%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN036+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 03:18:45 PM UTC 2026
% Result : Theorem 0.14s 5.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN036+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 10:39:40 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.41 fof(f1,conjecture,(
% 0.14/5.41 ( ( (? [X] :(! [Y] :( big_p(X)<=> big_p(Y) )))<=> ( (? [U] : big_q(U))<=> (! [W] : big_q(W) )) )<=> ( (? [X1] :(! [Y1] :( big_q(X1)<=> big_q(Y1) )))<=> ( (? [U1] : big_p(U1))<=> (! [W1] : big_p(W1) )) ) ) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f2,negated_conjecture,(
% 0.14/5.41 ~(( ( (? [X] :(! [Y] :( big_p(X)<=> big_p(Y) )))<=> ( (? [U] : big_q(U))<=> (! [W] : big_q(W) )) )<=> ( (? [X1] :(! [Y1] :( big_q(X1)<=> big_q(Y1) )))<=> ( (? [U1] : big_p(U1))<=> (! [W1] : big_p(W1) )) ) ) )),
% 0.14/5.41 inference(negated_conjecture,[status(cth)],[f1])).
% 0.14/5.41 fof(f3,plain,(
% 0.14/5.41 (((?[X]: ![Y]: (big_p(X)<=>big_p(Y)))<=>((?[U]: big_q(U))<=>(![W]: big_q(W))))<~>((?[X1]: ![Y1]: (big_q(X1)<=>big_q(Y1)))<=>((?[U1]: big_p(U1))<=>(![W1]: big_p(W1)))))),
% 0.14/5.41 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.14/5.41 fof(f4,definition,(
% 0.14/5.41 sP0_prd<=>((?[X]: ![Y]: (big_p(X)<=>big_p(Y)))<=>((?[U]: big_q(U))<=>(![W]: big_q(W))))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.14/5.41 fof(f5,plain,(
% 0.14/5.41 sP0_prd<~>((?[X1]: ![Y1]: (big_q(X1)<=>big_q(Y1)))<=>((?[U1]: big_p(U1))<=>(![W1]: big_p(W1))))),
% 0.14/5.41 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.14/5.41 fof(f6,definition,(
% 0.14/5.41 ![X1,Y1]: (sP1_prd(Y1,X1)<=>(big_q(X1)<=>big_q(Y1)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.14/5.41 fof(f7,definition,(
% 0.14/5.41 sP2_prd<=>((?[U1]: big_p(U1))<=>(![W1]: big_p(W1)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 0.14/5.41 fof(f8,plain,(
% 0.14/5.41 sP0_prd<~>((?[X1]: ![Y1]: sP1_prd(Y1,X1))<=>sP2_prd)),
% 0.14/5.41 inference(formula_renaming,[status(thm)],[f5,f7,f6])).
% 0.14/5.41 fof(f9,plain,(
% 0.14/5.41 (sP0_prd|(((![X1]: ?[Y1]: ~sP1_prd(Y1,X1))|sP2_prd)&((?[X1]: ![Y1]: sP1_prd(Y1,X1))|~sP2_prd)))&(~sP0_prd|(((![X1]: ?[Y1]: ~sP1_prd(Y1,X1))|~sP2_prd)&((?[X1]: ![Y1]: sP1_prd(Y1,X1))|sP2_prd)))),
% 0.14/5.41 inference(NNF_transformation,[status(thm)],[f8])).
% 0.14/5.41 fof(f10,plain,(
% 0.14/5.41 (sP0_prd|(((![X1]: ~sP1_prd(sK0_skl(X1),X1))|sP2_prd)&(![Y1]: sP1_prd(Y1,sK1_skl)|~sP2_prd)))&(~sP0_prd|(((![X1]: ~sP1_prd(sK2_skl(X1),X1))|~sP2_prd)&(![Y1]: sP1_prd(Y1,sK3_skl)|sP2_prd)))),
% 0.14/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(Y1,sK0_skl(X1)),skolemize(X1,sK1_skl),skolemize(Y1,sK2_skl(X1)),skolemize(X1,sK3_skl)],[f9])).
