%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO007-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 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 12:23:44 PM UTC 2026
% Result : Unsatisfiable 8.95s 1.80s
% Output : CNFRefutation 8.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 117 ( 31 unt; 17 def)
% Number of atoms : 252 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 240 ( 105 ~; 118 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 18 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 102 ( 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z,V] :
( between(X,V,Z)
| between(X,Z,V)
| X = Y
| ~ between(X,Y,V)
| ~ between(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
between(d,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
between(e,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
~ between(d,e,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ between(e,d,a),
file('/export/starexec/sandbox/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(f29,plain,
! [X,Z,V] :
( between(X,V,Z)
| between(X,Z,V)
| ! [Y] :
( X = Y
| ~ between(X,Y,V)
| ~ between(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( between(X0,X3,X2)
| between(X0,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
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(f53,plain,
between(d,a,c),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f54,plain,
between(e,a,c),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f55,plain,
~ between(d,e,a),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f56,plain,
~ between(e,d,a),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f58,plain,
! [X0] :
( between(X0,d,a)
| ~ between(X0,d,c) ),
inference(resolution,[status(thm)],[f28,f53]) ).
fof(f59,plain,
! [X0] :
( between(e,c,X0)
| between(e,X0,c)
| e = a
| ~ between(e,a,X0) ),
inference(resolution,[status(thm)],[f30,f54]) ).
fof(f61,definition,
! [X0] :
( sQ0_spl
<=> ( between(e,c,X0)
| between(e,X0,c)
| ~ between(e,a,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0] :
( ~ sQ0_spl
| between(e,c,X0)
| between(e,X0,c)
| ~ between(e,a,X0) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ1_spl
<=> e = a ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ1_spl
| e = a ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f61,f64]) ).
fof(f76,definition,
( sQ4_spl
<=> between(d,c,c) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( sQ4_spl
| ~ between(d,c,c) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f113,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f44,f33]) ).
fof(f115,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f113,f43]) ).
fof(f125,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(f134,plain,
! [X0,X1,X2] :
( X0 = outer_pasch(X1,X0,X0,X2,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f125,f115]) ).
fof(f139,plain,
! [X0,X1] : X0 = outer_pasch(X1,X0,X0,X1,X1),
inference(resolution,[status(thm)],[f134,f115]) ).
fof(f140,plain,
! [X0,X1] :
( between(X1,X1,X0)
| ~ between(X0,X1,X1)
| ~ between(X0,X1,X1) ),
inference(paramodulation,[status(thm)],[f139,f37]) ).
fof(f142,plain,
! [X0,X1] :
( between(X1,X1,X0)
| ~ between(X0,X1,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f140]) ).
fof(f143,plain,
! [X0,X1] : between(X0,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f142,f115]) ).
fof(f158,plain,
d = outer_pasch(a,d,d,c,c),
inference(resolution,[status(thm)],[f53,f134]) ).
fof(f163,plain,
e = outer_pasch(a,e,e,c,c),
inference(resolution,[status(thm)],[f54,f134]) ).
fof(f164,plain,
! [X0] :
( e = outer_pasch(X0,e,e,c,a)
| ~ between(e,X0,a) ),
inference(resolution,[status(thm)],[f54,f125]) ).
fof(f166,plain,
! [X0] :
( between(X0,e,a)
| ~ between(X0,e,c) ),
inference(resolution,[status(thm)],[f54,f28]) ).
fof(f178,plain,
( between(c,a,d)
| ~ between(d,c,c)
| ~ between(d,a,c) ),
inference(paramodulation,[status(thm)],[f158,f37]) ).
fof(f180,definition,
( sQ9_spl
<=> between(d,a,c) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( sQ9_spl
| ~ between(d,a,c) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
( sQ10_spl
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ10_spl
| between(c,a,d) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ10_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f178,f180,f76,f183]) ).
fof(f191,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f53]) ).
fof(f192,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f193,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f115]) ).
fof(f194,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( ~ sQ0_spl
| between(e,c,c)
| between(e,c,c) ),
inference(resolution,[status(thm)],[f62,f54]) ).
fof(f199,definition,
( sQ12_spl
<=> between(e,c,c) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ0_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f195,f199,f61]) ).
fof(f203,definition,
( sQ13_spl
<=> between(e,a,c) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ13_spl
| ~ between(e,a,c) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f229,plain,
( ~ sQ1_spl
| ~ between(d,e,e) ),
inference(backward_demodulation,[status(thm)],[f65,f55]) ).
fof(f235,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f115]) ).
fof(f236,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f240,plain,
! [X0] :
( ~ sQ10_spl
| between(c,d,X0)
| between(c,X0,d)
| c = a
| ~ between(c,a,X0) ),
inference(resolution,[status(thm)],[f184,f30]) ).
