TSTP Solution File: SEU210+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:41:30 EDT 2024
% Result : Theorem 0.21s 0.47s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 19:37:33 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.21/0.47 % Refutation found
% 0.21/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.21/0.47 fof(f4,axiom,(
% 0.21/0.47 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f5,axiom,(
% 0.21/0.47 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f15,axiom,(
% 0.21/0.47 (! [A] :(? [B] : element(B,A) ))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f17,axiom,(
% 0.21/0.47 empty(empty_set) ),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f31,axiom,(
% 0.21/0.47 (! [A,B,C] :( relation(C)=> ( in(A,relation_inverse_image(C,B))<=> (? [D] :( in(D,relation_rng(C))& in(ordered_pair(A,D),C)& in(D,B) ) )) ) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f32,conjecture,(
% 0.21/0.47 (! [A,B] :( relation(B)=> ~ ( A != empty_set& subset(A,relation_rng(B))& relation_inverse_image(B,A) = empty_set ) ) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f33,negated_conjecture,(
% 0.21/0.47 ~((! [A,B] :( relation(B)=> ~ ( A != empty_set& subset(A,relation_rng(B))& relation_inverse_image(B,A) = empty_set ) ) ))),
% 0.21/0.47 inference(negated_conjecture,[status(cth)],[f32])).
% 0.21/0.47 fof(f35,axiom,(
% 0.21/0.47 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f39,axiom,(
% 0.21/0.47 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f40,axiom,(
% 0.21/0.47 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.47 fof(f47,plain,(
% 0.21/0.47 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.21/0.47 fof(f48,plain,(
% 0.21/0.47 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.21/0.47 inference(NNF_transformation,[status(esa)],[f47])).
% 0.21/0.47 fof(f49,plain,(
% 0.21/0.47 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.21/0.47 inference(miniscoping,[status(esa)],[f48])).
% 0.21/0.47 fof(f50,plain,(
% 0.21/0.47 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_0(B,A),A)&~in(sk0_0(B,A),B))))),
% 0.21/0.47 inference(skolemization,[status(esa)],[f49])).
% 0.21/0.47 fof(f51,plain,(
% 0.21/0.47 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f50])).
% 0.21/0.47 fof(f54,plain,(
% 0.21/0.47 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.21/0.47 fof(f55,plain,(
% 0.21/0.47 ![A]: (~relation(A)|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(D,C),A)))&(in(C,B)|(![D]: ~in(ordered_pair(D,C),A))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 0.21/0.47 inference(NNF_transformation,[status(esa)],[f54])).
% 0.21/0.47 fof(f56,plain,(
% 0.21/0.47 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(D,C),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 0.21/0.47 inference(miniscoping,[status(esa)],[f55])).
% 0.21/0.47 fof(f57,plain,(
% 0.21/0.47 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sk0_1(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sk0_2(B,A),B)|(![D]: ~in(ordered_pair(D,sk0_2(B,A)),A)))&(in(sk0_2(B,A),B)|in(ordered_pair(sk0_3(B,A),sk0_2(B,A)),A)))))))),
% 0.21/0.47 inference(skolemization,[status(esa)],[f56])).
% 0.21/0.47 fof(f58,plain,(
% 0.21/0.47 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sk0_1(X2,X1,X0),X2),X0))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f57])).
% 0.21/0.47 fof(f63,plain,(
% 0.21/0.47 ![A]: element(sk0_4(A),A)),
% 0.21/0.47 inference(skolemization,[status(esa)],[f15])).
% 0.21/0.47 fof(f64,plain,(
% 0.21/0.47 ![X0]: (element(sk0_4(X0),X0))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f63])).
% 0.21/0.47 fof(f66,plain,(
% 0.21/0.47 empty(empty_set)),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f17])).
% 0.21/0.47 fof(f96,plain,(
% 0.21/0.47 ![A,B,C]: (~relation(C)|(in(A,relation_inverse_image(C,B))<=>(?[D]: ((in(D,relation_rng(C))&in(ordered_pair(A,D),C))&in(D,B)))))),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 0.21/0.47 fof(f97,plain,(
% 0.21/0.47 ![A,B,C]: (~relation(C)|((~in(A,relation_inverse_image(C,B))|(?[D]: ((in(D,relation_rng(C))&in(ordered_pair(A,D),C))&in(D,B))))&(in(A,relation_inverse_image(C,B))|(![D]: ((~in(D,relation_rng(C))|~in(ordered_pair(A,D),C))|~in(D,B))))))),
% 0.21/0.47 inference(NNF_transformation,[status(esa)],[f96])).
% 0.21/0.47 fof(f98,plain,(
% 0.21/0.47 ![C]: (~relation(C)|((![A,B]: (~in(A,relation_inverse_image(C,B))|(?[D]: ((in(D,relation_rng(C))&in(ordered_pair(A,D),C))&in(D,B)))))&(![A,B]: (in(A,relation_inverse_image(C,B))|(![D]: ((~in(D,relation_rng(C))|~in(ordered_pair(A,D),C))|~in(D,B)))))))),
% 0.21/0.47 inference(miniscoping,[status(esa)],[f97])).