% 0.14/5.41 fof(f11,plain,(
% 0.14/5.41 ![X0]: (sP0_prd|~sP1_prd(sK0_skl(X0),X0)|sP2_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/5.41 fof(f12,plain,(
% 0.14/5.41 ![X0]: (sP0_prd|sP1_prd(X0,sK1_skl)|~sP2_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/5.41 fof(f13,plain,(
% 0.14/5.41 ![X0]: (~sP0_prd|~sP1_prd(sK2_skl(X0),X0)|~sP2_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/5.41 fof(f14,plain,(
% 0.14/5.41 ![X0]: (~sP0_prd|sP1_prd(X0,sK3_skl)|sP2_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/5.41 fof(f15,definition,(
% 0.14/5.41 ![X,Y]: (sP3_prd(Y,X)<=>(big_p(X)<=>big_p(Y)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sP3_prd])],[])).
% 0.14/5.41 fof(f16,definition,(
% 0.14/5.41 sP4_prd<=>((?[U]: big_q(U))<=>(![W]: big_q(W)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sP4_prd])],[])).
% 0.14/5.41 fof(f17,plain,(
% 0.14/5.41 sP0_prd<=>((?[X]: ![Y]: sP3_prd(Y,X))<=>sP4_prd)),
% 0.14/5.41 inference(formula_renaming,[status(thm)],[f4,f16,f15])).
% 0.14/5.41 fof(f18,plain,(
% 0.14/5.41 (~sP0_prd|(((![X]: ?[Y]: ~sP3_prd(Y,X))|sP4_prd)&((?[X]: ![Y]: sP3_prd(Y,X))|~sP4_prd)))&(sP0_prd|(((![X]: ?[Y]: ~sP3_prd(Y,X))|~sP4_prd)&((?[X]: ![Y]: sP3_prd(Y,X))|sP4_prd)))),
% 0.14/5.41 inference(NNF_transformation,[status(thm)],[f17])).
% 0.14/5.41 fof(f19,plain,(
% 0.14/5.41 (~sP0_prd|(((![X]: ~sP3_prd(sK4_skl(X),X))|sP4_prd)&(![Y]: sP3_prd(Y,sK5_skl)|~sP4_prd)))&(sP0_prd|(((![X]: ~sP3_prd(sK6_skl(X),X))|~sP4_prd)&(![Y]: sP3_prd(Y,sK7_skl)|sP4_prd)))),
% 0.14/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y,sK4_skl(X)),skolemize(X,sK5_skl),skolemize(Y,sK6_skl(X)),skolemize(X,sK7_skl)],[f18])).
% 0.14/5.41 fof(f20,plain,(
% 0.14/5.41 ![X0]: (~sP0_prd|~sP3_prd(sK4_skl(X0),X0)|sP4_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/5.41 fof(f21,plain,(
% 0.14/5.41 ![X0]: (~sP0_prd|sP3_prd(X0,sK5_skl)|~sP4_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/5.41 fof(f22,plain,(
% 0.14/5.41 ![X0]: (sP0_prd|~sP3_prd(sK6_skl(X0),X0)|~sP4_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/5.41 fof(f23,plain,(
% 0.14/5.41 ![X0]: (sP0_prd|sP3_prd(X0,sK7_skl)|sP4_prd)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/5.41 fof(f24,plain,(
% 0.14/5.41 ![X1,Y1]: ((~sP1_prd(Y1,X1)|((~big_q(X1)|big_q(Y1))&(big_q(X1)|~big_q(Y1))))&(sP1_prd(Y1,X1)|((~big_q(X1)|~big_q(Y1))&(big_q(X1)|big_q(Y1)))))),
% 0.14/5.41 inference(NNF_transformation,[status(thm)],[f6])).
% 0.14/5.41 fof(f25,plain,(
% 0.14/5.41 (![X1,Y1]: (~sP1_prd(Y1,X1)|((~big_q(X1)|big_q(Y1))&(big_q(X1)|~big_q(Y1)))))&(![X1,Y1]: (sP1_prd(Y1,X1)|((~big_q(X1)|~big_q(Y1))&(big_q(X1)|big_q(Y1)))))),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f24])).
