%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:16:29 PM UTC 2026
% Result : Unsatisfiable 12.65s 2.12s
% Output : Proof 12.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 45 unt; 0 def)
% Number of atoms : 53 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 22 ~; 4 |; 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 : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 85 ( 18 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f18,negated_conjecture,
~ between(a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_a_and_b) ).
fof(f18_nnf,plain,
~ between(a,b,b),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ between(a,b,b),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ between(a,b,b),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t5,plain,
between(a,b,b) = false,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t175,plain,
between(a,b,b) = false,
inference(orient,[status(thm)],[t5]) ).
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(t12,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t51,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t12]) ).
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(t19,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t32,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(orient,[status(thm)],[t19]) ).
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(t18,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t87,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t88,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t32,t87]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t233,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t88,t30]) ).
cnf(t196,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t233]) ).
cnf(t198,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t51,t196]) ).
cnf(t199,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t198]) ).
cnf(t234,plain,
true = false,
inference(step,[status(thm)],[t175,t199]) ).
cnf(t219,plain,
true = false,
inference(rw,[status(thm)],[t234]) ).
cnf(t220,plain,
false = true,
inference(orient,[status(thm)],[t219]) ).
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,c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t220]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n018.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 : Wed Sep 23 10:19:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.65/2.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.65/2.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------