%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% 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 01:16:29 PM UTC 2026
% Result : Unsatisfiable 26.67s 4.05s
% Output : Proof 26.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 100 ( 26 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 94 ( 43 ~; 51 |; 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 : 76 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f47,axiom,
( U = V
| ~ between(V,U,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
fof(f47_nnf,plain,
! [U,V,W] :
( U = V
| ~ between(V,U,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [U,V,W] :
( U = V
| ~ between(V,U,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c47,plain,
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(f8,axiom,
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f8_nnf,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f53,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_between_others) ).
fof(f53_nnf,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(p100,plain,
( between(a,d,c)
| between(X1,inner_pasch(c,a,d,X1,X0),c)
| ~ between(X0,X1,d) ),
inference(resolution,[status(thm)],[c8,c53]) ).
cnf(f52,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f52_nnf,plain,
between(a,c,d),
inference(nnf_transformation,[status(thm)],[f52]) ).
cnf(c52,plain,
between(a,c,d),
inference(cnf_transformation,[status(esa)],[f52_nnf]) ).
cnf(p231,plain,
( between(a,d,c)
| between(c,inner_pasch(c,a,d,c,a),c) ),
inference(resolution,[status(thm)],[p100,c52]) ).
cnf(f6,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f6_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p258,plain,
( c = inner_pasch(c,a,d,c,a)
| between(a,d,c) ),
inference(resolution,[status(thm)],[p231,c6]) ).
cnf(f7,axiom,
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f7_nnf,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p78,plain,
( between(a,d,c)
| between(a,inner_pasch(c,a,d,X1,X0),X0)
| ~ between(X0,X1,d) ),
inference(resolution,[status(thm)],[c7,c53]) ).
cnf(p90,plain,
( between(a,d,c)
| between(a,inner_pasch(c,a,d,c,a),a) ),
inference(resolution,[status(thm)],[p78,c52]) ).
cnf(p112,plain,
( a = inner_pasch(c,a,d,c,a)
| between(a,d,c) ),
inference(resolution,[status(thm)],[p90,c6]) ).
cnf(p271,plain,
( a = c
| between(a,d,c)
| between(a,d,c) ),
inference(superposition,[status(thm)],[p258,p112]) ).
cnf(p273,plain,
( a = c
| between(a,d,c) ),
inference(factoring,[status(thm)],[p271]) ).
cnf(f45,axiom,
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f45_nnf,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p274,plain,
( between(c,d,a)
| a = c ),
inference(resolution,[status(thm)],[p273,c45]) ).
cnf(p721,plain,
( a = c
| c = d
| ~ between(d,c,a) ),
inference(resolution,[status(thm)],[c47,p274]) ).
cnf(p75,plain,
between(d,c,a),
inference(resolution,[status(thm)],[c45,c52]) ).
cnf(p764,plain,
( a = c
| c = d ),
inference(resolution,[status(thm)],[p721,p75]) ).
cnf(f51,hypothesis,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_d) ).
fof(f51_nnf,plain,
c != d,
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
c != d,
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c51,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p765,plain,
a = c,
inference(resolution,[status(thm)],[p764,c51]) ).
cnf(f49,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
fof(f49_nnf,plain,
a != c,
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
a != c,
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c49,plain,
a != c,
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(p803,plain,
$false,
inference(resolution,[status(thm)],[p765,c49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:24:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.67/4.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.67/4.05 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------