%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG203+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 : 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 11:49:48 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG203+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:03:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.38 fof(f1,axiom,(
% 0.13/0.38 (! [U] :( sorti1(U)=> (! [V] :( sorti1(V)=> sorti1(op1(U,V)) ) )) )),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f3,axiom,(
% 0.13/0.38 ( (? [U] :( sorti1(U)& op1(U,U) = U ))& (? [V] :( sorti1(V)& op1(V,V) != V ) )) ),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f4,axiom,(
% 0.13/0.38 ~ ( (? [U] :( sorti2(U)& op2(U,U) = U ))& (? [V] :( sorti2(V)& op2(V,V) != V ) )) ),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f5,conjecture,(
% 0.13/0.38 ( ( (! [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 ) )) ) ),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f6,negated_conjecture,(
% 0.13/0.38 ~(( ( (! [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 ) )) ) )),
% 0.13/0.38 inference(negated_conjecture,[status(cth)],[f5])).
% 0.13/0.38 fof(f7,plain,(
% 0.13/0.38 ![U]: (~sorti1(U)|(![V]: (~sorti1(V)|sorti1(op1(U,V)))))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.38 fof(f8,plain,(
% 0.13/0.38 ![X0,X1]: (~sorti1(X0)|~sorti1(X1)|sorti1(op1(X0,X1)))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.38 fof(f11,plain,(
% 0.13/0.38 (sorti1(sK0_skl)&op1(sK0_skl,sK0_skl)=sK0_skl)&(sorti1(sK1_skl)&~op1(sK1_skl,sK1_skl)=sK1_skl)),
% 0.13/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f3])).
% 0.13/0.38 fof(f12,plain,(
% 0.13/0.38 sorti1(sK0_skl)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.38 fof(f13,plain,(
% 0.13/0.38 op1(sK0_skl,sK0_skl)=sK0_skl),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.38 fof(f14,plain,(
% 0.13/0.38 sorti1(sK1_skl)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.38 fof(f15,plain,(
% 0.13/0.38 ~op1(sK1_skl,sK1_skl)=sK1_skl),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.38 fof(f16,plain,(
% 0.13/0.38 ((![U]: (~sorti2(U)|~op2(U,U)=U))|(![V]: (~sorti2(V)|op2(V,V)=V)))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.38 fof(f17,plain,(
% 0.13/0.38 ![X0,X1]: (~sorti2(X0)|~op2(X0,X0)=X0|~sorti2(X1)|op2(X1,X1)=X1)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.38 fof(f18,plain,(
% 0.13/0.38 (((![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))))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f19,plain,(
% 0.13/0.38 ![X0]: (~sorti1(X0)|sorti2(h(X0)))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.38 fof(f21,plain,(
% 0.13/0.38 ![X0,X1]: (~sorti1(X0)|~sorti1(X1)|h(op1(X0,X1))=op2(h(X0),h(X1)))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.38 fof(f24,plain,(
% 0.13/0.38 ![X0]: (~sorti1(X0)|j(h(X0))=X0)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.38 fof(f25,definition,(
% 0.13/0.38 ![X0]: (sQ0_spl <=> (~sorti2(X0)|~op2(X0,X0)=X0))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f26,plain,(
% 0.13/0.38 ![X0]: (~sorti2(X0)|~op2(X0,X0)=X0|~sQ0_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f25])).
% 0.13/0.38 fof(f28,definition,(
% 0.13/0.38 ![X1]: (sQ1_spl <=> (~sorti2(X1)|op2(X1,X1)=X1))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f29,plain,(
% 0.13/0.38 ![X0]: (~sorti2(X0)|op2(X0,X0)=X0|~sQ1_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f28])).
% 0.13/0.38 fof(f31,plain,(
% 0.13/0.38 sQ0_spl|sQ1_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f17,f25,f28])).
% 0.13/0.38 fof(f36,plain,(
% 0.13/0.38 sorti1(op1(sK1_skl,sK1_skl))),
% 0.13/0.38 inference(resolution,[status(thm)],[f14,f8])).
