%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO065-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:16:52 PM UTC 2026
% Result : Unsatisfiable 8.54s 11.89s
% Output : Proof 8.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 94 ( 74 unt; 0 def)
% Number of atoms : 122 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 46 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-5 aty)
% Number of variables : 184 ( 18 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,axiom,
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity2) ).
fof(f19_nnf,plain,
! [Y,Z,X] :
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Y,Z,X] :
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t23,plain,
ifeq(between(X1,X2,X3),true,colinear(X3,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t46,plain,
ifeq(between(X1,X2,X3),true,colinear(X3,X1,X2),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(f7,axiom,
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/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(t26,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(t42,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)],[t26]) ).
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(t14,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t36,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/sandbox2/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(t27,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(t41,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)],[t27]) ).
cnf(f22,hypothesis,
between(u,w,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_v) ).
fof(f22_nnf,plain,
between(u,w,v),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
between(u,w,v),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(t8,plain,
between(u,w,v) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t86,plain,
between(u,w,v) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t91,plain,
true = ifeq(between(X1,X2,v),true,ifeq(true,true,between(w,inner_pasch(X1,X2,v,w,u),X1),true),true),
inference(cp,[status(thm)],[t41,t86]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t649,plain,
true = ifeq(between(X1,X2,v),true,between(w,inner_pasch(X1,X2,v,w,u),X1),true),
inference(step,[status(thm)],[t91,t35]) ).
cnf(t522,plain,
ifeq(between(X1,X2,v),true,between(w,inner_pasch(X1,X2,v,w,u),X1),true) = true,
inference(orient,[status(thm)],[t649]) ).
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(t13,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t60,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/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(t20,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t37,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/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(t19,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t128,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t129,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t37,t128]) ).
cnf(t605,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t129,t35]) ).
cnf(t249,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t605]) ).
cnf(t251,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t60,t249]) ).
cnf(t252,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t251]) ).
cnf(t523,plain,
true = ifeq(true,true,between(w,inner_pasch(X1,v,v,w,u),X1),true),
inference(cp,[status(thm)],[t522,t252]) ).
cnf(t650,plain,
true = between(w,inner_pasch(X1,v,v,w,u),X1),
inference(step,[status(thm)],[t523,t35]) ).
cnf(t524,plain,
between(w,inner_pasch(X1,v,v,w,u),X1) = true,
inference(orient,[status(thm)],[t650]) ).
cnf(t525,plain,
inner_pasch(w,v,v,w,u) = ifeq(true,true,w,inner_pasch(w,v,v,w,u)),
inference(cp,[status(thm)],[t36,t524]) ).
cnf(t651,plain,
inner_pasch(w,v,v,w,u) = w,
inference(step,[status(thm)],[t525,t35]) ).
cnf(t553,plain,
inner_pasch(w,v,v,w,u) = w,
inference(orient,[status(thm)],[t651]) ).
cnf(t554,plain,
true = ifeq(between(w,v,v),true,ifeq(between(u,w,v),true,between(v,w,u),true),true),
inference(cp,[status(thm)],[t42,t553]) ).
cnf(t652,plain,
true = ifeq(true,true,ifeq(between(u,w,v),true,between(v,w,u),true),true),
inference(step,[status(thm)],[t554,t252]) ).
cnf(t653,plain,
true = ifeq(between(u,w,v),true,between(v,w,u),true),
inference(step,[status(thm)],[t652,t35]) ).
cnf(t654,plain,
true = ifeq(true,true,between(v,w,u),true),
inference(step,[status(thm)],[t653,t86]) ).
cnf(t655,plain,
true = between(v,w,u),
inference(step,[status(thm)],[t654,t35]) ).
cnf(t555,plain,
between(v,w,u) = true,
inference(orient,[status(thm)],[t655]) ).
cnf(t558,plain,
true = ifeq(true,true,colinear(u,v,w),true),
inference(cp,[status(thm)],[t46,t555]) ).
cnf(t658,plain,
true = colinear(u,v,w),
inference(step,[status(thm)],[t558,t35]) ).
cnf(f23,negated_conjecture,
~ colinear(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_uvw_colinear) ).
fof(f23_nnf,plain,
~ colinear(u,v,w),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
~ colinear(u,v,w),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
~ colinear(u,v,w),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t9,plain,
colinear(u,v,w) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t234,plain,
colinear(u,v,w) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t659,plain,
true = false,
inference(step,[status(thm)],[t658,t234]) ).
cnf(t581,plain,
false = true,
inference(orient,[status(thm)],[t659]) ).
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,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t581]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO065-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.58 % Computer : n019.cluster.edu
% 0.09/10.58 % Model : x86_64 x86_64
% 0.09/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.58 % Memory : 8046.5625MB
% 0.09/10.58 % OS : Linux 6.8.0-71-generic
% 0.09/10.58 % CPULimit : 300
% 0.09/10.58 % WCLimit : 300
% 0.09/10.58 % DateTime : Wed Sep 23 10:40:18 UTC 2026
% 0.09/10.58 % CPUTime :
% 0.09/10.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.54/11.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.54/11.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------