%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:22:03 PM UTC 2026
% Result : Theorem 0.15s 5.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.58 % Computer : n019.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Mon Sep 21 06:00:11 UTC 2026
% 0.11/5.58 % CPUTime :
% 0.15/5.60 % Drodi V4.1.1
% 0.15/5.62 % Refutation found
% 0.15/5.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.62 % SZS output start CNFRefutation for theBenchmark
% 0.15/5.62 fof(f6,axiom,(
% 0.15/5.62 (! [A,B,C] :( C = set_intersection2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& in(D,B) ) ) )) )),
% 0.15/5.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.62 fof(f11,axiom,(
% 0.15/5.62 (! [A,B] :( relation(A)=> relation(relation_dom_restriction(A,B)) ) )),
% 0.15/5.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.62 fof(f18,axiom,(
% 0.15/5.62 (! [A,B] :( ( relation(A)& function(A) )=> ( relation(relation_dom_restriction(A,B))& function(relation_dom_restriction(A,B)) ) ) )),
% 0.15/5.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.62 fof(f23,conjecture,(
% 0.15/5.62 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))<=> ( in(B,relation_dom(C))& in(B,A) ) ) ) )),
% 0.15/5.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.62 fof(f24,negated_conjecture,(
% 0.15/5.62 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))<=> ( in(B,relation_dom(C))& in(B,A) ) ) ) ))),
% 0.15/5.62 inference(negated_conjecture,[status(cth)],[f23])).
% 0.15/5.62 fof(f36,axiom,(
% 0.15/5.62 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( B = relation_dom_restriction(C,A)<=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)& (! [D] :( in(D,relation_dom(B))=> apply(B,D) = apply(C,D) ) )) ) ) )) )),
% 0.15/5.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.62 fof(f51,plain,(
% 0.15/5.62 ![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 0.15/5.62 inference(NNF_transformation,[status(thm)],[f6])).
% 0.15/5.62 fof(f52,plain,(
% 0.15/5.62 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 0.15/5.62 inference(miniscoping,[status(thm)],[f51])).
% 0.15/5.62 fof(f53,plain,(
% 0.15/5.62 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|((~in(sK0_skl(C,B,A),C)|(~in(sK0_skl(C,B,A),A)|~in(sK0_skl(C,B,A),B)))&(in(sK0_skl(C,B,A),C)|(in(sK0_skl(C,B,A),A)&in(sK0_skl(C,B,A),B))))))),
% 0.15/5.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f52])).
% 0.15/5.62 fof(f54,plain,(
% 0.15/5.62 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f53])).
% 0.15/5.62 fof(f55,plain,(
% 0.15/5.62 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X2))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f53])).
% 0.15/5.62 fof(f56,plain,(
% 0.15/5.62 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|in(X3,X0)|~in(X3,X1)|~in(X3,X2))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f53])).
% 0.15/5.62 fof(f60,plain,(
% 0.15/5.62 ![A,B]: (~relation(A)|relation(relation_dom_restriction(A,B)))),
% 0.15/5.62 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.15/5.62 fof(f61,plain,(
% 0.15/5.62 ![A]: (~relation(A)|(![B]: relation(relation_dom_restriction(A,B))))),
% 0.15/5.62 inference(miniscoping,[status(thm)],[f60])).
% 0.15/5.62 fof(f62,plain,(
% 0.15/5.62 ![X0,X1]: (~relation(X0)|relation(relation_dom_restriction(X0,X1)))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f61])).
% 0.15/5.62 fof(f75,plain,(
% 0.15/5.62 ![A,B]: ((~relation(A)|~function(A))|(relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))))),
% 0.15/5.62 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.15/5.62 fof(f76,plain,(
% 0.15/5.62 ![A]: ((~relation(A)|~function(A))|((![B]: relation(relation_dom_restriction(A,B)))&(![B]: function(relation_dom_restriction(A,B)))))),
% 0.15/5.62 inference(miniscoping,[status(thm)],[f75])).
% 0.15/5.62 fof(f78,plain,(
% 0.15/5.62 ![X0,X1]: (~relation(X0)|~function(X0)|function(relation_dom_restriction(X0,X1)))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f76])).