% 0.14/5.41 fof(f26,plain,(
% 0.14/5.41 ![X0,X1]: (~sP1_prd(X0,X1)|~big_q(X1)|big_q(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/5.41 fof(f27,plain,(
% 0.14/5.41 ![X0,X1]: (~sP1_prd(X0,X1)|big_q(X1)|~big_q(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/5.41 fof(f28,plain,(
% 0.14/5.41 ![X0,X1]: (sP1_prd(X0,X1)|~big_q(X1)|~big_q(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/5.41 fof(f29,plain,(
% 0.14/5.41 ![X0,X1]: (sP1_prd(X0,X1)|big_q(X1)|big_q(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/5.41 fof(f30,plain,(
% 0.14/5.41 (~sP2_prd|(((![U1]: ~big_p(U1))|(![W1]: big_p(W1)))&((?[U1]: big_p(U1))|(?[W1]: ~big_p(W1)))))&(sP2_prd|(((![U1]: ~big_p(U1))|(?[W1]: ~big_p(W1)))&((?[U1]: big_p(U1))|(![W1]: big_p(W1)))))),
% 0.14/5.41 inference(NNF_transformation,[status(thm)],[f7])).
% 0.14/5.41 fof(f31,plain,(
% 0.14/5.41 (~sP2_prd|(((![U1]: ~big_p(U1))|(![W1]: big_p(W1)))&(big_p(sK8_skl)|~big_p(sK9_skl))))&(sP2_prd|(((![U1]: ~big_p(U1))|~big_p(sK10_skl))&(big_p(sK11_skl)|(![W1]: big_p(W1)))))),
% 0.14/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(U1,sK8_skl),skolemize(W1,sK9_skl),skolemize(W1,sK10_skl),skolemize(U1,sK11_skl)],[f30])).
% 0.14/5.41 fof(f32,plain,(
% 0.14/5.41 ![X0,X1]: (~sP2_prd|~big_p(X0)|big_p(X1))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/5.41 fof(f33,plain,(
% 0.14/5.41 ~sP2_prd|big_p(sK8_skl)|~big_p(sK9_skl)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/5.41 fof(f34,plain,(
% 0.14/5.41 ![X0]: (sP2_prd|~big_p(X0)|~big_p(sK10_skl))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/5.41 fof(f35,plain,(
% 0.14/5.41 ![X0]: (sP2_prd|big_p(sK11_skl)|big_p(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/5.41 fof(f36,plain,(
% 0.14/5.41 ![X,Y]: ((~sP3_prd(Y,X)|((~big_p(X)|big_p(Y))&(big_p(X)|~big_p(Y))))&(sP3_prd(Y,X)|((~big_p(X)|~big_p(Y))&(big_p(X)|big_p(Y)))))),
% 0.14/5.41 inference(NNF_transformation,[status(thm)],[f15])).
% 0.14/5.41 fof(f37,plain,(
% 0.14/5.41 (![X,Y]: (~sP3_prd(Y,X)|((~big_p(X)|big_p(Y))&(big_p(X)|~big_p(Y)))))&(![X,Y]: (sP3_prd(Y,X)|((~big_p(X)|~big_p(Y))&(big_p(X)|big_p(Y)))))),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f36])).
% 0.14/5.41 fof(f38,plain,(
% 0.14/5.41 ![X0,X1]: (~sP3_prd(X0,X1)|~big_p(X1)|big_p(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/5.41 fof(f39,plain,(
% 0.14/5.41 ![X0,X1]: (~sP3_prd(X0,X1)|big_p(X1)|~big_p(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/5.41 fof(f40,plain,(
% 0.14/5.41 ![X0,X1]: (sP3_prd(X0,X1)|~big_p(X1)|~big_p(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/5.41 fof(f41,plain,(
% 0.14/5.41 ![X0,X1]: (sP3_prd(X0,X1)|big_p(X1)|big_p(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/5.41 fof(f42,plain,(
% 0.14/5.41 (~sP4_prd|(((![U]: ~big_q(U))|(![W]: big_q(W)))&((?[U]: big_q(U))|(?[W]: ~big_q(W)))))&(sP4_prd|(((![U]: ~big_q(U))|(?[W]: ~big_q(W)))&((?[U]: big_q(U))|(![W]: big_q(W)))))),
% 0.14/5.41 inference(NNF_transformation,[status(thm)],[f16])).
