%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN084+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 : n016.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 03:18:55 PM UTC 2026
% Result : Theorem 0.15s 15.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN084+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
% 0.11/15.39 % Computer : n016.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 10:48:08 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.15/15.40 % Drodi V4.1.1
% 0.15/15.42 % Refutation found
% 0.15/15.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/15.42 % SZS output start CNFRefutation for theBenchmark
% 0.15/15.42 fof(f1,conjecture,(
% 0.15/15.42 ( (! [X] :( ( big_p(a)& ( big_p(X)=> big_p(f(X)) ) )=> big_p(f(f(X))) ))<=> (! [X1] :( ( ~ big_p(a)| big_p(X1)| big_p(f(f(X1))) )& ( ~ big_p(a)| ~ big_p(f(X1))| big_p(f(f(X1))) ) ) )) ),
% 0.15/15.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/15.42 fof(f2,negated_conjecture,(
% 0.15/15.42 ~(( (! [X] :( ( big_p(a)& ( big_p(X)=> big_p(f(X)) ) )=> big_p(f(f(X))) ))<=> (! [X1] :( ( ~ big_p(a)| big_p(X1)| big_p(f(f(X1))) )& ( ~ big_p(a)| ~ big_p(f(X1))| big_p(f(f(X1))) ) ) )) )),
% 0.15/15.42 inference(negated_conjecture,[status(cth)],[f1])).
% 0.15/15.42 fof(f3,plain,(
% 0.15/15.42 ((![X]: ((~big_p(a)|(big_p(X)&~big_p(f(X))))|big_p(f(f(X)))))<~>(![X1]: (((~big_p(a)|big_p(X1))|big_p(f(f(X1))))&((~big_p(a)|~big_p(f(X1)))|big_p(f(f(X1)))))))),
% 0.15/15.42 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/15.42 fof(f4,definition,(
% 0.15/15.42 ![X]: (sP0_prd(X)<=>((~big_p(a)|(big_p(X)&~big_p(f(X))))|big_p(f(f(X)))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/15.42 fof(f5,definition,(
% 0.15/15.42 ![X1]: (sP1_prd(X1)<=>((~big_p(a)|big_p(X1))|big_p(f(f(X1)))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.15/15.42 fof(f6,plain,(
% 0.15/15.42 (![X]: sP0_prd(X))<~>(![X1]: (sP1_prd(X1)&((~big_p(a)|~big_p(f(X1)))|big_p(f(f(X1))))))),
% 0.15/15.42 inference(formula_renaming,[status(thm)],[f3,f5,f4])).
% 0.15/15.42 fof(f7,plain,(
% 0.15/15.42 ((![X]: sP0_prd(X))|(![X1]: (sP1_prd(X1)&((~big_p(a)|~big_p(f(X1)))|big_p(f(f(X1)))))))&((?[X]: ~sP0_prd(X))|(?[X1]: (~sP1_prd(X1)|((big_p(a)&big_p(f(X1)))&~big_p(f(f(X1)))))))),
% 0.15/15.42 inference(NNF_transformation,[status(thm)],[f6])).
% 0.15/15.42 fof(f8,plain,(
% 0.15/15.42 ((![X]: sP0_prd(X))|((![X1]: sP1_prd(X1))&(![X1]: ((~big_p(a)|~big_p(f(X1)))|big_p(f(f(X1)))))))&((?[X]: ~sP0_prd(X))|((?[X1]: ~sP1_prd(X1))|(?[X1]: ((big_p(a)&big_p(f(X1)))&~big_p(f(f(X1)))))))),
% 0.15/15.42 inference(miniscoping,[status(thm)],[f7])).
% 0.15/15.42 fof(f9,plain,(
% 0.15/15.42 ((![X]: sP0_prd(X))|((![X1]: sP1_prd(X1))&(![X1]: ((~big_p(a)|~big_p(f(X1)))|big_p(f(f(X1)))))))&(~sP0_prd(sK0_skl)|(~sP1_prd(sK1_skl)|((big_p(a)&big_p(f(sK2_skl)))&~big_p(f(f(sK2_skl))))))),
% 0.15/15.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(X1,sK1_skl),skolemize(X1,sK2_skl)],[f8])).
