%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN056+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 : n006.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 03:18:49 PM UTC 2026
% Result : Theorem 0.18s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 10:41:14 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.45 % Refutation found
% 0.18/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.45 fof(f1,axiom,(
% 0.18/0.45 ( (? [X] : big_p(X))<=> (? [Y] : big_q(Y) )) ),
% 0.18/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.45 fof(f2,axiom,(
% 0.18/0.45 (! [X,Y] :( ( big_p(X)& big_q(Y) )=> ( big_r(X)<=> big_s(Y) ) ) )),
% 0.18/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.45 fof(f3,conjecture,(
% 0.18/0.45 ( (! [X] :( big_p(X)=> big_r(X) ))<=> (! [Y] :( big_q(Y)=> big_s(Y) ) )) ),
% 0.18/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.45 fof(f4,negated_conjecture,(
% 0.18/0.45 ~(( (! [X] :( big_p(X)=> big_r(X) ))<=> (! [Y] :( big_q(Y)=> big_s(Y) ) )) )),
% 0.18/0.45 inference(negated_conjecture,[status(cth)],[f3])).
% 0.18/0.45 fof(f5,plain,(
% 0.18/0.45 ((![X]: ~big_p(X))|(?[Y]: big_q(Y)))&((?[X]: big_p(X))|(![Y]: ~big_q(Y)))),
% 0.18/0.45 inference(NNF_transformation,[status(thm)],[f1])).
% 0.18/0.45 fof(f6,plain,(
% 0.18/0.45 ((![X]: ~big_p(X))|big_q(sK0_skl))&(big_p(sK1_skl)|(![Y]: ~big_q(Y)))),
% 0.18/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f5])).
% 0.18/0.45 fof(f7,plain,(
% 0.18/0.45 ![X0]: (~big_p(X0)|big_q(sK0_skl))),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f6])).
% 0.18/0.45 fof(f8,plain,(
% 0.18/0.45 ![X0]: (big_p(sK1_skl)|~big_q(X0))),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f6])).
% 0.18/0.45 fof(f9,plain,(
% 0.18/0.45 ![X,Y]: ((~big_p(X)|~big_q(Y))|(big_r(X)<=>big_s(Y)))),
% 0.18/0.45 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.18/0.45 fof(f10,plain,(
% 0.18/0.45 ![X,Y]: ((~big_p(X)|~big_q(Y))|((~big_r(X)|big_s(Y))&(big_r(X)|~big_s(Y))))),
% 0.18/0.45 inference(NNF_transformation,[status(thm)],[f9])).
% 0.18/0.45 fof(f11,plain,(
% 0.18/0.45 ![X0,X1]: (~big_p(X0)|~big_q(X1)|~big_r(X0)|big_s(X1))),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f10])).
% 0.18/0.45 fof(f12,plain,(
% 0.18/0.45 ![X0,X1]: (~big_p(X0)|~big_q(X1)|big_r(X0)|~big_s(X1))),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f10])).
% 0.18/0.45 fof(f13,plain,(
% 0.18/0.45 ((![X]: (~big_p(X)|big_r(X)))<~>(![Y]: (~big_q(Y)|big_s(Y))))),
% 0.18/0.45 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.18/0.45 fof(f14,plain,(
% 0.18/0.45 ((![X]: (~big_p(X)|big_r(X)))|(![Y]: (~big_q(Y)|big_s(Y))))&((?[X]: (big_p(X)&~big_r(X)))|(?[Y]: (big_q(Y)&~big_s(Y))))),
% 0.18/0.45 inference(NNF_transformation,[status(thm)],[f13])).
% 0.18/0.45 fof(f15,plain,(
% 0.18/0.45 ((![X]: (~big_p(X)|big_r(X)))|(![Y]: (~big_q(Y)|big_s(Y))))&((big_p(sK2_skl)&~big_r(sK2_skl))|(big_q(sK3_skl)&~big_s(sK3_skl)))),
% 0.18/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f14])).
% 0.18/0.45 fof(f16,plain,(
% 0.18/0.45 ![X0,X1]: (~big_p(X0)|big_r(X0)|~big_q(X1)|big_s(X1))),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f15])).
% 0.18/0.45 fof(f17,plain,(
% 0.18/0.45 big_p(sK2_skl)|big_q(sK3_skl)),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f15])).
% 0.18/0.45 fof(f18,plain,(
% 0.18/0.45 big_p(sK2_skl)|~big_s(sK3_skl)),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f15])).
% 0.18/0.45 fof(f19,plain,(
% 0.18/0.45 ~big_r(sK2_skl)|big_q(sK3_skl)),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f15])).
% 0.18/0.45 fof(f20,plain,(
% 0.18/0.45 ~big_r(sK2_skl)|~big_s(sK3_skl)),
% 0.18/0.45 inference(cnf_transformation,[status(thm)],[f15])).
% 0.18/0.45 fof(f21,definition,(
% 0.18/0.45 ![X0]: (sQ0_spl <=> (~big_p(X0)))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f22,plain,(
% 0.18/0.45 ![X0]: (~big_p(X0)|~sQ0_spl)),
% 0.18/0.45 inference(component_clause,[status(thm)],[f21])).
