%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO039-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 6.01s 1.25s
% Output : Proof 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 12 ( 4 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f46,negated_conjecture,
~ between(v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary) ).
fof(f46_nnf,plain,
~ between(v,w,x),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
~ between(v,w,x),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
~ between(v,w,x),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t11,plain,
between(v,w,x) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t70,plain,
between(v,w,x) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t57,axiom,
sF0 = between(v,w,x),
introduced(definition) ).
cnf(t118,plain,
sF0 = false,
inference(step,[status(thm)],[t57,t70]) ).
cnf(t71,plain,
false = sF0,
inference(orient,[status(thm)],[t118]) ).
cnf(t127,plain,
between(v,w,x) = sF0,
inference(step,[status(thm)],[t70,t71]) ).
cnf(t80,plain,
between(v,w,x) = sF0,
inference(orient,[status(thm)],[t127]) ).
cnf(t99,plain,
between(v,x,x) = sF0,
inference(rw,[status(thm)],[t80]) ).
cnf(f43,axiom,
between(U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
fof(f43_nnf,plain,
! [U,V] : between(U,V,V),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [U,V] : between(U,V,V),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
between(X0,X1,X1),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t6,plain,
between(X1,X2,X2) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t65,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t132,plain,
true = sF0,
inference(step,[status(thm)],[t99,t65]) ).
cnf(t100,plain,
true = sF0,
inference(orient,[status(thm)],[t132]) ).
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,c46]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t100]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t71]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 10:34:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.01/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.01/1.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------