TSTP Solution File: SEU053+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:57 EDT 2024
% Result : Theorem 4.40s 0.93s
% Output : CNFRefutation 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 19:37:19 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 4.40/0.93 % Refutation found
% 4.40/0.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.40/0.93 % SZS output start CNFRefutation for theBenchmark
% 4.40/0.93 fof(f5,axiom,(
% 4.40/0.93 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f7,axiom,(
% 4.40/0.93 (! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f8,axiom,(
% 4.40/0.93 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)<=> (! [B,C] :( ( in(B,relation_dom(A))& in(C,relation_dom(A))& apply(A,B) = apply(A,C) )=> B = C ) )) ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f10,axiom,(
% 4.40/0.93 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f12,axiom,(
% 4.40/0.93 (! [A] : ~ empty(powerset(A)) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f14,axiom,(
% 4.40/0.93 (! [A] : ~ empty(singleton(A)) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f18,axiom,(
% 4.40/0.93 (! [A,B] : set_intersection2(A,A) = A )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f20,axiom,(
% 4.40/0.93 (? [A] :( relation(A)& function(A) ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f28,axiom,(
% 4.40/0.93 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f34,axiom,(
% 4.40/0.93 (! [A,B] :( ( relation(B)& function(B) )=> ( in(A,relation_dom(B))=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f35,conjecture,(
% 4.40/0.93 (! [A] :( ( relation(A)& function(A) )=> ( (! [B,C] : relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C)))=> one_to_one(A) ) ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f36,negated_conjecture,(
% 4.40/0.93 ~((! [A] :( ( relation(A)& function(A) )=> ( (! [B,C] : relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C)))=> one_to_one(A) ) ) ))),
% 4.40/0.93 inference(negated_conjecture,[status(cth)],[f35])).
% 4.40/0.93 fof(f37,axiom,(
% 4.40/0.93 (! [A] :( relation(A)=> relation_image(A,empty_set) = empty_set ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f38,axiom,(
% 4.40/0.93 (! [A,B] :( A != B=> disjoint(singleton(A),singleton(B)) ) )),
% 4.40/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.40/0.93 fof(f58,plain,(
% 4.40/0.93 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f5])).
% 4.40/0.93 fof(f66,plain,(
% 4.40/0.93 ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 4.40/0.93 inference(NNF_transformation,[status(esa)],[f7])).
% 4.40/0.93 fof(f67,plain,(
% 4.40/0.93 (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 4.40/0.93 inference(miniscoping,[status(esa)],[f66])).
% 4.40/0.93 fof(f68,plain,(
% 4.40/0.93 ![X0,X1]: (~disjoint(X0,X1)|set_intersection2(X0,X1)=empty_set)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f67])).
% 4.40/0.93 fof(f70,plain,(
% 4.40/0.93 ![A]: ((~relation(A)|~function(A))|(one_to_one(A)<=>(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C))))),
% 4.40/0.93 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 4.40/0.93 fof(f71,plain,(
% 4.40/0.93 ![A]: ((~relation(A)|~function(A))|((~one_to_one(A)|(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C)))&(one_to_one(A)|(?[B,C]: (((in(B,relation_dom(A))&in(C,relation_dom(A)))&apply(A,B)=apply(A,C))&~B=C)))))),
% 4.40/0.93 inference(NNF_transformation,[status(esa)],[f70])).
% 4.40/0.93 fof(f72,plain,(
% 4.40/0.93 ![A]: ((~relation(A)|~function(A))|((~one_to_one(A)|(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C)))&(one_to_one(A)|(((in(sk0_1(A),relation_dom(A))&in(sk0_2(A),relation_dom(A)))&apply(A,sk0_1(A))=apply(A,sk0_2(A)))&~sk0_1(A)=sk0_2(A)))))),
% 4.40/0.93 inference(skolemization,[status(esa)],[f71])).
% 4.40/0.93 fof(f74,plain,(
% 4.40/0.93 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|in(sk0_1(X0),relation_dom(X0)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f72])).
% 4.40/0.93 fof(f75,plain,(
% 4.40/0.93 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|in(sk0_2(X0),relation_dom(X0)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f72])).
% 4.40/0.93 fof(f76,plain,(
% 4.40/0.93 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|apply(X0,sk0_1(X0))=apply(X0,sk0_2(X0)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f72])).
