%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO011-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 : Fri Sep 25 01:16:30 PM UTC 2026
% Result : Unsatisfiable 36.49s 5.14s
% Output : Proof 36.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 27 unt; 0 def)
% Number of atoms : 124 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 104 ( 42 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 121 ( 11 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,axiom,
( between(X,Z,Y)
| between(Y,X,Z)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
fof(f20_nnf,plain,
! [X,Y,Z] :
( between(X,Z,Y)
| between(Y,X,Z)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y,Z] :
( between(X,Z,Y)
| between(Y,X,Z)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( between(X0,X2,X1)
| between(X1,X0,X2)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f24,negated_conjecture,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
fof(f24_nnf,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p163,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[c20,c24]) ).
cnf(f6,axiom,
( 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',outer_pasch1) ).
fof(f6_nnf,plain,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f13,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f13_nnf,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(f4,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p25,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c13,c4]) ).
cnf(f12,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f12_nnf,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p28,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[p25,c12]) ).
cnf(p43,plain,
( between(X3,outer_pasch(X1,X3,X0,X2,X1),X0)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c6,p28]) ).
cnf(p170,plain,
( between(X0,outer_pasch(lower_dimension_point_1,X0,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p163,p43]) ).
cnf(f0,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f0_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p185,plain,
( lower_dimension_point_2 = outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p170,c0]) ).
cnf(f7,axiom,
( 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',outer_pasch2) ).
fof(f7_nnf,plain,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p50,plain,
( between(X2,X1,outer_pasch(X1,X3,X0,X2,X1))
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,p28]) ).
cnf(p174,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,outer_pasch(lower_dimension_point_1,X0,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1))
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p163,p50]) ).
cnf(p213,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(superposition,[status(thm)],[p185,p174]) ).
cnf(p869,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(factoring,[status(thm)],[p213]) ).
cnf(p871,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(factoring,[status(thm)],[p869]) ).
cnf(f16,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f16_nnf,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p872,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p871,c16]) ).
cnf(p906,plain,
( between(X0,outer_pasch(lower_dimension_point_3,X0,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p872,p43]) ).
cnf(p932,plain,
( lower_dimension_point_1 = outer_pasch(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p906,c0]) ).
cnf(p910,plain,
( between(lower_dimension_point_2,lower_dimension_point_3,outer_pasch(lower_dimension_point_3,X0,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3))
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[p872,p50]) ).
cnf(p980,plain,
( between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(superposition,[status(thm)],[p932,p910]) ).
cnf(p1093,plain,
( between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(factoring,[status(thm)],[p980]) ).
cnf(f15,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f15_nnf,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p1094,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(resolution,[status(thm)],[p1093,c15]) ).
cnf(f14,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f14_nnf,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p1095,plain,
$false,
inference(resolution,[status(thm)],[p1094,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO011-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 10:20:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.49/5.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.49/5.14 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------