%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO033-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:16:38 PM UTC 2026
% Result : Unsatisfiable 0.15s 6.03s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 70 unt; 0 def)
% Number of atoms : 118 ( 35 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 114 ( 74 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-4 aty)
% Number of variables : 84 ( 4 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f73,negated_conjecture,
~ equidistant(v,x,v1,x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_to_x_equals_v1_to_x1) ).
fof(f73_nnf,plain,
~ equidistant(v,x,v1,x1),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
~ equidistant(v,x,v1,x1),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
~ equidistant(v,x,v1,x1),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t143,plain,
ifeq(equidistant(v,x,v1,x1),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(f36,axiom,
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
fof(f36_nnf,plain,
! [U,V,U1,V1,W,W1] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [U,V,U1,V1,W,W1] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
( equidistant(X0,X4,X2,X5)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi33,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X1,X4,X3,X5),true,ifeq(between(X0,X1,X4),true,ifeq(between(X2,X3,X5),true,equidistant(X0,X4,X2,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(f67,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f67_nnf,plain,
equidistant(u,v,u1,v1),
inference(nnf_transformation,[status(thm)],[f67]) ).
cnf(c67,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(esa)],[f67_nnf]) ).
cnf(hi59,axiom,
equidistant(u,v,u1,v1) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(f68,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f68_nnf,plain,
equidistant(v,w,v1,w1),
inference(nnf_transformation,[status(thm)],[f68]) ).
cnf(c68,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(esa)],[f68_nnf]) ).
cnf(hi60,axiom,
equidistant(v,w,v1,w1) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(f71,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f71_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f71]) ).
cnf(c71,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f71_nnf]) ).
cnf(hi63,axiom,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(f72,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
fof(f72_nnf,plain,
between(u1,v1,w1),
inference(nnf_transformation,[status(thm)],[f72]) ).
cnf(c72,plain,
between(u1,v1,w1),
inference(cnf_transformation,[status(esa)],[f72_nnf]) ).
cnf(hi64,axiom,
between(u1,v1,w1) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(h319,plain,
equidistant(u,w,u1,w1) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi59,hi60,hi63,hi64]) ).
cnf(f65,axiom,
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12) ).
fof(f65_nnf,plain,
! [U,V,U1,V1,W,W1,X,X1] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [U,V,U1,V1,W,W1,X,X1] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( equidistant(X1,X6,X3,X7)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi57,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X0,X4,X2,X5),true,ifeq(equidistant(X0,X6,X2,X7),true,ifeq(equidistant(X4,X6,X5,X7),true,ifeq(between(X0,X1,X4),true,ifeq(between(X2,X3,X5),true,equidistant(X1,X6,X3,X7),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(f69,hypothesis,
equidistant(u,x,u1,x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_x_equals_u1_to_x1) ).
fof(f69_nnf,plain,
equidistant(u,x,u1,x1),
inference(nnf_transformation,[status(thm)],[f69]) ).
cnf(c69,plain,
equidistant(u,x,u1,x1),
inference(cnf_transformation,[status(esa)],[f69_nnf]) ).
cnf(hi61,axiom,
equidistant(u,x,u1,x1) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(f70,hypothesis,
equidistant(w,x,w1,x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_to_x_equals_w1_to_x1) ).
fof(f70_nnf,plain,
equidistant(w,x,w1,x1),
inference(nnf_transformation,[status(thm)],[f70]) ).
cnf(c70,plain,
equidistant(w,x,w1,x1),
inference(cnf_transformation,[status(esa)],[f70_nnf]) ).
cnf(hi62,axiom,
equidistant(w,x,w1,x1) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(t39,plain,
equidistant(v,x,v1,x1) = true,
inference(hyper_resolution,[status(thm)],[hi57,hi59,h319,hi61,hi62,hi63,hi64]) ).
cnf(t283,plain,
equidistant(v,x,v1,x1) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(t2073,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t143,t283]) ).
cnf(t65,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t65]) ).
cnf(t2074,plain,
false = true,
inference(step,[status(thm)],[t2073,t256]) ).
cnf(t2055,plain,
false = true,
inference(orient,[status(thm)],[t2074]) ).
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(f57,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
fof(f57_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(f58,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
fof(f58_nnf,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(f59,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
fof(f59_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c59,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(f60,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
fof(f60_nnf,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
X0 != extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c57,c58,c59,c60,c73]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2055]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO033-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n007.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Wed Sep 23 10:27:28 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/6.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/6.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------