%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 01:16:29 PM UTC 2026
% Result : Unsatisfiable 26.79s 3.87s
% Output : Proof 26.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 8
% Syntax : Number of formulae : 91 ( 14 unt; 0 def)
% Number of atoms : 200 ( 85 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 159 ( 50 ~; 109 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 84 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,plain,
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f23,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f23_nnf,plain,
between(a,c,d),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
between(a,c,d),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p59,plain,
( between(a,outer_pasch(c,a,X0,X1,d),X0)
| ~ between(X0,d,X1) ),
inference(resolution,[status(thm)],[c6,c23]) ).
cnf(f1,axiom,
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
fof(f1_nnf,plain,
! [X,Y,V,Z] :
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,V,Z] :
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f24,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
fof(f24_nnf,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p26,plain,
( between(a,d,c)
| between(c,a,X0)
| ~ between(a,X0,d) ),
inference(resolution,[status(thm)],[c1,c24]) ).
cnf(p28,plain,
( between(a,d,c)
| between(c,a,c) ),
inference(resolution,[status(thm)],[p26,c23]) ).
cnf(f0,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f0_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p29,plain,
( c = a
| between(a,d,c) ),
inference(resolution,[status(thm)],[p28,c0]) ).
cnf(p61,plain,
( c = a
| between(a,outer_pasch(d,a,X0,X1,c),X0)
| ~ between(X0,c,X1) ),
inference(resolution,[status(thm)],[c6,p29]) ).
cnf(p66,plain,
( c = a
| between(a,outer_pasch(d,a,a,d,c),a) ),
inference(resolution,[status(thm)],[p61,c23]) ).
cnf(p69,plain,
( a = outer_pasch(d,a,a,d,c)
| c = a ),
inference(resolution,[status(thm)],[p66,c0]) ).
cnf(f7,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(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c7,plain,
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p78,plain,
( c = a
| between(X1,d,outer_pasch(d,a,X0,X1,c))
| ~ between(X0,c,X1) ),
inference(resolution,[status(thm)],[c7,p29]) ).
cnf(p106,plain,
( c = a
| between(d,d,outer_pasch(d,a,a,d,c)) ),
inference(resolution,[status(thm)],[p78,c23]) ).
cnf(p111,plain,
( c = a
| between(d,d,a)
| c = a ),
inference(superposition,[status(thm)],[p69,p106]) ).
cnf(p121,plain,
( between(d,d,a)
| c = a ),
inference(factoring,[status(thm)],[p111]) ).
cnf(p122,plain,
( between(d,d,X0)
| ~ between(d,X0,a)
| c = a ),
inference(resolution,[status(thm)],[p121,c1]) ).
cnf(p125,plain,
( c = a
| between(d,d,d)
| c = a ),
inference(resolution,[status(thm)],[p122,p121]) ).
cnf(p126,plain,
( between(d,d,d)
| c = a ),
inference(factoring,[status(thm)],[p125]) ).
cnf(p136,plain,
( between(d,outer_pasch(d,d,X0,X1,d),X0)
| ~ between(X0,d,X1)
| c = a ),
inference(resolution,[status(thm)],[p126,c6]) ).
cnf(p229,plain,
( c = a
| between(d,outer_pasch(d,d,d,a,d),d)
| c = a ),
inference(resolution,[status(thm)],[p136,p121]) ).
cnf(p265,plain,
( between(d,outer_pasch(d,d,d,a,d),d)
| c = a ),
inference(factoring,[status(thm)],[p229]) ).
cnf(p266,plain,
( d = outer_pasch(d,d,d,a,d)
| c = a ),
inference(resolution,[status(thm)],[p265,c0]) ).
cnf(p137,plain,
( between(X1,d,outer_pasch(d,d,X0,X1,d))
| ~ between(X0,d,X1)
| c = a ),
inference(resolution,[status(thm)],[p126,c7]) ).
cnf(p302,plain,
( c = a
| between(a,d,outer_pasch(d,d,d,a,d))
| c = a ),
inference(resolution,[status(thm)],[p137,p121]) ).
cnf(p330,plain,
( between(a,d,outer_pasch(d,d,d,a,d))
| c = a ),
inference(factoring,[status(thm)],[p302]) ).
cnf(p340,plain,
( between(a,d,d)
| c = a
| c = a ),
inference(superposition,[status(thm)],[p266,p330]) ).
cnf(p343,plain,
( between(a,d,d)
| c = a ),
inference(factoring,[status(thm)],[p340]) ).
cnf(p466,plain,
( c = a
| between(a,outer_pasch(c,a,a,d,d),a) ),
inference(resolution,[status(thm)],[p59,p343]) ).
cnf(p497,plain,
( a = outer_pasch(c,a,a,d,d)
| c = a ),
inference(resolution,[status(thm)],[p466,c0]) ).
cnf(p76,plain,
( between(X1,c,outer_pasch(c,a,X0,X1,d))
| ~ between(X0,d,X1) ),
inference(resolution,[status(thm)],[c7,c23]) ).
cnf(p705,plain,
( c = a
| between(d,c,outer_pasch(c,a,a,d,d)) ),
inference(resolution,[status(thm)],[p76,p343]) ).
