%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN063+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 : n018.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 03:18:51 PM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN063+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 10:43:43 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.37 fof(f1,conjecture,(
% 0.11/0.37 ( (! [X] :( ( big_p(a)& ( big_p(X)=> big_p(b) ) )=> big_p(c) ))<=> (! [X1] :( ( ~ big_p(a)| big_p(X1)| big_p(c) )& ( ~ big_p(a)| ~ big_p(b)| big_p(c) ) ) )) ),
% 0.11/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f2,negated_conjecture,(
% 0.11/0.37 ~(( (! [X] :( ( big_p(a)& ( big_p(X)=> big_p(b) ) )=> big_p(c) ))<=> (! [X1] :( ( ~ big_p(a)| big_p(X1)| big_p(c) )& ( ~ big_p(a)| ~ big_p(b)| big_p(c) ) ) )) )),
% 0.11/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.37 fof(f3,plain,(
% 0.11/0.37 ((![X]: ((~big_p(a)|(big_p(X)&~big_p(b)))|big_p(c)))<~>(![X1]: (((~big_p(a)|big_p(X1))|big_p(c))&((~big_p(a)|~big_p(b))|big_p(c)))))),
% 0.11/0.37 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.11/0.37 fof(f4,definition,(
% 0.11/0.37 ![X]: (sP0_prd(X)<=>((~big_p(a)|(big_p(X)&~big_p(b)))|big_p(c)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.11/0.37 fof(f5,definition,(
% 0.11/0.37 ![X1]: (sP1_prd(X1)<=>((~big_p(a)|big_p(X1))|big_p(c)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.11/0.37 fof(f6,plain,(
% 0.11/0.37 (![X]: sP0_prd(X))<~>(![X1]: (sP1_prd(X1)&((~big_p(a)|~big_p(b))|big_p(c))))),
% 0.11/0.37 inference(formula_renaming,[status(thm)],[f3,f5,f4])).
% 0.11/0.37 fof(f7,plain,(
% 0.11/0.37 ((![X]: sP0_prd(X))|(![X1]: (sP1_prd(X1)&((~big_p(a)|~big_p(b))|big_p(c)))))&((?[X]: ~sP0_prd(X))|(?[X1]: (~sP1_prd(X1)|((big_p(a)&big_p(b))&~big_p(c)))))),
% 0.11/0.37 inference(NNF_transformation,[status(thm)],[f6])).
% 0.11/0.37 fof(f8,plain,(
% 0.11/0.37 ((![X]: sP0_prd(X))|((![X1]: sP1_prd(X1))&((~big_p(a)|~big_p(b))|big_p(c))))&((?[X]: ~sP0_prd(X))|((?[X1]: ~sP1_prd(X1))|((big_p(a)&big_p(b))&~big_p(c))))),
% 0.11/0.37 inference(miniscoping,[status(thm)],[f7])).
% 0.11/0.37 fof(f9,plain,(
% 0.11/0.37 ((![X]: sP0_prd(X))|((![X1]: sP1_prd(X1))&((~big_p(a)|~big_p(b))|big_p(c))))&(~sP0_prd(sK0_skl)|(~sP1_prd(sK1_skl)|((big_p(a)&big_p(b))&~big_p(c))))),
% 0.11/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X1,sK1_skl)],[f8])).
% 0.11/0.37 fof(f10,plain,(
% 0.11/0.37 ![X0,X1]: (sP0_prd(X0)|sP1_prd(X1))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.11/0.37 fof(f11,plain,(
% 0.11/0.37 ![X0]: (sP0_prd(X0)|~big_p(a)|~big_p(b)|big_p(c))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.11/0.37 fof(f12,plain,(
% 0.11/0.37 ~sP0_prd(sK0_skl)|~sP1_prd(sK1_skl)|big_p(a)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.11/0.37 fof(f13,plain,(
% 0.11/0.37 ~sP0_prd(sK0_skl)|~sP1_prd(sK1_skl)|big_p(b)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.11/0.37 fof(f14,plain,(
% 0.11/0.37 ~sP0_prd(sK0_skl)|~sP1_prd(sK1_skl)|~big_p(c)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.11/0.37 fof(f15,plain,(
% 0.11/0.37 ![X]: ((~sP0_prd(X)|((~big_p(a)|(big_p(X)&~big_p(b)))|big_p(c)))&(sP0_prd(X)|((big_p(a)&(~big_p(X)|big_p(b)))&~big_p(c))))),
% 0.11/0.37 inference(NNF_transformation,[status(thm)],[f4])).
