%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 03:21:37 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 11:30:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f1,conjecture,(
% 0.10/0.40 ( (! [X,Y] :( eq(X,Y)<=> (! [Z] :( a_member_of(Z,X)<=> a_member_of(Z,Y) ) )))=> (! [A,B] :( eq(A,B)=> eq(B,A) ) )) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f2,negated_conjecture,(
% 0.10/0.40 ~(( (! [X,Y] :( eq(X,Y)<=> (! [Z] :( a_member_of(Z,X)<=> a_member_of(Z,Y) ) )))=> (! [A,B] :( eq(A,B)=> eq(B,A) ) )) )),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.40 fof(f3,plain,(
% 0.10/0.40 ((![X,Y]: (eq(X,Y)<=>(![Z]: (a_member_of(Z,X)<=>a_member_of(Z,Y)))))&(?[A,B]: (eq(A,B)&~eq(B,A))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.10/0.40 fof(f4,plain,(
% 0.10/0.40 (![X,Y]: ((~eq(X,Y)|(![Z]: ((~a_member_of(Z,X)|a_member_of(Z,Y))&(a_member_of(Z,X)|~a_member_of(Z,Y)))))&(eq(X,Y)|(?[Z]: ((~a_member_of(Z,X)|~a_member_of(Z,Y))&(a_member_of(Z,X)|a_member_of(Z,Y)))))))&(?[A,B]: (eq(A,B)&~eq(B,A)))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f3])).
% 0.10/0.40 fof(f5,plain,(
% 0.10/0.40 ((![X,Y]: (~eq(X,Y)|((![Z]: (~a_member_of(Z,X)|a_member_of(Z,Y)))&(![Z]: (a_member_of(Z,X)|~a_member_of(Z,Y))))))&(![X,Y]: (eq(X,Y)|(?[Z]: ((~a_member_of(Z,X)|~a_member_of(Z,Y))&(a_member_of(Z,X)|a_member_of(Z,Y)))))))&(?[A,B]: (eq(A,B)&~eq(B,A)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f4])).
% 0.10/0.40 fof(f6,plain,(
% 0.10/0.40 ((![X,Y]: (~eq(X,Y)|((![Z]: (~a_member_of(Z,X)|a_member_of(Z,Y)))&(![Z]: (a_member_of(Z,X)|~a_member_of(Z,Y))))))&(![X,Y]: (eq(X,Y)|((~a_member_of(sK0_skl(Y,X),X)|~a_member_of(sK0_skl(Y,X),Y))&(a_member_of(sK0_skl(Y,X),X)|a_member_of(sK0_skl(Y,X),Y))))))&(eq(sK1_skl,sK2_skl)&~eq(sK2_skl,sK1_skl))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Z,sK0_skl(Y,X)),skolemize(A,sK1_skl),skolemize(B,sK2_skl)],[f5])).
% 0.10/0.40 fof(f7,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~eq(X0,X1)|~a_member_of(X2,X0)|a_member_of(X2,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f8,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~eq(X0,X1)|a_member_of(X2,X0)|~a_member_of(X2,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f9,plain,(
% 0.10/0.40 ![X0,X1]: (eq(X0,X1)|~a_member_of(sK0_skl(X1,X0),X0)|~a_member_of(sK0_skl(X1,X0),X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f10,plain,(
% 0.10/0.40 ![X0,X1]: (eq(X0,X1)|a_member_of(sK0_skl(X1,X0),X0)|a_member_of(sK0_skl(X1,X0),X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f11,plain,(
% 0.10/0.40 eq(sK1_skl,sK2_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f12,plain,(
% 0.10/0.40 ~eq(sK2_skl,sK1_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f13,plain,(
% 0.10/0.40 ![X0,X1,X2]: (eq(X0,X1)|~a_member_of(sK0_skl(X1,X0),X0)|~eq(X1,X2)|~a_member_of(sK0_skl(X1,X0),X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f9,f8])).
% 0.10/0.40 fof(f15,plain,(
% 0.10/0.40 ![X0]: (eq(X0,sK1_skl)|~a_member_of(sK0_skl(sK1_skl,X0),X0)|~a_member_of(sK0_skl(sK1_skl,X0),sK2_skl))),
% 0.10/0.40 inference(resolution,[status(thm)],[f13,f11])).
% 0.10/0.40 fof(f24,plain,(
% 0.10/0.40 eq(sK2_skl,sK1_skl)|a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|eq(sK2_skl,sK1_skl)|~a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f10,f15])).
% 0.10/0.40 fof(f38,definition,(
% 0.10/0.40 sQ3_spl <=> (eq(sK2_skl,sK1_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f39,plain,(
% 0.10/0.40 eq(sK2_skl,sK1_skl)|~sQ3_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f38])).
% 0.10/0.40 fof(f41,definition,(
% 0.10/0.40 sQ4_spl <=> (a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f42,plain,(
% 0.10/0.40 a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|~sQ4_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f41])).
% 0.10/0.40 fof(f44,definition,(
% 0.10/0.40 sQ5_spl <=> (a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f46,plain,(
% 0.10/0.40 ~a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl)|sQ5_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f44])).
% 0.10/0.40 fof(f47,plain,(
% 0.10/0.40 sQ3_spl|sQ4_spl|~sQ5_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f24,f38,f41,f44])).
% 0.10/0.40 fof(f49,plain,(
% 0.10/0.40 $false|~sQ3_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f39,f12])).
% 0.10/0.40 fof(f50,plain,(
% 0.10/0.40 ~sQ3_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f49])).
% 0.10/0.40 fof(f51,plain,(
% 0.10/0.40 eq(sK2_skl,sK1_skl)|a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|sQ5_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f46,f10])).
% 0.10/0.40 fof(f53,plain,(
% 0.10/0.40 ![X0]: (~eq(X0,sK2_skl)|~a_member_of(sK0_skl(sK1_skl,sK2_skl),X0)|sQ5_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f46,f7])).
% 0.10/0.40 fof(f54,plain,(
% 0.10/0.40 sQ3_spl|sQ4_spl|sQ5_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f51,f38,f41,f44])).
% 0.10/0.40 fof(f71,plain,(
% 0.10/0.40 eq(sK2_skl,sK1_skl)|~a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl)|~sQ4_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f42,f9])).
% 0.10/0.40 fof(f72,plain,(
% 0.10/0.40 sQ3_spl|~sQ5_spl|~sQ4_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f71,f38,f44,f41])).
% 0.10/0.40 fof(f84,plain,(
% 0.10/0.40 ~a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|sQ5_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f53,f11])).
% 0.10/0.40 fof(f86,plain,(
% 0.10/0.40 $false|~sQ4_spl|sQ5_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f84,f42])).
% 0.10/0.40 fof(f87,plain,(
% 0.10/0.40 ~sQ4_spl|sQ5_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f86])).
% 0.10/0.40 fof(f88,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f47,f50,f54,f72,f87])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.050509 seconds
% 0.10/0.43 % CPU time: 0.118985 seconds
% 0.10/0.43 % Total memory used: 16.723 MB
% 0.10/0.43 % Net memory used: 16.217 MB
%------------------------------------------------------------------------------