%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:11:12 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:44:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.40 fof(f1,axiom,(
% 0.13/0.40 (![X]: (member(X,singleton_set(X)) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f2,axiom,(
% 0.13/0.40 (![X,Y]: (( ~ member(X,singleton_set(Y))| X = Y ) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f3,axiom,(
% 0.13/0.40 (![X,Y]: (member(X,unordered_pair(X,Y)) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f4,axiom,(
% 0.13/0.40 (![Y,X]: (member(Y,unordered_pair(X,Y)) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f5,axiom,(
% 0.13/0.40 (![X,Y,Z]: (( ~ member(X,unordered_pair(Y,Z))| X = Y| X = Z ) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f6,axiom,(
% 0.13/0.40 (![X,Y]: (ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f7,hypothesis,(
% 0.13/0.40 ordered_pair(m1,r1) = ordered_pair(m2,r2) ),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f8,negated_conjecture,(
% 0.13/0.40 r1 != r2 ),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f9,plain,(
% 0.13/0.40 ![X0]: (member(X0,singleton_set(X0)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.40 fof(f10,plain,(
% 0.13/0.40 ![X0,X1]: (~member(X0,singleton_set(X1))|X0=X1)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.40 fof(f11,plain,(
% 0.13/0.40 ![X0,X1]: (member(X0,unordered_pair(X0,X1)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.40 fof(f12,plain,(
% 0.13/0.40 ![X0,X1]: (member(X0,unordered_pair(X1,X0)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.40 fof(f13,plain,(
% 0.13/0.40 ![X,Z]: ((![Y]: (~member(X,unordered_pair(Y,Z))|X=Y))|X=Z)),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f5])).
% 0.13/0.40 fof(f14,plain,(
% 0.13/0.40 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.40 fof(f15,plain,(
% 0.13/0.40 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton_set(X0),unordered_pair(X0,X1)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.40 fof(f16,plain,(
% 0.13/0.40 ordered_pair(m1,r1)=ordered_pair(m2,r2)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.40 fof(f17,plain,(
% 0.13/0.40 ~r1=r2),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.40 fof(f22,plain,(
% 0.13/0.40 ![X0,X1,X2]: (~member(X0,ordered_pair(X1,X2))|X0=singleton_set(X1)|X0=unordered_pair(X1,X2))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f15,f14])).
% 0.13/0.40 fof(f23,plain,(
% 0.13/0.40 ![X0,X1]: (member(unordered_pair(X0,X1),ordered_pair(X0,X1)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f15,f12])).
% 0.13/0.40 fof(f24,plain,(
% 0.13/0.40 ![X0,X1]: (member(singleton_set(X0),ordered_pair(X0,X1)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f15,f11])).
% 0.13/0.40 fof(f25,plain,(
% 0.13/0.40 member(singleton_set(m1),ordered_pair(m2,r2))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f16,f24])).
% 0.13/0.40 fof(f27,plain,(
% 0.13/0.40 member(unordered_pair(m1,r1),ordered_pair(m2,r2))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f16,f23])).
% 0.13/0.40 fof(f31,plain,(
% 0.13/0.40 unordered_pair(m1,r1)=singleton_set(m2)|unordered_pair(m1,r1)=unordered_pair(m2,r2)),
% 0.13/0.40 inference(resolution,[status(thm)],[f22,f27])).
% 0.13/0.40 fof(f33,plain,(
% 0.13/0.40 singleton_set(m1)=singleton_set(m2)|singleton_set(m1)=unordered_pair(m2,r2)),
% 0.13/0.40 inference(resolution,[status(thm)],[f22,f25])).
% 0.13/0.40 fof(f35,plain,(
% 0.13/0.40 ![X0]: (~member(X0,ordered_pair(m2,r2))|X0=singleton_set(m1)|X0=unordered_pair(m1,r1))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f16,f22])).
% 0.13/0.40 fof(f36,definition,(
% 0.13/0.40 sQ0_spl <=> (unordered_pair(m1,r1)=singleton_set(m2))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f37,plain,(
% 0.13/0.40 unordered_pair(m1,r1)=singleton_set(m2)|~sQ0_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f36])).
% 0.13/0.40 fof(f39,definition,(
% 0.13/0.40 sQ1_spl <=> (unordered_pair(m1,r1)=unordered_pair(m2,r2))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f40,plain,(
% 0.13/0.40 unordered_pair(m1,r1)=unordered_pair(m2,r2)|~sQ1_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f39])).
% 0.13/0.40 fof(f42,plain,(
% 0.13/0.40 sQ0_spl|sQ1_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f31,f36,f39])).