% 0.11/0.37 fof(f16,plain,(
% 0.11/0.37 (![X]: (~sP0_prd(X)|((~big_p(a)|(big_p(X)&~big_p(b)))|big_p(c))))&(![X]: (sP0_prd(X)|((big_p(a)&(~big_p(X)|big_p(b)))&~big_p(c))))),
% 0.11/0.37 inference(miniscoping,[status(thm)],[f15])).
% 0.11/0.37 fof(f17,plain,(
% 0.11/0.37 ![X0]: (~sP0_prd(X0)|~big_p(a)|big_p(X0)|big_p(c))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.37 fof(f18,plain,(
% 0.11/0.37 ![X0]: (~sP0_prd(X0)|~big_p(a)|~big_p(b)|big_p(c))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.37 fof(f19,plain,(
% 0.11/0.37 ![X0]: (sP0_prd(X0)|big_p(a))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.37 fof(f21,plain,(
% 0.11/0.37 ![X0]: (sP0_prd(X0)|~big_p(c))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.37 fof(f22,plain,(
% 0.11/0.37 ![X1]: ((~sP1_prd(X1)|((~big_p(a)|big_p(X1))|big_p(c)))&(sP1_prd(X1)|((big_p(a)&~big_p(X1))&~big_p(c))))),
% 0.11/0.37 inference(NNF_transformation,[status(thm)],[f5])).
% 0.11/0.37 fof(f23,plain,(
% 0.11/0.37 (![X1]: (~sP1_prd(X1)|((~big_p(a)|big_p(X1))|big_p(c))))&(![X1]: (sP1_prd(X1)|((big_p(a)&~big_p(X1))&~big_p(c))))),
% 0.11/0.37 inference(miniscoping,[status(thm)],[f22])).
% 0.11/0.37 fof(f24,plain,(
% 0.11/0.37 ![X0]: (~sP1_prd(X0)|~big_p(a)|big_p(X0)|big_p(c))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f23])).
% 0.11/0.37 fof(f25,plain,(
% 0.11/0.37 ![X0]: (sP1_prd(X0)|big_p(a))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f23])).
% 0.11/0.37 fof(f27,plain,(
% 0.11/0.37 ![X0]: (sP1_prd(X0)|~big_p(c))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f23])).
% 0.11/0.37 fof(f28,definition,(
% 0.11/0.37 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f29,plain,(
% 0.11/0.37 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.11/0.37 inference(component_clause,[status(thm)],[f28])).
% 0.11/0.37 fof(f31,definition,(
% 0.11/0.37 ![X1]: (sQ1_spl <=> (sP1_prd(X1)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f32,plain,(
% 0.11/0.37 ![X0]: (sP1_prd(X0)|~sQ1_spl)),
% 0.11/0.37 inference(component_clause,[status(thm)],[f31])).
% 0.11/0.37 fof(f34,plain,(
% 0.11/0.37 sQ0_spl|sQ1_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f10,f28,f31])).
% 0.11/0.37 fof(f35,definition,(
% 0.11/0.37 sQ2_spl <=> (big_p(a))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f38,definition,(
% 0.11/0.37 sQ3_spl <=> (big_p(b))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f40,plain,(
% 0.11/0.37 ~big_p(b)|sQ3_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f38])).
% 0.11/0.37 fof(f41,definition,(
% 0.11/0.37 sQ4_spl <=> (big_p(c))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f44,plain,(
% 0.11/0.37 sQ0_spl|~sQ2_spl|~sQ3_spl|sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f11,f28,f35,f38,f41])).
% 0.11/0.37 fof(f45,definition,(
% 0.11/0.37 sQ5_spl <=> (sP0_prd(sK0_skl))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f47,plain,(
% 0.11/0.37 ~sP0_prd(sK0_skl)|sQ5_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f45])).
% 0.11/0.37 fof(f48,definition,(
% 0.11/0.37 sQ6_spl <=> (sP1_prd(sK1_skl))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f50,plain,(
% 0.11/0.37 ~sP1_prd(sK1_skl)|sQ6_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f48])).
% 0.11/0.37 fof(f51,plain,(
% 0.11/0.37 ~sQ5_spl|~sQ6_spl|sQ2_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f12,f45,f48,f35])).
% 0.11/0.37 fof(f52,plain,(
% 0.11/0.37 ~sQ5_spl|~sQ6_spl|sQ3_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f13,f45,f48,f38])).
% 0.11/0.37 fof(f53,plain,(
% 0.11/0.37 ~sQ5_spl|~sQ6_spl|~sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f14,f45,f48,f41])).
