%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:16:25 PM UTC 2026
% Result : Unsatisfiable 13.69s 2.26s
% Output : Proof 13.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 69 unt; 0 def)
% Number of atoms : 109 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 42 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-5 aty)
% Number of variables : 166 ( 18 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f7_nnf,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t22,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t38,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(f6,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/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(t14,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(f8,axiom,
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f8_nnf,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t23,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t37,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(f18,hypothesis,
between(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_between_a_and_c) ).
fof(f18_nnf,plain,
between(a,b,c),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
between(a,b,c),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t5,plain,
between(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t72,plain,
between(a,b,c) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t74,plain,
true = ifeq(between(X1,X2,c),true,ifeq(true,true,between(b,inner_pasch(X1,X2,c,b,a),X1),true),true),
inference(cp,[status(thm)],[t37,t72]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t562,plain,
true = ifeq(between(X1,X2,c),true,between(b,inner_pasch(X1,X2,c,b,a),X1),true),
inference(step,[status(thm)],[t74,t31]) ).
cnf(t493,plain,
ifeq(between(X1,X2,c),true,between(b,inner_pasch(X1,X2,c,b,a),X1),true) = true,
inference(orient,[status(thm)],[t562]) ).
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(t13,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t52,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t13]) ).
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(t33,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(t108,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t109,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t33,t108]) ).
cnf(t538,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t109,t31]) ).
cnf(t217,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t538]) ).
cnf(t219,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t52,t217]) ).
cnf(t220,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t219]) ).
cnf(t494,plain,
true = ifeq(true,true,between(b,inner_pasch(X1,c,c,b,a),X1),true),
inference(cp,[status(thm)],[t493,t220]) ).
cnf(t563,plain,
true = between(b,inner_pasch(X1,c,c,b,a),X1),
inference(step,[status(thm)],[t494,t31]) ).
cnf(t497,plain,
between(b,inner_pasch(X1,c,c,b,a),X1) = true,
inference(orient,[status(thm)],[t563]) ).
cnf(t498,plain,
inner_pasch(b,c,c,b,a) = ifeq(true,true,b,inner_pasch(b,c,c,b,a)),
inference(cp,[status(thm)],[t32,t497]) ).
cnf(t564,plain,
inner_pasch(b,c,c,b,a) = b,
inference(step,[status(thm)],[t498,t31]) ).
cnf(t521,plain,
inner_pasch(b,c,c,b,a) = b,
inference(orient,[status(thm)],[t564]) ).
cnf(t522,plain,
true = ifeq(between(b,c,c),true,ifeq(between(a,b,c),true,between(c,b,a),true),true),
inference(cp,[status(thm)],[t38,t521]) ).
cnf(t565,plain,
true = ifeq(true,true,ifeq(between(a,b,c),true,between(c,b,a),true),true),
inference(step,[status(thm)],[t522,t220]) ).
cnf(t566,plain,
true = ifeq(between(a,b,c),true,between(c,b,a),true),
inference(step,[status(thm)],[t565,t31]) ).
cnf(t567,plain,
true = ifeq(true,true,between(c,b,a),true),
inference(step,[status(thm)],[t566,t72]) ).
cnf(t568,plain,
true = between(c,b,a),
inference(step,[status(thm)],[t567,t31]) ).
cnf(f19,negated_conjecture,
~ between(c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_c_and_a) ).
fof(f19_nnf,plain,
~ between(c,b,a),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ between(c,b,a),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ between(c,b,a),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t6,plain,
between(c,b,a) = false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t196,plain,
between(c,b,a) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t569,plain,
true = false,
inference(step,[status(thm)],[t568,t196]) ).
cnf(t523,plain,
false = true,
inference(orient,[status(thm)],[t569]) ).
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,c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t523]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.46 % Computer : n003.cluster.edu
% 0.10/0.46 % Model : x86_64 x86_64
% 0.10/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.46 % Memory : 8046.5625MB
% 0.10/0.46 % OS : Linux 6.8.0-71-generic
% 0.10/0.46 % CPULimit : 300
% 0.10/0.46 % WCLimit : 300
% 0.10/0.46 % DateTime : Wed Sep 23 10:18:49 UTC 2026
% 0.10/0.46 % CPUTime :
% 0.10/0.46 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.69/2.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.69/2.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------