%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU353+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 : n020.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 02:22:24 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU353+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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 06:15:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.41 fof(f10,axiom,(
% 0.14/0.41 (! [A] :( one_sorted_str(A)=> identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)) ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f17,axiom,(
% 0.14/0.41 (! [A] :( one_sorted_str(A)=> ( function(identity_on_carrier(A))& quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))& relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)) ) ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f28,axiom,(
% 0.14/0.41 (! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> ~ empty(the_carrier(A)) ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f44,axiom,(
% 0.14/0.41 (! [A] : identity_as_relation_of(A) = identity_relation(A) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f45,axiom,(
% 0.14/0.41 (! [A,B,C,D] :( ( ~ empty(A)& function(C)& quasi_total(C,A,B)& relation_of2(C,A,B)& element(D,A) )=> apply_as_element(A,B,C,D) = apply(C,D) ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f46,axiom,(
% 0.14/0.41 (! [A,B,C] :( relation_of2_as_subset(C,A,B)<=> relation_of2(C,A,B) ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f49,axiom,(
% 0.14/0.41 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f50,axiom,(
% 0.14/0.41 (! [A,B] :( in(B,A)=> apply(identity_relation(A),B) = B ) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f57,conjecture,(
% 0.14/0.41 (! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( element(B,the_carrier(A))=> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f58,negated_conjecture,(
% 0.14/0.41 ~((! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( element(B,the_carrier(A))=> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B ) )) ))),
% 0.14/0.41 inference(negated_conjecture,[status(cth)],[f57])).
% 0.14/0.41 fof(f95,plain,(
% 0.14/0.41 ![A]: (~one_sorted_str(A)|identity_on_carrier(A)=identity_as_relation_of(the_carrier(A)))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.14/0.41 fof(f96,plain,(
% 0.14/0.41 ![X0]: (~one_sorted_str(X0)|identity_on_carrier(X0)=identity_as_relation_of(the_carrier(X0)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f95])).
% 0.14/0.41 fof(f101,plain,(
% 0.14/0.41 ![A]: (~one_sorted_str(A)|((function(identity_on_carrier(A))&quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)))&relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.14/0.41 fof(f102,plain,(
% 0.14/0.41 ![X0]: (~one_sorted_str(X0)|function(identity_on_carrier(X0)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f101])).
% 0.14/0.41 fof(f103,plain,(
% 0.14/0.41 ![X0]: (~one_sorted_str(X0)|quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f101])).
% 0.14/0.41 fof(f104,plain,(
% 0.14/0.41 ![X0]: (~one_sorted_str(X0)|relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f101])).
% 0.14/0.41 fof(f117,plain,(
% 0.14/0.41 ![A]: ((empty_carrier(A)|~one_sorted_str(A))|~empty(the_carrier(A)))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.14/0.41 fof(f118,plain,(
% 0.14/0.41 ![X0]: (empty_carrier(X0)|~one_sorted_str(X0)|~empty(the_carrier(X0)))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f117])).
% 0.14/0.41 fof(f178,plain,(
% 0.14/0.41 ![X0]: (identity_as_relation_of(X0)=identity_relation(X0))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f44])).
% 0.14/0.41 fof(f179,plain,(
% 0.14/0.41 ![A,B,C,D]: (((((empty(A)|~function(C))|~quasi_total(C,A,B))|~relation_of2(C,A,B))|~element(D,A))|apply_as_element(A,B,C,D)=apply(C,D))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.14/0.41 fof(f180,plain,(
% 0.14/0.41 ![X0,X1,X2,X3]: (empty(X0)|~function(X1)|~quasi_total(X1,X0,X2)|~relation_of2(X1,X0,X2)|~element(X3,X0)|apply_as_element(X0,X2,X1,X3)=apply(X1,X3))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f179])).
% 0.14/0.41 fof(f181,plain,(
% 0.14/0.41 ![A,B,C]: ((~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B))&(relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 0.14/0.41 inference(NNF_transformation,[status(thm)],[f46])).
% 0.14/0.41 fof(f182,plain,(
% 0.14/0.41 (![A,B,C]: (~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B)))&(![A,B,C]: (relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f181])).
% 0.14/0.41 fof(f183,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|relation_of2(X0,X1,X2))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f182])).
% 0.14/0.41 fof(f189,plain,(
% 0.14/0.41 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f49])).
% 0.14/0.41 fof(f190,plain,(
% 0.14/0.41 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f189])).
% 0.14/0.41 fof(f191,plain,(
% 0.14/0.41 ![A,B]: (~in(B,A)|apply(identity_relation(A),B)=B)),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 0.14/0.41 fof(f192,plain,(
% 0.14/0.41 ![X0,X1]: (~in(X0,X1)|apply(identity_relation(X1),X0)=X0)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f191])).
% 0.14/0.41 fof(f211,plain,(
% 0.14/0.41 (?[A]: ((~empty_carrier(A)&one_sorted_str(A))&(?[B]: (element(B,the_carrier(A))&~apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B)=B))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 0.14/0.41 fof(f212,plain,(
% 0.14/0.41 ((~empty_carrier(sK15_skl)&one_sorted_str(sK15_skl))&(element(sK16_skl,the_carrier(sK15_skl))&~apply_as_element(the_carrier(sK15_skl),the_carrier(sK15_skl),identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl))),
% 0.14/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(A,sK15_skl),skolemize(B,sK16_skl)],[f211])).
% 0.14/0.41 fof(f213,plain,(
% 0.14/0.41 ~empty_carrier(sK15_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f212])).
% 0.14/0.41 fof(f214,plain,(
% 0.14/0.41 one_sorted_str(sK15_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f212])).
