%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO068-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:23:58 PM UTC 2026
% Result : Unsatisfiable 164.34s 21.03s
% Output : CNFRefutation 164.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 106 ( 26 unt; 16 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 257 ( 116 ~; 125 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 17 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U,V,W,X] :
( equidistant(V,U,X,W)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U,V] : equidistant(U,U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U,V,U1,V1,W,W1] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U,V] : between(U,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U,V,U1,V1,W,W1,X,X1] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U,V,U1,V1,W,W1] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [U,W,V] :
( colinear(U,V,W)
| ~ between(U,W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [V,U,W] :
( colinear(U,V,W)
| ~ between(V,U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,hypothesis,
colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,negated_conjecture,
~ colinear(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f128,plain,
! [X0,X1,X2] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f131,plain,
! [X0,X1,X2] :
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f152,plain,
! [X0,X1] : equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f153,plain,
! [U,U1,W,W1] :
( equidistant(U,W,U1,W1)
| ! [V1] :
( ~ between(U1,V1,W1)
| ! [V] :
( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X0,X4,X2,X5)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f166,plain,
! [X0,X1,X2] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f167,plain,
! [X0,X1] : between(X0,X0,X1),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f201,plain,
! [V,V1,X,X1] :
( equidistant(V,X,V1,X1)
| ! [U1,W1] :
( ~ between(U1,V1,W1)
| ! [U,W] :
( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f202,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( equidistant(X1,X6,X3,X7)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f212,plain,
! [U1,V1,W1] :
( between(U1,V1,W1)
| ! [U,V,W] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f213,plain,
! [X0,X1,X2,X3,X4,X5] :
( between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f229,plain,
! [X0,X1,X2] :
( colinear(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f230,plain,
! [X0,X1,X2] :
( colinear(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f242,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f243,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f244,plain,
equidistant(u,w,u1,w1),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f245,plain,
colinear(u,v,w),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f246,plain,
~ colinear(u1,v1,w1),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f359,plain,
( between(w,u,v)
| between(v,w,u)
| between(u,v,w) ),
inference(resolution,[status(thm)],[f245,f131]) ).
fof(f365,definition,
( sQ0_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f368,definition,
( sQ1_spl
<=> between(v,w,u) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( ~ sQ1_spl
| between(v,w,u) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,definition,
( sQ2_spl
<=> between(w,u,v) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ2_spl
| between(w,u,v) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f359,f365,f368,f371]) ).
fof(f437,definition,
( sQ3_spl
<=> between(v,u,w) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f440,definition,
( sQ4_spl
<=> between(u,w,v) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f490,definition,
( sQ6_spl
<=> equidistant(v,v,v1,v1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ6_spl
| ~ equidistant(v,v,v1,v1) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,definition,
( sQ7_spl
<=> between(v,v,w) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ7_spl
| ~ between(v,v,w) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ8_spl
<=> between(v1,v1,w1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ8_spl
| ~ between(v1,v1,w1) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f502,definition,
( sQ10_spl
<=> equidistant(w,w,w1,w1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ10_spl
| ~ equidistant(w,w,w1,w1) ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f552,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f167]) ).
fof(f553,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f554,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f167]) ).
fof(f555,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f660,definition,
( sQ22_spl
<=> equidistant(w,v,w1,v1) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f705,definition,
( sQ29_spl
<=> between(w,w,v) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f707,plain,
( sQ29_spl
| ~ between(w,w,v) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f717,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f167]) ).
fof(f718,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f717]) ).
fof(f757,definition,
( sQ39_spl
<=> equidistant(v,w,v1,w1) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f931,definition,
( sQ57_spl
<=> between(w1,w1,v1) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( sQ57_spl
| ~ between(w1,w1,v1) ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f937,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f933,f167]) ).
fof(f938,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f937]) ).
fof(f1363,plain,
( ~ sQ1_spl
| between(u,w,v) ),
inference(resolution,[status(thm)],[f369,f166]) ).
fof(f1391,plain,
( ~ sQ2_spl
| between(v,u,w) ),
inference(resolution,[status(thm)],[f372,f166]) ).
fof(f1460,plain,
equidistant(w,v,w1,v1),
inference(resolution,[status(thm)],[f138,f243]) ).
fof(f1796,plain,
! [X0,X1] :
( equidistant(X0,w,X1,w1)
| ~ between(X1,v1,w1)
| ~ between(X0,v,w)
| ~ equidistant(X0,v,X1,v1) ),
inference(resolution,[status(thm)],[f154,f243]) ).
fof(f2256,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1363,f440,f368]) ).
fof(f2277,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f152]) ).
fof(f2278,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f2277]) ).
fof(f2996,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f152]) ).
fof(f2997,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f2996]) ).
fof(f3339,plain,
( equidistant(w,v,w1,v1)
| ~ between(w1,w1,v1)
| ~ between(w,w,v)
| ~ equidistant(v,v,v1,v1)
| ~ equidistant(w,w,w1,w1) ),
inference(resolution,[status(thm)],[f1460,f202]) ).
fof(f3367,plain,
( sQ22_spl
| ~ sQ57_spl
| ~ sQ29_spl
| ~ sQ6_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3339,f502,f490,f705,f931,f660]) ).