% 0.13/0.40 fof(f43,definition,(
% 0.13/0.40 sQ2_spl <=> (singleton_set(m1)=singleton_set(m2))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f44,plain,(
% 0.13/0.40 singleton_set(m1)=singleton_set(m2)|~sQ2_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f43])).
% 0.13/0.40 fof(f45,plain,(
% 0.13/0.40 ~singleton_set(m1)=singleton_set(m2)|sQ2_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f43])).
% 0.13/0.40 fof(f46,definition,(
% 0.13/0.40 sQ3_spl <=> (singleton_set(m1)=unordered_pair(m2,r2))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f47,plain,(
% 0.13/0.40 singleton_set(m1)=unordered_pair(m2,r2)|~sQ3_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f46])).
% 0.13/0.40 fof(f49,plain,(
% 0.13/0.40 sQ2_spl|sQ3_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f33,f43,f46])).
% 0.13/0.40 fof(f55,plain,(
% 0.13/0.40 member(m1,singleton_set(m2))|~sQ2_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f44,f9])).
% 0.13/0.40 fof(f56,plain,(
% 0.13/0.40 m1=m2|~sQ2_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f55,f10])).
% 0.13/0.40 fof(f70,plain,(
% 0.13/0.40 ![X0]: (~member(X0,ordered_pair(m2,r2))|X0=singleton_set(m2)|X0=unordered_pair(m1,r1)|~sQ2_spl)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f44,f35])).
% 0.13/0.40 fof(f72,plain,(
% 0.13/0.40 unordered_pair(m2,r2)=singleton_set(m2)|unordered_pair(m2,r2)=unordered_pair(m1,r1)|~sQ2_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f70,f23])).
% 0.13/0.40 fof(f78,definition,(
% 0.13/0.40 sQ5_spl <=> (unordered_pair(m2,r2)=singleton_set(m2))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f79,plain,(
% 0.13/0.40 unordered_pair(m2,r2)=singleton_set(m2)|~sQ5_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f78])).
% 0.13/0.40 fof(f81,plain,(
% 0.13/0.40 sQ5_spl|sQ1_spl|~sQ2_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f72,f78,f39,f43])).
% 0.13/0.40 fof(f91,plain,(
% 0.13/0.40 unordered_pair(m2,r1)=singleton_set(m2)|~sQ2_spl|~sQ0_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f56,f37])).
% 0.13/0.40 fof(f96,plain,(
% 0.13/0.40 member(r1,singleton_set(m2))|~sQ2_spl|~sQ0_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f91,f12])).
% 0.13/0.40 fof(f98,plain,(
% 0.13/0.40 r1=m2|~sQ2_spl|~sQ0_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f96,f10])).
% 0.13/0.40 fof(f100,plain,(
% 0.13/0.40 unordered_pair(m2,m2)=singleton_set(m2)|~sQ2_spl|~sQ0_spl),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f98,f91])).
% 0.13/0.40 fof(f101,plain,(
% 0.13/0.40 ~m2=r2|~sQ2_spl|~sQ0_spl),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f98,f17])).
% 0.13/0.40 fof(f111,plain,(
% 0.13/0.40 unordered_pair(m2,r1)=unordered_pair(m2,r2)|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f56,f40])).
% 0.13/0.40 fof(f112,plain,(
% 0.13/0.40 unordered_pair(m2,m2)=unordered_pair(m2,r2)|~sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f98,f111])).
% 0.13/0.40 fof(f113,plain,(
% 0.13/0.40 singleton_set(m2)=unordered_pair(m2,r2)|~sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f100,f112])).
% 0.13/0.40 fof(f118,plain,(
% 0.13/0.40 member(r2,singleton_set(m2))|~sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f113,f12])).
% 0.13/0.40 fof(f120,plain,(
% 0.13/0.40 r2=m2|~sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f118,f10])).
% 0.13/0.40 fof(f121,plain,(
% 0.13/0.40 $false|~sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f120,f101])).
% 0.13/0.40 fof(f122,plain,(
% 0.13/0.40 ~sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f121])).
% 0.13/0.40 fof(f130,plain,(
% 0.13/0.40 member(r2,singleton_set(m2))|~sQ5_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f79,f12])).
% 0.13/0.40 fof(f132,plain,(
% 0.13/0.40 r2=m2|~sQ5_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f130,f10])).
% 0.13/0.40 fof(f133,plain,(
% 0.13/0.40 $false|~sQ2_spl|~sQ0_spl|~sQ5_spl),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f132,f101])).
