%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 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 11:49:34 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 12:57:03 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.47 fof(f3,axiom,(
% 0.17/0.47 (? [U] :( sorti1(U)& (? [V] :( sorti1(V)& op1(U,U) = V& op1(V,V) = U& op1(U,V) != U ) )) )),
% 0.17/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f4,axiom,(
% 0.17/0.47 ~ (? [U] :( sorti2(U)& (? [V] :( sorti2(V)& op2(U,U) = V& op2(V,V) = U& op2(U,V) != U ) )) )),
% 0.17/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f5,conjecture,(
% 0.17/0.47 ( ( (! [U] :( sorti1(U)=> sorti2(h(U)) ))& (! [V] :( sorti2(V)=> sorti1(j(V)) ) ))=> ~ ( (! [W] :( sorti1(W)=> (! [X] :( sorti1(X)=> h(op1(W,X)) = op2(h(W),h(X)) ) )))& (! [Y] :( sorti2(Y)=> (! [Z] :( sorti2(Z)=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )))& (! [X1] :( sorti2(X1)=> h(j(X1)) = X1 ))& (! [X2] :( sorti1(X2)=> j(h(X2)) = X2 ) )) ) ),
% 0.17/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f6,negated_conjecture,(
% 0.17/0.47 ~(( ( (! [U] :( sorti1(U)=> sorti2(h(U)) ))& (! [V] :( sorti2(V)=> sorti1(j(V)) ) ))=> ~ ( (! [W] :( sorti1(W)=> (! [X] :( sorti1(X)=> h(op1(W,X)) = op2(h(W),h(X)) ) )))& (! [Y] :( sorti2(Y)=> (! [Z] :( sorti2(Z)=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )))& (! [X1] :( sorti2(X1)=> h(j(X1)) = X1 ))& (! [X2] :( sorti1(X2)=> j(h(X2)) = X2 ) )) ) )),
% 0.17/0.47 inference(negated_conjecture,[status(cth)],[f5])).
% 0.17/0.47 fof(f11,plain,(
% 0.17/0.47 (sorti1(sK0_skl)&(((sorti1(sK1_skl)&op1(sK0_skl,sK0_skl)=sK1_skl)&op1(sK1_skl,sK1_skl)=sK0_skl)&~op1(sK0_skl,sK1_skl)=sK0_skl))),
% 0.17/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f3])).
% 0.17/0.47 fof(f12,plain,(
% 0.17/0.47 sorti1(sK0_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f11])).
% 0.17/0.47 fof(f13,plain,(
% 0.17/0.47 sorti1(sK1_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f11])).
% 0.17/0.47 fof(f14,plain,(
% 0.17/0.47 op1(sK0_skl,sK0_skl)=sK1_skl),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f11])).
% 0.17/0.47 fof(f15,plain,(
% 0.17/0.47 op1(sK1_skl,sK1_skl)=sK0_skl),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f11])).
% 0.17/0.47 fof(f16,plain,(
% 0.17/0.47 ~op1(sK0_skl,sK1_skl)=sK0_skl),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f11])).
% 0.17/0.47 fof(f17,plain,(
% 0.17/0.47 (![U]: (~sorti2(U)|(![V]: (((~sorti2(V)|~op2(U,U)=V)|~op2(V,V)=U)|op2(U,V)=U))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.17/0.47 fof(f18,plain,(
% 0.17/0.47 ![X0,X1]: (~sorti2(X0)|~sorti2(X1)|~op2(X0,X0)=X1|~op2(X1,X1)=X0|op2(X0,X1)=X0)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f17])).
% 0.17/0.47 fof(f19,plain,(
% 0.17/0.47 (((![U]: (~sorti1(U)|sorti2(h(U))))&(![V]: (~sorti2(V)|sorti1(j(V)))))&((((![W]: (~sorti1(W)|(![X]: (~sorti1(X)|h(op1(W,X))=op2(h(W),h(X))))))&(![Y]: (~sorti2(Y)|(![Z]: (~sorti2(Z)|j(op2(Y,Z))=op1(j(Y),j(Z)))))))&(![X1]: (~sorti2(X1)|h(j(X1))=X1)))&(![X2]: (~sorti1(X2)|j(h(X2))=X2))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.17/0.47 fof(f20,plain,(
% 0.17/0.47 ![X0]: (~sorti1(X0)|sorti2(h(X0)))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.47 fof(f22,plain,(
% 0.17/0.47 ![X0,X1]: (~sorti1(X0)|~sorti1(X1)|h(op1(X0,X1))=op2(h(X0),h(X1)))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.47 fof(f23,plain,(
% 0.17/0.47 ![X0,X1]: (~sorti2(X0)|~sorti2(X1)|j(op2(X0,X1))=op1(j(X0),j(X1)))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.47 fof(f25,plain,(
% 0.17/0.47 ![X0]: (~sorti1(X0)|j(h(X0))=X0)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.47 fof(f26,plain,(
% 0.17/0.47 ![X0]: (~sorti2(X0)|~sorti2(op2(X0,X0))|~op2(op2(X0,X0),op2(X0,X0))=X0|op2(X0,op2(X0,X0))=X0)),
% 0.17/0.47 inference(destructive_equality_resolution,[status(thm)],[f18])).