% 0.15/15.42 fof(f10,plain,(
% 0.15/15.42 ![X0,X1]: (sP0_prd(X0)|sP1_prd(X1))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/15.42 fof(f11,plain,(
% 0.15/15.42 ![X0,X1]: (sP0_prd(X0)|~big_p(a)|~big_p(f(X1))|big_p(f(f(X1))))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/15.42 fof(f12,plain,(
% 0.15/15.42 ~sP0_prd(sK0_skl)|~sP1_prd(sK1_skl)|big_p(a)),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/15.42 fof(f13,plain,(
% 0.15/15.42 ~sP0_prd(sK0_skl)|~sP1_prd(sK1_skl)|big_p(f(sK2_skl))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/15.42 fof(f14,plain,(
% 0.15/15.42 ~sP0_prd(sK0_skl)|~sP1_prd(sK1_skl)|~big_p(f(f(sK2_skl)))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/15.42 fof(f15,plain,(
% 0.15/15.42 ![X]: ((~sP0_prd(X)|((~big_p(a)|(big_p(X)&~big_p(f(X))))|big_p(f(f(X)))))&(sP0_prd(X)|((big_p(a)&(~big_p(X)|big_p(f(X))))&~big_p(f(f(X))))))),
% 0.15/15.42 inference(NNF_transformation,[status(thm)],[f4])).
% 0.15/15.42 fof(f16,plain,(
% 0.15/15.42 (![X]: (~sP0_prd(X)|((~big_p(a)|(big_p(X)&~big_p(f(X))))|big_p(f(f(X))))))&(![X]: (sP0_prd(X)|((big_p(a)&(~big_p(X)|big_p(f(X))))&~big_p(f(f(X))))))),
% 0.15/15.42 inference(miniscoping,[status(thm)],[f15])).
% 0.15/15.42 fof(f17,plain,(
% 0.15/15.42 ![X0]: (~sP0_prd(X0)|~big_p(a)|big_p(X0)|big_p(f(f(X0))))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/15.42 fof(f18,plain,(
% 0.15/15.42 ![X0]: (~sP0_prd(X0)|~big_p(a)|~big_p(f(X0))|big_p(f(f(X0))))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/15.42 fof(f19,plain,(
% 0.15/15.42 ![X0]: (sP0_prd(X0)|big_p(a))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/15.42 fof(f20,plain,(
% 0.15/15.42 ![X0]: (sP0_prd(X0)|~big_p(X0)|big_p(f(X0)))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/15.42 fof(f21,plain,(
% 0.15/15.42 ![X0]: (sP0_prd(X0)|~big_p(f(f(X0))))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/15.42 fof(f22,plain,(
% 0.15/15.42 ![X1]: ((~sP1_prd(X1)|((~big_p(a)|big_p(X1))|big_p(f(f(X1)))))&(sP1_prd(X1)|((big_p(a)&~big_p(X1))&~big_p(f(f(X1))))))),
% 0.15/15.42 inference(NNF_transformation,[status(thm)],[f5])).
% 0.15/15.42 fof(f23,plain,(
% 0.15/15.42 (![X1]: (~sP1_prd(X1)|((~big_p(a)|big_p(X1))|big_p(f(f(X1))))))&(![X1]: (sP1_prd(X1)|((big_p(a)&~big_p(X1))&~big_p(f(f(X1))))))),
% 0.15/15.42 inference(miniscoping,[status(thm)],[f22])).
% 0.15/15.42 fof(f24,plain,(
% 0.15/15.42 ![X0]: (~sP1_prd(X0)|~big_p(a)|big_p(X0)|big_p(f(f(X0))))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/15.42 fof(f25,plain,(
% 0.15/15.42 ![X0]: (sP1_prd(X0)|big_p(a))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/15.42 fof(f26,plain,(
% 0.15/15.42 ![X0]: (sP1_prd(X0)|~big_p(X0))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/15.42 fof(f27,plain,(
% 0.15/15.42 ![X0]: (sP1_prd(X0)|~big_p(f(f(X0))))),
% 0.15/15.42 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/15.42 fof(f28,definition,(
% 0.15/15.42 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f29,plain,(
% 0.15/15.42 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.15/15.42 inference(component_clause,[status(thm)],[f28])).
% 0.15/15.42 fof(f31,definition,(
% 0.15/15.42 ![X1]: (sQ1_spl <=> (sP1_prd(X1)))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f32,plain,(
% 0.15/15.42 ![X0]: (sP1_prd(X0)|~sQ1_spl)),
% 0.15/15.42 inference(component_clause,[status(thm)],[f31])).
% 0.15/15.42 fof(f34,plain,(
% 0.15/15.42 sQ0_spl|sQ1_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f10,f28,f31])).
% 0.15/15.42 fof(f35,definition,(
% 0.15/15.42 sQ2_spl <=> (big_p(a))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f38,definition,(
% 0.15/15.42 ![X1]: (sQ3_spl <=> (~big_p(f(X1))|big_p(f(f(X1)))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f39,plain,(
% 0.15/15.42 ![X0]: (~big_p(f(X0))|big_p(f(f(X0)))|~sQ3_spl)),
% 0.15/15.42 inference(component_clause,[status(thm)],[f38])).