% 0.14/0.41 fof(f215,plain,(
% 0.14/0.41 element(sK16_skl,the_carrier(sK15_skl))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f212])).
% 0.14/0.41 fof(f216,plain,(
% 0.14/0.41 ~apply_as_element(the_carrier(sK15_skl),the_carrier(sK15_skl),identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f212])).
% 0.14/0.41 fof(f224,plain,(
% 0.14/0.41 identity_on_carrier(sK15_skl)=identity_as_relation_of(the_carrier(sK15_skl))),
% 0.14/0.41 inference(resolution,[status(thm)],[f96,f214])).
% 0.14/0.41 fof(f281,plain,(
% 0.14/0.41 ![X0,X1,X2,X3]: (empty(X0)|~quasi_total(identity_on_carrier(X1),X0,X2)|~relation_of2(identity_on_carrier(X1),X0,X2)|~element(X3,X0)|apply_as_element(X0,X2,identity_on_carrier(X1),X3)=apply(identity_on_carrier(X1),X3)|~one_sorted_str(X1))),
% 0.14/0.41 inference(resolution,[status(thm)],[f180,f102])).
% 0.14/0.41 fof(f285,plain,(
% 0.14/0.41 ![X0]: (relation_of2(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))|~one_sorted_str(X0))),
% 0.14/0.41 inference(resolution,[status(thm)],[f183,f104])).
% 0.14/0.41 fof(f300,plain,(
% 0.14/0.41 ![X0,X1]: (empty(the_carrier(X0))|~relation_of2(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))|~element(X1,the_carrier(X0))|apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1)=apply(identity_on_carrier(X0),X1)|~one_sorted_str(X0)|~one_sorted_str(X0))),
% 0.14/0.41 inference(resolution,[status(thm)],[f281,f103])).
% 0.14/0.41 fof(f302,plain,(
% 0.14/0.41 ![X0,X1]: (empty(the_carrier(X0))|~relation_of2(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))|~element(X1,the_carrier(X0))|apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1)=apply(identity_on_carrier(X0),X1)|~one_sorted_str(X0))),
% 0.14/0.41 inference(duplicate_literals_removal,[status(thm)],[f300])).
% 0.14/0.41 fof(f303,plain,(
% 0.14/0.41 ![X0,X1]: (empty(the_carrier(X0))|~element(X1,the_carrier(X0))|apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1)=apply(identity_on_carrier(X0),X1)|~one_sorted_str(X0))),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f302,f285])).
% 0.14/0.41 fof(f313,plain,(
% 0.14/0.41 ![X0]: (empty(the_carrier(sK15_skl))|~element(X0,the_carrier(sK15_skl))|apply_as_element(the_carrier(sK15_skl),the_carrier(sK15_skl),identity_on_carrier(sK15_skl),X0)=apply(identity_on_carrier(sK15_skl),X0))),
% 0.14/0.41 inference(resolution,[status(thm)],[f303,f214])).
% 0.14/0.41 fof(f323,plain,(
% 0.14/0.41 empty(the_carrier(sK15_skl))|in(sK16_skl,the_carrier(sK15_skl))),
% 0.14/0.41 inference(resolution,[status(thm)],[f190,f215])).
% 0.14/0.41 fof(f329,plain,(
% 0.14/0.41 ![X0,X1]: (~in(X0,X1)|apply(identity_as_relation_of(X1),X0)=X0)),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f178,f192])).
% 0.14/0.41 fof(f339,plain,(
% 0.14/0.41 empty(the_carrier(sK15_skl))|apply(identity_as_relation_of(the_carrier(sK15_skl)),sK16_skl)=sK16_skl),
% 0.14/0.41 inference(resolution,[status(thm)],[f323,f329])).
% 0.14/0.41 fof(f342,plain,(
% 0.14/0.41 empty(the_carrier(sK15_skl))|apply(identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f224,f339])).
% 0.14/0.41 fof(f376,plain,(
% 0.14/0.41 apply(identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl|empty_carrier(sK15_skl)|~one_sorted_str(sK15_skl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f342,f118])).
% 0.14/0.41 fof(f379,plain,(
% 0.14/0.41 apply(identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl|~one_sorted_str(sK15_skl)),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f376,f213])).
% 0.14/0.41 fof(f381,plain,(
% 0.14/0.41 apply(identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f379,f214])).
% 0.14/0.41 fof(f483,plain,(
% 0.14/0.41 empty(the_carrier(sK15_skl))|apply_as_element(the_carrier(sK15_skl),the_carrier(sK15_skl),identity_on_carrier(sK15_skl),sK16_skl)=apply(identity_on_carrier(sK15_skl),sK16_skl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f313,f215])).
% 0.14/0.41 fof(f485,plain,(
% 0.14/0.41 empty(the_carrier(sK15_skl))|apply_as_element(the_carrier(sK15_skl),the_carrier(sK15_skl),identity_on_carrier(sK15_skl),sK16_skl)=sK16_skl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f381,f483])).
% 0.14/0.41 fof(f486,plain,(
% 0.14/0.41 empty(the_carrier(sK15_skl))),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f485,f216])).
% 0.14/0.41 fof(f489,plain,(
% 0.14/0.41 empty_carrier(sK15_skl)|~one_sorted_str(sK15_skl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f486,f118])).
% 0.14/0.41 fof(f493,plain,(
% 0.14/0.41 ~one_sorted_str(sK15_skl)),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f489,f213])).
% 0.14/0.41 fof(f494,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f493,f214])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.45 % Elapsed time: 0.070947 seconds
% 0.14/0.45 % CPU time: 0.221534 seconds
% 0.14/0.45 % Total memory used: 105.979 MB
% 0.14/0.45 % Net memory used: 105.875 MB
%------------------------------------------------------------------------------