TSTP Solution File: SET964+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET964+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:40:48 EDT 2024
% Result : Theorem 0.13s 0.28s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SET964+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.26 % Computer : n007.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon Apr 29 21:26:32 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.13/0.27 % Drodi V3.6.0
% 0.13/0.28 % Refutation found
% 0.13/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.28 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.28 fof(f3,axiom,(
% 0.13/0.28 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.13/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.28 fof(f5,axiom,(
% 0.13/0.28 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.13/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.28 fof(f9,axiom,(
% 0.13/0.28 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.13/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.28 fof(f13,conjecture,(
% 0.13/0.28 (! [A,B,C] :~ ( A != empty_set& ( subset(cartesian_product2(B,A),cartesian_product2(C,A))| subset(cartesian_product2(A,B),cartesian_product2(A,C)) )& ~ subset(B,C) ) )),
% 0.13/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.28 fof(f14,negated_conjecture,(
% 0.13/0.28 ~((! [A,B,C] :~ ( A != empty_set& ( subset(cartesian_product2(B,A),cartesian_product2(C,A))| subset(cartesian_product2(A,B),cartesian_product2(A,C)) )& ~ subset(B,C) ) ))),
% 0.13/0.28 inference(negated_conjecture,[status(cth)],[f13])).
% 0.13/0.28 fof(f18,plain,(
% 0.13/0.28 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.13/0.28 inference(NNF_transformation,[status(esa)],[f3])).
% 0.13/0.28 fof(f19,plain,(
% 0.13/0.28 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.13/0.28 inference(miniscoping,[status(esa)],[f18])).
% 0.13/0.28 fof(f20,plain,(
% 0.13/0.28 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_0(A),A)))),
% 0.13/0.28 inference(skolemization,[status(esa)],[f19])).
% 0.13/0.28 fof(f22,plain,(
% 0.13/0.28 ![X0]: (X0=empty_set|in(sk0_0(X0),X0))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f20])).
% 0.13/0.28 fof(f32,plain,(
% 0.13/0.28 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.13/0.28 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.13/0.28 fof(f33,plain,(
% 0.13/0.28 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/0.28 inference(NNF_transformation,[status(esa)],[f32])).
% 0.13/0.28 fof(f34,plain,(
% 0.13/0.28 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/0.28 inference(miniscoping,[status(esa)],[f33])).
% 0.13/0.28 fof(f35,plain,(
% 0.13/0.28 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_6(B,A),A)&~in(sk0_6(B,A),B))))),
% 0.13/0.28 inference(skolemization,[status(esa)],[f34])).
% 0.13/0.28 fof(f36,plain,(
% 0.13/0.28 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f35])).
% 0.13/0.28 fof(f37,plain,(
% 0.13/0.28 ![X0,X1]: (subset(X0,X1)|in(sk0_6(X1,X0),X0))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f35])).
% 0.13/0.28 fof(f38,plain,(
% 0.13/0.28 ![X0,X1]: (subset(X0,X1)|~in(sk0_6(X1,X0),X1))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f35])).
% 0.13/0.28 fof(f42,plain,(
% 0.13/0.28 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.13/0.28 inference(NNF_transformation,[status(esa)],[f9])).
% 0.13/0.28 fof(f43,plain,(
% 0.13/0.28 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.13/0.28 inference(miniscoping,[status(esa)],[f42])).
% 0.13/0.28 fof(f44,plain,(
% 0.13/0.28 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f43])).
% 0.13/0.28 fof(f45,plain,(
% 0.13/0.28 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f43])).
% 0.13/0.28 fof(f46,plain,(
% 0.13/0.28 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f43])).
% 0.13/0.28 fof(f53,plain,(
% 0.13/0.28 (?[A,B,C]: ((~A=empty_set&(subset(cartesian_product2(B,A),cartesian_product2(C,A))|subset(cartesian_product2(A,B),cartesian_product2(A,C))))&~subset(B,C)))),
% 0.13/0.28 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.13/0.28 fof(f54,plain,(
% 0.13/0.28 ?[B,C]: ((?[A]: (~A=empty_set&(subset(cartesian_product2(B,A),cartesian_product2(C,A))|subset(cartesian_product2(A,B),cartesian_product2(A,C)))))&~subset(B,C))),
% 0.13/0.28 inference(miniscoping,[status(esa)],[f53])).