% 4.40/0.93 fof(f77,plain,(
% 4.40/0.93 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|~sk0_1(X0)=sk0_2(X0))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f72])).
% 4.40/0.93 fof(f80,plain,(
% 4.40/0.93 empty(empty_set)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f10])).
% 4.40/0.93 fof(f85,plain,(
% 4.40/0.93 ![X0]: (~empty(powerset(X0)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f12])).
% 4.40/0.93 fof(f87,plain,(
% 4.40/0.93 ![X0]: (~empty(singleton(X0)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f14])).
% 4.40/0.93 fof(f95,plain,(
% 4.40/0.93 ![A]: set_intersection2(A,A)=A),
% 4.40/0.93 inference(miniscoping,[status(esa)],[f18])).
% 4.40/0.93 fof(f96,plain,(
% 4.40/0.93 ![X0]: (set_intersection2(X0,X0)=X0)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f95])).
% 4.40/0.93 fof(f100,plain,(
% 4.40/0.93 (relation(sk0_4)&function(sk0_4))),
% 4.40/0.93 inference(skolemization,[status(esa)],[f20])).
% 4.40/0.93 fof(f101,plain,(
% 4.40/0.93 relation(sk0_4)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f100])).
% 4.40/0.93 fof(f124,plain,(
% 4.40/0.93 ((relation(sk0_12)&function(sk0_12))&one_to_one(sk0_12))),
% 4.40/0.93 inference(skolemization,[status(esa)],[f28])).
% 4.40/0.93 fof(f125,plain,(
% 4.40/0.93 relation(sk0_12)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f124])).
% 4.40/0.93 fof(f141,plain,(
% 4.40/0.93 ![A,B]: ((~relation(B)|~function(B))|(~in(A,relation_dom(B))|relation_image(B,singleton(A))=singleton(apply(B,A))))),
% 4.40/0.93 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 4.40/0.93 fof(f142,plain,(
% 4.40/0.93 ![B]: ((~relation(B)|~function(B))|(![A]: (~in(A,relation_dom(B))|relation_image(B,singleton(A))=singleton(apply(B,A)))))),
% 4.40/0.93 inference(miniscoping,[status(esa)],[f141])).
% 4.40/0.93 fof(f143,plain,(
% 4.40/0.93 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|relation_image(X0,singleton(X1))=singleton(apply(X0,X1)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f142])).
% 4.40/0.93 fof(f144,plain,(
% 4.40/0.93 (?[A]: ((relation(A)&function(A))&((![B,C]: relation_image(A,set_intersection2(B,C))=set_intersection2(relation_image(A,B),relation_image(A,C)))&~one_to_one(A))))),
% 4.40/0.93 inference(pre_NNF_transformation,[status(esa)],[f36])).
% 4.40/0.93 fof(f145,plain,(
% 4.40/0.93 ((relation(sk0_14)&function(sk0_14))&((![B,C]: relation_image(sk0_14,set_intersection2(B,C))=set_intersection2(relation_image(sk0_14,B),relation_image(sk0_14,C)))&~one_to_one(sk0_14)))),
% 4.40/0.93 inference(skolemization,[status(esa)],[f144])).
% 4.40/0.93 fof(f146,plain,(
% 4.40/0.93 relation(sk0_14)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f145])).
% 4.40/0.93 fof(f147,plain,(
% 4.40/0.93 function(sk0_14)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f145])).
% 4.40/0.93 fof(f148,plain,(
% 4.40/0.93 ![X0,X1]: (relation_image(sk0_14,set_intersection2(X0,X1))=set_intersection2(relation_image(sk0_14,X0),relation_image(sk0_14,X1)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f145])).
% 4.40/0.93 fof(f149,plain,(
% 4.40/0.93 ~one_to_one(sk0_14)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f145])).
% 4.40/0.93 fof(f150,plain,(
% 4.40/0.93 ![A]: (~relation(A)|relation_image(A,empty_set)=empty_set)),
% 4.40/0.93 inference(pre_NNF_transformation,[status(esa)],[f37])).
% 4.40/0.93 fof(f151,plain,(
% 4.40/0.93 ![X0]: (~relation(X0)|relation_image(X0,empty_set)=empty_set)),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f150])).
