%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO011-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:16:31 PM UTC 2026
% Result : Unsatisfiable 5.97s 1.31s
% Output : Proof 5.97s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t107,axiom,
sF0 = colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
introduced(definition) ).
cnf(f95,negated_conjecture,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
fof(f95_nnf,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f95]) ).
cnf(c95,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f95_nnf]) ).
cnf(t13,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = true,
inference(equality_encoding,[status(esa)],[c95]) ).
cnf(t121,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t766,plain,
sF0 = true,
inference(step,[status(thm)],[t107,t121]) ).
cnf(t122,plain,
true = sF0,
inference(orient,[status(thm)],[t766]) ).
cnf(f21,axiom,
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity4) ).
fof(f21_nnf,plain,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t73,plain,
ifeq(colinear(X1,X2,X3),true,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t1005,plain,
ifeq(colinear(X1,X2,X3),sF0,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),true) = true,
inference(step,[status(thm)],[t73,t122]) ).
cnf(t1006,plain,
ifeq(colinear(X1,X2,X3),sF0,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),sF0) = true,
inference(step,[status(thm)],[t1005,t122]) ).
cnf(t1007,plain,
ifeq(colinear(X1,X2,X3),sF0,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),sF0) = sF0,
inference(step,[status(thm)],[t1006,t122]) ).
cnf(t669,plain,
ifeq(colinear(X1,X2,X3),sF0,or(between(X1,X2,X3),or(between(X2,X3,X1),between(X3,X1,X2))),sF0) = sF0,
inference(orient,[status(thm)],[t1007]) ).
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(t10,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t118,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t670,plain,
sF0 = ifeq(colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),sF0,or(false,or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2))),sF0),
inference(cp,[status(thm)],[t669,t118]) ).
cnf(t773,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(step,[status(thm)],[t121,t122]) ).
cnf(t131,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(orient,[status(thm)],[t773]) ).
cnf(t1008,plain,
sF0 = ifeq(sF0,sF0,or(false,or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2))),sF0),
inference(step,[status(thm)],[t670,t131]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t141,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t1009,plain,
sF0 = or(false,or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2))),
inference(step,[status(thm)],[t1008,t141]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t114,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t1010,plain,
sF0 = or(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)),
inference(step,[status(thm)],[t1009,t114]) ).
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(t11,plain,
between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = false,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t119,plain,
between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t1011,plain,
sF0 = or(false,between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)),
inference(step,[status(thm)],[t1010,t119]) ).
cnf(t1012,plain,
sF0 = between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(step,[status(thm)],[t1011,t114]) ).
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(t12,plain,
between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) = false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t120,plain,
between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t1013,plain,
sF0 = false,
inference(step,[status(thm)],[t1012,t120]) ).
cnf(t674,plain,
false = sF0,
inference(orient,[status(thm)],[t1013]) ).
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]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t122]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t674]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO011-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 10:19:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.97/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.97/1.31 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------