%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 03:32:09 PM UTC 2026
% Result : Theorem 29.18s 4.96s
% Output : Proof 29.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 67 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 22 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 10 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34,axiom,
! [X,Z,X3,Tx3] :
( index(X,X3) = just(Tx3)
=> ( tc(X,var(X3),Z)
<=> Tx3 = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
fof(f34_nnf,plain,
! [X,Z,X3,Tx3] :
( ( ( Tx3 != Z
| tc(X,var(X3),Z) )
& ( Tx3 = Z
| ~ tc(X,var(X3),Z) ) )
| index(X,X3) != just(Tx3) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X,X3,Tx3,Z] :
( ( ( Tx3 != Z
| tc(X,var(X3),Z) )
& ( Tx3 = Z
| ~ tc(X,var(X3),Z) ) )
| index(X,X3) != just(Tx3) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c41,plain,
( X3 != X1
| tc(X0,var(X2),X1)
| index(X0,X2) != just(X3) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
fof(f28,axiom,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
fof(f28_nnf,plain,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c31,plain,
index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p80,plain,
( X0 != X2
| tc(cons(X0,X1),var(zero),X2) ),
inference(resolution,[status(thm)],[c41,c31]) ).
cnf(p83,plain,
tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[p80]) ).
fof(f32,axiom,
! [X,E,Tx2,T1] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
fof(f32_nnf,plain,
! [X,E,Tx2,T1] :
( ( ~ tc(cons(Tx2,X),E,T1)
| tc(X,lam(E),arr(Tx2,T1)) )
& ( tc(cons(Tx2,X),E,T1)
| ~ tc(X,lam(E),arr(Tx2,T1)) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,E,Tx2,T1] :
( ( ~ tc(cons(Tx2,X),E,T1)
| tc(X,lam(E),arr(Tx2,T1)) )
& ( tc(cons(Tx2,X),E,T1)
| ~ tc(X,lam(E),arr(Tx2,T1)) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c38,plain,
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p85,plain,
tc(X0,lam(var(zero)),arr(X1,X1)),
inference(resolution,[status(thm)],[p83,c38]) ).
cnf(p87,plain,
tc(X0,lam(lam(var(zero))),arr(X1,arr(X2,X2))),
inference(resolution,[status(thm)],[p85,c38]) ).
fof(f35,conjecture,
? [E] :
( tc(nil,E,arr(a,arr(b,b)))
& nf(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_036) ).
fof(f35_neg,negated_conjecture,
~ ? [E] :
( tc(nil,E,arr(a,arr(b,b)))
& nf(E) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
! [E] :
( ~ tc(nil,E,arr(a,arr(b,b)))
| ~ nf(E) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
! [E] :
( ~ tc(nil,E,arr(a,arr(b,b)))
| ~ nf(E) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c42,plain,
( ~ tc(nil,X0,arr(a,arr(b,b)))
| ~ nf(X0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f25,axiom,
! [E] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(f25_nnf,plain,
! [E] :
( ( ~ nf(E)
| nf(lam(E)) )
& ( nf(E)
| ~ nf(lam(E)) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [E] :
( ( ~ nf(E)
| nf(lam(E)) )
& ( nf(E)
| ~ nf(lam(E)) ) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c28,plain,
( ~ nf(X0)
| nf(lam(X0)) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f26,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
fof(f26_nnf,plain,
! [X4] : nf(var(X4)),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X4] : nf(var(X4)),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c29,plain,
nf(var(X0)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p43,plain,
nf(lam(var(X0))),
inference(resolution,[status(thm)],[c28,c29]) ).
cnf(p44,plain,
nf(lam(lam(var(X0)))),
inference(resolution,[status(thm)],[p43,c28]) ).
cnf(p55,plain,
~ tc(nil,lam(lam(var(X0))),arr(a,arr(b,b))),
inference(resolution,[status(thm)],[c42,p44]) ).
cnf(p88,plain,
$false,
inference(resolution,[status(thm)],[p87,p55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 23:43:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.18/4.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.18/4.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------