fof(f242,definition,
( sQ17_spl
<=> c = a ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ17_spl
| c = a ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f249,definition,
! [X0] :
( sQ19_spl
<=> ( between(c,d,X0)
| between(c,X0,d)
| ~ between(c,a,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f250,plain,
! [X0] :
( ~ sQ19_spl
| between(c,d,X0)
| between(c,X0,d)
| ~ between(c,a,X0) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,plain,
( ~ sQ10_spl
| sQ17_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f240,f249,f242,f183]) ).
fof(f253,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f52]) ).
fof(f254,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f277,plain,
( between(c,a,e)
| ~ between(e,c,c)
| ~ between(e,a,c) ),
inference(paramodulation,[status(thm)],[f163,f37]) ).
fof(f279,definition,
( sQ20_spl
<=> between(c,a,e) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ20_spl
| between(c,a,e) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( sQ20_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f277,f203,f199,f279]) ).
fof(f287,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f54]) ).
fof(f288,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f325,definition,
( sQ24_spl
<=> between(c,d,d) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ24_spl
| ~ between(c,d,d) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f333,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f115]) ).
fof(f334,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f373,definition,
( sQ32_spl
<=> between(c,e,e) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f517,plain,
e = outer_pasch(e,e,e,c,a),
inference(resolution,[status(thm)],[f164,f143]) ).
fof(f520,plain,
( between(c,e,e)
| ~ between(e,a,c)
| ~ between(e,e,a) ),
inference(paramodulation,[status(thm)],[f517,f37]) ).
fof(f522,definition,
( sQ42_spl
<=> between(e,e,a) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ42_spl
| ~ between(e,e,a) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f529,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f520,f522,f203,f373]) ).
fof(f531,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f143]) ).
fof(f532,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f963,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| between(c,d,e)
| between(c,e,d) ),
inference(resolution,[status(thm)],[f250,f280]) ).
fof(f970,definition,
( sQ65_spl
<=> between(c,e,d) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f971,plain,
( ~ sQ65_spl
| between(c,e,d) ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f973,definition,
( sQ66_spl
<=> between(c,d,e) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f974,plain,
( ~ sQ66_spl
| between(c,d,e) ),
inference(component_clause,[status(thm)],[f973]) ).
fof(f976,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| sQ66_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f963,f970,f973,f249,f279]) ).
fof(f989,plain,
( ~ sQ65_spl
| c = outer_pasch(e,c,c,d,d) ),
inference(resolution,[status(thm)],[f971,f134]) ).
fof(f1108,plain,
( ~ sQ66_spl
| c = outer_pasch(d,c,c,e,e) ),
inference(resolution,[status(thm)],[f974,f134]) ).
fof(f1521,plain,
( ~ sQ66_spl
| between(e,d,c)
| ~ between(c,e,e)
| ~ between(c,d,e) ),
inference(paramodulation,[status(thm)],[f1108,f37]) ).
fof(f1527,definition,
( sQ87_spl
<=> between(e,d,c) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1528,plain,
( ~ sQ87_spl
| between(e,d,c) ),
inference(component_clause,[status(thm)],[f1527]) ).
fof(f1530,plain,
( sQ87_spl
| ~ sQ32_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f1521,f973,f373,f1527]) ).
fof(f1667,plain,
( ~ sQ65_spl
| between(d,e,c)
| ~ between(c,d,d)
| ~ between(c,e,d) ),
inference(paramodulation,[status(thm)],[f989,f37]) ).
fof(f1673,definition,
( sQ91_spl
<=> between(d,e,c) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1674,plain,
( ~ sQ91_spl
| between(d,e,c) ),
inference(component_clause,[status(thm)],[f1673]) ).
fof(f1676,plain,
( sQ91_spl
| ~ sQ24_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f1667,f970,f325,f1673]) ).
fof(f1678,plain,
( ~ sQ91_spl
| between(d,e,a) ),
inference(resolution,[status(thm)],[f1674,f166]) ).
fof(f1694,plain,
( ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1678,f55]) ).
fof(f1695,plain,
~ sQ91_spl,
inference(contradiction_clause,[status(thm)],[f1694]) ).
fof(f1696,plain,
( ~ sQ87_spl
| between(e,d,a) ),
inference(resolution,[status(thm)],[f1528,f58]) ).
fof(f1712,plain,
( ~ sQ87_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1696,f56]) ).
fof(f1713,plain,
~ sQ87_spl,
inference(contradiction_clause,[status(thm)],[f1712]) ).
fof(f1714,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f186,f192,f194,f202,f236,f252,f254,f282,f288,f334,f529,f532,f976,f1530,f1676,f1695,f1713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO007-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 08:15:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 8.95/1.80 % Refutation found
% 8.95/1.80 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.95/1.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.95/1.82 % Elapsed time: 1.444983 seconds
% 8.95/1.82 % CPU time: 11.195014 seconds
% 8.95/1.82 % Total memory used: 126.273 MB
% 8.95/1.82 % Net memory used: 118.095 MB
%------------------------------------------------------------------------------