% 0.13/0.28 fof(f55,plain,(
% 0.13/0.28 ((~sk0_11=empty_set&(subset(cartesian_product2(sk0_9,sk0_11),cartesian_product2(sk0_10,sk0_11))|subset(cartesian_product2(sk0_11,sk0_9),cartesian_product2(sk0_11,sk0_10))))&~subset(sk0_9,sk0_10))),
% 0.13/0.28 inference(skolemization,[status(esa)],[f54])).
% 0.13/0.28 fof(f56,plain,(
% 0.13/0.28 ~sk0_11=empty_set),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f55])).
% 0.13/0.28 fof(f57,plain,(
% 0.13/0.28 subset(cartesian_product2(sk0_9,sk0_11),cartesian_product2(sk0_10,sk0_11))|subset(cartesian_product2(sk0_11,sk0_9),cartesian_product2(sk0_11,sk0_10))),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f55])).
% 0.13/0.28 fof(f58,plain,(
% 0.13/0.28 ~subset(sk0_9,sk0_10)),
% 0.13/0.28 inference(cnf_transformation,[status(esa)],[f55])).
% 0.13/0.28 fof(f65,plain,(
% 0.13/0.28 spl0_0 <=> subset(cartesian_product2(sk0_9,sk0_11),cartesian_product2(sk0_10,sk0_11))),
% 0.13/0.28 introduced(split_symbol_definition)).
% 0.13/0.28 fof(f66,plain,(
% 0.13/0.28 subset(cartesian_product2(sk0_9,sk0_11),cartesian_product2(sk0_10,sk0_11))|~spl0_0),
% 0.13/0.28 inference(component_clause,[status(thm)],[f65])).
% 0.13/0.28 fof(f68,plain,(
% 0.13/0.28 spl0_1 <=> subset(cartesian_product2(sk0_11,sk0_9),cartesian_product2(sk0_11,sk0_10))),
% 0.13/0.28 introduced(split_symbol_definition)).
% 0.13/0.28 fof(f69,plain,(
% 0.13/0.28 subset(cartesian_product2(sk0_11,sk0_9),cartesian_product2(sk0_11,sk0_10))|~spl0_1),
% 0.13/0.28 inference(component_clause,[status(thm)],[f68])).
% 0.13/0.28 fof(f71,plain,(
% 0.13/0.28 spl0_0|spl0_1),
% 0.13/0.28 inference(split_clause,[status(thm)],[f57,f65,f68])).
% 0.13/0.28 fof(f144,plain,(
% 0.13/0.28 ![X0]: (~in(X0,cartesian_product2(sk0_9,sk0_11))|in(X0,cartesian_product2(sk0_10,sk0_11))|~spl0_0)),
% 0.13/0.28 inference(resolution,[status(thm)],[f66,f36])).
% 0.13/0.28 fof(f147,plain,(
% 0.13/0.28 ![X0,X1]: (in(ordered_pair(X0,X1),cartesian_product2(sk0_10,sk0_11))|~in(X0,sk0_9)|~in(X1,sk0_11)|~spl0_0)),
% 0.13/0.28 inference(resolution,[status(thm)],[f144,f46])).
% 0.13/0.28 fof(f190,plain,(
% 0.13/0.28 spl0_11 <=> sk0_11=empty_set),
% 0.13/0.28 introduced(split_symbol_definition)).
% 0.13/0.28 fof(f191,plain,(
% 0.13/0.28 sk0_11=empty_set|~spl0_11),
% 0.13/0.28 inference(component_clause,[status(thm)],[f190])).
% 0.13/0.28 fof(f195,plain,(
% 0.13/0.28 $false|~spl0_11),
% 0.13/0.28 inference(forward_subsumption_resolution,[status(thm)],[f191,f56])).
% 0.13/0.28 fof(f196,plain,(
% 0.13/0.28 ~spl0_11),
% 0.13/0.28 inference(contradiction_clause,[status(thm)],[f195])).
% 0.13/0.28 fof(f197,plain,(
% 0.13/0.28 ![X0]: (~in(X0,cartesian_product2(sk0_11,sk0_9))|in(X0,cartesian_product2(sk0_11,sk0_10))|~spl0_1)),
% 0.13/0.28 inference(resolution,[status(thm)],[f69,f36])).
% 0.13/0.28 fof(f201,plain,(
% 0.13/0.28 ![X0,X1]: (in(ordered_pair(X0,X1),cartesian_product2(sk0_11,sk0_10))|~in(X0,sk0_11)|~in(X1,sk0_9)|~spl0_1)),
% 0.13/0.28 inference(resolution,[status(thm)],[f197,f46])).