% 0.14/5.41 fof(f43,plain,(
% 0.14/5.41 (~sP4_prd|(((![U]: ~big_q(U))|(![W]: big_q(W)))&(big_q(sK12_skl)|~big_q(sK13_skl))))&(sP4_prd|(((![U]: ~big_q(U))|~big_q(sK14_skl))&(big_q(sK15_skl)|(![W]: big_q(W)))))),
% 0.14/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl,sK15_skl]),skolemize(U,sK12_skl),skolemize(W,sK13_skl),skolemize(W,sK14_skl),skolemize(U,sK15_skl)],[f42])).
% 0.14/5.41 fof(f44,plain,(
% 0.14/5.41 ![X0,X1]: (~sP4_prd|~big_q(X0)|big_q(X1))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/5.41 fof(f46,plain,(
% 0.14/5.41 ![X0]: (sP4_prd|~big_q(X0)|~big_q(sK14_skl))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/5.41 fof(f47,plain,(
% 0.14/5.41 ![X0]: (sP4_prd|big_q(sK15_skl)|big_q(X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/5.41 fof(f48,definition,(
% 0.14/5.41 sQ0_spl <=> (sP0_prd)),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f51,definition,(
% 0.14/5.41 ![X0]: (sQ1_spl <=> (~sP1_prd(sK0_skl(X0),X0)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f52,plain,(
% 0.14/5.41 ![X0]: (~sP1_prd(sK0_skl(X0),X0)|~sQ1_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f51])).
% 0.14/5.41 fof(f54,definition,(
% 0.14/5.41 sQ2_spl <=> (sP2_prd)),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f57,plain,(
% 0.14/5.41 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f11,f48,f51,f54])).
% 0.14/5.41 fof(f58,definition,(
% 0.14/5.41 ![X0]: (sQ3_spl <=> (sP1_prd(X0,sK1_skl)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f59,plain,(
% 0.14/5.41 ![X0]: (sP1_prd(X0,sK1_skl)|~sQ3_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f58])).
% 0.14/5.41 fof(f61,plain,(
% 0.14/5.41 sQ0_spl|sQ3_spl|~sQ2_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f12,f48,f58,f54])).
% 0.14/5.41 fof(f62,definition,(
% 0.14/5.41 ![X0]: (sQ4_spl <=> (~sP1_prd(sK2_skl(X0),X0)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f63,plain,(
% 0.14/5.41 ![X0]: (~sP1_prd(sK2_skl(X0),X0)|~sQ4_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f62])).
% 0.14/5.41 fof(f65,plain,(
% 0.14/5.41 ~sQ0_spl|sQ4_spl|~sQ2_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f13,f48,f62,f54])).
% 0.14/5.41 fof(f66,definition,(
% 0.14/5.41 ![X0]: (sQ5_spl <=> (sP1_prd(X0,sK3_skl)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f67,plain,(
% 0.14/5.41 ![X0]: (sP1_prd(X0,sK3_skl)|~sQ5_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f66])).
% 0.14/5.41 fof(f69,plain,(
% 0.14/5.41 ~sQ0_spl|sQ5_spl|sQ2_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f14,f48,f66,f54])).
% 0.14/5.41 fof(f70,definition,(
% 0.14/5.41 ![X0]: (sQ6_spl <=> (~sP3_prd(sK4_skl(X0),X0)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f71,plain,(
% 0.14/5.41 ![X0]: (~sP3_prd(sK4_skl(X0),X0)|~sQ6_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f70])).
% 0.14/5.41 fof(f73,definition,(
% 0.14/5.41 sQ7_spl <=> (sP4_prd)),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f76,plain,(
% 0.14/5.41 ~sQ0_spl|sQ6_spl|sQ7_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f20,f48,f70,f73])).
% 0.14/5.41 fof(f77,definition,(
% 0.14/5.41 ![X0]: (sQ8_spl <=> (sP3_prd(X0,sK5_skl)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f78,plain,(
% 0.14/5.41 ![X0]: (sP3_prd(X0,sK5_skl)|~sQ8_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f77])).
% 0.14/5.41 fof(f80,plain,(
% 0.14/5.41 ~sQ0_spl|sQ8_spl|~sQ7_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f21,f48,f77,f73])).
% 0.14/5.41 fof(f81,definition,(
% 0.14/5.41 ![X0]: (sQ9_spl <=> (~sP3_prd(sK6_skl(X0),X0)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f82,plain,(
% 0.14/5.41 ![X0]: (~sP3_prd(sK6_skl(X0),X0)|~sQ9_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f81])).
