%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:25:31 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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
% 0.09/0.36 % DateTime : Sun Sep 20 08:15:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.48 fof(f3,axiom,(
% 0.13/0.48 (![X,Y,Z]: (( ~ equidistant(X,Y,Z,Z)| X = Y ) ))),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f4,axiom,(
% 0.13/0.48 (![X,Y,W,V]: (between(X,Y,extension(X,Y,W,V)) ))),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f5,axiom,(
% 0.13/0.48 (![Y,X,W,V]: (equidistant(Y,extension(X,Y,W,V),W,V) ))),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f7,axiom,(
% 0.13/0.48 (![X,Y]: (( ~ between(X,Y,X)| X = Y ) ))),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f8,axiom,(
% 0.13/0.48 (![U,V,W,Y,X]: (( ~ between(U,V,W)| ~ between(Y,X,W)| between(V,inner_pasch(U,V,W,X,Y),Y) ) ))),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f9,axiom,(
% 0.13/0.48 (![U,V,W,Y,X]: (( ~ between(U,V,W)| ~ between(Y,X,W)| between(X,inner_pasch(U,V,W,X,Y),U) ) ))),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f19,hypothesis,(
% 0.13/0.48 a != c ),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f21,hypothesis,(
% 0.13/0.48 c != d ),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f22,hypothesis,(
% 0.13/0.48 between(a,c,d) ),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f23,negated_conjecture,(
% 0.13/0.48 ( between(c,a,d)| between(a,d,c) ) ),
% 0.13/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.48 fof(f27,plain,(
% 0.13/0.48 ![X,Y]: ((![Z]: ~equidistant(X,Y,Z,Z))|X=Y)),
% 0.13/0.48 inference(miniscoping,[status(thm)],[f3])).
% 0.13/0.48 fof(f28,plain,(
% 0.13/0.48 ![X0,X1,X2]: (~equidistant(X0,X1,X2,X2)|X0=X1)),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.48 fof(f29,plain,(
% 0.13/0.48 ![X0,X1,X2,X3]: (between(X0,X1,extension(X0,X1,X2,X3)))),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.48 fof(f30,plain,(
% 0.13/0.48 ![X0,X1,X2,X3]: (equidistant(X0,extension(X1,X0,X2,X3),X2,X3))),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.48 fof(f33,plain,(
% 0.13/0.48 ![X0,X1]: (~between(X0,X1,X0)|X0=X1)),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.48 fof(f34,plain,(
% 0.13/0.48 ![X0,X1,X2,X3,X4]: (~between(X0,X1,X2)|~between(X3,X4,X2)|between(X1,inner_pasch(X0,X1,X2,X4,X3),X3))),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.48 fof(f35,plain,(
% 0.13/0.48 ![X0,X1,X2,X3,X4]: (~between(X0,X1,X2)|~between(X3,X4,X2)|between(X4,inner_pasch(X0,X1,X2,X4,X3),X0))),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f9])).
% 0.13/0.48 fof(f46,plain,(
% 0.13/0.48 ~a=c),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.48 fof(f48,plain,(
% 0.13/0.48 ~c=d),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f21])).
% 0.13/0.48 fof(f49,plain,(
% 0.13/0.48 between(a,c,d)),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f22])).
% 0.13/0.48 fof(f50,plain,(
% 0.13/0.48 between(c,a,d)|between(a,d,c)),
% 0.13/0.48 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.48 fof(f51,definition,(
% 0.13/0.48 sQ0_spl <=> (between(c,a,d))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f52,plain,(
% 0.13/0.48 between(c,a,d)|~sQ0_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f51])).
% 0.13/0.48 fof(f54,definition,(
% 0.13/0.48 sQ1_spl <=> (between(a,d,c))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f55,plain,(
% 0.13/0.48 between(a,d,c)|~sQ1_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f54])).
% 0.13/0.48 fof(f57,plain,(
% 0.13/0.48 sQ0_spl|sQ1_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f50,f51,f54])).
% 0.13/0.48 fof(f59,plain,(
% 0.13/0.48 ![X0,X1,X2]: (X0=extension(X1,X0,X2,X2))),
% 0.13/0.48 inference(resolution,[status(thm)],[f30,f28])).
% 0.13/0.48 fof(f63,plain,(
% 0.13/0.48 ![X0,X1]: (between(X0,X1,X1))),
% 0.13/0.48 inference(paramodulation,[status(thm)],[f59,f29])).
