%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.10s 0.52s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 67 ( 19 unt; 9 def)
% Number of atoms : 131 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 119 ( 55 ~; 55 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,V,Z] :
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X,Y,Z] :
( between(X,Y,Z)
| ! [V] :
( ~ between(Y,Z,V)
| ~ between(X,Y,V) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f32,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f44,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
a != c,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f55,plain,
between(a,c,d),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f56,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f57,definition,
( sQ0_spl
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f60,definition,
( sQ1_spl
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ1_spl
| between(a,d,c) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f57,f60]) ).
fof(f64,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f65,plain,
( c = a
| ~ between(c,a,d) ),
inference(resolution,[status(thm)],[f64,f55]) ).
fof(f68,definition,
( sQ2_spl
<=> c = a ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ2_spl
| c = a ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f57,f68]) ).
fof(f72,definition,
( sQ3_spl
<=> between(a,c,d) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( sQ3_spl
| ~ between(a,c,d) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f76,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f52]) ).
fof(f77,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f130,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f44,f33]) ).
fof(f132,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f130,f43]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( X0 = outer_pasch(X1,X0,X0,X3,X2)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f36,f26]) ).
fof(f296,definition,
( sQ15_spl
<=> between(a,d,d) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ15_spl
| ~ between(a,d,d) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f315,definition,
( sQ18_spl
<=> c = d ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( ~ sQ18_spl
| c = d ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f326,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f54]) ).
fof(f327,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f426,plain,
! [X0,X1,X2] :
( X0 = outer_pasch(X1,X0,X0,X2,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f148,f132]) ).
fof(f429,plain,
( ~ sQ1_spl
| a = outer_pasch(d,a,a,c,c) ),
inference(resolution,[status(thm)],[f426,f61]) ).
fof(f430,plain,
a = outer_pasch(c,a,a,d,d),
inference(resolution,[status(thm)],[f426,f55]) ).
fof(f516,plain,
( ~ sQ1_spl
| between(c,d,a)
| ~ between(a,c,c)
| ~ between(a,d,c) ),
inference(paramodulation,[status(thm)],[f429,f37]) ).
fof(f518,definition,
( sQ31_spl
<=> between(a,c,c) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ31_spl
| ~ between(a,c,c) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f525,definition,
( sQ33_spl
<=> between(c,d,a) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ33_spl
| between(c,d,a) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( sQ33_spl
| ~ sQ31_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f516,f60,f518,f525]) ).
fof(f530,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f132]) ).
fof(f531,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f541,plain,
( ~ sQ33_spl
| d = c
| ~ between(d,c,a) ),
inference(resolution,[status(thm)],[f526,f64]) ).
fof(f554,definition,
( sQ37_spl
<=> between(d,c,a) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( ~ sQ33_spl
| sQ18_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f541,f554,f315,f525]) ).
fof(f645,plain,
( between(d,c,a)
| ~ between(a,d,d)
| ~ between(a,c,d) ),
inference(paramodulation,[status(thm)],[f430,f37]) ).
fof(f651,plain,
( sQ37_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f645,f72,f296,f554]) ).
fof(f653,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f55]) ).
fof(f654,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f653]) ).
fof(f655,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f132]) ).
fof(f656,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f657,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f71,f77,f327,f528,f531,f557,f651,f654,f656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 08:18:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.52 % Refutation found
% 0.10/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.52 % Elapsed time: 0.149522 seconds
% 0.10/0.52 % CPU time: 0.879918 seconds
% 0.10/0.52 % Total memory used: 90.123 MB
% 0.10/0.52 % Net memory used: 88.727 MB
%------------------------------------------------------------------------------