% 0.11/0.37 fof(f54,definition,(
% 0.11/0.37 ![X0]: (sQ7_spl <=> (~sP0_prd(X0)|big_p(X0)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f55,plain,(
% 0.11/0.37 ![X0]: (~sP0_prd(X0)|big_p(X0)|~sQ7_spl)),
% 0.11/0.37 inference(component_clause,[status(thm)],[f54])).
% 0.11/0.37 fof(f57,plain,(
% 0.11/0.37 sQ7_spl|~sQ2_spl|sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f17,f54,f35,f41])).
% 0.11/0.37 fof(f58,definition,(
% 0.11/0.37 ![X0]: (sQ8_spl <=> (~sP0_prd(X0)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f59,plain,(
% 0.11/0.37 ![X0]: (~sP0_prd(X0)|~sQ8_spl)),
% 0.11/0.37 inference(component_clause,[status(thm)],[f58])).
% 0.11/0.37 fof(f61,plain,(
% 0.11/0.37 sQ8_spl|~sQ2_spl|~sQ3_spl|sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f18,f58,f35,f38,f41])).
% 0.11/0.37 fof(f62,plain,(
% 0.11/0.37 sQ0_spl|sQ2_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f19,f28,f35])).
% 0.11/0.37 fof(f67,plain,(
% 0.11/0.37 sQ0_spl|~sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f21,f28,f41])).
% 0.11/0.37 fof(f68,definition,(
% 0.11/0.37 ![X0]: (sQ10_spl <=> (~sP1_prd(X0)|big_p(X0)))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f69,plain,(
% 0.11/0.37 ![X0]: (~sP1_prd(X0)|big_p(X0)|~sQ10_spl)),
% 0.11/0.37 inference(component_clause,[status(thm)],[f68])).
% 0.11/0.37 fof(f71,plain,(
% 0.11/0.37 sQ10_spl|~sQ2_spl|sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f24,f68,f35,f41])).
% 0.11/0.37 fof(f72,plain,(
% 0.11/0.37 sQ1_spl|sQ2_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f25,f31,f35])).
% 0.11/0.37 fof(f73,plain,(
% 0.11/0.37 sQ1_spl|~sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f27,f31,f41])).
% 0.11/0.37 fof(f74,plain,(
% 0.11/0.37 $false|~sQ1_spl|sQ6_spl),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f50,f32])).
% 0.11/0.37 fof(f75,plain,(
% 0.11/0.37 ~sQ1_spl|sQ6_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f74])).
% 0.11/0.37 fof(f76,plain,(
% 0.11/0.37 $false|~sQ0_spl|sQ5_spl),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f47,f29])).
% 0.11/0.37 fof(f77,plain,(
% 0.11/0.37 ~sQ0_spl|sQ5_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f76])).
% 0.11/0.37 fof(f78,plain,(
% 0.11/0.37 ![X0]: (big_p(X0)|~sQ1_spl|~sQ10_spl)),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f69,f32])).
% 0.11/0.37 fof(f79,plain,(
% 0.11/0.37 $false|~sQ1_spl|~sQ10_spl|sQ3_spl),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f40,f78])).
% 0.11/0.37 fof(f82,plain,(
% 0.11/0.37 ~sQ1_spl|~sQ10_spl|sQ3_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f79])).
% 0.11/0.37 fof(f83,plain,(
% 0.11/0.37 $false|~sQ8_spl|~sQ0_spl),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f29,f59])).
% 0.11/0.37 fof(f84,plain,(
% 0.11/0.37 ~sQ8_spl|~sQ0_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f83])).
% 0.11/0.37 fof(f85,plain,(
% 0.11/0.37 ![X0]: (big_p(X0)|~sQ0_spl|~sQ7_spl)),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f55,f29])).
% 0.11/0.37 fof(f86,plain,(
% 0.11/0.37 $false|~sQ0_spl|~sQ7_spl|sQ3_spl),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f40,f85])).
% 0.11/0.37 fof(f89,plain,(
% 0.11/0.37 ~sQ0_spl|~sQ7_spl|sQ3_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f86])).
% 0.11/0.37 fof(f90,plain,(
% 0.11/0.37 $false),
% 0.11/0.37 inference(sat_refutation,[status(thm)],[f34,f44,f51,f52,f53,f57,f61,f62,f67,f71,f72,f73,f75,f77,f82,f84,f89])).
% 0.11/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.40 % Elapsed time: 0.042169 seconds
% 0.11/0.40 % CPU time: 0.103523 seconds
% 0.11/0.40 % Total memory used: 16.770 MB
% 0.11/0.40 % Net memory used: 16.336 MB
%------------------------------------------------------------------------------