%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO043-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:16:43 PM UTC 2026
% Result : Unsatisfiable 12.22s 5.70s
% Output : Proof 12.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 22 unt; 0 def)
% Number of atoms : 86 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 44 ~; 40 |; 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 : 5 ( 5 usr; 4 con; 0-5 aty)
% Number of variables : 98 ( 6 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f45,axiom,
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/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(f53,hypothesis,
between(u,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
fof(f53_nnf,plain,
between(u,w,x),
inference(nnf_transformation,[status(thm)],[f53]) ).
cnf(c53,plain,
between(u,w,x),
inference(cnf_transformation,[status(esa)],[f53_nnf]) ).
cnf(p84,plain,
between(x,w,u),
inference(resolution,[status(thm)],[c45,c53]) ).
cnf(f7,axiom,
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/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(p87,plain,
( between(w,inner_pasch(x,w,u,X1,X0),X0)
| ~ between(X0,X1,u) ),
inference(resolution,[status(thm)],[p84,c7]) ).
cnf(f52,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f52_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f52]) ).
cnf(c52,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f52_nnf]) ).
cnf(p83,plain,
between(w,v,u),
inference(resolution,[status(thm)],[c45,c52]) ).
cnf(p1299,plain,
between(w,inner_pasch(x,w,u,v,w),w),
inference(resolution,[status(thm)],[p87,p83]) ).
cnf(f44,axiom,
( between(V,W,X)
| U != X
| ~ between(U,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
fof(f44_nnf,plain,
! [U,W,X,V] :
( between(V,W,X)
| U != X
| ~ between(U,W,X) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [U,W,X,V] :
( between(V,W,X)
| U != X
| ~ between(U,W,X) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( between(X3,X1,X2)
| X0 != X2
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p271,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X0) ),
inference(equality_resolution,[status(thm)],[c44]) ).
cnf(p1930,plain,
between(X0,inner_pasch(x,w,u,v,w),w),
inference(resolution,[status(thm)],[p1299,p271]) ).
cnf(f47,axiom,
( U = V
| ~ between(V,U,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/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(f43,axiom,
between(U,V,V),
file('/export/starexec/sandbox2/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(p337,plain,
( X1 = X0
| ~ between(X0,X1,X0) ),
inference(resolution,[status(thm)],[c47,c43]) ).
cnf(p2918,plain,
inner_pasch(x,w,u,v,w) = w,
inference(resolution,[status(thm)],[p1930,p337]) ).
cnf(f8,axiom,
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/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(p97,plain,
( between(X1,inner_pasch(x,w,u,X1,X0),x)
| ~ between(X0,X1,u) ),
inference(resolution,[status(thm)],[c8,p84]) ).
cnf(p2234,plain,
between(v,inner_pasch(x,w,u,v,w),x),
inference(resolution,[status(thm)],[p97,p83]) ).
cnf(p2919,plain,
between(v,w,x),
inference(demodulation,[status(thm)],[p2918,p2234]) ).
cnf(f54,negated_conjecture,
~ between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_between_v_and_x) ).
fof(f54_nnf,plain,
~ between(v,w,x),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
~ between(v,w,x),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c54,plain,
~ between(v,w,x),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(p2920,plain,
$false,
inference(resolution,[status(thm)],[p2919,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO043-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 10:34:53 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.22/5.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.22/5.70 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------