%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO002-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:16:27 PM UTC 2026
% Result : Unsatisfiable 14.99s 2.39s
% Output : Proof 14.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 68 unt; 0 def)
% Number of atoms : 108 ( 51 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 : 10 ( 10 usr; 7 con; 0-5 aty)
% Number of variables : 209 ( 29 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
fof(f20_nnf,plain,
~ between(a,a,b),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ between(a,a,b),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ between(a,a,b),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t5,plain,
between(a,a,b) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t208,plain,
between(a,a,b) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(f7,axiom,
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).
fof(f7_nnf,plain,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t23,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X3,X5),true,between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t39,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X3,X5),true,between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)),true),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(f12,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f12_nnf,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t12,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t38,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(f4,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t19,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t34,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(f13,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f13_nnf,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t18,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t98,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t99,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t34,t98]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t629,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t99,t32]) ).
cnf(t236,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t629]) ).
cnf(t238,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t38,t236]) ).
cnf(t239,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t238]) ).
cnf(t243,plain,
true = ifeq(true,true,ifeq(between(X1,X2,X3),true,between(X3,X2,outer_pasch(X2,X4,X1,X3,X2)),true),true),
inference(cp,[status(thm)],[t39,t239]) ).
cnf(t657,plain,
true = ifeq(between(X1,X2,X3),true,between(X3,X2,outer_pasch(X2,X4,X1,X3,X2)),true),
inference(step,[status(thm)],[t243,t32]) ).
cnf(t476,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,outer_pasch(X2,X4,X1,X3,X2)),true) = true,
inference(orient,[status(thm)],[t657]) ).
cnf(t477,plain,
true = ifeq(true,true,between(X1,X1,outer_pasch(X1,X2,X3,X1,X1)),true),
inference(cp,[status(thm)],[t476,t239]) ).
cnf(t658,plain,
true = between(X1,X1,outer_pasch(X1,X2,X3,X1,X1)),
inference(step,[status(thm)],[t477,t32]) ).
cnf(t483,plain,
between(X1,X1,outer_pasch(X1,X2,X3,X1,X1)) = true,
inference(orient,[status(thm)],[t658]) ).
cnf(f0,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f0_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t13,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t33,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(f6,axiom,
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).
fof(f6_nnf,plain,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t22,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X3,X5),true,between(X1,outer_pasch(X2,X1,X4,X5,X3),X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t42,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X3,X5),true,between(X1,outer_pasch(X2,X1,X4,X5,X3),X4),true),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t245,plain,
true = ifeq(true,true,ifeq(between(X1,X2,X3),true,between(X4,outer_pasch(X2,X4,X1,X3,X2),X1),true),true),
inference(cp,[status(thm)],[t42,t239]) ).
cnf(t661,plain,
true = ifeq(between(X1,X2,X3),true,between(X4,outer_pasch(X2,X4,X1,X3,X2),X1),true),
inference(step,[status(thm)],[t245,t32]) ).
cnf(t520,plain,
ifeq(between(X1,X2,X3),true,between(X4,outer_pasch(X2,X4,X1,X3,X2),X1),true) = true,
inference(orient,[status(thm)],[t661]) ).
cnf(t521,plain,
true = ifeq(true,true,between(X1,outer_pasch(X2,X1,X3,X2,X2),X3),true),
inference(cp,[status(thm)],[t520,t239]) ).
cnf(t662,plain,
true = between(X1,outer_pasch(X2,X1,X3,X2,X2),X3),
inference(step,[status(thm)],[t521,t32]) ).
cnf(t528,plain,
between(X1,outer_pasch(X2,X1,X3,X2,X2),X3) = true,
inference(orient,[status(thm)],[t662]) ).
cnf(t529,plain,
outer_pasch(X1,X2,X2,X1,X1) = ifeq(true,true,X2,outer_pasch(X1,X2,X2,X1,X1)),
inference(cp,[status(thm)],[t33,t528]) ).
cnf(t663,plain,
outer_pasch(X1,X2,X2,X1,X1) = X2,
inference(step,[status(thm)],[t529,t32]) ).
cnf(t562,plain,
outer_pasch(X1,X2,X2,X1,X1) = X2,
inference(orient,[status(thm)],[t663]) ).
cnf(t563,plain,
true = between(X1,X1,X2),
inference(cp,[status(thm)],[t483,t562]) ).
cnf(t577,plain,
between(X1,X1,X2) = true,
inference(orient,[status(thm)],[t563]) ).
cnf(t665,plain,
true = false,
inference(step,[status(thm)],[t208,t577]) ).
cnf(t599,plain,
true = false,
inference(rw,[status(thm)],[t665]) ).
cnf(t602,plain,
false = true,
inference(orient,[status(thm)],[t599]) ).
cnf(f14,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f14_nnf,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f15,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f15_nnf,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f16,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f16_nnf,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c15,c16,c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t602]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO002-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 10:18:20 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.99/2.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.99/2.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------