% 0.18/0.45 fof(f24,definition,(
% 0.18/0.45 sQ1_spl <=> (big_q(sK0_skl))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f25,plain,(
% 0.18/0.45 big_q(sK0_skl)|~sQ1_spl),
% 0.18/0.45 inference(component_clause,[status(thm)],[f24])).
% 0.18/0.45 fof(f27,plain,(
% 0.18/0.45 sQ0_spl|sQ1_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f7,f21,f24])).
% 0.18/0.45 fof(f28,definition,(
% 0.18/0.45 sQ2_spl <=> (big_p(sK1_skl))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f29,plain,(
% 0.18/0.45 big_p(sK1_skl)|~sQ2_spl),
% 0.18/0.45 inference(component_clause,[status(thm)],[f28])).
% 0.18/0.45 fof(f31,definition,(
% 0.18/0.45 ![X0]: (sQ3_spl <=> (~big_q(X0)))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f32,plain,(
% 0.18/0.45 ![X0]: (~big_q(X0)|~sQ3_spl)),
% 0.18/0.45 inference(component_clause,[status(thm)],[f31])).
% 0.18/0.45 fof(f34,plain,(
% 0.18/0.45 sQ2_spl|sQ3_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f8,f28,f31])).
% 0.18/0.45 fof(f35,definition,(
% 0.18/0.45 ![X0]: (sQ4_spl <=> (~big_p(X0)|~big_r(X0)))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f36,plain,(
% 0.18/0.45 ![X0]: (~big_p(X0)|~big_r(X0)|~sQ4_spl)),
% 0.18/0.45 inference(component_clause,[status(thm)],[f35])).
% 0.18/0.45 fof(f38,definition,(
% 0.18/0.45 ![X1]: (sQ5_spl <=> (~big_q(X1)|big_s(X1)))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f39,plain,(
% 0.18/0.45 ![X0]: (~big_q(X0)|big_s(X0)|~sQ5_spl)),
% 0.18/0.45 inference(component_clause,[status(thm)],[f38])).
% 0.18/0.45 fof(f41,plain,(
% 0.18/0.45 sQ4_spl|sQ5_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f11,f35,f38])).
% 0.18/0.45 fof(f42,definition,(
% 0.18/0.45 ![X0]: (sQ6_spl <=> (~big_p(X0)|big_r(X0)))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f43,plain,(
% 0.18/0.45 ![X0]: (~big_p(X0)|big_r(X0)|~sQ6_spl)),
% 0.18/0.45 inference(component_clause,[status(thm)],[f42])).
% 0.18/0.45 fof(f45,definition,(
% 0.18/0.45 ![X1]: (sQ7_spl <=> (~big_q(X1)|~big_s(X1)))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f46,plain,(
% 0.18/0.45 ![X0]: (~big_q(X0)|~big_s(X0)|~sQ7_spl)),
% 0.18/0.45 inference(component_clause,[status(thm)],[f45])).
% 0.18/0.45 fof(f48,plain,(
% 0.18/0.45 sQ6_spl|sQ7_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f12,f42,f45])).
% 0.18/0.45 fof(f49,plain,(
% 0.18/0.45 sQ6_spl|sQ5_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f16,f42,f38])).
% 0.18/0.45 fof(f50,definition,(
% 0.18/0.45 sQ8_spl <=> (big_p(sK2_skl))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f51,plain,(
% 0.18/0.45 big_p(sK2_skl)|~sQ8_spl),
% 0.18/0.45 inference(component_clause,[status(thm)],[f50])).
% 0.18/0.45 fof(f53,definition,(
% 0.18/0.45 sQ9_spl <=> (big_q(sK3_skl))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f54,plain,(
% 0.18/0.45 big_q(sK3_skl)|~sQ9_spl),
% 0.18/0.45 inference(component_clause,[status(thm)],[f53])).
% 0.18/0.45 fof(f56,plain,(
% 0.18/0.45 sQ8_spl|sQ9_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f17,f50,f53])).
% 0.18/0.45 fof(f57,definition,(
% 0.18/0.45 sQ10_spl <=> (big_s(sK3_skl))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f59,plain,(
% 0.18/0.45 ~big_s(sK3_skl)|sQ10_spl),
% 0.18/0.45 inference(component_clause,[status(thm)],[f57])).
% 0.18/0.45 fof(f60,plain,(
% 0.18/0.45 sQ8_spl|~sQ10_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f18,f50,f57])).
% 0.18/0.45 fof(f61,definition,(
% 0.18/0.45 sQ11_spl <=> (big_r(sK2_skl))),
% 0.18/0.45 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.18/0.45 fof(f63,plain,(
% 0.18/0.45 ~big_r(sK2_skl)|sQ11_spl),
% 0.18/0.45 inference(component_clause,[status(thm)],[f61])).
% 0.18/0.45 fof(f64,plain,(
% 0.18/0.45 ~sQ11_spl|sQ9_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f19,f61,f53])).
