%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG070+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 : n007.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 11:49:33 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG070+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
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 12:52:52 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.37 fof(f2,axiom,(
% 0.13/0.37 (! [U] :( sorti2(U)=> (! [V] :( sorti2(V)=> sorti2(op2(U,V)) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f3,axiom,(
% 0.13/0.37 (! [U] :( sorti1(U)=> (! [V] :( sorti1(V)=> ( op1(U,U) != V| op1(U,V) = U ) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f4,axiom,(
% 0.13/0.37 ~ (! [U] :( sorti2(U)=> (! [V] :( sorti2(V)=> ( op2(U,U) != V| op2(U,V) = U ) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f5,conjecture,(
% 0.13/0.37 ( ( (! [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 ) )) ) ),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f6,negated_conjecture,(
% 0.13/0.37 ~(( ( (! [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 ) )) ) )),
% 0.13/0.37 inference(negated_conjecture,[status(cth)],[f5])).
% 0.13/0.37 fof(f9,plain,(
% 0.13/0.37 ![U]: (~sorti2(U)|(![V]: (~sorti2(V)|sorti2(op2(U,V)))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.13/0.37 fof(f10,plain,(
% 0.13/0.37 ![X0,X1]: (~sorti2(X0)|~sorti2(X1)|sorti2(op2(X0,X1)))),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.13/0.37 fof(f11,plain,(
% 0.13/0.37 ![U]: (~sorti1(U)|(![V]: (~sorti1(V)|(~op1(U,U)=V|op1(U,V)=U))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.13/0.37 fof(f12,plain,(
% 0.13/0.37 ![X0,X1]: (~sorti1(X0)|~sorti1(X1)|~op1(X0,X0)=X1|op1(X0,X1)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.37 fof(f13,plain,(
% 0.13/0.37 (?[U]: (sorti2(U)&(?[V]: (sorti2(V)&(op2(U,U)=V&~op2(U,V)=U)))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.37 fof(f14,plain,(
% 0.13/0.37 (sorti2(sK0_skl)&(sorti2(sK1_skl)&(op2(sK0_skl,sK0_skl)=sK1_skl&~op2(sK0_skl,sK1_skl)=sK0_skl)))),
% 0.13/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f13])).
% 0.13/0.37 fof(f15,plain,(
% 0.13/0.37 sorti2(sK0_skl)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.37 fof(f16,plain,(
% 0.13/0.37 sorti2(sK1_skl)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.37 fof(f17,plain,(
% 0.13/0.37 op2(sK0_skl,sK0_skl)=sK1_skl),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.37 fof(f18,plain,(
% 0.13/0.37 ~op2(sK0_skl,sK1_skl)=sK0_skl),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.37 fof(f19,plain,(
% 0.13/0.37 (((![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))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.37 fof(f21,plain,(
% 0.13/0.37 ![X0]: (~sorti2(X0)|sorti1(j(X0)))),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.37 fof(f23,plain,(
% 0.13/0.37 ![X0,X1]: (~sorti2(X0)|~sorti2(X1)|j(op2(X0,X1))=op1(j(X0),j(X1)))),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.37 fof(f24,plain,(
% 0.13/0.37 ![X0]: (~sorti2(X0)|h(j(X0))=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.37 fof(f29,plain,(
% 0.13/0.37 ![X0]: (~sorti2(X0)|sorti2(op2(sK0_skl,X0)))),
% 0.13/0.37 inference(resolution,[status(thm)],[f10,f15])).
% 0.13/0.37 fof(f33,plain,(
% 0.13/0.37 sorti1(j(sK1_skl))),
% 0.13/0.37 inference(resolution,[status(thm)],[f21,f16])).
% 0.13/0.37 fof(f34,plain,(
% 0.13/0.37 sorti1(j(sK0_skl))),
% 0.13/0.37 inference(resolution,[status(thm)],[f21,f15])).
% 0.13/0.37 fof(f41,plain,(
% 0.13/0.37 ![X0]: (~sorti1(X0)|~op1(X0,X0)=j(sK1_skl)|op1(X0,j(sK1_skl))=X0)),
% 0.13/0.37 inference(resolution,[status(thm)],[f33,f12])).
% 0.13/0.37 fof(f55,plain,(
% 0.13/0.37 j(op2(sK0_skl,sK0_skl))=op1(j(sK0_skl),j(sK0_skl))),
% 0.13/0.37 inference(resolution,[status(thm)],[f23,f15])).
% 0.13/0.37 fof(f56,plain,(
% 0.13/0.37 ![X0]: (~sorti2(X0)|j(op2(sK0_skl,X0))=op1(j(sK0_skl),j(X0)))),
% 0.13/0.37 inference(resolution,[status(thm)],[f23,f15])).
