%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 4.08s 0.94s
% Output : Proof 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 65 unt; 0 def)
% Number of atoms : 93 ( 32 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 82 ( 58 ~; 24 |; 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 : 13 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 64 ( 4 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f70,negated_conjecture,
~ equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f70_nnf,plain,
~ equidistant(v,w,v1,w1),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
~ equidistant(v,w,v1,w1),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
~ equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(t126,plain,
ifeq(equidistant(v,w,v1,w1),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
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(f68,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f68_nnf,plain,
equidistant(u,v,u1,v1),
inference(nnf_transformation,[status(thm)],[f68]) ).
cnf(c68,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(esa)],[f68_nnf]) ).
cnf(hi60,axiom,
equidistant(u,v,u1,v1) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(f69,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
fof(f69_nnf,plain,
equidistant(u,w,u1,w1),
inference(nnf_transformation,[status(thm)],[f69]) ).
cnf(c69,plain,
equidistant(u,w,u1,w1),
inference(cnf_transformation,[status(esa)],[f69_nnf]) ).
cnf(hi61,axiom,
equidistant(u,w,u1,w1) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(f35,axiom,
equidistant(U,U,V,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
fof(f35_nnf,plain,
! [U,V] : equidistant(U,U,V,V),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [U,V] : equidistant(U,U,V,V),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi32,axiom,
equidistant(X0,X0,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(f66,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f66_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f66]) ).
cnf(c66,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f66_nnf]) ).
cnf(hi58,axiom,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(f67,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
fof(f67_nnf,plain,
between(u1,v1,w1),
inference(nnf_transformation,[status(thm)],[f67]) ).
cnf(c67,plain,
between(u1,v1,w1),
inference(cnf_transformation,[status(esa)],[f67_nnf]) ).
cnf(hi59,axiom,
between(u1,v1,w1) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t33,plain,
equidistant(v,w,v1,w1) = true,
inference(hyper_resolution,[status(thm)],[hi57,hi60,hi61,hi61,hi32,hi58,hi59]) ).
cnf(t289,plain,
equidistant(v,w,v1,w1) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t2341,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t126,t289]) ).
cnf(t41,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t41]) ).
cnf(t2342,plain,
false = true,
inference(step,[status(thm)],[t2341,t256]) ).
cnf(t2322,plain,
false = true,
inference(orient,[status(thm)],[t2342]) ).
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,c70]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2322]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 10:29:13 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.08/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/0.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------