% 0.14/5.41 fof(f84,plain,(
% 0.14/5.41 sQ0_spl|sQ9_spl|~sQ7_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f22,f48,f81,f73])).
% 0.14/5.41 fof(f85,definition,(
% 0.14/5.41 ![X0]: (sQ10_spl <=> (sP3_prd(X0,sK7_skl)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f86,plain,(
% 0.14/5.41 ![X0]: (sP3_prd(X0,sK7_skl)|~sQ10_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f85])).
% 0.14/5.41 fof(f88,plain,(
% 0.14/5.41 sQ0_spl|sQ10_spl|sQ7_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f23,f48,f85,f73])).
% 0.14/5.41 fof(f89,definition,(
% 0.14/5.41 ![X0]: (sQ11_spl <=> (~big_p(X0)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f90,plain,(
% 0.14/5.41 ![X0]: (~big_p(X0)|~sQ11_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f89])).
% 0.14/5.41 fof(f92,definition,(
% 0.14/5.41 ![X1]: (sQ12_spl <=> (big_p(X1)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f93,plain,(
% 0.14/5.41 ![X0]: (big_p(X0)|~sQ12_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f92])).
% 0.14/5.41 fof(f95,plain,(
% 0.14/5.41 ~sQ2_spl|sQ11_spl|sQ12_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f32,f54,f89,f92])).
% 0.14/5.41 fof(f96,definition,(
% 0.14/5.41 sQ13_spl <=> (big_p(sK8_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f97,plain,(
% 0.14/5.41 big_p(sK8_skl)|~sQ13_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f96])).
% 0.14/5.41 fof(f99,definition,(
% 0.14/5.41 sQ14_spl <=> (big_p(sK9_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f101,plain,(
% 0.14/5.41 ~big_p(sK9_skl)|sQ14_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f99])).
% 0.14/5.41 fof(f102,plain,(
% 0.14/5.41 ~sQ2_spl|sQ13_spl|~sQ14_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f33,f54,f96,f99])).
% 0.14/5.41 fof(f103,definition,(
% 0.14/5.41 sQ15_spl <=> (big_p(sK10_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f105,plain,(
% 0.14/5.41 ~big_p(sK10_skl)|sQ15_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f103])).
% 0.14/5.41 fof(f106,plain,(
% 0.14/5.41 sQ2_spl|sQ11_spl|~sQ15_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f34,f54,f89,f103])).
% 0.14/5.41 fof(f107,definition,(
% 0.14/5.41 sQ16_spl <=> (big_p(sK11_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f108,plain,(
% 0.14/5.41 big_p(sK11_skl)|~sQ16_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f107])).
% 0.14/5.41 fof(f110,plain,(
% 0.14/5.41 sQ2_spl|sQ16_spl|sQ12_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f35,f54,f107,f92])).
% 0.14/5.41 fof(f111,definition,(
% 0.14/5.41 ![X0]: (sQ17_spl <=> (~big_q(X0)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f112,plain,(
% 0.14/5.41 ![X0]: (~big_q(X0)|~sQ17_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f111])).
% 0.14/5.41 fof(f114,definition,(
% 0.14/5.41 ![X1]: (sQ18_spl <=> (big_q(X1)))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f115,plain,(
% 0.14/5.41 ![X0]: (big_q(X0)|~sQ18_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f114])).
% 0.14/5.41 fof(f117,plain,(
% 0.14/5.41 ~sQ7_spl|sQ17_spl|sQ18_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f44,f73,f111,f114])).
% 0.14/5.41 fof(f125,definition,(
% 0.14/5.41 sQ21_spl <=> (big_q(sK14_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f127,plain,(
% 0.14/5.41 ~big_q(sK14_skl)|sQ21_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f125])).
% 0.14/5.41 fof(f128,plain,(
% 0.14/5.41 sQ7_spl|sQ17_spl|~sQ21_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f46,f73,f111,f125])).
% 0.14/5.41 fof(f129,definition,(
% 0.14/5.41 sQ22_spl <=> (big_q(sK15_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f130,plain,(
% 0.14/5.41 big_q(sK15_skl)|~sQ22_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f129])).
% 0.14/5.41 fof(f132,plain,(
% 0.14/5.41 sQ7_spl|sQ22_spl|sQ18_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f47,f73,f129,f114])).
