%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 20.90s 3.16s
% Output : Proof 20.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 83 ( 71 unt; 0 def)
% Number of atoms : 135 ( 41 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 138 ( 86 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 134 ( 8 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f67,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(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14) ).
fof(f67_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(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_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(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,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(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(hi59,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X1,X4,X3,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)],[c67]) ).
cnf(f19,axiom,
equidistant(U,V,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f19_nnf,plain,
! [U,V] : equidistant(U,V,U,V),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U,V] : equidistant(U,V,U,V),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi15,axiom,
equidistant(X0,X1,X0,X1) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f69,hypothesis,
equidistant(u,v,u,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u_to_x) ).
fof(f69_nnf,plain,
equidistant(u,v,u,x),
inference(nnf_transformation,[status(thm)],[f69]) ).
cnf(c69,plain,
equidistant(u,v,u,x),
inference(cnf_transformation,[status(esa)],[f69_nnf]) ).
cnf(hi61,axiom,
equidistant(u,v,u,x) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(f70,hypothesis,
equidistant(w,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_v_equals_w_to_x) ).
fof(f70_nnf,plain,
equidistant(w,v,w,x),
inference(nnf_transformation,[status(thm)],[f70]) ).
cnf(c70,plain,
equidistant(w,v,w,x),
inference(cnf_transformation,[status(esa)],[f70_nnf]) ).
cnf(hi62,axiom,
equidistant(w,v,w,x) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(f68,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f68_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f68]) ).
cnf(c68,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f68_nnf]) ).
cnf(hi60,axiom,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h249,plain,
equidistant(v,v,v,x) = true,
inference(hyper_resolution,[status(thm)],[hi59,hi15,hi15,hi61,hi62,hi60,hi60]) ).
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/sandbox/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(f46,axiom,
between(U,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
fof(f46_nnf,plain,
! [U,V] : between(U,U,V),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [U,V] : between(U,U,V),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
between(X0,X0,X1),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi43,axiom,
between(X0,X0,X1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(f43,axiom,
between(U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
fof(f43_nnf,plain,
! [U,V] : between(U,V,V),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [U,V] : between(U,V,V),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
between(X0,X1,X1),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi40,axiom,
between(X0,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(h390,plain,
equidistant(v,V0,x,V0) = true,
inference(hyper_resolution,[status(thm)],[hi57,h249,hi15,hi15,hi15,hi43,hi40]) ).
cnf(f2,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(equidistant(X0,X1,X2,X2),true,X0,X1) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h550,plain,
v = x,
inference(hyper_resolution,[status(thm)],[hi2,h390]) ).
cnf(f71,negated_conjecture,
v != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_is_x) ).
fof(f71_nnf,plain,
v != x,
inference(nnf_transformation,[status(thm)],[f71]) ).
fof(f71_sk,plain,
v != x,
inference(skolemisation,[status(esa)],[f71_nnf]) ).
cnf(c71,plain,
v != x,
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
cnf(hi70,negated_conjecture,
ifeq(v,x,false,true) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi70,h550]) ).
cnf(t4015,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(f57,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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,c71]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4015]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 % Computer : n026.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Wed Sep 23 10:32:38 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.90/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.90/3.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------