% 0.13/0.37 fof(f62,plain,(
% 0.13/0.37 j(sK1_skl)=op1(j(sK0_skl),j(sK0_skl))),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f17,f55])).
% 0.13/0.37 fof(f87,plain,(
% 0.13/0.37 h(j(sK0_skl))=sK0_skl),
% 0.13/0.37 inference(resolution,[status(thm)],[f24,f15])).
% 0.13/0.37 fof(f115,plain,(
% 0.13/0.37 sorti2(op2(sK0_skl,sK1_skl))),
% 0.13/0.37 inference(resolution,[status(thm)],[f29,f16])).
% 0.13/0.37 fof(f137,plain,(
% 0.13/0.37 h(j(op2(sK0_skl,sK1_skl)))=op2(sK0_skl,sK1_skl)),
% 0.13/0.37 inference(resolution,[status(thm)],[f115,f24])).
% 0.13/0.37 fof(f260,plain,(
% 0.13/0.37 j(op2(sK0_skl,sK1_skl))=op1(j(sK0_skl),j(sK1_skl))),
% 0.13/0.37 inference(resolution,[status(thm)],[f56,f16])).
% 0.13/0.37 fof(f311,plain,(
% 0.13/0.37 ~op1(j(sK0_skl),j(sK0_skl))=j(sK1_skl)|op1(j(sK0_skl),j(sK1_skl))=j(sK0_skl)),
% 0.13/0.37 inference(resolution,[status(thm)],[f41,f34])).
% 0.13/0.37 fof(f334,definition,(
% 0.13/0.37 sQ11_spl <=> (op1(j(sK0_skl),j(sK0_skl))=j(sK1_skl))),
% 0.13/0.37 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.13/0.37 fof(f336,plain,(
% 0.13/0.37 ~op1(j(sK0_skl),j(sK0_skl))=j(sK1_skl)|sQ11_spl),
% 0.13/0.37 inference(component_clause,[status(thm)],[f334])).
% 0.13/0.37 fof(f337,definition,(
% 0.13/0.37 sQ12_spl <=> (op1(j(sK0_skl),j(sK1_skl))=j(sK0_skl))),
% 0.13/0.37 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.13/0.37 fof(f338,plain,(
% 0.13/0.37 op1(j(sK0_skl),j(sK1_skl))=j(sK0_skl)|~sQ12_spl),
% 0.13/0.37 inference(component_clause,[status(thm)],[f337])).
% 0.13/0.37 fof(f340,plain,(
% 0.13/0.37 ~sQ11_spl|sQ12_spl),
% 0.13/0.37 inference(split_clause,[status(thm)],[f311,f334,f337])).
% 0.13/0.37 fof(f342,plain,(
% 0.13/0.37 ~j(sK1_skl)=j(sK1_skl)|sQ11_spl),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f62,f336])).
% 0.13/0.37 fof(f343,plain,(
% 0.13/0.37 $false|sQ11_spl),
% 0.13/0.37 inference(trivial_equality_resolution,[status(thm)],[f342])).
% 0.13/0.37 fof(f344,plain,(
% 0.13/0.37 sQ11_spl),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f343])).
% 0.13/0.37 fof(f348,plain,(
% 0.13/0.37 j(op2(sK0_skl,sK1_skl))=j(sK0_skl)|~sQ12_spl),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f338,f260])).
% 0.13/0.37 fof(f363,plain,(
% 0.13/0.37 h(j(sK0_skl))=op2(sK0_skl,sK1_skl)|~sQ12_spl),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f348,f137])).
% 0.13/0.37 fof(f378,plain,(
% 0.13/0.37 sK0_skl=op2(sK0_skl,sK1_skl)|~sQ12_spl),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f87,f363])).
% 0.13/0.37 fof(f379,plain,(
% 0.13/0.37 $false|~sQ12_spl),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f378,f18])).
% 0.13/0.37 fof(f380,plain,(
% 0.13/0.37 ~sQ12_spl),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f379])).
% 0.13/0.37 fof(f381,plain,(
% 0.13/0.37 $false),
% 0.13/0.37 inference(sat_refutation,[status(thm)],[f340,f344,f380])).
% 0.13/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.39 % Elapsed time: 0.034552 seconds
% 0.13/0.39 % CPU time: 0.089091 seconds
% 0.13/0.39 % Total memory used: 15.155 MB
% 0.13/0.39 % Net memory used: 15.060 MB
%------------------------------------------------------------------------------