% 0.14/5.41 fof(f133,plain,(
% 0.14/5.41 $false|~sQ18_spl|~sQ17_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f112,f115])).
% 0.14/5.41 fof(f134,plain,(
% 0.14/5.41 ~sQ18_spl|~sQ17_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f133])).
% 0.14/5.41 fof(f135,plain,(
% 0.14/5.41 $false|~sQ12_spl|~sQ11_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f90,f93])).
% 0.14/5.41 fof(f136,plain,(
% 0.14/5.41 ~sQ12_spl|~sQ11_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f135])).
% 0.14/5.41 fof(f137,plain,(
% 0.14/5.41 $false|~sQ17_spl|~sQ22_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f130,f112])).
% 0.14/5.41 fof(f138,plain,(
% 0.14/5.41 ~sQ17_spl|~sQ22_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f137])).
% 0.14/5.41 fof(f139,plain,(
% 0.14/5.41 $false|~sQ18_spl|sQ21_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f127,f115])).
% 0.14/5.41 fof(f140,plain,(
% 0.14/5.41 ~sQ18_spl|sQ21_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f139])).
% 0.14/5.41 fof(f143,plain,(
% 0.14/5.41 $false|~sQ11_spl|~sQ16_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f108,f90])).
% 0.14/5.41 fof(f144,plain,(
% 0.14/5.41 ~sQ11_spl|~sQ16_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f143])).
% 0.14/5.41 fof(f145,plain,(
% 0.14/5.41 $false|~sQ12_spl|sQ15_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f105,f93])).
% 0.14/5.41 fof(f146,plain,(
% 0.14/5.41 ~sQ12_spl|sQ15_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f145])).
% 0.14/5.41 fof(f148,plain,(
% 0.14/5.41 ![X0]: (~sP1_prd(sK15_skl,X0)|big_q(X0)|~sQ22_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f130,f27])).
% 0.14/5.41 fof(f149,plain,(
% 0.14/5.41 ![X0]: (~sP3_prd(sK11_skl,X0)|big_p(X0)|~sQ16_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f108,f39])).
% 0.14/5.41 fof(f152,plain,(
% 0.14/5.41 ![X0]: (~big_p(X0)|~big_p(sK4_skl(X0))|~sQ6_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f71,f40])).
% 0.14/5.41 fof(f154,plain,(
% 0.14/5.41 $false|~sQ1_spl|~sQ3_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f52,f59])).
% 0.14/5.41 fof(f156,plain,(
% 0.14/5.41 ~sQ1_spl|~sQ3_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f154])).
% 0.14/5.41 fof(f158,plain,(
% 0.14/5.41 $false|~sQ4_spl|~sQ5_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f63,f67])).
% 0.14/5.41 fof(f160,plain,(
% 0.14/5.41 ~sQ4_spl|~sQ5_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f158])).
% 0.14/5.41 fof(f165,plain,(
% 0.14/5.41 ![X0,X1]: (sP3_prd(X0,X1)|big_p(X1)|~sQ11_spl)),
% 0.14/5.41 inference(backward_subsumption_resolution,[status(thm)],[f41,f90])).
% 0.14/5.41 fof(f166,plain,(
% 0.14/5.41 ![X0,X1]: (sP3_prd(X0,X1)|~sQ11_spl)),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f165,f90])).
% 0.14/5.41 fof(f167,plain,(
% 0.14/5.41 $false|~sQ11_spl|~sQ13_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f97,f90])).
% 0.14/5.41 fof(f168,plain,(
% 0.14/5.41 ~sQ11_spl|~sQ13_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f167])).
% 0.14/5.41 fof(f171,plain,(
% 0.14/5.41 ![X0,X1]: (sP1_prd(X0,X1)|big_q(X1)|~sQ17_spl)),
% 0.14/5.41 inference(backward_subsumption_resolution,[status(thm)],[f29,f112])).
% 0.14/5.41 fof(f172,plain,(
% 0.14/5.41 ![X0,X1]: (sP1_prd(X0,X1)|~sQ17_spl)),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f171,f112])).
% 0.14/5.41 fof(f176,plain,(
% 0.14/5.41 $false|~sQ11_spl|~sQ6_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f71,f166])).