% 4.40/0.93 fof(f152,plain,(
% 4.40/0.93 ![A,B]: (A=B|disjoint(singleton(A),singleton(B)))),
% 4.40/0.93 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 4.40/0.93 fof(f153,plain,(
% 4.40/0.93 ![X0,X1]: (X0=X1|disjoint(singleton(X0),singleton(X1)))),
% 4.40/0.93 inference(cnf_transformation,[status(esa)],[f152])).
% 4.40/0.93 fof(f188,plain,(
% 4.40/0.93 ![X0,X1]: (relation_image(sk0_14,set_intersection2(X0,X1))=set_intersection2(relation_image(sk0_14,X1),relation_image(sk0_14,X0)))),
% 4.40/0.93 inference(paramodulation,[status(thm)],[f148,f58])).
% 4.40/0.93 fof(f189,plain,(
% 4.40/0.93 ![X0,X1]: (relation_image(sk0_14,set_intersection2(X0,X1))=relation_image(sk0_14,set_intersection2(X1,X0)))),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f148,f188])).
% 4.40/0.93 fof(f204,plain,(
% 4.40/0.93 relation_image(sk0_14,empty_set)=empty_set),
% 4.40/0.93 inference(resolution,[status(thm)],[f151,f146])).
% 4.40/0.93 fof(f215,plain,(
% 4.40/0.93 spl0_3 <=> one_to_one(sk0_14)),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f216,plain,(
% 4.40/0.93 one_to_one(sk0_14)|~spl0_3),
% 4.40/0.93 inference(component_clause,[status(thm)],[f215])).
% 4.40/0.93 fof(f712,plain,(
% 4.40/0.93 spl0_8 <=> empty(empty_set)),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f714,plain,(
% 4.40/0.93 ~empty(empty_set)|spl0_8),
% 4.40/0.93 inference(component_clause,[status(thm)],[f712])).
% 4.40/0.93 fof(f720,plain,(
% 4.40/0.93 $false|spl0_8),
% 4.40/0.93 inference(forward_subsumption_resolution,[status(thm)],[f714,f80])).
% 4.40/0.93 fof(f721,plain,(
% 4.40/0.93 spl0_8),
% 4.40/0.93 inference(contradiction_clause,[status(thm)],[f720])).
% 4.40/0.93 fof(f2382,plain,(
% 4.40/0.93 spl0_82 <=> function(sk0_14)),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f2384,plain,(
% 4.40/0.93 ~function(sk0_14)|spl0_82),
% 4.40/0.93 inference(component_clause,[status(thm)],[f2382])).
% 4.40/0.93 fof(f2385,plain,(
% 4.40/0.93 spl0_83 <=> in(sk0_1(sk0_14),relation_dom(sk0_14))),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f2386,plain,(
% 4.40/0.93 in(sk0_1(sk0_14),relation_dom(sk0_14))|~spl0_83),
% 4.40/0.93 inference(component_clause,[status(thm)],[f2385])).
% 4.40/0.93 fof(f2388,plain,(
% 4.40/0.93 ~function(sk0_14)|one_to_one(sk0_14)|in(sk0_1(sk0_14),relation_dom(sk0_14))),
% 4.40/0.93 inference(resolution,[status(thm)],[f74,f146])).
% 4.40/0.93 fof(f2389,plain,(
% 4.40/0.93 ~spl0_82|spl0_3|spl0_83),
% 4.40/0.93 inference(split_clause,[status(thm)],[f2388,f2382,f215,f2385])).
% 4.40/0.93 fof(f2390,plain,(
% 4.40/0.93 $false|spl0_82),
% 4.40/0.93 inference(forward_subsumption_resolution,[status(thm)],[f2384,f147])).
% 4.40/0.93 fof(f2391,plain,(
% 4.40/0.93 spl0_82),
% 4.40/0.93 inference(contradiction_clause,[status(thm)],[f2390])).
% 4.40/0.93 fof(f2396,plain,(
% 4.40/0.93 $false|~spl0_3),
% 4.40/0.93 inference(forward_subsumption_resolution,[status(thm)],[f216,f149])).
% 4.40/0.93 fof(f2397,plain,(
% 4.40/0.93 ~spl0_3),
% 4.40/0.93 inference(contradiction_clause,[status(thm)],[f2396])).
