%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:12:19 PM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n010.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 05:30:17 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.14/5.40 % Refutation found
% 0.14/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.40 fof(f1,axiom,(
% 0.14/5.40 (! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) )),
% 0.14/5.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.40 fof(f2,axiom,(
% 0.14/5.40 (! [B] : union(B,empty_set) = B )),
% 0.14/5.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.40 fof(f3,axiom,(
% 0.14/5.40 (! [B] : difference(B,empty_set) = B )),
% 0.14/5.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.40 fof(f4,axiom,(
% 0.14/5.40 (! [B] : difference(empty_set,B) = empty_set )),
% 0.14/5.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.40 fof(f8,axiom,(
% 0.14/5.40 (! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) )),
% 0.14/5.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.40 fof(f13,conjecture,(
% 0.14/5.40 (! [B] :( symmetric_difference(B,empty_set) = B& symmetric_difference(empty_set,B) = B ) )),
% 0.14/5.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.40 fof(f14,negated_conjecture,(
% 0.14/5.40 ~((! [B] :( symmetric_difference(B,empty_set) = B& symmetric_difference(empty_set,B) = B ) ))),
% 0.14/5.40 inference(negated_conjecture,[status(cth)],[f13])).
% 0.14/5.40 fof(f15,plain,(
% 0.14/5.40 ![X0,X1]: (symmetric_difference(X0,X1)=union(difference(X0,X1),difference(X1,X0)))),
% 0.14/5.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/5.40 fof(f16,plain,(
% 0.14/5.40 ![X0]: (union(X0,empty_set)=X0)),
% 0.14/5.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/5.40 fof(f17,plain,(
% 0.14/5.40 ![X0]: (difference(X0,empty_set)=X0)),
% 0.14/5.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/5.40 fof(f18,plain,(
% 0.14/5.40 ![X0]: (difference(empty_set,X0)=empty_set)),
% 0.14/5.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/5.40 fof(f26,plain,(
% 0.14/5.40 ![X0,X1]: (symmetric_difference(X0,X1)=symmetric_difference(X1,X0))),
% 0.14/5.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/5.40 fof(f47,plain,(
% 0.14/5.40 (?[B]: (~symmetric_difference(B,empty_set)=B|~symmetric_difference(empty_set,B)=B))),
% 0.14/5.40 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.14/5.40 fof(f48,plain,(
% 0.14/5.40 (?[B]: ~symmetric_difference(B,empty_set)=B)|(?[B]: ~symmetric_difference(empty_set,B)=B)),
% 0.14/5.40 inference(miniscoping,[status(thm)],[f47])).
% 0.14/5.40 fof(f49,plain,(
% 0.14/5.40 ~symmetric_difference(sK3_skl,empty_set)=sK3_skl|~symmetric_difference(empty_set,sK4_skl)=sK4_skl),
% 0.14/5.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(B,sK4_skl)],[f48])).
% 0.14/5.40 fof(f50,plain,(
% 0.14/5.40 ~symmetric_difference(sK3_skl,empty_set)=sK3_skl|~symmetric_difference(empty_set,sK4_skl)=sK4_skl),
% 0.14/5.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.14/5.40 fof(f51,definition,(
% 0.14/5.40 sQ0_spl <=> (symmetric_difference(sK3_skl,empty_set)=sK3_skl)),
% 0.14/5.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/5.40 fof(f53,plain,(
% 0.14/5.40 ~symmetric_difference(sK3_skl,empty_set)=sK3_skl|sQ0_spl),
% 0.14/5.40 inference(component_clause,[status(thm)],[f51])).
% 0.14/5.40 fof(f54,definition,(
% 0.14/5.40 sQ1_spl <=> (symmetric_difference(empty_set,sK4_skl)=sK4_skl)),
% 0.14/5.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/5.40 fof(f56,plain,(
% 0.14/5.40 ~symmetric_difference(empty_set,sK4_skl)=sK4_skl|sQ1_spl),
% 0.14/5.40 inference(component_clause,[status(thm)],[f54])).
% 0.14/5.40 fof(f57,plain,(
% 0.14/5.40 ~sQ0_spl|~sQ1_spl),
% 0.14/5.40 inference(split_clause,[status(thm)],[f50,f51,f54])).
% 0.14/5.40 fof(f68,plain,(
% 0.14/5.40 ![X0]: (symmetric_difference(X0,empty_set)=union(difference(X0,empty_set),empty_set))),
% 0.14/5.40 inference(paramodulation,[status(thm)],[f18,f15])).
% 0.14/5.40 fof(f70,plain,(
% 0.14/5.40 ![X0]: (symmetric_difference(X0,empty_set)=difference(X0,empty_set))),
% 0.14/5.40 inference(forward_demodulation,[status(thm)],[f16,f68])).
% 0.14/5.40 fof(f71,plain,(
% 0.14/5.40 ![X0]: (symmetric_difference(X0,empty_set)=X0)),
% 0.14/5.40 inference(forward_demodulation,[status(thm)],[f17,f70])).
% 0.14/5.40 fof(f73,plain,(
% 0.14/5.40 ~sK3_skl=sK3_skl|sQ0_spl),
% 0.14/5.40 inference(backward_demodulation,[status(thm)],[f71,f53])).
% 0.14/5.40 fof(f74,plain,(
% 0.14/5.40 ![X0]: (symmetric_difference(empty_set,X0)=X0)),
% 0.14/5.40 inference(paramodulation,[status(thm)],[f26,f71])).
% 0.14/5.40 fof(f78,plain,(
% 0.14/5.40 $false|sQ0_spl),
% 0.14/5.40 inference(trivial_equality_resolution,[status(thm)],[f73])).
% 0.14/5.40 fof(f79,plain,(
% 0.14/5.40 sQ0_spl),
% 0.14/5.40 inference(contradiction_clause,[status(thm)],[f78])).
% 0.14/5.40 fof(f86,plain,(
% 0.14/5.40 ~sK4_skl=sK4_skl|sQ1_spl),
% 0.14/5.40 inference(forward_demodulation,[status(thm)],[f74,f56])).
% 0.14/5.40 fof(f87,plain,(
% 0.14/5.40 $false|sQ1_spl),
% 0.14/5.40 inference(trivial_equality_resolution,[status(thm)],[f86])).
% 0.14/5.40 fof(f88,plain,(
% 0.14/5.40 sQ1_spl),
% 0.14/5.40 inference(contradiction_clause,[status(thm)],[f87])).
% 0.14/5.40 fof(f89,plain,(
% 0.14/5.40 $false),
% 0.14/5.40 inference(sat_refutation,[status(thm)],[f57,f79,f88])).
% 0.14/5.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.44 % Elapsed time: 0.053736 seconds
% 0.14/5.44 % CPU time: 0.155521 seconds
% 0.14/5.44 % Total memory used: 101.566 MB
% 0.14/5.44 % Net memory used: 101.219 MB
%------------------------------------------------------------------------------