% 0.21/0.47 fof(f99,plain,(
% 0.21/0.47 ![C]: (~relation(C)|((![A,B]: (~in(A,relation_inverse_image(C,B))|((in(sk0_11(B,A,C),relation_rng(C))&in(ordered_pair(A,sk0_11(B,A,C)),C))&in(sk0_11(B,A,C),B))))&(![A,B]: (in(A,relation_inverse_image(C,B))|(![D]: ((~in(D,relation_rng(C))|~in(ordered_pair(A,D),C))|~in(D,B)))))))),
% 0.21/0.47 inference(skolemization,[status(esa)],[f98])).
% 0.21/0.47 fof(f103,plain,(
% 0.21/0.47 ![X0,X1,X2,X3]: (~relation(X0)|in(X1,relation_inverse_image(X0,X2))|~in(X3,relation_rng(X0))|~in(ordered_pair(X1,X3),X0)|~in(X3,X2))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f99])).
% 0.21/0.47 fof(f104,plain,(
% 0.21/0.47 (?[A,B]: (relation(B)&((~A=empty_set&subset(A,relation_rng(B)))&relation_inverse_image(B,A)=empty_set)))),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 0.21/0.47 fof(f105,plain,(
% 0.21/0.47 ?[B]: (relation(B)&(?[A]: ((~A=empty_set&subset(A,relation_rng(B)))&relation_inverse_image(B,A)=empty_set)))),
% 0.21/0.47 inference(miniscoping,[status(esa)],[f104])).
% 0.21/0.47 fof(f106,plain,(
% 0.21/0.47 (relation(sk0_12)&((~sk0_13=empty_set&subset(sk0_13,relation_rng(sk0_12)))&relation_inverse_image(sk0_12,sk0_13)=empty_set))),
% 0.21/0.47 inference(skolemization,[status(esa)],[f105])).
% 0.21/0.47 fof(f107,plain,(
% 0.21/0.47 relation(sk0_12)),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f106])).
% 0.21/0.47 fof(f108,plain,(
% 0.21/0.47 ~sk0_13=empty_set),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f106])).
% 0.21/0.47 fof(f109,plain,(
% 0.21/0.47 subset(sk0_13,relation_rng(sk0_12))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f106])).
% 0.21/0.47 fof(f110,plain,(
% 0.21/0.47 relation_inverse_image(sk0_12,sk0_13)=empty_set),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f106])).
% 0.21/0.47 fof(f113,plain,(
% 0.21/0.47 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 0.21/0.47 fof(f114,plain,(
% 0.21/0.47 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f113])).
% 0.21/0.47 fof(f125,plain,(
% 0.21/0.47 ![A]: (~empty(A)|A=empty_set)),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 0.21/0.47 fof(f126,plain,(
% 0.21/0.47 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f125])).
% 0.21/0.47 fof(f127,plain,(
% 0.21/0.47 ![A,B]: (~in(A,B)|~empty(B))),
% 0.21/0.47 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 0.21/0.47 fof(f128,plain,(
% 0.21/0.47 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.21/0.47 inference(miniscoping,[status(esa)],[f127])).
% 0.21/0.47 fof(f129,plain,(
% 0.21/0.47 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.21/0.47 inference(cnf_transformation,[status(esa)],[f128])).
% 0.21/0.47 fof(f133,plain,(
% 0.21/0.47 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sk0_1(X1,relation_rng(X0),X0),X1),X0))),
% 0.21/0.47 inference(destructive_equality_resolution,[status(esa)],[f58])).
% 0.21/0.47 fof(f138,plain,(
% 0.21/0.47 ![X0]: (~in(X0,sk0_13)|in(X0,relation_rng(sk0_12)))),
% 0.21/0.47 inference(resolution,[status(thm)],[f51,f109])).
% 0.21/0.47 fof(f246,plain,(
% 0.21/0.47 spl0_4 <=> ~in(X0,sk0_13)),
% 0.21/0.47 introduced(split_symbol_definition)).
% 0.21/0.47 fof(f247,plain,(
% 0.21/0.47 ![X0]: (~in(X0,sk0_13)|~spl0_4)),
% 0.21/0.47 inference(component_clause,[status(thm)],[f246])).
% 0.21/0.47 fof(f361,plain,(
% 0.21/0.47 ![X0]: (empty(X0)|in(sk0_4(X0),X0))),
% 0.21/0.47 inference(resolution,[status(thm)],[f114,f64])).
% 0.21/0.47 fof(f364,plain,(
% 0.21/0.47 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_rng(X0))|~relation(X0)|in(sk0_1(X1,relation_rng(X0),X0),relation_inverse_image(X0,X2))|~in(X1,relation_rng(X0))|~in(X1,X2))),
% 0.21/0.47 inference(resolution,[status(thm)],[f133,f103])).
% 0.21/0.47 fof(f365,plain,(
% 0.21/0.47 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_rng(X0))|in(sk0_1(X1,relation_rng(X0),X0),relation_inverse_image(X0,X2))|~in(X1,X2))),
% 0.21/0.47 inference(duplicate_literals_removal,[status(esa)],[f364])).