% 0.14/5.41 fof(f177,plain,(
% 0.14/5.41 ~sQ11_spl|~sQ6_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f176])).
% 0.14/5.41 fof(f182,plain,(
% 0.14/5.41 big_q(sK3_skl)|~sQ22_spl|~sQ5_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f148,f67])).
% 0.14/5.41 fof(f190,plain,(
% 0.14/5.41 ![X0]: (~sP1_prd(X0,sK3_skl)|big_q(X0)|~sQ22_spl|~sQ5_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f182,f26])).
% 0.14/5.41 fof(f191,plain,(
% 0.14/5.41 ![X0]: (big_q(X0)|~sQ22_spl|~sQ5_spl)),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f190,f67])).
% 0.14/5.41 fof(f200,plain,(
% 0.14/5.41 $false|~sQ22_spl|~sQ5_spl|sQ21_spl),
% 0.14/5.41 inference(backward_subsumption_resolution,[status(thm)],[f127,f191])).
% 0.14/5.41 fof(f202,plain,(
% 0.14/5.41 ~sQ22_spl|~sQ5_spl|sQ21_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f200])).
% 0.14/5.41 fof(f205,plain,(
% 0.14/5.41 ![X0]: (~sP3_prd(sK11_skl,X0)|big_p(X0)|~sQ16_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f39,f108])).
% 0.14/5.41 fof(f206,plain,(
% 0.14/5.41 $false|~sQ17_spl|~sQ1_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f52,f172])).
% 0.14/5.41 fof(f207,plain,(
% 0.14/5.41 ~sQ17_spl|~sQ1_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f206])).
% 0.14/5.41 fof(f208,plain,(
% 0.14/5.41 big_p(sK7_skl)|~sQ16_spl|~sQ10_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f149,f86])).
% 0.14/5.41 fof(f215,plain,(
% 0.14/5.41 ![X0]: (~sP3_prd(X0,sK7_skl)|big_p(X0)|~sQ16_spl|~sQ10_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f208,f38])).
% 0.14/5.41 fof(f217,plain,(
% 0.14/5.41 ![X0]: (big_p(X0)|~sQ16_spl|~sQ10_spl)),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f215,f86])).
% 0.14/5.41 fof(f219,plain,(
% 0.14/5.41 $false|~sQ16_spl|~sQ10_spl|sQ15_spl),
% 0.14/5.41 inference(backward_subsumption_resolution,[status(thm)],[f105,f217])).
% 0.14/5.41 fof(f221,plain,(
% 0.14/5.41 ~sQ16_spl|~sQ10_spl|sQ15_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f219])).
% 0.14/5.41 fof(f223,plain,(
% 0.14/5.41 ![X0]: (~big_q(sK1_skl)|big_q(X0)|~sQ3_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f59,f26])).
% 0.14/5.41 fof(f224,plain,(
% 0.14/5.41 ![X0]: (big_q(sK1_skl)|~big_q(X0)|~sQ3_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f59,f27])).
% 0.14/5.41 fof(f225,definition,(
% 0.14/5.41 sQ26_spl <=> (big_q(sK1_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f228,plain,(
% 0.14/5.41 ~sQ26_spl|sQ18_spl|~sQ3_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f223,f225,f114,f58])).
% 0.14/5.41 fof(f229,plain,(
% 0.14/5.41 sQ26_spl|sQ17_spl|~sQ3_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f224,f225,f111,f58])).
% 0.14/5.41 fof(f236,plain,(
% 0.14/5.41 $false|~sQ17_spl|~sQ4_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f63,f172])).
% 0.14/5.41 fof(f237,plain,(
% 0.14/5.41 ~sQ17_spl|~sQ4_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f236])).
% 0.14/5.41 fof(f240,plain,(
% 0.14/5.41 $false|~sQ11_spl|~sQ9_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f82,f166])).
% 0.14/5.42 fof(f241,plain,(
% 0.14/5.42 ~sQ11_spl|~sQ9_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f240])).
% 0.14/5.42 fof(f248,plain,(
% 0.14/5.42 big_p(sK5_skl)|~sQ16_spl|~sQ8_spl),
% 0.14/5.42 inference(resolution,[status(thm)],[f205,f78])).
