%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO063-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 11.18s 9.30s
% Output : Proof 11.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 71 unt; 0 def)
% Number of atoms : 83 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 38 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 82 ( 6 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f61,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
fof(f61_nnf,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c61,plain,
X0 != extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(t44,plain,
eq(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2)) = false,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(t2181,plain,
eq(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2)) = false,
inference(orient,[status(thm)],[t44]) ).
cnf(t45,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t317,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t45]) ).
cnf(f40,axiom,
( U = V
| extension(U,V,W,X) = extension(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
fof(f40_nnf,plain,
! [W,X,Y,Z,U,V] :
( U = V
| extension(U,V,W,X) = extension(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [W,X,Y,Z,U,V] :
( U = V
| extension(U,V,W,X) = extension(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( X4 = X5
| extension(X4,X5,X0,X1) = extension(X4,X5,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t216,plain,
ifeq(equidistant(X1,X2,X3,X4),true,or(eq(extension(X5,X6,X1,X2),extension(X5,X6,X3,X4)),eq(X5,X6)),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t1695,plain,
ifeq(equidistant(X1,X2,X3,X4),true,or(eq(extension(X5,X6,X1,X2),extension(X5,X6,X3,X4)),eq(X5,X6)),true) = true,
inference(orient,[status(thm)],[t216]) ).
cnf(f75,negated_conjecture,
insertion(u,v,w,x) != insertion(u,v,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality_of_insertions) ).
fof(f75_nnf,plain,
insertion(u,v,w,x) != insertion(u,v,y,z),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
insertion(u,v,w,x) != insertion(u,v,y,z),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
insertion(u,v,w,x) != insertion(u,v,y,z),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(u12,axiom,
eq(insertion(u,v,w,x),insertion(u,v,y,z)) = false,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(f19,axiom,
insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',insertion) ).
fof(f19_nnf,plain,
! [U1,W1,U,V] : insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U1,W1,U,V] : insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
insertion(X0,X1,X2,X3) = extension(extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X2,X3),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(d1,axiom,
insertion(X0,X1,X2,X3) = extension(extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X2,X3),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t198,plain,
eq(extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x),extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z)) = false,
inference(definition_unfolding,[status(thm)],[u12,d1]) ).
cnf(t2201,plain,
eq(extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x),extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z)) = false,
inference(orient,[status(thm)],[t198]) ).
cnf(t2204,plain,
true = ifeq(equidistant(w,x,y,z),true,or(false,eq(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u)),true),
inference(cp,[status(thm)],[t1695,t2201]) ).
cnf(f74,hypothesis,
equidistant(w,x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
fof(f74_nnf,plain,
equidistant(w,x,y,z),
inference(nnf_transformation,[status(thm)],[f74]) ).
cnf(c74,plain,
equidistant(w,x,y,z),
inference(cnf_transformation,[status(esa)],[f74_nnf]) ).
cnf(t36,plain,
equidistant(w,x,y,z) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t590,plain,
equidistant(w,x,y,z) = true,
inference(orient,[status(thm)],[t36]) ).
cnf(t2728,plain,
true = ifeq(true,true,or(false,eq(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u)),true),
inference(step,[status(thm)],[t2204,t590]) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t304,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t2729,plain,
true = or(false,eq(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u)),
inference(step,[status(thm)],[t2728,t304]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t319,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t2730,plain,
true = eq(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u),
inference(step,[status(thm)],[t2729,t319]) ).
cnf(t2644,plain,
eq(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u) = true,
inference(orient,[status(thm)],[t2730]) ).
cnf(t2645,plain,
u = ifeq(true,true,extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u),
inference(cp,[status(thm)],[t317,t2644]) ).
cnf(t2731,plain,
u = extension(v,u,lower_dimension_point_1,lower_dimension_point_2),
inference(step,[status(thm)],[t2645,t304]) ).
cnf(t2648,plain,
extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u,
inference(orient,[status(thm)],[t2731]) ).
cnf(t2649,plain,
false = eq(u,u),
inference(cp,[status(thm)],[t2181,t2648]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t591,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t2736,plain,
false = true,
inference(step,[status(thm)],[t2649,t591]) ).
cnf(t2671,plain,
false = true,
inference(orient,[status(thm)],[t2736]) ).
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(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(f58,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
fof(f58_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(f59,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
fof(f59_nnf,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c59,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(f60,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
fof(f60_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c58,c59,c60,c61,c75]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2671]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO063-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n016.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 10:44:02 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.18/9.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.18/9.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------