% 0.18/0.45 fof(f65,plain,(
% 0.18/0.45 ~sQ11_spl|~sQ10_spl),
% 0.18/0.45 inference(split_clause,[status(thm)],[f20,f61,f57])).
% 0.18/0.45 fof(f66,plain,(
% 0.18/0.45 ~big_p(sK2_skl)|~sQ6_spl|sQ11_spl),
% 0.18/0.45 inference(resolution,[status(thm)],[f43,f63])).
% 0.18/0.45 fof(f67,plain,(
% 0.18/0.45 $false|~sQ8_spl|~sQ6_spl|sQ11_spl),
% 0.18/0.45 inference(forward_subsumption_resolution,[status(thm)],[f66,f51])).
% 0.18/0.45 fof(f68,plain,(
% 0.18/0.45 ~sQ8_spl|~sQ6_spl|sQ11_spl),
% 0.18/0.45 inference(contradiction_clause,[status(thm)],[f67])).
% 0.18/0.45 fof(f69,plain,(
% 0.18/0.45 ~big_q(sK3_skl)|~sQ5_spl|sQ10_spl),
% 0.18/0.45 inference(resolution,[status(thm)],[f39,f59])).
% 0.18/0.45 fof(f70,plain,(
% 0.18/0.45 $false|~sQ9_spl|~sQ5_spl|sQ10_spl),
% 0.18/0.45 inference(forward_subsumption_resolution,[status(thm)],[f69,f54])).
% 0.18/0.45 fof(f71,plain,(
% 0.18/0.45 ~sQ9_spl|~sQ5_spl|sQ10_spl),
% 0.18/0.45 inference(contradiction_clause,[status(thm)],[f70])).
% 0.18/0.45 fof(f72,plain,(
% 0.18/0.45 ![X0]: (~big_q(X0)|~sQ5_spl|~sQ7_spl)),
% 0.18/0.45 inference(forward_subsumption_resolution,[status(thm)],[f46,f39])).
% 0.18/0.45 fof(f73,plain,(
% 0.18/0.45 $false|~sQ0_spl|~sQ2_spl),
% 0.18/0.45 inference(backward_subsumption_resolution,[status(thm)],[f29,f22])).
% 0.18/0.45 fof(f74,plain,(
% 0.18/0.45 $false|~sQ0_spl|~sQ8_spl),
% 0.18/0.45 inference(backward_subsumption_resolution,[status(thm)],[f51,f22])).
% 0.18/0.45 fof(f75,plain,(
% 0.18/0.45 ~sQ0_spl|~sQ2_spl),
% 0.18/0.45 inference(contradiction_clause,[status(thm)],[f73])).
% 0.18/0.45 fof(f76,plain,(
% 0.18/0.45 $false|~sQ5_spl|~sQ7_spl|~sQ1_spl),
% 0.18/0.45 inference(forward_subsumption_resolution,[status(thm)],[f25,f72])).
% 0.18/0.45 fof(f77,plain,(
% 0.18/0.45 ~sQ5_spl|~sQ7_spl|~sQ1_spl),
% 0.18/0.45 inference(contradiction_clause,[status(thm)],[f76])).
% 0.18/0.45 fof(f78,plain,(
% 0.18/0.47 ~sQ0_spl|~sQ8_spl),
% 0.18/0.47 inference(contradiction_clause,[status(thm)],[f74])).
% 0.18/0.47 fof(f79,plain,(
% 0.18/0.47 $false|~sQ3_spl|~sQ9_spl),
% 0.18/0.47 inference(forward_subsumption_resolution,[status(thm)],[f54,f32])).
% 0.18/0.47 fof(f80,plain,(
% 0.18/0.47 ~sQ3_spl|~sQ9_spl),
% 0.18/0.47 inference(contradiction_clause,[status(thm)],[f79])).
% 0.18/0.47 fof(f82,plain,(
% 0.18/0.47 $false|~sQ4_spl|~sQ6_spl|~sQ2_spl),
% 0.18/0.47 inference(backward_subsumption_resolution,[status(thm)],[f29,f83])).
% 0.18/0.47 fof(f83,plain,(
% 0.18/0.47 ![X0]: (~big_p(X0)|~sQ4_spl|~sQ6_spl)),
% 0.18/0.47 inference(forward_subsumption_resolution,[status(thm)],[f43,f36])).
% 0.18/0.47 fof(f84,plain,(
% 0.18/0.47 ~sQ4_spl|~sQ6_spl|~sQ2_spl),
% 0.18/0.47 inference(contradiction_clause,[status(thm)],[f82])).
% 0.18/0.47 fof(f85,plain,(
% 0.18/0.47 $false),
% 0.18/0.47 inference(sat_refutation,[status(thm)],[f27,f34,f41,f48,f49,f56,f60,f64,f65,f68,f71,f75,f77,f78,f80,f84])).
% 0.18/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.53 % Elapsed time: 0.087040 seconds
% 0.18/0.53 % CPU time: 0.059379 seconds
% 0.18/0.53 % Total memory used: 1.041 MB
% 0.18/0.53 % Net memory used: 1.041 MB
%------------------------------------------------------------------------------