% 0.15/5.62 fof(f88,plain,(
% 0.15/5.62 (?[A,B,C]: ((relation(C)&function(C))&(in(B,relation_dom(relation_dom_restriction(C,A)))<~>(in(B,relation_dom(C))&in(B,A)))))),
% 0.15/5.62 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.15/5.62 fof(f89,plain,(
% 0.15/5.62 ?[A,B,C]: ((relation(C)&function(C))&((in(B,relation_dom(relation_dom_restriction(C,A)))|(in(B,relation_dom(C))&in(B,A)))&(~in(B,relation_dom(relation_dom_restriction(C,A)))|(~in(B,relation_dom(C))|~in(B,A)))))),
% 0.15/5.62 inference(NNF_transformation,[status(thm)],[f88])).
% 0.15/5.62 fof(f90,plain,(
% 0.15/5.62 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(B,relation_dom(relation_dom_restriction(C,A)))|(in(B,relation_dom(C))&in(B,A)))&(~in(B,relation_dom(relation_dom_restriction(C,A)))|(~in(B,relation_dom(C))|~in(B,A))))))),
% 0.15/5.62 inference(miniscoping,[status(thm)],[f89])).
% 0.15/5.62 fof(f91,plain,(
% 0.15/5.62 ((relation(sK2_skl)&function(sK2_skl))&((in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl)))|(in(sK4_skl,relation_dom(sK2_skl))&in(sK4_skl,sK3_skl)))&(~in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl)))|(~in(sK4_skl,relation_dom(sK2_skl))|~in(sK4_skl,sK3_skl)))))),
% 0.15/5.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(C,sK2_skl),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f90])).
% 0.15/5.62 fof(f92,plain,(
% 0.15/5.62 relation(sK2_skl)),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/5.62 fof(f93,plain,(
% 0.15/5.62 function(sK2_skl)),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/5.62 fof(f94,plain,(
% 0.15/5.62 in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl)))|in(sK4_skl,relation_dom(sK2_skl))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/5.62 fof(f95,plain,(
% 0.15/5.62 in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl)))|in(sK4_skl,sK3_skl)),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/5.62 fof(f96,plain,(
% 0.15/5.62 ~in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl)))|~in(sK4_skl,relation_dom(sK2_skl))|~in(sK4_skl,sK3_skl)),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/5.62 fof(f126,plain,(
% 0.15/5.62 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_dom_restriction(C,A)<=>(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.15/5.62 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.15/5.62 fof(f127,plain,(
% 0.15/5.62 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D)))))&(B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D)))))))))),
% 0.15/5.62 inference(NNF_transformation,[status(thm)],[f126])).
% 0.15/5.62 fof(f128,plain,(
% 0.15/5.62 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D))))))))))),
% 0.15/5.62 inference(miniscoping,[status(thm)],[f127])).
% 0.15/5.62 fof(f129,plain,(
% 0.15/5.62 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(in(sK13_skl(A,C,B),relation_dom(B))&~apply(B,sK13_skl(A,C,B))=apply(C,sK13_skl(A,C,B))))))))))),
% 0.15/5.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(D,sK13_skl(A,C,B))],[f128])).
% 0.15/5.62 fof(f130,plain,(
% 0.15/5.62 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_dom_restriction(X1,X2)|relation_dom(X0)=set_intersection2(relation_dom(X1),X2))),
% 0.15/5.62 inference(cnf_transformation,[status(thm)],[f129])).
% 0.15/5.62 fof(f143,plain,(
% 0.15/5.62 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X1))),
% 0.15/5.62 inference(destructive_equality_resolution,[status(thm)],[f54])).
% 0.15/5.62 fof(f144,plain,(
% 0.15/5.62 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X2))),
% 0.15/5.62 inference(destructive_equality_resolution,[status(thm)],[f55])).
% 0.15/5.62 fof(f145,plain,(
% 0.15/5.62 ![X0,X1,X2]: (in(X0,set_intersection2(X1,X2))|~in(X0,X1)|~in(X0,X2))),
% 0.15/5.62 inference(destructive_equality_resolution,[status(thm)],[f56])).
% 0.15/5.62 fof(f146,plain,(
% 0.15/5.62 ![X1,X2]: (~relation(relation_dom_restriction(X1,X2))|~function(relation_dom_restriction(X1,X2))|~relation(X1)|~function(X1)|relation_dom(relation_dom_restriction(X1,X2))=set_intersection2(relation_dom(X1),X2))),
% 0.15/5.62 inference(destructive_equality_resolution,[status(thm)],[f130])).