% 4.40/0.93 fof(f2398,plain,(
% 4.40/0.93 spl0_84 <=> relation(sk0_14)),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f2400,plain,(
% 4.40/0.93 ~relation(sk0_14)|spl0_84),
% 4.40/0.93 inference(component_clause,[status(thm)],[f2398])).
% 4.40/0.93 fof(f2406,plain,(
% 4.40/0.93 spl0_86 <=> relation_image(sk0_14,singleton(sk0_1(sk0_14)))=singleton(apply(sk0_14,sk0_1(sk0_14)))),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f2407,plain,(
% 4.40/0.93 relation_image(sk0_14,singleton(sk0_1(sk0_14)))=singleton(apply(sk0_14,sk0_1(sk0_14)))|~spl0_86),
% 4.40/0.93 inference(component_clause,[status(thm)],[f2406])).
% 4.40/0.93 fof(f2409,plain,(
% 4.40/0.93 ~relation(sk0_14)|~function(sk0_14)|relation_image(sk0_14,singleton(sk0_1(sk0_14)))=singleton(apply(sk0_14,sk0_1(sk0_14)))|~spl0_83),
% 4.40/0.93 inference(resolution,[status(thm)],[f2386,f143])).
% 4.40/0.93 fof(f2410,plain,(
% 4.40/0.93 ~spl0_84|~spl0_82|spl0_86|~spl0_83),
% 4.40/0.93 inference(split_clause,[status(thm)],[f2409,f2398,f2382,f2406,f2385])).
% 4.40/0.93 fof(f2413,plain,(
% 4.40/0.93 $false|spl0_84),
% 4.40/0.93 inference(forward_subsumption_resolution,[status(thm)],[f2400,f146])).
% 4.40/0.93 fof(f2414,plain,(
% 4.40/0.93 spl0_84),
% 4.40/0.93 inference(contradiction_clause,[status(thm)],[f2413])).
% 4.40/0.93 fof(f2437,plain,(
% 4.40/0.93 ![X0]: (relation_image(sk0_14,set_intersection2(X0,singleton(sk0_1(sk0_14))))=set_intersection2(relation_image(sk0_14,X0),singleton(apply(sk0_14,sk0_1(sk0_14))))|~spl0_86)),
% 4.40/0.93 inference(paramodulation,[status(thm)],[f2407,f148])).
% 4.40/0.93 fof(f2438,plain,(
% 4.40/0.93 ![X0]: (relation_image(sk0_14,set_intersection2(X0,singleton(sk0_1(sk0_14))))=set_intersection2(singleton(apply(sk0_14,sk0_1(sk0_14))),relation_image(sk0_14,X0))|~spl0_86)),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f58,f2437])).
% 4.40/0.93 fof(f2566,plain,(
% 4.40/0.93 spl0_88 <=> relation_image(sk0_14,empty_set)=empty_set),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f2568,plain,(
% 4.40/0.93 ~relation_image(sk0_14,empty_set)=empty_set|spl0_88),
% 4.40/0.93 inference(component_clause,[status(thm)],[f2566])).
% 4.40/0.93 fof(f2576,plain,(
% 4.40/0.93 spl0_90 <=> relation_image(sk0_14,singleton(sk0_1(sk0_14)))=empty_set),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f2577,plain,(
% 4.40/0.93 relation_image(sk0_14,singleton(sk0_1(sk0_14)))=empty_set|~spl0_90),
% 4.40/0.93 inference(component_clause,[status(thm)],[f2576])).
% 4.40/0.93 fof(f2581,plain,(
% 4.40/0.93 ~empty_set=empty_set|spl0_88),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f204,f2568])).
% 4.40/0.93 fof(f2582,plain,(
% 4.40/0.93 $false|spl0_88),
% 4.40/0.93 inference(trivial_equality_resolution,[status(esa)],[f2581])).
% 4.40/0.93 fof(f2583,plain,(
% 4.40/0.93 spl0_88),
% 4.40/0.93 inference(contradiction_clause,[status(thm)],[f2582])).
% 4.40/0.93 fof(f3089,plain,(
% 4.40/0.93 spl0_138 <=> in(sk0_2(sk0_14),relation_dom(sk0_14))),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f3090,plain,(
% 4.40/0.93 in(sk0_2(sk0_14),relation_dom(sk0_14))|~spl0_138),
% 4.40/0.93 inference(component_clause,[status(thm)],[f3089])).