% 0.13/0.48 fof(f86,plain,(
% 0.13/0.48 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|~between(X1,X3,X2)|X1=inner_pasch(X0,X1,X2,X3,X1))),
% 0.13/0.48 inference(resolution,[status(thm)],[f34,f33])).
% 0.13/0.48 fof(f87,plain,(
% 0.13/0.48 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|~between(X3,X0,X2)|X0=inner_pasch(X0,X1,X2,X0,X3))),
% 0.13/0.48 inference(resolution,[status(thm)],[f35,f33])).
% 0.13/0.48 fof(f104,plain,(
% 0.13/0.48 ![X0]: (~between(X0,c,d)|c=inner_pasch(X0,c,d,a,c)|~sQ0_spl)),
% 0.13/0.48 inference(resolution,[status(thm)],[f86,f52])).
% 0.13/0.48 fof(f109,plain,(
% 0.13/0.48 ![X0,X1,X2]: (~between(X0,X1,X2)|X1=inner_pasch(X0,X1,X2,X2,X1))),
% 0.13/0.48 inference(resolution,[status(thm)],[f86,f63])).
% 0.13/0.48 fof(f110,plain,(
% 0.13/0.48 c=inner_pasch(a,c,d,a,c)|~sQ0_spl),
% 0.13/0.48 inference(resolution,[status(thm)],[f104,f49])).
% 0.13/0.48 fof(f111,plain,(
% 0.13/0.48 ~between(a,c,d)|~between(c,a,d)|between(a,c,a)|~sQ0_spl),
% 0.13/0.48 inference(paramodulation,[status(thm)],[f110,f35])).
% 0.13/0.48 fof(f113,definition,(
% 0.13/0.48 sQ2_spl <=> (between(a,c,d))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f115,plain,(
% 0.13/0.48 ~between(a,c,d)|sQ2_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f113])).
% 0.13/0.48 fof(f116,definition,(
% 0.13/0.48 sQ3_spl <=> (between(a,c,a))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f117,plain,(
% 0.13/0.48 between(a,c,a)|~sQ3_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f116])).
% 0.13/0.48 fof(f119,plain,(
% 0.13/0.48 ~sQ2_spl|~sQ0_spl|sQ3_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f111,f113,f51,f116])).
% 0.13/0.48 fof(f124,plain,(
% 0.13/0.48 $false|sQ2_spl),
% 0.13/0.48 inference(forward_subsumption_resolution,[status(thm)],[f115,f49])).
% 0.13/0.48 fof(f125,plain,(
% 0.13/0.48 sQ2_spl),
% 0.13/0.48 inference(contradiction_clause,[status(thm)],[f124])).
% 0.13/0.48 fof(f127,plain,(
% 0.13/0.48 d=inner_pasch(a,d,c,c,d)|~sQ1_spl),
% 0.13/0.48 inference(resolution,[status(thm)],[f109,f55])).
% 0.13/0.48 fof(f128,plain,(
% 0.13/0.48 c=inner_pasch(a,c,d,d,c)),
% 0.13/0.48 inference(resolution,[status(thm)],[f109,f49])).
% 0.13/0.48 fof(f237,plain,(
% 0.13/0.48 ~between(a,d,c)|~between(d,c,c)|between(c,d,a)|~sQ1_spl),
% 0.13/0.48 inference(paramodulation,[status(thm)],[f127,f35])).
% 0.13/0.48 fof(f239,definition,(
% 0.13/0.48 sQ5_spl <=> (between(d,c,c))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f241,plain,(
% 0.13/0.48 ~between(d,c,c)|sQ5_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f239])).
% 0.13/0.48 fof(f242,definition,(
% 0.13/0.48 sQ6_spl <=> (between(c,d,a))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f243,plain,(
% 0.13/0.48 between(c,d,a)|~sQ6_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f242])).
% 0.13/0.48 fof(f245,plain,(
% 0.13/0.48 ~sQ1_spl|~sQ5_spl|sQ6_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f237,f54,f239,f242])).
% 0.13/0.48 fof(f250,plain,(
% 0.13/0.48 $false|sQ5_spl),
% 0.13/0.48 inference(forward_subsumption_resolution,[status(thm)],[f241,f63])).
