%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 01:16:55 PM UTC 2026
% Result : Unsatisfiable 9.04s 2.40s
% Output : Proof 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 14
% Syntax : Number of formulae : 105 ( 81 unt; 0 def)
% Number of atoms : 145 ( 68 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 98 ( 58 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 159 ( 27 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f23,negated_conjecture,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_2) ).
fof(f23_nnf,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t29,plain,
or(not(colinear(x,x,y)),or(not(colinear(x,y,x)),or(not(colinear(y,x,x)),not(colinear(x,z,y))))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t124,plain,
or(not(colinear(x,x,y)),or(not(colinear(x,y,x)),or(not(colinear(y,x,x)),not(colinear(x,z,y))))) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(f18,axiom,
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
fof(f18_nnf,plain,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t21,plain,
ifeq(between(X1,X2,X3),true,colinear(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t51,plain,
ifeq(between(X1,X2,X3),true,colinear(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f3,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f3_nnf,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t14,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t63,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f2,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t20,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t40,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(f4,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f4_nnf,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t19,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t105,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t106,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t40,t105]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t38,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t2857,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t106,t38]) ).
cnf(t217,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t2857]) ).
cnf(t219,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t63,t217]) ).
cnf(t220,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t219]) ).
cnf(t221,plain,
true = ifeq(true,true,colinear(X1,X2,X2),true),
inference(cp,[status(thm)],[t51,t220]) ).
cnf(t2858,plain,
true = colinear(X1,X2,X2),
inference(step,[status(thm)],[t221,t38]) ).
cnf(t246,plain,
colinear(X1,X2,X2) = true,
inference(orient,[status(thm)],[t2858]) ).
cnf(t2861,plain,
or(not(colinear(x,x,y)),or(not(colinear(x,y,x)),or(not(true),not(colinear(x,z,y))))) = true,
inference(step,[status(thm)],[t124,t246]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t215,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t2862,plain,
or(not(colinear(x,x,y)),or(not(colinear(x,y,x)),or(false,not(colinear(x,z,y))))) = true,
inference(step,[status(thm)],[t2861,t215]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t43,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t2863,plain,
or(not(colinear(x,x,y)),or(not(colinear(x,y,x)),not(colinear(x,z,y)))) = true,
inference(step,[status(thm)],[t2862,t43]) ).
cnf(t250,plain,
or(not(colinear(x,x,y)),or(not(colinear(x,y,x)),not(colinear(x,z,y)))) = true,
inference(rw,[status(thm)],[t2863]) ).
cnf(f20,axiom,
( colinear(X,Y,Z)
| ~ between(Z,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).
fof(f20_nnf,plain,
! [Z,X,Y] :
( colinear(X,Y,Z)
| ~ between(Z,X,Y) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Z,X,Y] :
( colinear(X,Y,Z)
| ~ between(Z,X,Y) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t22,plain,
ifeq(between(X1,X2,X3),true,colinear(X2,X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t50,plain,
ifeq(between(X1,X2,X3),true,colinear(X2,X3,X1),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t222,plain,
true = ifeq(true,true,colinear(X1,X1,X2),true),
inference(cp,[status(thm)],[t50,t220]) ).
cnf(t2866,plain,
true = colinear(X1,X1,X2),
inference(step,[status(thm)],[t222,t38]) ).
cnf(t252,plain,
colinear(X1,X1,X2) = true,
inference(orient,[status(thm)],[t2866]) ).
cnf(t3144,plain,
or(not(true),or(not(colinear(x,y,x)),not(colinear(x,z,y)))) = true,
inference(step,[status(thm)],[t250,t252]) ).
cnf(t3145,plain,
or(false,or(not(colinear(x,y,x)),not(colinear(x,z,y)))) = true,
inference(step,[status(thm)],[t3144,t215]) ).
cnf(t3146,plain,
or(not(colinear(x,y,x)),not(colinear(x,z,y))) = true,
inference(step,[status(thm)],[t3145,t43]) ).
cnf(f19,axiom,
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).
fof(f19_nnf,plain,
! [Y,Z,X] :
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Y,Z,X] :
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t23,plain,
ifeq(between(X1,X2,X3),true,colinear(X3,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t49,plain,
ifeq(between(X1,X2,X3),true,colinear(X3,X1,X2),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t223,plain,
true = ifeq(true,true,colinear(X1,X2,X1),true),
inference(cp,[status(thm)],[t49,t220]) ).
cnf(t2867,plain,
true = colinear(X1,X2,X1),
inference(step,[status(thm)],[t223,t38]) ).
cnf(t255,plain,
colinear(X1,X2,X1) = true,
inference(orient,[status(thm)],[t2867]) ).
cnf(t3147,plain,
or(not(true),not(colinear(x,z,y))) = true,
inference(step,[status(thm)],[t3146,t255]) ).
cnf(t3148,plain,
or(false,not(colinear(x,z,y))) = true,
inference(step,[status(thm)],[t3147,t215]) ).
cnf(t3149,plain,
not(colinear(x,z,y)) = true,
inference(step,[status(thm)],[t3148,t43]) ).
cnf(f22,negated_conjecture,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_1) ).
fof(f22_nnf,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t26,plain,
ifeq(colinear(x,x,y),true,ifeq(colinear(x,y,x),true,ifeq(colinear(y,x,x),true,x,y),y),y) = y,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t132,plain,
ifeq(colinear(x,x,y),true,ifeq(colinear(x,y,x),true,ifeq(colinear(y,x,x),true,x,y),y),y) = y,
inference(orient,[status(thm)],[t26]) ).
cnf(t2859,plain,
ifeq(colinear(x,x,y),true,ifeq(colinear(x,y,x),true,ifeq(true,true,x,y),y),y) = y,
inference(step,[status(thm)],[t132,t246]) ).
cnf(t2860,plain,
ifeq(colinear(x,x,y),true,ifeq(colinear(x,y,x),true,x,y),y) = y,
inference(step,[status(thm)],[t2859,t38]) ).
cnf(t249,plain,
ifeq(colinear(x,x,y),true,ifeq(colinear(x,y,x),true,x,y),y) = y,
inference(rw,[status(thm)],[t2860]) ).
cnf(t2899,plain,
ifeq(true,true,ifeq(colinear(x,y,x),true,x,y),y) = y,
inference(step,[status(thm)],[t249,t252]) ).
cnf(t2900,plain,
ifeq(colinear(x,y,x),true,x,y) = y,
inference(step,[status(thm)],[t2899,t38]) ).
cnf(t2901,plain,
ifeq(true,true,x,y) = y,
inference(step,[status(thm)],[t2900,t255]) ).
cnf(t2902,plain,
x = y,
inference(step,[status(thm)],[t2901,t38]) ).
cnf(t428,plain,
x = y,
inference(orient,[status(thm)],[t2902]) ).
cnf(t3150,plain,
not(colinear(y,z,y)) = true,
inference(step,[status(thm)],[t3149,t428]) ).
cnf(t3151,plain,
not(true) = true,
inference(step,[status(thm)],[t3150,t255]) ).
cnf(t3152,plain,
false = true,
inference(step,[status(thm)],[t3151,t215]) ).
cnf(t2812,plain,
false = true,
inference(orient,[status(thm)],[t3152]) ).
cnf(f9,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f9_nnf,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f10,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f10_nnf,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f11,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f11_nnf,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2812]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:38:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.04/2.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.04/2.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------