% 0.15/5.62 fof(f147,plain,(
% 0.15/5.62 ![X0,X1]: (~function(relation_dom_restriction(X0,X1))|~relation(X0)|~function(X0)|relation_dom(relation_dom_restriction(X0,X1))=set_intersection2(relation_dom(X0),X1))),
% 0.15/5.62 inference(forward_subsumption_resolution,[status(thm)],[f146,f62])).
% 0.15/5.62 fof(f157,plain,(
% 0.15/5.62 ![X0,X1]: (~relation(X0)|~function(X0)|relation_dom(relation_dom_restriction(X0,X1))=set_intersection2(relation_dom(X0),X1)|~relation(X0)|~function(X0))),
% 0.15/5.62 inference(resolution,[status(thm)],[f147,f78])).
% 0.15/5.62 fof(f159,plain,(
% 0.15/5.62 ![X0,X1]: (~relation(X0)|~function(X0)|relation_dom(relation_dom_restriction(X0,X1))=set_intersection2(relation_dom(X0),X1))),
% 0.15/5.62 inference(duplicate_literals_removal,[status(thm)],[f157])).
% 0.15/5.62 fof(f162,plain,(
% 0.15/5.62 ![X0]: (~relation(sK2_skl)|relation_dom(relation_dom_restriction(sK2_skl,X0))=set_intersection2(relation_dom(sK2_skl),X0))),
% 0.15/5.62 inference(resolution,[status(thm)],[f159,f93])).
% 0.15/5.62 fof(f167,plain,(
% 0.15/5.62 ~in(sK4_skl,set_intersection2(relation_dom(sK2_skl),sK3_skl))|~in(sK4_skl,relation_dom(sK2_skl))|~in(sK4_skl,sK3_skl)),
% 0.15/5.62 inference(backward_demodulation,[status(thm)],[f171,f96])).
% 0.15/5.62 fof(f169,plain,(
% 0.15/5.62 in(sK4_skl,set_intersection2(relation_dom(sK2_skl),sK3_skl))|in(sK4_skl,sK3_skl)),
% 0.15/5.62 inference(backward_demodulation,[status(thm)],[f171,f95])).
% 0.15/5.62 fof(f170,plain,(
% 0.15/5.62 in(sK4_skl,set_intersection2(relation_dom(sK2_skl),sK3_skl))|in(sK4_skl,relation_dom(sK2_skl))),
% 0.15/5.62 inference(backward_demodulation,[status(thm)],[f171,f94])).
% 0.15/5.62 fof(f171,plain,(
% 0.15/5.62 ![X0]: (relation_dom(relation_dom_restriction(sK2_skl,X0))=set_intersection2(relation_dom(sK2_skl),X0))),
% 0.15/5.62 inference(forward_subsumption_resolution,[status(thm)],[f162,f92])).
% 0.15/5.62 fof(f173,plain,(
% 0.15/5.62 ~in(sK4_skl,relation_dom(sK2_skl))|~in(sK4_skl,sK3_skl)),
% 0.15/5.62 inference(forward_subsumption_resolution,[status(thm)],[f167,f145])).
% 0.15/5.62 fof(f174,plain,(
% 0.15/5.62 ~in(sK4_skl,relation_dom(sK2_skl))),
% 0.15/5.62 inference(backward_subsumption_resolution,[status(thm)],[f173,f175])).
% 0.15/5.62 fof(f175,plain,(
% 0.15/5.62 in(sK4_skl,sK3_skl)),
% 0.15/5.62 inference(forward_subsumption_resolution,[status(thm)],[f169,f144])).
% 0.15/5.62 fof(f176,plain,(
% 0.15/5.62 in(sK4_skl,relation_dom(sK2_skl))),
% 0.15/5.62 inference(forward_subsumption_resolution,[status(thm)],[f170,f143])).
% 0.15/5.62 fof(f177,plain,(
% 0.15/5.62 $false),
% 0.15/5.62 inference(forward_subsumption_resolution,[status(thm)],[f174,f176])).
% 0.15/5.62 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/5.64 % Elapsed time: 0.047336 seconds
% 0.15/5.64 % CPU time: 0.136787 seconds
% 0.15/5.64 % Total memory used: 68.005 MB
% 0.15/5.64 % Net memory used: 67.973 MB
%------------------------------------------------------------------------------