%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 01:16:32 PM UTC 2026
% Result : Unsatisfiable 18.76s 2.87s
% Output : Proof 18.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 42 unt; 0 def)
% Number of atoms : 58 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 28 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity4) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t22,plain,
ifeq(colinear(X1,X2,X3),true,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t56,plain,
ifeq(colinear(X1,X2,X3),true,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(f15,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f15_nnf,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t7,plain,
between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t183,plain,
between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t191,plain,
true = ifeq(colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,or(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),false)),true),
inference(cp,[status(thm)],[t56,t183]) ).
cnf(f22,negated_conjecture,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
fof(f22_nnf,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(t8,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t124,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t222,plain,
true = ifeq(true,true,or(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),false)),true),
inference(step,[status(thm)],[t191,t124]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t223,plain,
true = or(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),false)),
inference(step,[status(thm)],[t222,t33]) ).
cnf(f13,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f13_nnf,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t5,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t129,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t224,plain,
true = or(false,or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),false)),
inference(step,[status(thm)],[t223,t129]) ).
cnf(t3,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t38,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t225,plain,
true = or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),false),
inference(step,[status(thm)],[t224,t38]) ).
cnf(t1,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t37,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t226,plain,
true = between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(step,[status(thm)],[t225,t37]) ).
cnf(f14,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f14_nnf,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t6,plain,
between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t156,plain,
between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t227,plain,
true = false,
inference(step,[status(thm)],[t226,t156]) ).
cnf(t210,plain,
false = true,
inference(orient,[status(thm)],[t227]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13,c14,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t210]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 10:19:13 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 18.76/2.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.76/2.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------