% 0.13/0.40 fof(f134,plain,(
% 0.13/0.40 ~sQ2_spl|~sQ0_spl|~sQ5_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f133])).
% 0.13/0.40 fof(f185,plain,(
% 0.13/0.40 member(r1,unordered_pair(m2,r2))|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f111,f12])).
% 0.13/0.40 fof(f192,plain,(
% 0.13/0.40 r1=m2|r1=r2|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f185,f14])).
% 0.13/0.40 fof(f193,definition,(
% 0.13/0.40 sQ7_spl <=> (r1=m2)),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f194,plain,(
% 0.13/0.40 r1=m2|~sQ7_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f193])).
% 0.13/0.40 fof(f196,definition,(
% 0.13/0.40 sQ8_spl <=> (r1=r2)),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f197,plain,(
% 0.13/0.40 r1=r2|~sQ8_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f196])).
% 0.13/0.40 fof(f199,plain,(
% 0.13/0.40 sQ7_spl|sQ8_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f192,f193,f196,f43,f39])).
% 0.13/0.40 fof(f201,plain,(
% 0.13/0.40 unordered_pair(m2,m2)=unordered_pair(m2,r2)|~sQ7_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f194,f111])).
% 0.13/0.40 fof(f203,plain,(
% 0.13/0.40 ~m2=r2|~sQ7_spl),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f194,f17])).
% 0.13/0.40 fof(f216,plain,(
% 0.13/0.40 ![X0]: (~member(X0,unordered_pair(m2,r2))|X0=m2|X0=m2|~sQ7_spl|~sQ2_spl|~sQ1_spl)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f201,f14])).
% 0.13/0.40 fof(f224,plain,(
% 0.13/0.40 ![X0]: (~member(X0,unordered_pair(m2,r2))|X0=m2|~sQ7_spl|~sQ2_spl|~sQ1_spl)),
% 0.13/0.40 inference(duplicate_literals_removal,[status(thm)],[f216])).
% 0.13/0.40 fof(f225,plain,(
% 0.13/0.40 r2=m2|~sQ7_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f224,f12])).
% 0.13/0.40 fof(f227,plain,(
% 0.13/0.40 $false|~sQ7_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f225,f203])).
% 0.13/0.40 fof(f228,plain,(
% 0.13/0.40 ~sQ7_spl|~sQ2_spl|~sQ1_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f227])).
% 0.13/0.40 fof(f229,plain,(
% 0.13/0.40 $false|~sQ8_spl),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f197,f17])).
% 0.13/0.40 fof(f230,plain,(
% 0.13/0.40 ~sQ8_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f229])).
% 0.13/0.40 fof(f237,plain,(
% 0.13/0.40 member(r2,singleton_set(m1))|~sQ3_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f47,f12])).
% 0.13/0.40 fof(f238,plain,(
% 0.13/0.40 member(m2,singleton_set(m1))|~sQ3_spl),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f47,f11])).
% 0.13/0.40 fof(f239,plain,(
% 0.13/0.40 r2=m1|~sQ3_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f237,f10])).
% 0.13/0.40 fof(f242,plain,(
% 0.13/0.40 ~singleton_set(r2)=singleton_set(m2)|~sQ3_spl|sQ2_spl),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f239,f45])).
% 0.13/0.40 fof(f243,plain,(
% 0.13/0.40 member(m2,singleton_set(r2))|~sQ3_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f239,f238])).
% 0.13/0.40 fof(f244,plain,(
% 0.13/0.40 m2=r2|~sQ3_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f243,f10])).
% 0.13/0.40 fof(f265,plain,(
% 0.13/0.40 ~singleton_set(r2)=singleton_set(r2)|~sQ3_spl|sQ2_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f244,f242])).
% 0.13/0.40 fof(f266,plain,(
% 0.13/0.40 $false|~sQ3_spl|sQ2_spl),
% 0.13/0.40 inference(trivial_equality_resolution,[status(thm)],[f265])).
% 0.13/0.40 fof(f267,plain,(
% 0.13/0.40 ~sQ3_spl|sQ2_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f266])).
% 0.13/0.40 fof(f268,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(sat_refutation,[status(thm)],[f42,f49,f81,f122,f134,f199,f228,f230,f267])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.062453 seconds
% 0.13/0.43 % CPU time: 0.158459 seconds
% 0.13/0.43 % Total memory used: 101.731 MB
% 0.13/0.43 % Net memory used: 101.241 MB
%------------------------------------------------------------------------------