% 0.15/15.42 fof(f41,plain,(
% 0.15/15.42 sQ0_spl|~sQ2_spl|sQ3_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f11,f28,f35,f38])).
% 0.15/15.42 fof(f42,definition,(
% 0.15/15.42 sQ4_spl <=> (sP0_prd(sK0_skl))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f44,plain,(
% 0.15/15.42 ~sP0_prd(sK0_skl)|sQ4_spl),
% 0.15/15.42 inference(component_clause,[status(thm)],[f42])).
% 0.15/15.42 fof(f45,definition,(
% 0.15/15.42 sQ5_spl <=> (sP1_prd(sK1_skl))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f47,plain,(
% 0.15/15.42 ~sP1_prd(sK1_skl)|sQ5_spl),
% 0.15/15.42 inference(component_clause,[status(thm)],[f45])).
% 0.15/15.42 fof(f48,plain,(
% 0.15/15.42 ~sQ4_spl|~sQ5_spl|sQ2_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f12,f42,f45,f35])).
% 0.15/15.42 fof(f49,definition,(
% 0.15/15.42 sQ6_spl <=> (big_p(f(sK2_skl)))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f50,plain,(
% 0.15/15.42 big_p(f(sK2_skl))|~sQ6_spl),
% 0.15/15.42 inference(component_clause,[status(thm)],[f49])).
% 0.15/15.42 fof(f52,plain,(
% 0.15/15.42 ~sQ4_spl|~sQ5_spl|sQ6_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f13,f42,f45,f49])).
% 0.15/15.42 fof(f53,definition,(
% 0.15/15.42 sQ7_spl <=> (big_p(f(f(sK2_skl))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f55,plain,(
% 0.15/15.42 ~big_p(f(f(sK2_skl)))|sQ7_spl),
% 0.15/15.42 inference(component_clause,[status(thm)],[f53])).
% 0.15/15.42 fof(f56,plain,(
% 0.15/15.42 ~sQ4_spl|~sQ5_spl|~sQ7_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f14,f42,f45,f53])).
% 0.15/15.42 fof(f57,definition,(
% 0.15/15.42 ![X0]: (sQ8_spl <=> (~sP0_prd(X0)|big_p(X0)|big_p(f(f(X0)))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f58,plain,(
% 0.15/15.42 ![X0]: (~sP0_prd(X0)|big_p(X0)|big_p(f(f(X0)))|~sQ8_spl)),
% 0.15/15.42 inference(component_clause,[status(thm)],[f57])).
% 0.15/15.42 fof(f60,plain,(
% 0.15/15.42 sQ8_spl|~sQ2_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f17,f57,f35])).
% 0.15/15.42 fof(f61,definition,(
% 0.15/15.42 ![X0]: (sQ9_spl <=> (~sP0_prd(X0)|~big_p(f(X0))|big_p(f(f(X0)))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f62,plain,(
% 0.15/15.42 ![X0]: (~sP0_prd(X0)|~big_p(f(X0))|big_p(f(f(X0)))|~sQ9_spl)),
% 0.15/15.42 inference(component_clause,[status(thm)],[f61])).
% 0.15/15.42 fof(f64,plain,(
% 0.15/15.42 sQ9_spl|~sQ2_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f18,f61,f35])).
% 0.15/15.42 fof(f65,plain,(
% 0.15/15.42 sQ0_spl|sQ2_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f19,f28,f35])).
% 0.15/15.42 fof(f66,definition,(
% 0.15/15.42 ![X0]: (sQ10_spl <=> (~sP1_prd(X0)|big_p(X0)|big_p(f(f(X0)))))),
% 0.15/15.42 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.15/15.42 fof(f67,plain,(
% 0.15/15.42 ![X0]: (~sP1_prd(X0)|big_p(X0)|big_p(f(f(X0)))|~sQ10_spl)),
% 0.15/15.42 inference(component_clause,[status(thm)],[f66])).
% 0.15/15.42 fof(f69,plain,(
% 0.15/15.42 sQ10_spl|~sQ2_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f24,f66,f35])).
% 0.15/15.42 fof(f70,plain,(
% 0.15/15.42 sQ1_spl|sQ2_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f25,f31,f35])).
% 0.15/15.42 fof(f71,plain,(
% 0.15/15.42 $false|~sQ1_spl|sQ5_spl),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f47,f32])).
% 0.15/15.42 fof(f72,plain,(
% 0.15/15.42 ~sQ1_spl|sQ5_spl),
% 0.15/15.42 inference(contradiction_clause,[status(thm)],[f71])).