% 0.13/0.38 fof(f40,plain,(
% 0.13/0.38 sorti2(h(sK1_skl))),
% 0.13/0.38 inference(resolution,[status(thm)],[f19,f14])).
% 0.13/0.38 fof(f41,plain,(
% 0.13/0.38 sorti2(h(sK0_skl))),
% 0.13/0.38 inference(resolution,[status(thm)],[f19,f12])).
% 0.13/0.38 fof(f47,plain,(
% 0.13/0.38 h(op1(sK1_skl,sK1_skl))=op2(h(sK1_skl),h(sK1_skl))),
% 0.13/0.38 inference(resolution,[status(thm)],[f21,f14])).
% 0.13/0.38 fof(f49,plain,(
% 0.13/0.38 h(op1(sK0_skl,sK0_skl))=op2(h(sK0_skl),h(sK0_skl))),
% 0.13/0.38 inference(resolution,[status(thm)],[f21,f12])).
% 0.13/0.38 fof(f54,plain,(
% 0.13/0.38 h(sK0_skl)=op2(h(sK0_skl),h(sK0_skl))),
% 0.13/0.38 inference(forward_demodulation,[status(thm)],[f13,f49])).
% 0.13/0.38 fof(f70,plain,(
% 0.13/0.38 ~op2(h(sK0_skl),h(sK0_skl))=h(sK0_skl)|~sQ0_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f26,f41])).
% 0.13/0.38 fof(f72,plain,(
% 0.13/0.38 ~h(sK0_skl)=h(sK0_skl)|~sQ0_spl),
% 0.13/0.38 inference(forward_demodulation,[status(thm)],[f54,f70])).
% 0.13/0.38 fof(f73,plain,(
% 0.13/0.38 $false|~sQ0_spl),
% 0.13/0.38 inference(trivial_equality_resolution,[status(thm)],[f72])).
% 0.13/0.38 fof(f74,plain,(
% 0.13/0.38 ~sQ0_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f73])).
% 0.13/0.38 fof(f86,plain,(
% 0.13/0.38 j(h(op1(sK1_skl,sK1_skl)))=op1(sK1_skl,sK1_skl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f24,f36])).
% 0.13/0.38 fof(f87,plain,(
% 0.13/0.38 j(h(sK1_skl))=sK1_skl),
% 0.13/0.38 inference(resolution,[status(thm)],[f24,f14])).
% 0.13/0.38 fof(f103,plain,(
% 0.13/0.38 op2(h(sK1_skl),h(sK1_skl))=h(sK1_skl)|~sQ1_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f29,f40])).
% 0.13/0.38 fof(f104,plain,(
% 0.13/0.38 h(op1(sK1_skl,sK1_skl))=h(sK1_skl)|~sQ1_spl),
% 0.13/0.38 inference(backward_demodulation,[status(thm)],[f103,f47])).
% 0.13/0.38 fof(f105,plain,(
% 0.13/0.38 j(h(sK1_skl))=op1(sK1_skl,sK1_skl)|~sQ1_spl),
% 0.13/0.38 inference(backward_demodulation,[status(thm)],[f104,f86])).
% 0.13/0.38 fof(f110,plain,(
% 0.13/0.38 sK1_skl=op1(sK1_skl,sK1_skl)|~sQ1_spl),
% 0.13/0.38 inference(forward_demodulation,[status(thm)],[f87,f105])).
% 0.13/0.38 fof(f111,plain,(
% 0.13/0.38 $false|~sQ1_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f110,f15])).
% 0.13/0.38 fof(f112,plain,(
% 0.13/0.38 ~sQ1_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f111])).
% 0.13/0.38 fof(f113,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f31,f74,f112])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.41 % Elapsed time: 0.046855 seconds
% 0.13/0.41 % CPU time: 0.134341 seconds
% 0.13/0.41 % Total memory used: 54.328 MB
% 0.13/0.41 % Net memory used: 53.823 MB
%------------------------------------------------------------------------------