% 0.21/0.47 fof(f804,plain,(
% 0.21/0.47 spl0_47 <=> relation(sk0_12)),
% 0.21/0.47 introduced(split_symbol_definition)).
% 0.21/0.47 fof(f806,plain,(
% 0.21/0.47 ~relation(sk0_12)|spl0_47),
% 0.21/0.47 inference(component_clause,[status(thm)],[f804])).
% 0.21/0.47 fof(f807,plain,(
% 0.21/0.47 spl0_48 <=> ~in(X0,relation_rng(sk0_12))|in(sk0_1(X0,relation_rng(sk0_12),sk0_12),empty_set)|~in(X0,sk0_13)),
% 0.21/0.47 introduced(split_symbol_definition)).
% 0.21/0.47 fof(f808,plain,(
% 0.21/0.47 ![X0]: (~in(X0,relation_rng(sk0_12))|in(sk0_1(X0,relation_rng(sk0_12),sk0_12),empty_set)|~in(X0,sk0_13)|~spl0_48)),
% 0.21/0.47 inference(component_clause,[status(thm)],[f807])).
% 0.21/0.47 fof(f810,plain,(
% 0.21/0.47 ![X0]: (~relation(sk0_12)|~in(X0,relation_rng(sk0_12))|in(sk0_1(X0,relation_rng(sk0_12),sk0_12),empty_set)|~in(X0,sk0_13))),
% 0.21/0.47 inference(paramodulation,[status(thm)],[f110,f365])).
% 0.21/0.47 fof(f811,plain,(
% 0.21/0.47 ~spl0_47|spl0_48),
% 0.21/0.47 inference(split_clause,[status(thm)],[f810,f804,f807])).
% 0.21/0.47 fof(f812,plain,(
% 0.21/0.47 $false|spl0_47),
% 0.21/0.47 inference(forward_subsumption_resolution,[status(thm)],[f806,f107])).
% 0.21/0.47 fof(f813,plain,(
% 0.21/0.47 spl0_47),
% 0.21/0.47 inference(contradiction_clause,[status(thm)],[f812])).
% 0.21/0.47 fof(f814,plain,(
% 0.21/0.47 ![X0]: (in(sk0_1(X0,relation_rng(sk0_12),sk0_12),empty_set)|~in(X0,sk0_13)|~spl0_48)),
% 0.21/0.47 inference(forward_subsumption_resolution,[status(thm)],[f808,f138])).
% 0.21/0.47 fof(f852,plain,(
% 0.21/0.47 spl0_49 <=> empty(empty_set)),
% 0.21/0.47 introduced(split_symbol_definition)).
% 0.21/0.47 fof(f854,plain,(
% 0.21/0.47 ~empty(empty_set)|spl0_49),
% 0.21/0.47 inference(component_clause,[status(thm)],[f852])).
% 0.21/0.47 fof(f1004,plain,(
% 0.21/0.47 ![X0]: (~in(X0,sk0_13)|~empty(empty_set)|~spl0_48)),
% 0.21/0.47 inference(resolution,[status(thm)],[f814,f129])).
% 0.21/0.47 fof(f1005,plain,(
% 0.21/0.47 spl0_4|~spl0_49|~spl0_48),
% 0.21/0.47 inference(split_clause,[status(thm)],[f1004,f246,f852,f807])).
% 0.21/0.47 fof(f1009,plain,(
% 0.21/0.47 empty(sk0_13)|~spl0_4),
% 0.21/0.47 inference(resolution,[status(thm)],[f247,f361])).
% 0.21/0.47 fof(f1049,plain,(
% 0.21/0.47 sk0_13=empty_set|~spl0_4),
% 0.21/0.47 inference(resolution,[status(thm)],[f1009,f126])).
% 0.21/0.47 fof(f1050,plain,(
% 0.21/0.47 $false|~spl0_4),
% 0.21/0.47 inference(forward_subsumption_resolution,[status(thm)],[f1049,f108])).
% 0.21/0.47 fof(f1051,plain,(
% 0.21/0.47 ~spl0_4),
% 0.21/0.47 inference(contradiction_clause,[status(thm)],[f1050])).
% 0.21/0.47 fof(f1052,plain,(
% 0.21/0.47 $false|spl0_49),
% 0.21/0.47 inference(forward_subsumption_resolution,[status(thm)],[f854,f66])).
% 0.21/0.47 fof(f1053,plain,(
% 0.21/0.47 spl0_49),
% 0.21/0.47 inference(contradiction_clause,[status(thm)],[f1052])).
% 0.21/0.47 fof(f1054,plain,(
% 0.21/0.47 $false),
% 0.21/0.47 inference(sat_refutation,[status(thm)],[f811,f813,f1005,f1051,f1053])).
% 0.21/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.49 % Elapsed time: 0.131951 seconds
% 0.21/0.49 % CPU time: 0.911618 seconds
% 0.21/0.49 % Total memory used: 72.933 MB
% 0.21/0.49 % Net memory used: 72.390 MB
%------------------------------------------------------------------------------