%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO013-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 01:16:33 PM UTC 2026
% Result : Unsatisfiable 109.85s 16.98s
% Output : Proof 109.85s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t125,axiom,
sF1 = ifeq(colinear(d1,d2,d3),true,false,true),
introduced(definition) ).
cnf(f109,negated_conjecture,
~ colinear(d1,d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d1d2d3_colinear) ).
fof(f109_nnf,plain,
~ colinear(d1,d2,d3),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
~ colinear(d1,d2,d3),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
~ colinear(d1,d2,d3),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(t20,plain,
colinear(d1,d2,d3) = false,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(t146,plain,
colinear(d1,d2,d3) = false,
inference(orient,[status(thm)],[t20]) ).
cnf(t124,axiom,
sF0 = colinear(d1,d2,d3),
introduced(definition) ).
cnf(t18633,plain,
sF0 = false,
inference(step,[status(thm)],[t124,t146]) ).
cnf(t148,plain,
false = sF0,
inference(orient,[status(thm)],[t18633]) ).
cnf(t18650,plain,
colinear(d1,d2,d3) = sF0,
inference(step,[status(thm)],[t146,t148]) ).
cnf(t165,plain,
colinear(d1,d2,d3) = sF0,
inference(orient,[status(thm)],[t18650]) ).
cnf(t18663,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t125,t165]) ).
cnf(t18664,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t18663,t148]) ).
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(t39,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(t11,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t137,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t18644,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(step,[status(thm)],[t137,t148]) ).
cnf(t159,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(orient,[status(thm)],[t18644]) ).
cnf(t18661,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t39,t159]) ).
cnf(t18662,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t18661,t148]) ).
cnf(t202,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t18662]) ).
cnf(t18665,plain,
sF1 = true,
inference(step,[status(thm)],[t18664,t202]) ).
cnf(t203,plain,
true = sF1,
inference(orient,[status(thm)],[t18665]) ).
cnf(f101,axiom,
( U = V
| colinear(U,W,X)
| ~ colinear(U,V,X)
| ~ colinear(U,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_1) ).
fof(f101_nnf,plain,
! [U,V,W,X] :
( U = V
| colinear(U,W,X)
| ~ colinear(U,V,X)
| ~ colinear(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [U,V,W,X] :
( U = V
| colinear(U,W,X)
| ~ colinear(U,V,X)
| ~ colinear(U,V,W) ),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
( X0 = X1
| colinear(X0,X2,X3)
| ~ colinear(X0,X1,X3)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(t90,plain,
ifeq(colinear(X1,X2,X3),true,ifeq(colinear(X1,X2,X4),true,or(colinear(X1,X3,X4),eq(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c101]) ).
cnf(t18986,plain,
ifeq(colinear(X1,X2,X3),sF1,ifeq(colinear(X1,X2,X4),true,or(colinear(X1,X3,X4),eq(X1,X2)),true),true) = true,
inference(step,[status(thm)],[t90,t203]) ).
cnf(t18987,plain,
ifeq(colinear(X1,X2,X3),sF1,ifeq(colinear(X1,X2,X4),sF1,or(colinear(X1,X3,X4),eq(X1,X2)),true),true) = true,
inference(step,[status(thm)],[t18986,t203]) ).
cnf(t18988,plain,
ifeq(colinear(X1,X2,X3),sF1,ifeq(colinear(X1,X2,X4),sF1,or(colinear(X1,X3,X4),eq(X1,X2)),sF1),true) = true,
inference(step,[status(thm)],[t18987,t203]) ).
cnf(t18989,plain,
ifeq(colinear(X1,X2,X3),sF1,ifeq(colinear(X1,X2,X4),sF1,or(colinear(X1,X3,X4),eq(X1,X2)),sF1),sF1) = true,
inference(step,[status(thm)],[t18988,t203]) ).
cnf(t18990,plain,
ifeq(colinear(X1,X2,X3),sF1,ifeq(colinear(X1,X2,X4),sF1,or(colinear(X1,X3,X4),eq(X1,X2)),sF1),sF1) = sF1,
inference(step,[status(thm)],[t18989,t203]) ).
cnf(t1104,plain,
ifeq(colinear(X1,X2,X3),sF1,ifeq(colinear(X1,X2,X4),sF1,or(colinear(X1,X3,X4),eq(X1,X2)),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t18990]) ).
cnf(f107,hypothesis,
colinear(a,b,d2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd2_colinear) ).
fof(f107_nnf,plain,
colinear(a,b,d2),
inference(nnf_transformation,[status(thm)],[f107]) ).
cnf(c107,plain,
colinear(a,b,d2),
inference(cnf_transformation,[status(esa)],[f107_nnf]) ).