fof(f4424,plain,
! [X0,X1] :
( between(X1,u1,w1)
| ~ between(X0,u,w)
| ~ equidistant(X0,w,X1,w1)
| ~ equidistant(X0,u,X1,u1) ),
inference(resolution,[status(thm)],[f213,f244]) ).
fof(f4486,plain,
! [X0,X1] :
( between(u1,X1,w1)
| ~ between(u,X0,w)
| ~ equidistant(X0,w,X1,w1)
| ~ equidistant(u,X0,u1,X1) ),
inference(resolution,[status(thm)],[f213,f244]) ).
fof(f4488,plain,
! [X0,X1] :
( between(u1,X1,v1)
| ~ between(u,X0,v)
| ~ equidistant(X0,v,X1,v1)
| ~ equidistant(u,X0,u1,X1) ),
inference(resolution,[status(thm)],[f213,f242]) ).
fof(f6385,plain,
equidistant(v,u,v1,u1),
inference(resolution,[status(thm)],[f242,f138]) ).
fof(f15095,plain,
( equidistant(v,w,v1,w1)
| ~ between(v1,v1,w1)
| ~ between(v,v,w) ),
inference(resolution,[status(thm)],[f1796,f152]) ).
fof(f15104,definition,
( sQ633_spl
<=> between(u1,v1,w1) ),
introduced(definition,[new_symbols(definition,[sQ633_spl])],[split_symbol_definition]) ).
fof(f15105,plain,
( ~ sQ633_spl
| between(u1,v1,w1) ),
inference(component_clause,[status(thm)],[f15104]) ).
fof(f15120,plain,
( sQ39_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f15095,f493,f496,f757]) ).
fof(f15136,definition,
( sQ637_spl
<=> between(v1,u1,w1) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f15137,plain,
( ~ sQ637_spl
| between(v1,u1,w1) ),
inference(component_clause,[status(thm)],[f15136]) ).
fof(f16508,definition,
( sQ698_spl
<=> between(u1,w1,v1) ),
introduced(definition,[new_symbols(definition,[sQ698_spl])],[split_symbol_definition]) ).
fof(f16509,plain,
( ~ sQ698_spl
| between(u1,w1,v1) ),
inference(component_clause,[status(thm)],[f16508]) ).
fof(f23195,plain,
( between(v1,u1,w1)
| ~ between(v,u,w)
| ~ equidistant(v,w,v1,w1) ),
inference(resolution,[status(thm)],[f4424,f6385]) ).
fof(f23211,plain,
( sQ637_spl
| ~ sQ3_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f23195,f757,f437,f15136]) ).
fof(f23522,plain,
( between(u1,w1,v1)
| ~ between(u,w,v)
| ~ equidistant(w,v,w1,v1) ),
inference(resolution,[status(thm)],[f4488,f244]) ).
fof(f23544,plain,
( sQ698_spl
| ~ sQ4_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f23522,f660,f440,f16508]) ).
fof(f23577,plain,
( ~ sQ633_spl
| colinear(u1,v1,w1) ),
inference(resolution,[status(thm)],[f15105,f128]) ).
fof(f23602,plain,
( ~ sQ633_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23577,f246]) ).
fof(f23603,plain,
~ sQ633_spl,
inference(contradiction_clause,[status(thm)],[f23602]) ).
fof(f23607,plain,
( ~ sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1391,f437,f371]) ).
fof(f23800,plain,
( between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1) ),
inference(resolution,[status(thm)],[f4486,f242]) ).
fof(f23822,plain,
( sQ633_spl
| ~ sQ0_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f23800,f757,f365,f15104]) ).
fof(f24069,plain,
( ~ sQ637_spl
| colinear(u1,v1,w1) ),
inference(resolution,[status(thm)],[f15137,f230]) ).
fof(f24104,plain,
( ~ sQ637_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24069,f246]) ).
fof(f24105,plain,
~ sQ637_spl,
inference(contradiction_clause,[status(thm)],[f24104]) ).
fof(f24817,plain,
( ~ sQ698_spl
| colinear(u1,v1,w1) ),
inference(resolution,[status(thm)],[f16509,f229]) ).
fof(f24846,plain,
( ~ sQ698_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24817,f246]) ).
fof(f24847,plain,
~ sQ698_spl,
inference(contradiction_clause,[status(thm)],[f24846]) ).
fof(f24848,plain,
$false,
inference(sat_refutation,[status(thm)],[f374,f553,f555,f718,f938,f2256,f2278,f2997,f3367,f15120,f23211,f23544,f23603,f23607,f23822,f24105,f24847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO068-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 20 09:31:24 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.32 % Drodi V4.1.1
% 164.34/21.03 % Refutation found
% 164.34/21.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 164.34/21.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 164.34/21.07 % Elapsed time: 20.745820 seconds
% 164.34/21.07 % CPU time: 164.834319 seconds
% 164.34/21.07 % Total memory used: 375.310 MB
% 164.34/21.07 % Net memory used: 322.706 MB
%------------------------------------------------------------------------------