2_prd(sK10_skl(X0))|~big_p(sK10_skl(X0))|~big_p(X0))),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f359,f27])).
% 0.09/0.42 fof(f365,definition,(
% 0.09/0.42 ![X0]: (sQ47_spl <=> (sP0_prd(X0)|~big_r(X0,sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f376,definition,(
% 0.09/0.42 ![X0]: (sQ49_spl <=> (~big_p(X0)|~big_r(sK4_skl,X0)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f377,plain,(
% 0.09/0.42 ![X0]: (~big_p(X0)|~big_r(sK4_skl,X0)|~sQ49_spl)),
% 0.09/0.42 inference(component_clause,[status(thm)],[f376])).
% 0.09/0.42 fof(f393,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_p(X1)|~big_r(X0,X1)|~big_p(sK10_skl(X0))|sP2_prd(X0)|~big_p(X0)|~sQ3_spl|~sQ5_spl|~sQ4_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f348,f44])).
% 0.09/0.42 fof(f397,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_p(X1)|~big_r(X0,X1)|~big_p(sK10_skl(X0))|sP2_prd(X0)|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ3_spl|~sQ5_spl|~sQ4_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f393,f344])).
% 0.09/0.42 fof(f401,plain,(
% 0.09/0.42 ~big_p(sK10_skl(sK4_skl))|sP2_prd(sK4_skl)|~big_p(sK4_skl)|~sQ49_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f377,f44])).
% 0.09/0.42 fof(f404,plain,(
% 0.09/0.42 ~sQ40_spl|sQ18_spl|~sQ19_spl|~sQ49_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f401,f277,f140,f143,f376])).
% 0.09/0.42 fof(f412,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP2_prd(sK10_skl(X0))|~big_p(X0)|sP2_prd(X0)|~big_p(X0))),
% 0.09/0.42 inference(resolution,[status(thm)],[f363,f43])).
% 0.09/0.42 fof(f413,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP2_prd(sK10_skl(X0))|~big_p(X0)|sP2_prd(X0))),
% 0.09/0.42 inference(duplicate_literals_removal,[status(thm)],[f412])).
% 0.09/0.42 fof(f414,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP2_prd(sK10_skl(X0))|~big_p(X0))),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f413,f27])).
% 0.09/0.42 fof(f415,plain,(
% 0.09/0.42 sP0_prd(sK4_skl)|~big_p(sK4_skl)|sQ44_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f414,f312])).
% 0.09/0.42 fof(f417,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|~big_p(X0)|big_p(sK10_skl(X0)))),
% 0.09/0.42 inference(resolution,[status(thm)],[f414,f41])).
% 0.09/0.42 fof(f418,definition,(
% 0.09/0.42 sQ50_spl <=> (sP0_prd(sK4_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f419,plain,(
% 0.09/0.42 sP0_prd(sK4_skl)|~sQ50_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f418])).
% 0.09/0.42 fof(f421,plain,(
% 0.09/0.42 sQ50_spl|~sQ19_spl|sQ44_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f415,f418,f143,f310])).
% 0.09/0.42 fof(f423,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_p(X1)|~big_r(X0,X1)|sP2_prd(X0)|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ3_spl|~sQ5_spl|~sQ4_spl)),
% 0.09/0.42 inference(backward_subsumption_resolution,[status(thm)],[f397,f424])).
% 0.09/0.42 fof(f424,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|big_p(sK10_skl(X0))|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f417,f344])).
% 0.09/0.42 fof(f427,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_p(X1)|~big_r(X0,X1)|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ3_spl|~sQ5_spl|~sQ4_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f423,f27])).
% 0.09/0.42 fof(f428,plain,(
% 0.09/0.42 sP2_prd(sK4_skl)|big_r(sK4_skl,sK7_skl(sK4_skl))|~sQ50_spl|~sQ12_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f419,f91])).
% 0.09/0.42 fof(f429,definition,(
% 0.09/0.42 sQ51_spl <=> (big_r(sK4_skl,sK7_skl(sK4_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f430,plain,(
% 0.09/0.42 big_r(sK4_skl,sK7_skl(sK4_skl))|~sQ51_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f429])).