% 4.40/0.93 fof(f3092,plain,(
% 4.40/0.93 ~function(sk0_14)|one_to_one(sk0_14)|in(sk0_2(sk0_14),relation_dom(sk0_14))),
% 4.40/0.93 inference(resolution,[status(thm)],[f75,f146])).
% 4.40/0.93 fof(f3093,plain,(
% 4.40/0.93 ~spl0_82|spl0_3|spl0_138),
% 4.40/0.93 inference(split_clause,[status(thm)],[f3092,f2382,f215,f3089])).
% 4.40/0.93 fof(f3229,plain,(
% 4.40/0.93 spl0_166 <=> apply(sk0_14,sk0_1(sk0_14))=apply(sk0_14,sk0_2(sk0_14))),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f3230,plain,(
% 4.40/0.93 apply(sk0_14,sk0_1(sk0_14))=apply(sk0_14,sk0_2(sk0_14))|~spl0_166),
% 4.40/0.93 inference(component_clause,[status(thm)],[f3229])).
% 4.40/0.93 fof(f3232,plain,(
% 4.40/0.93 ~function(sk0_14)|one_to_one(sk0_14)|apply(sk0_14,sk0_1(sk0_14))=apply(sk0_14,sk0_2(sk0_14))),
% 4.40/0.93 inference(resolution,[status(thm)],[f76,f146])).
% 4.40/0.93 fof(f3233,plain,(
% 4.40/0.93 ~spl0_82|spl0_3|spl0_166),
% 4.40/0.93 inference(split_clause,[status(thm)],[f3232,f2382,f215,f3229])).
% 4.40/0.93 fof(f3369,plain,(
% 4.40/0.93 spl0_194 <=> sk0_1(sk0_14)=sk0_2(sk0_14)),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f3372,plain,(
% 4.40/0.93 ~function(sk0_14)|one_to_one(sk0_14)|~sk0_1(sk0_14)=sk0_2(sk0_14)),
% 4.40/0.93 inference(resolution,[status(thm)],[f77,f146])).
% 4.40/0.93 fof(f3373,plain,(
% 4.40/0.93 ~spl0_82|spl0_3|~spl0_194),
% 4.40/0.93 inference(split_clause,[status(thm)],[f3372,f2382,f215,f3369])).
% 4.40/0.93 fof(f3379,plain,(
% 4.40/0.93 spl0_196 <=> relation_image(sk0_14,singleton(sk0_2(sk0_14)))=singleton(apply(sk0_14,sk0_2(sk0_14)))),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f3380,plain,(
% 4.40/0.93 relation_image(sk0_14,singleton(sk0_2(sk0_14)))=singleton(apply(sk0_14,sk0_2(sk0_14)))|~spl0_196),
% 4.40/0.93 inference(component_clause,[status(thm)],[f3379])).
% 4.40/0.93 fof(f3382,plain,(
% 4.40/0.93 ~relation(sk0_14)|~function(sk0_14)|relation_image(sk0_14,singleton(sk0_2(sk0_14)))=singleton(apply(sk0_14,sk0_2(sk0_14)))|~spl0_138),
% 4.40/0.93 inference(resolution,[status(thm)],[f3090,f143])).
% 4.40/0.93 fof(f3383,plain,(
% 4.40/0.93 ~spl0_84|~spl0_82|spl0_196|~spl0_138),
% 4.40/0.93 inference(split_clause,[status(thm)],[f3382,f2398,f2382,f3379,f3089])).
% 4.40/0.93 fof(f3390,plain,(
% 4.40/0.93 relation_image(sk0_14,singleton(sk0_2(sk0_14)))=singleton(apply(sk0_14,sk0_1(sk0_14)))|~spl0_166|~spl0_196),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f3230,f3380])).
% 4.40/0.93 fof(f3397,plain,(
% 4.40/0.93 ![X0]: (relation_image(sk0_14,set_intersection2(singleton(sk0_2(sk0_14)),X0))=set_intersection2(singleton(apply(sk0_14,sk0_1(sk0_14))),relation_image(sk0_14,X0))|~spl0_166|~spl0_196)),
% 4.40/0.93 inference(paramodulation,[status(thm)],[f3390,f148])).
