%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:16:28 PM UTC 2026
% Result : Unsatisfiable 6.60s 21.48s
% Output : Proof 6.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 31 unt; 0 def)
% Number of atoms : 87 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-5 aty)
% Number of variables : 167 ( 17 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
fof(f0_nnf,plain,
! [X,Y,V,Z] :
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,V,Z] :
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(between(X0,X1,X2),true,ifeq(between(X1,X3,X2),true,between(X0,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f4,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
fof(f4_nnf,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2,plain,
between(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4,hi4]) ).
cnf(f1,axiom,
( equalish(X,Y)
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f1_nnf,plain,
! [X,Y,Z] :
( equalish(X,Y)
| ~ equidistant(X,Y,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] :
( equalish(X,Y)
| ~ equidistant(X,Y,Z,Z) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(equidistant(X0,X1,X2,X2),true,equalish(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f5,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
fof(f5_nnf,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h3,plain,
equalish(V0,extension(V1,V0,V2,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi5]) ).
cnf(f6,axiom,
( between(W,Z,Y)
| ~ between(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_substitution3) ).
fof(f6_nnf,plain,
! [X,Y,W,Z] :
( between(W,Z,Y)
| ~ between(W,Z,X)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,W,Z] :
( between(W,Z,Y)
| ~ between(W,Z,X)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( between(X2,X3,X1)
| ~ between(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(equalish(X0,X1),true,ifeq(between(X2,X3,X0),true,between(X2,X3,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h30,plain,
between(V0,V0,extension(V1,V0,V2,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3,h2]) ).
cnf(h59,plain,
between(V0,V1,V1) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4,h30]) ).
cnf(f2,axiom,
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch1) ).
fof(f2_nnf,plain,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(between(X0,X1,X2),true,ifeq(between(X3,X2,X4),true,between(X0,outer_pasch(X1,X0,X3,X4,X2),X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h111,plain,
between(V0,outer_pasch(V1,V0,V2,V1,V1),V2) = true,
inference(hyper_resolution,[status(thm)],[hi2,h59,h59]) ).
cnf(h1270,plain,
between(V0,V1,outer_pasch(V2,V1,V1,V2,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59,h111]) ).
cnf(f3,axiom,
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch2) ).
fof(f3_nnf,plain,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(between(X0,X1,X2),true,ifeq(between(X3,X2,X4),true,between(X4,X1,outer_pasch(X1,X0,X3,X4,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h93,plain,
between(V0,V0,outer_pasch(V0,V1,V2,V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h59,h59]) ).
cnf(t1,plain,
between(X1,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi0,h93,h1270]) ).
cnf(t263,plain,
between(X1,X1,X2) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f7,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
fof(f7_nnf,plain,
~ between(a,a,b),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ between(a,a,b),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ between(a,a,b),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
between(a,a,b) != true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t263]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.13/20.48 % CPULimit : 300
% 0.13/20.48 % WCLimit : 300
% 0.13/20.48 % DateTime : Wed Sep 23 10:18:39 UTC 2026
% 0.13/20.48 % CPUTime :
% 0.13/20.48 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.60/21.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.60/21.48 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------