%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:23:43 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 19 unt; 9 def)
% Number of atoms : 142 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 62 ~; 62 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f46,plain,
a != c,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f49,plain,
between(a,c,d),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f50,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f51,definition,
( sQ0_spl
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ0_spl
| between(c,a,d) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ1_spl
| between(a,d,c) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f51,f54]) ).
fof(f59,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f61,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f59,f29]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( X1 = inner_pasch(X0,X1,X2,X3,X1)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f33]) ).
fof(f87,plain,
! [X0] :
( a = inner_pasch(X0,a,d,c,a)
| ~ between(X0,a,d) ),
inference(resolution,[status(thm)],[f86,f49]) ).
fof(f91,plain,
! [X0,X1,X2] :
( X1 = inner_pasch(X0,X1,X2,X2,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f86,f61]) ).
fof(f92,plain,
c = inner_pasch(a,c,d,d,c),
inference(resolution,[status(thm)],[f91,f49]) ).
fof(f99,definition,
( sQ2_spl
<=> between(a,c,d) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ2_spl
| ~ between(a,c,d) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ3_spl
<=> between(c,d,d) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( sQ3_spl
| ~ between(c,d,d) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f119,plain,
( ~ sQ1_spl
| d = inner_pasch(a,d,c,c,d) ),
inference(resolution,[status(thm)],[f55,f91]) ).
fof(f124,plain,
( between(d,c,a)
| ~ between(c,d,d)
| ~ between(a,c,d) ),
inference(paramodulation,[status(thm)],[f92,f35]) ).
fof(f126,definition,
( sQ7_spl
<=> between(d,c,a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ7_spl
| between(d,c,a) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f124,f99,f102,f126]) ).
fof(f131,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f61]) ).
fof(f132,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f49]) ).
fof(f134,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f152,plain,
( ~ sQ1_spl
| between(c,d,a)
| ~ between(d,c,c)
| ~ between(a,d,c) ),
inference(paramodulation,[status(thm)],[f119,f35]) ).
fof(f154,definition,
( sQ8_spl
<=> between(d,c,c) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ8_spl
| ~ between(d,c,c) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
( sQ9_spl
<=> between(c,d,a) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ9_spl
| between(c,d,a) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f152,f54,f154,f157]) ).
fof(f165,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f61]) ).
fof(f166,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f177,plain,
! [X0] :
( ~ sQ9_spl
| c = inner_pasch(X0,c,a,d,c)
| ~ between(X0,c,a) ),
inference(resolution,[status(thm)],[f158,f86]) ).
fof(f359,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| c = inner_pasch(d,c,a,d,c) ),
inference(resolution,[status(thm)],[f177,f127]) ).
fof(f361,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| between(d,c,d)
| ~ between(c,d,a)
| ~ between(d,c,a) ),
inference(paramodulation,[status(thm)],[f359,f35]) ).
fof(f363,definition,
( sQ20_spl
<=> between(d,c,d) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( ~ sQ20_spl
| between(d,c,d) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f361,f126,f157,f363]) ).
fof(f373,plain,
( ~ sQ0_spl
| a = inner_pasch(c,a,d,c,a) ),
inference(resolution,[status(thm)],[f52,f87]) ).
fof(f402,plain,
( ~ sQ0_spl
| between(c,a,c)
| ~ between(a,c,d)
| ~ between(c,a,d) ),
inference(paramodulation,[status(thm)],[f373,f35]) ).
fof(f404,definition,
( sQ22_spl
<=> between(c,a,c) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ22_spl
| between(c,a,c) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f402,f51,f99,f404]) ).
fof(f415,plain,
( ~ sQ22_spl
| c = a ),
inference(resolution,[status(thm)],[f405,f33]) ).
fof(f417,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f46]) ).
fof(f418,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f430,plain,
( ~ sQ20_spl
| d = c ),
inference(resolution,[status(thm)],[f364,f33]) ).
fof(f432,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f48]) ).
fof(f433,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f434,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f129,f132,f134,f160,f166,f366,f407,f418,f433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 08:15:53 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.47 % Elapsed time: 0.105011 seconds
% 0.15/0.47 % CPU time: 0.544623 seconds
% 0.15/0.47 % Total memory used: 84.820 MB
% 0.15/0.47 % Net memory used: 83.977 MB
%------------------------------------------------------------------------------