cnf(p768,plain,
( c = a
| between(d,c,a)
| c = a ),
inference(superposition,[status(thm)],[p497,p705]) ).
cnf(p772,plain,
( between(d,c,a)
| c = a ),
inference(factoring,[status(thm)],[p768]) ).
cnf(p773,plain,
( between(d,c,X0)
| ~ between(c,X0,a)
| c = a ),
inference(resolution,[status(thm)],[p772,c1]) ).
cnf(p454,plain,
( c = a
| between(a,outer_pasch(c,a,a,c,d),a) ),
inference(resolution,[status(thm)],[p59,p29]) ).
cnf(p482,plain,
( a = outer_pasch(c,a,a,c,d)
| c = a ),
inference(resolution,[status(thm)],[p454,c0]) ).
cnf(p693,plain,
( c = a
| between(c,c,outer_pasch(c,a,a,c,d)) ),
inference(resolution,[status(thm)],[p76,p29]) ).
cnf(p729,plain,
( c = a
| between(c,c,a)
| c = a ),
inference(superposition,[status(thm)],[p482,p693]) ).
cnf(p734,plain,
( between(c,c,a)
| c = a ),
inference(factoring,[status(thm)],[p729]) ).
cnf(p816,plain,
( c = a
| between(d,c,c)
| c = a ),
inference(resolution,[status(thm)],[p773,p734]) ).
cnf(p820,plain,
( between(d,c,c)
| c = a ),
inference(factoring,[status(thm)],[p816]) ).
cnf(p57,plain,
( between(X0,outer_pasch(X1,X0,X0,X1,X1),X0)
| ~ between(X0,X1,X1) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(p829,plain,
( between(d,outer_pasch(c,d,d,c,c),d)
| c = a ),
inference(resolution,[status(thm)],[p820,p57]) ).
cnf(p836,plain,
( d = outer_pasch(c,d,d,c,c)
| c = a ),
inference(resolution,[status(thm)],[p829,c0]) ).
cnf(p74,plain,
( between(X1,X1,outer_pasch(X1,X0,X0,X1,X1))
| ~ between(X0,X1,X1) ),
inference(factoring,[status(thm)],[c7]) ).
cnf(p833,plain,
( between(c,c,outer_pasch(c,d,d,c,c))
| c = a ),
inference(resolution,[status(thm)],[p820,p74]) ).
cnf(p864,plain,
( between(c,c,d)
| c = a
| c = a ),
inference(superposition,[status(thm)],[p836,p833]) ).
cnf(p865,plain,
( between(c,c,d)
| c = a ),
inference(factoring,[status(thm)],[p864]) ).
cnf(p27,plain,
( between(a,c,X0)
| ~ between(c,X0,d) ),
inference(resolution,[status(thm)],[c1,c23]) ).
cnf(p871,plain,
( between(a,c,c)
| c = a ),
inference(resolution,[status(thm)],[p865,p27]) ).
cnf(p893,plain,
( c = a
| between(a,outer_pasch(d,a,a,c,c),a)
| c = a ),
inference(resolution,[status(thm)],[p871,p61]) ).
cnf(p1543,plain,
( between(a,outer_pasch(d,a,a,c,c),a)
| c = a ),
inference(factoring,[status(thm)],[p893]) ).
cnf(p1544,plain,
( a = outer_pasch(d,a,a,c,c)
| c = a ),
inference(resolution,[status(thm)],[p1543,c0]) ).
cnf(p896,plain,
( c = a
| between(c,d,outer_pasch(d,a,a,c,c))
| c = a ),
inference(resolution,[status(thm)],[p871,p78]) ).
cnf(p1553,plain,
( between(c,d,outer_pasch(d,a,a,c,c))
| c = a ),
inference(factoring,[status(thm)],[p896]) ).
cnf(p1572,plain,
( between(c,d,a)
| c = a
| c = a ),
inference(superposition,[status(thm)],[p1544,p1553]) ).
cnf(p1573,plain,
( between(c,d,a)
| c = a ),
inference(factoring,[status(thm)],[p1572]) ).
cnf(p1587,plain,
( between(d,c,d)
| c = a
| c = a ),
inference(resolution,[status(thm)],[p1573,p773]) ).
cnf(p1596,plain,
( between(d,c,d)
| c = a ),
inference(factoring,[status(thm)],[p1587]) ).
cnf(p1597,plain,
( d = c
| c = a ),
inference(resolution,[status(thm)],[p1596,c0]) ).
cnf(f22,hypothesis,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
fof(f22_nnf,plain,
c != d,
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
c != d,
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p1612,plain,
( c != c
| c = a ),
inference(superposition,[status(thm)],[p1597,c22]) ).
cnf(p1913,plain,
c = a,
inference(equality_resolution,[status(thm)],[p1612]) ).
cnf(f20,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
fof(f20_nnf,plain,
a != c,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
a != c,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
a != c,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p1914,plain,
a != a,
inference(demodulation,[status(thm)],[p1913,c20]) ).
cnf(p1958,plain,
$false,
inference(equality_resolution,[status(thm)],[p1914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 10:12:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.79/3.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.79/3.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------