% 0.15/15.42 fof(f73,plain,(
% 0.15/15.42 $false|~sQ0_spl|sQ4_spl),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f44,f29])).
% 0.15/15.42 fof(f74,plain,(
% 0.15/15.42 ~sQ0_spl|sQ4_spl),
% 0.15/15.42 inference(contradiction_clause,[status(thm)],[f73])).
% 0.15/15.42 fof(f76,plain,(
% 0.15/15.42 ![X0]: (~big_p(f(X0))|sP0_prd(X0)|~sQ3_spl)),
% 0.15/15.42 inference(resolution,[status(thm)],[f39,f21])).
% 0.15/15.42 fof(f77,plain,(
% 0.15/15.42 ![X0]: (big_p(X0)|big_p(f(f(X0)))|~sQ1_spl|~sQ10_spl)),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f67,f32])).
% 0.15/15.42 fof(f78,plain,(
% 0.15/15.42 ![X0]: (big_p(X0)|sP0_prd(X0)|~sQ1_spl|~sQ10_spl)),
% 0.15/15.42 inference(resolution,[status(thm)],[f77,f21])).
% 0.15/15.42 fof(f79,plain,(
% 0.15/15.42 ![X0]: (sP0_prd(X0)|big_p(f(X0))|~sQ1_spl|~sQ10_spl)),
% 0.15/15.42 inference(backward_subsumption_resolution,[status(thm)],[f20,f78])).
% 0.15/15.42 fof(f86,plain,(
% 0.15/15.42 ![X0]: (sP0_prd(X0)|~sQ3_spl|~sQ1_spl|~sQ10_spl)),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f79,f76])).
% 0.15/15.42 fof(f89,plain,(
% 0.15/15.42 ![X0]: (big_p(X0)|big_p(f(f(X0)))|~sQ0_spl|~sQ8_spl)),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f58,f29])).
% 0.15/15.42 fof(f91,plain,(
% 0.15/15.42 ![X0]: (sP1_prd(X0)|big_p(X0)|~sQ0_spl|~sQ8_spl)),
% 0.15/15.42 inference(resolution,[status(thm)],[f27,f89])).
% 0.15/15.42 fof(f92,plain,(
% 0.15/15.42 ![X0]: (sP1_prd(X0)|~sQ0_spl|~sQ8_spl)),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f91,f26])).
% 0.15/15.42 fof(f93,plain,(
% 0.15/15.42 $false|~sQ0_spl|~sQ8_spl|sQ5_spl),
% 0.15/15.42 inference(backward_subsumption_resolution,[status(thm)],[f47,f92])).
% 0.15/15.42 fof(f94,plain,(
% 0.15/15.42 ~sQ0_spl|~sQ8_spl|sQ5_spl),
% 0.15/15.42 inference(contradiction_clause,[status(thm)],[f93])).
% 0.15/15.42 fof(f96,plain,(
% 0.15/15.42 ![X0]: (~big_p(f(X0))|big_p(f(f(X0)))|~sQ0_spl|~sQ9_spl)),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f62,f29])).
% 0.15/15.42 fof(f97,plain,(
% 0.15/15.42 ~big_p(f(sK2_skl))|~sQ0_spl|~sQ9_spl|sQ7_spl),
% 0.15/15.42 inference(resolution,[status(thm)],[f96,f55])).
% 0.15/15.42 fof(f98,plain,(
% 0.15/15.42 $false|~sQ6_spl|~sQ0_spl|~sQ9_spl|sQ7_spl),
% 0.15/15.42 inference(forward_subsumption_resolution,[status(thm)],[f97,f50])).
% 0.15/15.42 fof(f99,plain,(
% 0.15/15.42 ~sQ6_spl|~sQ0_spl|~sQ9_spl|sQ7_spl),
% 0.15/15.42 inference(contradiction_clause,[status(thm)],[f98])).
% 0.15/15.42 fof(f100,plain,(
% 0.15/15.42 sQ0_spl|~sQ3_spl|~sQ1_spl|~sQ10_spl),
% 0.15/15.42 inference(split_clause,[status(thm)],[f86,f28,f38,f31,f66])).
% 0.15/15.42 fof(f101,plain,(
% 0.15/15.42 $false),
% 0.15/15.42 inference(sat_refutation,[status(thm)],[f34,f41,f48,f52,f56,f60,f64,f65,f69,f70,f72,f74,f94,f99,f100])).
% 0.15/15.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/15.43 % Elapsed time: 0.035183 seconds
% 0.15/15.43 % CPU time: 0.099078 seconds
% 0.15/15.43 % Total memory used: 13.265 MB
% 0.15/15.43 % Net memory used: 12.969 MB
%------------------------------------------------------------------------------