% 0.13/0.48 fof(f251,plain,(
% 0.13/0.48 sQ5_spl),
% 0.13/0.48 inference(contradiction_clause,[status(thm)],[f250])).
% 0.13/0.48 fof(f257,plain,(
% 0.13/0.48 ![X0]: (~between(d,X0,a)|d=inner_pasch(d,X0,a,d,c)|~sQ6_spl)),
% 0.13/0.48 inference(resolution,[status(thm)],[f243,f87])).
% 0.13/0.48 fof(f261,plain,(
% 0.13/0.48 ~between(a,c,d)|~between(c,d,d)|between(d,c,a)),
% 0.13/0.48 inference(paramodulation,[status(thm)],[f128,f35])).
% 0.13/0.48 fof(f263,definition,(
% 0.13/0.48 sQ8_spl <=> (between(c,d,d))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f265,plain,(
% 0.13/0.48 ~between(c,d,d)|sQ8_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f263])).
% 0.13/0.48 fof(f266,definition,(
% 0.13/0.48 sQ9_spl <=> (between(d,c,a))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f267,plain,(
% 0.13/0.48 between(d,c,a)|~sQ9_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f266])).
% 0.13/0.48 fof(f269,plain,(
% 0.13/0.48 ~sQ2_spl|~sQ8_spl|sQ9_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f261,f113,f263,f266])).
% 0.13/0.48 fof(f271,plain,(
% 0.13/0.48 $false|sQ8_spl),
% 0.13/0.48 inference(forward_subsumption_resolution,[status(thm)],[f265,f63])).
% 0.13/0.48 fof(f272,plain,(
% 0.13/0.48 sQ8_spl),
% 0.13/0.48 inference(contradiction_clause,[status(thm)],[f271])).
% 0.13/0.48 fof(f480,plain,(
% 0.13/0.48 d=inner_pasch(d,c,a,d,c)|~sQ6_spl|~sQ9_spl),
% 0.13/0.48 inference(resolution,[status(thm)],[f257,f267])).
% 0.13/0.48 fof(f486,plain,(
% 0.13/0.48 ~between(d,c,a)|~between(c,d,a)|between(c,d,c)|~sQ6_spl|~sQ9_spl),
% 0.13/0.48 inference(paramodulation,[status(thm)],[f480,f34])).
% 0.13/0.48 fof(f488,definition,(
% 0.13/0.48 sQ19_spl <=> (between(c,d,c))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f489,plain,(
% 0.13/0.48 between(c,d,c)|~sQ19_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f488])).
% 0.13/0.48 fof(f491,plain,(
% 0.13/0.48 ~sQ9_spl|~sQ6_spl|sQ19_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f486,f266,f242,f488])).
% 0.13/0.48 fof(f507,plain,(
% 0.13/0.48 a=c|~sQ3_spl),
% 0.13/0.48 inference(resolution,[status(thm)],[f117,f33])).
% 0.13/0.48 fof(f509,plain,(
% 0.13/0.48 $false|~sQ3_spl),
% 0.13/0.48 inference(forward_subsumption_resolution,[status(thm)],[f507,f46])).
% 0.13/0.48 fof(f510,plain,(
% 0.13/0.48 ~sQ3_spl),
% 0.13/0.48 inference(contradiction_clause,[status(thm)],[f509])).
% 0.13/0.49 fof(f526,plain,(
% 0.13/0.49 c=d|~sQ19_spl),
% 0.13/0.49 inference(resolution,[status(thm)],[f489,f33])).
% 0.13/0.49 fof(f528,plain,(
% 0.13/0.49 $false|~sQ19_spl),
% 0.13/0.49 inference(forward_subsumption_resolution,[status(thm)],[f526,f48])).
% 0.13/0.49 fof(f529,plain,(
% 0.13/0.49 ~sQ19_spl),
% 0.13/0.49 inference(contradiction_clause,[status(thm)],[f528])).
% 0.13/0.49 fof(f530,plain,(
% 0.13/0.49 $false),
% 0.13/0.49 inference(sat_refutation,[status(thm)],[f57,f119,f125,f245,f251,f269,f272,f491,f510,f529])).
% 0.13/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.50 % Elapsed time: 0.135723 seconds
% 0.13/0.50 % CPU time: 0.720194 seconds
% 0.13/0.50 % Total memory used: 89.027 MB
% 0.13/0.50 % Net memory used: 87.965 MB
%------------------------------------------------------------------------------