%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:16:41 PM UTC 2026
% Result : Unsatisfiable 7.01s 1.42s
% Output : Proof 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 66 unt; 0 def)
% Number of atoms : 82 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 26 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 97 ( 18 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,negated_conjecture,
~ between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary) ).
fof(f20_nnf,plain,
~ between(v,w,x),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ between(v,w,x),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ between(v,w,x),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t10,plain,
between(v,w,x) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t197,plain,
between(v,w,x) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(f6,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f6_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t15,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t33,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(f18,hypothesis,
between(u,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
fof(f18_nnf,plain,
between(u,w,x),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
between(u,w,x),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t9,plain,
between(u,w,x) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t73,plain,
between(u,w,x) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f19,hypothesis,
u = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_x) ).
fof(f19_nnf,plain,
u = x,
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
u = x,
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t0,plain,
x = u,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t218,plain,
u = x,
inference(orient,[status(thm)],[t0]) ).
cnf(t321,plain,
between(x,w,x) = true,
inference(step,[status(thm)],[t73,t218]) ).
cnf(t219,plain,
between(x,w,x) = true,
inference(rw,[status(thm)],[t321]) ).
cnf(t220,plain,
between(x,w,x) = true,
inference(orient,[status(thm)],[t219]) ).
cnf(t221,plain,
w = ifeq(true,true,x,w),
inference(cp,[status(thm)],[t33,t220]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t322,plain,
w = x,
inference(step,[status(thm)],[t221,t32]) ).
cnf(t241,plain,
w = x,
inference(orient,[status(thm)],[t322]) ).
cnf(t324,plain,
between(v,x,x) = false,
inference(step,[status(thm)],[t197,t241]) ).
cnf(t243,plain,
between(v,x,x) = false,
inference(rw,[status(thm)],[t324]) ).
cnf(t264,plain,
between(v,x,x) = false,
inference(orient,[status(thm)],[t243]) ).
cnf(f3,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/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(t53,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/sandbox2/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(t21,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t34,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(f4,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/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(t20,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t109,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t110,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t34,t109]) ).
cnf(t325,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t110,t32]) ).
cnf(t284,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t325]) ).
cnf(t286,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t53,t284]) ).
cnf(t287,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t286]) ).
cnf(t326,plain,
true = false,
inference(step,[status(thm)],[t264,t287]) ).
cnf(t307,plain,
true = false,
inference(rw,[status(thm)],[t326]) ).
cnf(t308,plain,
false = true,
inference(orient,[status(thm)],[t307]) ).
cnf(f9,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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,c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t308]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:33:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.01/1.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.01/1.42 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------