cnf(t18,plain,
colinear(a,b,d2) = true,
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t144,plain,
colinear(a,b,d2) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t18680,plain,
colinear(a,b,d2) = sF1,
inference(step,[status(thm)],[t144,t203]) ).
cnf(t220,plain,
colinear(a,b,d2) = sF1,
inference(orient,[status(thm)],[t18680]) ).
cnf(t1113,plain,
sF1 = ifeq(sF1,sF1,ifeq(colinear(a,b,X1),sF1,or(colinear(a,d2,X1),eq(a,b)),sF1),sF1),
inference(cp,[status(thm)],[t1104,t220]) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t177,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t27]) ).
cnf(t19031,plain,
sF1 = ifeq(colinear(a,b,X1),sF1,or(colinear(a,d2,X1),eq(a,b)),sF1),
inference(step,[status(thm)],[t1113,t177]) ).
cnf(f105,hypothesis,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_b) ).
fof(f105_nnf,plain,
a != b,
inference(nnf_transformation,[status(thm)],[f105]) ).
fof(f105_sk,plain,
a != b,
inference(skolemisation,[status(esa)],[f105_nnf]) ).
cnf(c105,plain,
a != b,
inference(cnf_transformation,[status(esa)],[f105_sk]) ).
cnf(t1,plain,
eq(a,b) = false,
inference(equality_encoding,[status(esa)],[c105]) ).
cnf(t127,plain,
eq(a,b) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t18634,plain,
eq(a,b) = sF0,
inference(step,[status(thm)],[t127,t148]) ).
cnf(t149,plain,
eq(a,b) = sF0,
inference(orient,[status(thm)],[t18634]) ).
cnf(t19032,plain,
sF1 = ifeq(colinear(a,b,X1),sF1,or(colinear(a,d2,X1),sF0),sF1),
inference(step,[status(thm)],[t19031,t149]) ).
cnf(t5,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t131,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t18642,plain,
or(X1,sF0) = X1,
inference(step,[status(thm)],[t131,t148]) ).
cnf(t157,plain,
or(X1,sF0) = X1,
inference(rw,[status(thm)],[t18642]) ).
cnf(t169,plain,
or(X1,sF0) = X1,
inference(orient,[status(thm)],[t157]) ).
cnf(t19033,plain,
sF1 = ifeq(colinear(a,b,X1),sF1,colinear(a,d2,X1),sF1),
inference(step,[status(thm)],[t19032,t169]) ).
cnf(t1551,plain,
ifeq(colinear(a,b,X1),sF1,colinear(a,d2,X1),sF1) = sF1,
inference(orient,[status(thm)],[t19033]) ).
cnf(f108,hypothesis,
colinear(a,b,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd3_colinear) ).
fof(f108_nnf,plain,
colinear(a,b,d3),
inference(nnf_transformation,[status(thm)],[f108]) ).
cnf(c108,plain,
colinear(a,b,d3),
inference(cnf_transformation,[status(esa)],[f108_nnf]) ).
cnf(t19,plain,
colinear(a,b,d3) = true,
inference(equality_encoding,[status(esa)],[c108]) ).
cnf(t145,plain,
colinear(a,b,d3) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t18682,plain,
colinear(a,b,d3) = sF1,
inference(step,[status(thm)],[t145,t203]) ).
cnf(t222,plain,
colinear(a,b,d3) = sF1,
inference(orient,[status(thm)],[t18682]) ).
cnf(t1552,plain,
sF1 = ifeq(sF1,sF1,colinear(a,d2,d3),sF1),
inference(cp,[status(thm)],[t1551,t222]) ).
cnf(t19034,plain,
sF1 = colinear(a,d2,d3),
inference(step,[status(thm)],[t1552,t177]) ).
cnf(t1557,plain,
colinear(a,d2,d3) = sF1,
inference(orient,[status(thm)],[t19034]) ).
cnf(t17564,plain,
colinear(d1,d2,d3) = sF1,
inference(rw,[status(thm)],[t1557]) ).
cnf(t20769,plain,
sF0 = sF1,
inference(step,[status(thm)],[t17564,t165]) ).
cnf(t17949,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t20769]) ).
cnf(t20790,plain,
true = sF0,
inference(step,[status(thm)],[t203,t17949]) ).
cnf(t17970,plain,
true = sF0,
inference(orient,[status(thm)],[t20790]) ).
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(f62,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f95,axiom,
~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11) ).
fof(f95_nnf,plain,
~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f95]) ).
fof(f95_sk,plain,
~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f95_nnf]) ).
cnf(c95,plain,
~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c62,c63,c64,c65,c95,c105,c109]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t17970]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t148]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO013-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n018.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 10:25:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 109.85/16.98 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 109.85/16.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------