% 0.17/0.47 fof(f27,plain,(
% 0.17/0.47 ![X0]: (~sorti1(X0)|h(op1(X0,sK0_skl))=op2(h(X0),h(sK0_skl)))),
% 0.17/0.47 inference(resolution,[status(thm)],[f12,f22])).
% 0.17/0.47 fof(f28,plain,(
% 0.17/0.47 j(h(sK0_skl))=sK0_skl),
% 0.17/0.47 inference(resolution,[status(thm)],[f12,f25])).
% 0.17/0.47 fof(f30,plain,(
% 0.17/0.47 sorti2(h(sK0_skl))),
% 0.17/0.47 inference(resolution,[status(thm)],[f12,f20])).
% 0.17/0.47 fof(f32,plain,(
% 0.17/0.47 ![X0]: (~sorti2(X0)|j(op2(X0,h(sK0_skl)))=op1(j(X0),j(h(sK0_skl))))),
% 0.17/0.47 inference(resolution,[status(thm)],[f30,f23])).
% 0.17/0.47 fof(f35,plain,(
% 0.17/0.47 ![X0]: (~sorti2(X0)|j(op2(X0,h(sK0_skl)))=op1(j(X0),sK0_skl))),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f28,f32])).
% 0.17/0.47 fof(f37,plain,(
% 0.17/0.47 h(op1(sK0_skl,sK0_skl))=op2(h(sK0_skl),h(sK0_skl))),
% 0.17/0.47 inference(resolution,[status(thm)],[f27,f12])).
% 0.17/0.47 fof(f38,plain,(
% 0.17/0.47 h(sK1_skl)=op2(h(sK0_skl),h(sK0_skl))),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f14,f37])).
% 0.17/0.47 fof(f39,plain,(
% 0.17/0.47 j(op2(h(sK0_skl),h(sK0_skl)))=op1(j(h(sK0_skl)),sK0_skl)),
% 0.17/0.47 inference(resolution,[status(thm)],[f35,f30])).
% 0.17/0.47 fof(f40,plain,(
% 0.17/0.47 j(h(sK1_skl))=op1(j(h(sK0_skl)),sK0_skl)),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f38,f39])).
% 0.17/0.47 fof(f41,plain,(
% 0.17/0.47 j(h(sK1_skl))=op1(sK0_skl,sK0_skl)),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f28,f40])).
% 0.17/0.47 fof(f42,plain,(
% 0.17/0.47 j(h(sK1_skl))=sK1_skl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f14,f41])).
% 0.17/0.47 fof(f44,plain,(
% 0.17/0.47 ![X0]: (~sorti1(X0)|h(op1(X0,sK1_skl))=op2(h(X0),h(sK1_skl)))),
% 0.17/0.47 inference(resolution,[status(thm)],[f13,f22])).
% 0.17/0.47 fof(f47,plain,(
% 0.17/0.47 sorti2(h(sK1_skl))),
% 0.17/0.47 inference(resolution,[status(thm)],[f13,f20])).
% 0.17/0.47 fof(f48,plain,(
% 0.17/0.47 ~sorti2(h(sK0_skl))|~sorti2(op2(h(sK0_skl),h(sK0_skl)))|~op2(h(sK1_skl),op2(h(sK0_skl),h(sK0_skl)))=h(sK0_skl)|op2(h(sK0_skl),op2(h(sK0_skl),h(sK0_skl)))=h(sK0_skl)),
% 0.17/0.47 inference(paramodulation,[status(thm)],[f38,f26])).
% 0.17/0.47 fof(f50,definition,(
% 0.17/0.47 sQ0_spl <=> (sorti2(h(sK0_skl)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f52,plain,(
% 0.17/0.47 ~sorti2(h(sK0_skl))|sQ0_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f50])).
% 0.17/0.47 fof(f53,definition,(
% 0.17/0.47 sQ1_spl <=> (sorti2(op2(h(sK0_skl),h(sK0_skl))))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f55,plain,(
% 0.17/0.47 ~sorti2(op2(h(sK0_skl),h(sK0_skl)))|sQ1_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f53])).
% 0.17/0.47 fof(f56,definition,(
% 0.17/0.47 sQ2_spl <=> (op2(h(sK1_skl),op2(h(sK0_skl),h(sK0_skl)))=h(sK0_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f58,plain,(
% 0.17/0.47 ~op2(h(sK1_skl),op2(h(sK0_skl),h(sK0_skl)))=h(sK0_skl)|sQ2_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f56])).