% 0.14/5.42 fof(f252,plain,(
% 0.14/5.42 ![X0]: (~sP3_prd(X0,sK5_skl)|big_p(X0)|~sQ16_spl|~sQ8_spl)),
% 0.14/5.42 inference(resolution,[status(thm)],[f248,f38])).
% 0.14/5.42 fof(f253,plain,(
% 0.14/5.42 ![X0]: (big_p(X0)|~sQ16_spl|~sQ8_spl)),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f252,f78])).
% 0.14/5.42 fof(f259,plain,(
% 0.14/5.42 $false|~sQ16_spl|~sQ8_spl|sQ15_spl),
% 0.14/5.42 inference(backward_subsumption_resolution,[status(thm)],[f105,f253])).
% 0.14/5.42 fof(f262,plain,(
% 0.14/5.42 ~sQ16_spl|~sQ8_spl|sQ15_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f259])).
% 0.14/5.42 fof(f268,plain,(
% 0.14/5.42 ![X0,X1]: (sP1_prd(X0,X1)|~big_q(X0)|~sQ18_spl)),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f28,f115])).
% 0.14/5.42 fof(f269,plain,(
% 0.14/5.42 ![X0,X1]: (sP1_prd(X0,X1)|~sQ18_spl)),
% 0.14/5.42 inference(resolution,[status(thm)],[f268,f115])).
% 0.14/5.42 fof(f274,plain,(
% 0.14/5.42 $false|~sQ18_spl|~sQ1_spl),
% 0.14/5.42 inference(backward_subsumption_resolution,[status(thm)],[f52,f269])).
% 0.14/5.42 fof(f275,plain,(
% 0.14/5.42 ~sQ18_spl|~sQ1_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f274])).
% 0.14/5.42 fof(f276,plain,(
% 0.14/5.42 $false|~sQ18_spl|~sQ4_spl),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f63,f269])).
% 0.14/5.42 fof(f277,plain,(
% 0.14/5.42 ~sQ18_spl|~sQ4_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f276])).
% 0.14/5.42 fof(f285,plain,(
% 0.14/5.42 $false|~sQ12_spl|sQ14_spl),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f101,f93])).
% 0.14/5.42 fof(f286,plain,(
% 0.14/5.42 ~sQ12_spl|sQ14_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f285])).
% 0.14/5.42 fof(f287,plain,(
% 0.14/5.42 ![X0,X1]: (sP3_prd(X0,X1)|~big_p(X0)|~sQ12_spl)),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f40,f93])).
% 0.14/5.42 fof(f288,plain,(
% 0.14/5.42 ![X0]: (~big_p(sK6_skl(X0))|~sQ9_spl|~sQ12_spl)),
% 0.14/5.42 inference(resolution,[status(thm)],[f82,f287])).
% 0.14/5.42 fof(f289,plain,(
% 0.14/5.42 $false|~sQ9_spl|~sQ12_spl),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f288,f93])).
% 0.14/5.42 fof(f290,plain,(
% 0.14/5.42 ~sQ9_spl|~sQ12_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f289])).
% 0.14/5.42 fof(f291,plain,(
% 0.14/5.42 ![X0]: (~big_p(sK4_skl(X0))|~sQ12_spl|~sQ6_spl)),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f152,f93])).
% 0.14/5.42 fof(f296,plain,(
% 0.14/5.42 $false|~sQ12_spl|~sQ6_spl),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f291,f93])).
% 0.14/5.42 fof(f297,plain,(
% 0.14/5.42 ~sQ12_spl|~sQ6_spl),
% 0.14/5.42 inference(contradiction_clause,[status(thm)],[f296])).
% 0.14/5.42 fof(f298,plain,(
% 0.14/5.42 $false),
% 0.14/5.42 inference(sat_refutation,[status(thm)],[f57,f61,f65,f69,f76,f80,f84,f88,f95,f102,f106,f110,f117,f128,f132,f134,f136,f138,f140,f144,f146,f156,f160,f168,f177,f202,f207,f221,f228,f229,f237,f241,f262,f275,f277,f286,f290,f297])).
% 0.14/5.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.44 % Elapsed time: 0.049283 seconds
% 0.14/5.44 % CPU time: 0.142379 seconds
% 0.14/5.44 % Total memory used: 17.696 MB
% 0.14/5.44 % Net memory used: 17.384 MB
%------------------------------------------------------------------------------