%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO064-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 01:16:51 PM UTC 2026
% Result : Unsatisfiable 6.72s 1.33s
% Output : Proof 6.72s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t102,axiom,
sF1 = ifeq(colinear(u,v,w),true,false,true),
introduced(definition) ).
cnf(f88,negated_conjecture,
~ colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_uvw_colinear) ).
fof(f88_nnf,plain,
~ colinear(u,v,w),
inference(nnf_transformation,[status(thm)],[f88]) ).
fof(f88_sk,plain,
~ colinear(u,v,w),
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c88,plain,
~ colinear(u,v,w),
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
cnf(t14,plain,
colinear(u,v,w) = false,
inference(equality_encoding,[status(esa)],[c88]) ).
cnf(t117,plain,
colinear(u,v,w) = false,
inference(orient,[status(thm)],[t14]) ).
cnf(t101,axiom,
sF0 = colinear(u,v,w),
introduced(definition) ).
cnf(t271,plain,
sF0 = false,
inference(step,[status(thm)],[t101,t117]) ).
cnf(t118,plain,
false = sF0,
inference(orient,[status(thm)],[t271]) ).
cnf(t286,plain,
colinear(u,v,w) = sF0,
inference(step,[status(thm)],[t117,t118]) ).
cnf(t133,plain,
colinear(u,v,w) = sF0,
inference(orient,[status(thm)],[t286]) ).
cnf(t296,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t102,t133]) ).
cnf(t297,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t296,t118]) ).
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(t30,plain,
ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t10,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t113,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t280,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(step,[status(thm)],[t113,t118]) ).
cnf(t127,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(orient,[status(thm)],[t280]) ).
cnf(t294,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t30,t127]) ).
cnf(t295,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t294,t118]) ).
cnf(t160,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t295]) ).
cnf(t298,plain,
sF1 = true,
inference(step,[status(thm)],[t297,t160]) ).
cnf(t161,plain,
true = sF1,
inference(orient,[status(thm)],[t298]) ).
cnf(f18,axiom,
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
fof(f18_nnf,plain,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t40,plain,
ifeq(between(X1,X2,X3),true,colinear(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t337,plain,
ifeq(between(X1,X2,X3),sF1,colinear(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t40,t161]) ).
cnf(t338,plain,
ifeq(between(X1,X2,X3),sF1,colinear(X1,X2,X3),sF1) = true,
inference(step,[status(thm)],[t337,t161]) ).
cnf(t339,plain,
ifeq(between(X1,X2,X3),sF1,colinear(X1,X2,X3),sF1) = sF1,
inference(step,[status(thm)],[t338,t161]) ).
cnf(t222,plain,
ifeq(between(X1,X2,X3),sF1,colinear(X1,X2,X3),sF1) = sF1,
inference(orient,[status(thm)],[t339]) ).
cnf(t229,plain,
sF1 = ifeq(between(u,v,w),sF1,sF0,sF1),
inference(cp,[status(thm)],[t222,t133]) ).
cnf(f50,axiom,
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f50_nnf,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c50,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t39,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t333,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),true) = true,
inference(step,[status(thm)],[t39,t161]) ).
cnf(t334,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = true,
inference(step,[status(thm)],[t333,t161]) ).
cnf(t335,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(step,[status(thm)],[t334,t161]) ).
cnf(t209,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(orient,[status(thm)],[t335]) ).
cnf(f87,hypothesis,
between(w,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_w_and_u) ).
fof(f87_nnf,plain,
between(w,v,u),
inference(nnf_transformation,[status(thm)],[f87]) ).
cnf(c87,plain,
between(w,v,u),
inference(cnf_transformation,[status(esa)],[f87_nnf]) ).
cnf(t13,plain,
between(w,v,u) = true,
inference(equality_encoding,[status(esa)],[c87]) ).
cnf(t116,plain,
between(w,v,u) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t305,plain,
between(w,v,u) = sF1,
inference(step,[status(thm)],[t116,t161]) ).
cnf(t170,plain,
between(w,v,u) = sF1,
inference(orient,[status(thm)],[t305]) ).
cnf(t216,plain,
sF1 = ifeq(sF1,sF1,between(u,v,w),sF1),
inference(cp,[status(thm)],[t209,t170]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t143,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t336,plain,
sF1 = between(u,v,w),
inference(step,[status(thm)],[t216,t143]) ).
cnf(t220,plain,
between(u,v,w) = sF1,
inference(orient,[status(thm)],[t336]) ).
cnf(t340,plain,
sF1 = ifeq(sF1,sF1,sF0,sF1),
inference(step,[status(thm)],[t229,t220]) ).
cnf(t341,plain,
sF1 = sF0,
inference(step,[status(thm)],[t340,t143]) ).
cnf(t231,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t341]) ).
cnf(t358,plain,
true = sF0,
inference(step,[status(thm)],[t161,t231]) ).
cnf(t248,plain,
true = sF0,
inference(orient,[status(thm)],[t358]) ).
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(f62,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
fof(f62_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(f63,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
fof(f63_nnf,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(f64,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
fof(f64_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(f65,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
fof(f65_nnf,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
X0 != extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c62,c63,c64,c65,c88]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t248]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t118]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO064-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:37:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.72/1.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/1.33 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------