%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 11:49:45 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:02:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.41 fof(f2,axiom,(
% 0.14/0.41 (! [U] :( sorti2(U)=> (! [V] :( sorti2(V)=> sorti2(op2(U,V)) ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f3,axiom,(
% 0.14/0.41 (! [U] :( sorti1(U)=> (! [V] :( sorti1(V)=> op1(U,op1(U,V)) = V ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f4,axiom,(
% 0.14/0.41 ~ (! [U] :( sorti2(U)=> (! [V] :( sorti2(V)=> op2(U,op2(U,V)) = V ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f5,conjecture,(
% 0.14/0.41 ( ( (! [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 ) )) ) ),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f6,negated_conjecture,(
% 0.14/0.41 ~(( ( (! [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 ) )) ) )),
% 0.14/0.41 inference(negated_conjecture,[status(cth)],[f5])).
% 0.14/0.41 fof(f9,plain,(
% 0.14/0.41 ![U]: (~sorti2(U)|(![V]: (~sorti2(V)|sorti2(op2(U,V)))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.14/0.41 fof(f10,plain,(
% 0.14/0.41 ![X0,X1]: (~sorti2(X0)|~sorti2(X1)|sorti2(op2(X0,X1)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/0.41 fof(f11,plain,(
% 0.14/0.41 ![U]: (~sorti1(U)|(![V]: (~sorti1(V)|op1(U,op1(U,V))=V)))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.14/0.41 fof(f12,plain,(
% 0.14/0.41 ![X0,X1]: (~sorti1(X0)|~sorti1(X1)|op1(X0,op1(X0,X1))=X1)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.41 fof(f13,plain,(
% 0.14/0.41 (?[U]: (sorti2(U)&(?[V]: (sorti2(V)&~op2(U,op2(U,V))=V))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.41 fof(f14,plain,(
% 0.14/0.41 (sorti2(sK0_skl)&(sorti2(sK1_skl)&~op2(sK0_skl,op2(sK0_skl,sK1_skl))=sK1_skl))),
% 0.14/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f13])).
% 0.14/0.41 fof(f15,plain,(
% 0.14/0.41 sorti2(sK0_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/0.41 fof(f16,plain,(
% 0.14/0.41 sorti2(sK1_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/0.41 fof(f17,plain,(
% 0.14/0.41 ~op2(sK0_skl,op2(sK0_skl,sK1_skl))=sK1_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/0.41 fof(f18,plain,(
% 0.14/0.41 (((![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))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.14/0.41 fof(f20,plain,(
% 0.14/0.41 ![X0]: (~sorti2(X0)|sorti1(j(X0)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/0.41 fof(f22,plain,(
% 0.14/0.41 ![X0,X1]: (~sorti2(X0)|~sorti2(X1)|j(op2(X0,X1))=op1(j(X0),j(X1)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/0.41 fof(f23,plain,(
% 0.14/0.41 ![X0]: (~sorti2(X0)|h(j(X0))=X0)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/0.41 fof(f25,plain,(
% 0.14/0.41 ![X0]: (~sorti2(X0)|sorti2(op2(sK0_skl,X0)))),
% 0.14/0.41 inference(resolution,[status(thm)],[f15,f10])).
% 0.14/0.41 fof(f27,plain,(
% 0.14/0.41 sorti1(j(sK1_skl))),
% 0.14/0.41 inference(resolution,[status(thm)],[f20,f16])).
% 0.14/0.41 fof(f28,plain,(
% 0.14/0.41 sorti1(j(sK0_skl))),
% 0.14/0.41 inference(resolution,[status(thm)],[f20,f15])).
% 0.14/0.41 fof(f29,plain,(
% 0.14/0.41 ![X0]: (~sorti2(X0)|j(op2(X0,sK1_skl))=op1(j(X0),j(sK1_skl)))),
% 0.14/0.41 inference(resolution,[status(thm)],[f22,f16])).
% 0.14/0.41 fof(f31,plain,(
% 0.14/0.41 h(j(sK1_skl))=sK1_skl),
% 0.14/0.41 inference(resolution,[status(thm)],[f23,f16])).
% 0.14/0.41 fof(f36,plain,(
% 0.14/0.41 ![X0]: (~sorti1(X0)|op1(X0,op1(X0,j(sK1_skl)))=j(sK1_skl))),
% 0.14/0.41 inference(resolution,[status(thm)],[f27,f12])).
% 0.14/0.41 fof(f40,plain,(
% 0.14/0.41 sorti2(op2(sK0_skl,sK1_skl))),
% 0.14/0.41 inference(resolution,[status(thm)],[f25,f16])).
% 0.14/0.41 fof(f52,plain,(
% 0.14/0.41 j(op2(sK0_skl,sK1_skl))=op1(j(sK0_skl),j(sK1_skl))),
% 0.14/0.42 inference(resolution,[status(thm)],[f29,f15])).
% 0.14/0.42 fof(f61,plain,(
% 0.14/0.42 op1(j(sK0_skl),op1(j(sK0_skl),j(sK1_skl)))=j(sK1_skl)),
% 0.14/0.42 inference(resolution,[status(thm)],[f36,f28])).
% 0.14/0.42 fof(f63,plain,(
% 0.14/0.42 op1(j(sK0_skl),j(op2(sK0_skl,sK1_skl)))=j(sK1_skl)),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f52,f61])).
% 0.14/0.42 fof(f72,plain,(
% 0.14/0.42 sorti2(op2(sK0_skl,op2(sK0_skl,sK1_skl)))),
% 0.14/0.42 inference(resolution,[status(thm)],[f40,f25])).
% 0.14/0.42 fof(f74,plain,(
% 0.14/0.42 ![X0]: (~sorti2(X0)|j(op2(X0,op2(sK0_skl,sK1_skl)))=op1(j(X0),j(op2(sK0_skl,sK1_skl))))),
% 0.14/0.42 inference(resolution,[status(thm)],[f40,f22])).
% 0.14/0.42 fof(f167,plain,(
% 0.14/0.42 h(j(op2(sK0_skl,op2(sK0_skl,sK1_skl))))=op2(sK0_skl,op2(sK0_skl,sK1_skl))),
% 0.14/0.42 inference(resolution,[status(thm)],[f72,f23])).
% 0.14/0.42 fof(f178,plain,(
% 0.14/0.42 j(op2(sK0_skl,op2(sK0_skl,sK1_skl)))=op1(j(sK0_skl),j(op2(sK0_skl,sK1_skl)))),
% 0.14/0.42 inference(resolution,[status(thm)],[f74,f15])).
% 0.14/0.42 fof(f182,plain,(
% 0.14/0.42 h(j(sK1_skl))=op2(sK0_skl,op2(sK0_skl,sK1_skl))),
% 0.14/0.42 inference(backward_demodulation,[status(thm)],[f185,f167])).
% 0.14/0.42 fof(f185,plain,(
% 0.14/0.42 j(op2(sK0_skl,op2(sK0_skl,sK1_skl)))=j(sK1_skl)),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f63,f178])).
% 0.14/0.42 fof(f187,plain,(
% 0.14/0.42 sK1_skl=op2(sK0_skl,op2(sK0_skl,sK1_skl))),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f31,f182])).
% 0.14/0.42 fof(f188,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(forward_subsumption_resolution,[status(thm)],[f187,f17])).
% 0.14/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.45 % Elapsed time: 0.067546 seconds
% 0.14/0.45 % CPU time: 0.275259 seconds
% 0.14/0.45 % Total memory used: 51.206 MB
% 0.14/0.45 % Net memory used: 50.287 MB
%------------------------------------------------------------------------------