% 0.17/0.47 fof(f59,definition,(
% 0.17/0.47 sQ3_spl <=> (op2(h(sK0_skl),op2(h(sK0_skl),h(sK0_skl)))=h(sK0_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f60,plain,(
% 0.17/0.47 op2(h(sK0_skl),op2(h(sK0_skl),h(sK0_skl)))=h(sK0_skl)|~sQ3_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f59])).
% 0.17/0.47 fof(f62,plain,(
% 0.17/0.47 ~sQ0_spl|~sQ1_spl|~sQ2_spl|sQ3_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f48,f50,f53,f56,f59])).
% 0.17/0.47 fof(f67,plain,(
% 0.17/0.47 op2(h(sK0_skl),h(sK1_skl))=h(sK0_skl)|~sQ3_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f38,f60])).
% 0.17/0.47 fof(f70,plain,(
% 0.17/0.47 ![X0]: (~sorti2(X0)|j(op2(X0,h(sK1_skl)))=op1(j(X0),j(h(sK1_skl))))),
% 0.17/0.47 inference(resolution,[status(thm)],[f47,f23])).
% 0.17/0.47 fof(f75,plain,(
% 0.17/0.47 ![X0]: (~sorti2(X0)|j(op2(X0,h(sK1_skl)))=op1(j(X0),sK1_skl))),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f42,f70])).
% 0.17/0.47 fof(f77,plain,(
% 0.17/0.47 h(op1(sK1_skl,sK1_skl))=op2(h(sK1_skl),h(sK1_skl))),
% 0.17/0.47 inference(resolution,[status(thm)],[f44,f13])).
% 0.17/0.47 fof(f79,plain,(
% 0.17/0.47 h(sK0_skl)=op2(h(sK1_skl),h(sK1_skl))),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f15,f77])).
% 0.17/0.47 fof(f112,plain,(
% 0.17/0.47 j(op2(h(sK0_skl),h(sK1_skl)))=op1(j(h(sK0_skl)),sK1_skl)),
% 0.17/0.47 inference(resolution,[status(thm)],[f75,f30])).
% 0.17/0.47 fof(f116,plain,(
% 0.17/0.47 j(h(sK0_skl))=op1(j(h(sK0_skl)),sK1_skl)|~sQ3_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f67,f112])).
% 0.17/0.47 fof(f117,plain,(
% 0.17/0.47 sK0_skl=op1(j(h(sK0_skl)),sK1_skl)|~sQ3_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f28,f116])).
% 0.17/0.47 fof(f118,plain,(
% 0.17/0.47 sK0_skl=op1(sK0_skl,sK1_skl)|~sQ3_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f28,f117])).
% 0.17/0.47 fof(f119,plain,(
% 0.17/0.47 $false|~sQ3_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f118,f16])).
% 0.17/0.47 fof(f120,plain,(
% 0.17/0.47 ~sQ3_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f119])).
% 0.17/0.47 fof(f121,plain,(
% 0.17/0.47 ~sorti2(h(sK1_skl))|sQ1_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f38,f55])).
% 0.17/0.47 fof(f122,plain,(
% 0.17/0.47 $false|sQ1_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f121,f47])).
% 0.17/0.47 fof(f123,plain,(
% 0.17/0.47 sQ1_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f122])).
% 0.17/0.47 fof(f128,plain,(
% 0.17/0.47 $false|sQ0_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f52,f30])).
% 0.17/0.47 fof(f129,plain,(
% 0.17/0.47 sQ0_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f128])).
% 0.17/0.47 fof(f131,plain,(
% 0.17/0.47 ~op2(h(sK1_skl),h(sK1_skl))=h(sK0_skl)|sQ2_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f38,f58])).
% 0.17/0.47 fof(f132,plain,(
% 0.17/0.47 ~h(sK0_skl)=h(sK0_skl)|sQ2_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f79,f131])).
% 0.17/0.47 fof(f133,plain,(
% 0.17/0.47 $false|sQ2_spl),
% 0.17/0.47 inference(trivial_equality_resolution,[status(thm)],[f132])).
% 0.17/0.47 fof(f134,plain,(
% 0.17/0.47 sQ2_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f133])).
% 0.17/0.47 fof(f135,plain,(
% 0.17/0.47 $false),
% 0.17/0.47 inference(sat_refutation,[status(thm)],[f62,f120,f123,f129,f134])).
% 0.17/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.50 % Elapsed time: 0.059051 seconds
% 0.17/0.50 % CPU time: 0.179255 seconds
% 0.17/0.50 % Total memory used: 34.242 MB
% 0.17/0.50 % Net memory used: 34.079 MB
%------------------------------------------------------------------------------