% 4.40/0.93 fof(f3398,plain,(
% 4.40/0.93 ![X0]: (relation_image(sk0_14,set_intersection2(singleton(sk0_2(sk0_14)),X0))=relation_image(sk0_14,set_intersection2(X0,singleton(sk0_1(sk0_14))))|~spl0_86|~spl0_166|~spl0_196)),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f2438,f3397])).
% 4.40/0.93 fof(f3509,plain,(
% 4.40/0.93 ![X0]: (relation_image(sk0_14,set_intersection2(singleton(sk0_2(sk0_14)),X0))=relation_image(sk0_14,set_intersection2(singleton(sk0_1(sk0_14)),X0))|~spl0_86|~spl0_166|~spl0_196)),
% 4.40/0.93 inference(paramodulation,[status(thm)],[f189,f3398])).
% 4.40/0.93 fof(f3821,plain,(
% 4.40/0.93 ![X0,X1]: (X0=X1|set_intersection2(singleton(X0),singleton(X1))=empty_set)),
% 4.40/0.93 inference(resolution,[status(thm)],[f153,f68])).
% 4.40/0.93 fof(f5204,plain,(
% 4.40/0.93 spl0_258 <=> relation_image(sk0_14,relation_image(sk0_14,empty_set))=empty_set),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f5206,plain,(
% 4.40/0.93 ~relation_image(sk0_14,relation_image(sk0_14,empty_set))=empty_set|spl0_258),
% 4.40/0.93 inference(component_clause,[status(thm)],[f5204])).
% 4.40/0.93 fof(f5218,plain,(
% 4.40/0.93 ~relation_image(sk0_14,empty_set)=empty_set|spl0_258),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f204,f5206])).
% 4.40/0.93 fof(f5219,plain,(
% 4.40/0.93 ~empty_set=empty_set|spl0_258),
% 4.40/0.93 inference(forward_demodulation,[status(thm)],[f204,f5218])).
% 4.40/0.93 fof(f5220,plain,(
% 4.40/0.93 $false|spl0_258),
% 4.40/0.93 inference(trivial_equality_resolution,[status(esa)],[f5219])).
% 4.40/0.93 fof(f5221,plain,(
% 4.40/0.93 spl0_258),
% 4.40/0.93 inference(contradiction_clause,[status(thm)],[f5220])).
% 4.40/0.93 fof(f7048,plain,(
% 4.40/0.93 spl0_412 <=> relation(sk0_4)),
% 4.40/0.93 introduced(split_symbol_definition)).
% 4.40/0.93 fof(f7050,plain,(
% 4.40/0.93 ~relation(sk0_4)|spl0_412),
% 4.40/0.93 inference(component_clause,[status(thm)],[f7048])).
% 4.40/0.93 fof(f7060,plain,(
% 4.58/0.95 $false|spl0_412),
% 4.58/0.95 inference(forward_subsumption_resolution,[status(thm)],[f7050,f101])).
% 4.58/0.95 fof(f7061,plain,(
% 4.58/0.95 spl0_412),
% 4.58/0.95 inference(contradiction_clause,[status(thm)],[f7060])).
% 4.58/0.95 fof(f7725,plain,(
% 4.58/0.95 spl0_413 <=> relation(sk0_12)),
% 4.58/0.95 introduced(split_symbol_definition)).
% 4.58/0.95 fof(f7727,plain,(
% 4.58/0.95 ~relation(sk0_12)|spl0_413),
% 4.58/0.95 inference(component_clause,[status(thm)],[f7725])).
% 4.58/0.95 fof(f7737,plain,(
% 4.58/0.95 $false|spl0_413),
% 4.58/0.95 inference(forward_subsumption_resolution,[status(thm)],[f7727,f125])).
% 4.58/0.95 fof(f7738,plain,(
% 4.58/0.95 spl0_413),
% 4.58/0.95 inference(contradiction_clause,[status(thm)],[f7737])).
% 4.58/0.95 fof(f9108,plain,(
% 4.58/0.95 ![X0]: (relation_image(sk0_14,empty_set)=relation_image(sk0_14,set_intersection2(singleton(sk0_1(sk0_14)),singleton(X0)))|sk0_2(sk0_14)=X0|~spl0_86|~spl0_166|~spl0_196)),
% 4.58/0.95 inference(paramodulation,[status(thm)],[f3821,f3509])).