% 0.09/0.42 fof(f432,plain,(
% 0.09/0.42 sQ18_spl|sQ51_spl|~sQ50_spl|~sQ12_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f428,f140,f429,f418,f90])).
% 0.09/0.42 fof(f436,plain,(
% 0.09/0.42 sP0_prd(sK4_skl)|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|sQ40_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f424,f279])).
% 0.09/0.42 fof(f437,plain,(
% 0.09/0.42 ~big_p(sK7_skl(sK4_skl))|big_p(sK4_skl)|~sQ18_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ12_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f157,f353])).
% 0.09/0.42 fof(f441,plain,(
% 0.09/0.42 ~sQ34_spl|sQ19_spl|~sQ18_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|~sQ12_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f437,f242,f143,f140,f99,f107,f48,f103,f90])).
% 0.09/0.42 fof(f449,plain,(
% 0.09/0.42 sP2_prd(sK4_skl)|big_r(sK4_skl,sK7_skl(sK4_skl))|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|sQ40_spl|~sQ12_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f436,f91])).
% 0.09/0.42 fof(f450,plain,(
% 0.09/0.42 sQ18_spl|sQ51_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl|sQ40_spl|~sQ12_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f449,f140,f429,f99,f107,f48,f103,f277,f90])).
% 0.09/0.42 fof(f454,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|~big_p(sK7_skl(sK4_skl))|~big_r(X0,sK4_skl)|~sQ51_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f430,f28])).
% 0.09/0.42 fof(f456,plain,(
% 0.09/0.42 sQ47_spl|~sQ34_spl|~sQ51_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f454,f365,f242,f429])).
% 0.09/0.42 fof(f472,plain,(
% 0.09/0.42 ![X0,X1]: (sP0_prd(X0)|~big_r(X0,sK10_skl(X1))|sP0_prd(X1)|~sQ3_spl|~sQ5_spl|~sQ4_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f427,f424])).
% 0.09/0.42 fof(f482,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP0_prd(X0)|sP2_prd(X0)|~big_p(X0)|~sQ3_spl|~sQ5_spl|~sQ4_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f472,f44])).
% 0.09/0.42 fof(f483,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|sP2_prd(X0)|~big_p(X0)|~sQ3_spl|~sQ5_spl|~sQ4_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(duplicate_literals_removal,[status(thm)],[f482])).
% 0.09/0.42 fof(f484,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|~sQ3_spl|~sQ5_spl|~sQ4_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(backward_subsumption_resolution,[status(thm)],[f344,f485])).
% 0.09/0.42 fof(f485,plain,(
% 0.09/0.42 ![X0]: (sP0_prd(X0)|~big_p(X0)|~sQ3_spl|~sQ5_spl|~sQ4_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl)),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f483,f27])).
% 0.09/0.42 fof(f486,plain,(
% 0.09/0.42 sQ0_spl|~sQ3_spl|~sQ5_spl|~sQ4_spl|~sQ14_spl|~sQ16_spl|~sQ1_spl|~sQ15_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f484,f45,f55,f63,f59,f99,f107,f48,f103])).
% 0.09/0.42 fof(f487,plain,(
% 0.09/0.42 $false),
% 0.09/0.42 inference(sat_refutation,[status(thm)],[f51,f58,f62,f66,f73,f77,f81,f85,f89,f93,f97,f98,f102,f106,f110,f111,f130,f132,f146,f163,f176,f186,f188,f193,f238,f256,f260,f262,f266,f313,f317,f332,f334,f336,f350,f404,f421,f432,f441,f450,f456,f486])).
% 0.09/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.44 % Elapsed time: 0.062093 seconds
% 0.09/0.44 % CPU time: 0.237961 seconds
% 0.09/0.44 % Total memory used: 14.809 MB
% 0.09/0.44 % Net memory used: 14.528 MB
%------------------------------------------------------------------------------