% 0.13/0.28 fof(f378,plain,(
% 0.13/0.28 spl0_15 <=> ~in(X0,sk0_11)),
% 0.13/0.28 introduced(split_symbol_definition)).
% 0.13/0.28 fof(f379,plain,(
% 0.13/0.28 ![X0]: (~in(X0,sk0_11)|~spl0_15)),
% 0.13/0.28 inference(component_clause,[status(thm)],[f378])).
% 0.13/0.28 fof(f381,plain,(
% 0.13/0.28 spl0_16 <=> ~in(X1,sk0_9)|in(X1,sk0_10)),
% 0.13/0.28 introduced(split_symbol_definition)).
% 0.13/0.28 fof(f382,plain,(
% 0.13/0.28 ![X0]: (~in(X0,sk0_9)|in(X0,sk0_10)|~spl0_16)),
% 0.13/0.28 inference(component_clause,[status(thm)],[f381])).
% 0.13/0.28 fof(f384,plain,(
% 0.13/0.28 ![X0,X1]: (~in(X0,sk0_11)|~in(X1,sk0_9)|in(X1,sk0_10)|~spl0_1)),
% 0.13/0.28 inference(resolution,[status(thm)],[f201,f45])).
% 0.13/0.28 fof(f385,plain,(
% 0.13/0.28 spl0_15|spl0_16|~spl0_1),
% 0.13/0.28 inference(split_clause,[status(thm)],[f384,f378,f381,f68])).
% 0.13/0.28 fof(f397,plain,(
% 0.13/0.28 ![X0,X1]: (~in(X0,sk0_9)|~in(X1,sk0_11)|in(X0,sk0_10)|~spl0_0)),
% 0.13/0.28 inference(resolution,[status(thm)],[f147,f44])).
% 0.13/0.28 fof(f398,plain,(
% 0.13/0.28 spl0_16|spl0_15|~spl0_0),
% 0.13/0.28 inference(split_clause,[status(thm)],[f397,f381,f378,f65])).
% 0.13/0.28 fof(f406,plain,(
% 0.13/0.28 ![X0]: (in(sk0_6(X0,sk0_9),sk0_10)|subset(sk0_9,X0)|~spl0_16)),
% 0.13/0.28 inference(resolution,[status(thm)],[f382,f37])).
% 0.13/0.28 fof(f428,plain,(
% 0.13/0.28 sk0_11=empty_set|~spl0_15),
% 0.13/0.28 inference(resolution,[status(thm)],[f379,f22])).
% 0.13/0.28 fof(f429,plain,(
% 0.13/0.28 spl0_11|~spl0_15),
% 0.13/0.28 inference(split_clause,[status(thm)],[f428,f190,f378])).
% 0.13/0.28 fof(f478,plain,(
% 0.13/0.28 spl0_19 <=> subset(sk0_9,sk0_10)),
% 0.13/0.28 introduced(split_symbol_definition)).
% 0.13/0.28 fof(f479,plain,(
% 0.13/0.28 subset(sk0_9,sk0_10)|~spl0_19),
% 0.13/0.28 inference(component_clause,[status(thm)],[f478])).
% 0.13/0.28 fof(f481,plain,(
% 0.13/0.28 subset(sk0_9,sk0_10)|subset(sk0_9,sk0_10)|~spl0_16),
% 0.13/0.28 inference(resolution,[status(thm)],[f406,f38])).
% 0.13/0.28 fof(f482,plain,(
% 0.13/0.28 spl0_19|~spl0_16),
% 0.13/0.28 inference(split_clause,[status(thm)],[f481,f478,f381])).
% 0.13/0.28 fof(f494,plain,(
% 0.13/0.28 $false|~spl0_19),
% 0.13/0.28 inference(forward_subsumption_resolution,[status(thm)],[f58,f479])).
% 0.13/0.28 fof(f495,plain,(
% 0.13/0.28 ~spl0_19),
% 0.13/0.28 inference(contradiction_clause,[status(thm)],[f494])).
% 0.13/0.28 fof(f496,plain,(
% 0.13/0.28 $false),
% 0.13/0.28 inference(sat_refutation,[status(thm)],[f71,f196,f385,f398,f429,f482,f495])).
% 0.13/0.28 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.29 % Elapsed time: 0.016711 seconds
% 0.13/0.29 % CPU time: 0.053759 seconds
% 0.13/0.29 % Total memory used: 16.006 MB
% 0.13/0.29 % Net memory used: 15.938 MB
%------------------------------------------------------------------------------