% 4.58/0.95 fof(f9109,plain,(
% 4.58/0.95 ![X0]: (empty_set=relation_image(sk0_14,set_intersection2(singleton(sk0_1(sk0_14)),singleton(X0)))|sk0_2(sk0_14)=X0|~spl0_86|~spl0_166|~spl0_196)),
% 4.58/0.95 inference(forward_demodulation,[status(thm)],[f204,f9108])).
% 4.58/0.95 fof(f10403,plain,(
% 4.58/0.95 spl0_476 <=> ~empty(X0)),
% 4.58/0.95 introduced(split_symbol_definition)).
% 4.58/0.95 fof(f10404,plain,(
% 4.58/0.95 ![X0]: (~empty(X0)|~spl0_476)),
% 4.58/0.95 inference(component_clause,[status(thm)],[f10403])).
% 4.58/0.95 fof(f10419,plain,(
% 4.58/0.95 spl0_477 <=> empty(powerset(empty_set))),
% 4.58/0.95 introduced(split_symbol_definition)).
% 4.58/0.95 fof(f10420,plain,(
% 4.58/0.95 empty(powerset(empty_set))|~spl0_477),
% 4.58/0.95 inference(component_clause,[status(thm)],[f10419])).
% 4.58/0.95 fof(f10433,plain,(
% 4.58/0.95 $false|~spl0_477),
% 4.58/0.95 inference(forward_subsumption_resolution,[status(thm)],[f10420,f85])).
% 4.58/0.95 fof(f10434,plain,(
% 4.58/0.95 ~spl0_477),
% 4.58/0.95 inference(contradiction_clause,[status(thm)],[f10433])).
% 4.58/0.95 fof(f10607,plain,(
% 4.58/0.95 $false|~spl0_476),
% 4.58/0.95 inference(backward_subsumption_resolution,[status(thm)],[f80,f10404])).
% 4.58/0.95 fof(f10608,plain,(
% 4.58/0.95 ~spl0_476),
% 4.58/0.95 inference(contradiction_clause,[status(thm)],[f10607])).
% 4.58/0.95 fof(f11228,plain,(
% 4.58/0.95 empty_set=relation_image(sk0_14,singleton(sk0_1(sk0_14)))|sk0_2(sk0_14)=sk0_1(sk0_14)|~spl0_86|~spl0_166|~spl0_196),
% 4.58/0.95 inference(paramodulation,[status(thm)],[f96,f9109])).
% 4.58/0.95 fof(f11229,plain,(
% 4.58/0.95 spl0_90|spl0_194|~spl0_86|~spl0_166|~spl0_196),
% 4.58/0.95 inference(split_clause,[status(thm)],[f11228,f2576,f3369,f2406,f3229,f3379])).
% 4.58/0.95 fof(f11252,plain,(
% 4.58/0.95 singleton(apply(sk0_14,sk0_1(sk0_14)))=empty_set|~spl0_86|~spl0_90),
% 4.58/0.95 inference(forward_demodulation,[status(thm)],[f2407,f2577])).
% 4.58/0.95 fof(f11310,plain,(
% 4.58/0.95 ~empty(empty_set)|~spl0_86|~spl0_90),
% 4.58/0.95 inference(paramodulation,[status(thm)],[f11252,f87])).
% 4.58/0.95 fof(f11311,plain,(
% 4.58/0.95 ~spl0_8|~spl0_86|~spl0_90),
% 4.58/0.95 inference(split_clause,[status(thm)],[f11310,f712,f2406,f2576])).
% 4.58/0.95 fof(f11317,plain,(
% 4.58/0.95 $false),
% 4.58/0.95 inference(sat_refutation,[status(thm)],[f721,f2389,f2391,f2397,f2410,f2414,f2583,f3093,f3233,f3373,f3383,f5221,f7061,f7738,f10434,f10608,f11229,f11311])).
% 4.58/0.95 % SZS output end CNFRefutation for theBenchmark.p
% 4.58/0.96 % Elapsed time: 0.607103 seconds
% 4.58/0.96 % CPU time: 4.681153 seconds
% 4.58/0.96 % Total memory used: 148.457 MB
% 4.58/0.96 % Net memory used: 147.291 MB
%------------------------------------------------------------------------------