%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX199+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 : n001.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 03:32:05 PM UTC 2026
% Result : Theorem 20.40s 3.08s
% Output : Proof 20.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 40 unt; 0 def)
% Number of atoms : 107 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 26 ~; 30 |; 2 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 156 ( 6 sgn 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f9_nnf,plain,
! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c10,plain,
merge(cons(X0,X1),nil) = cons(X0,X1),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f12,conjecture,
? [Xs,Ys,Zs] :
~ ( merge(Xs,Ys) = merge(Ys,Xs)
=> ( merge(Xs,Zs) = merge(Zs,Xs)
=> merge(Ys,Zs) = merge(Zs,Ys) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_013) ).
fof(f12_neg,negated_conjecture,
~ ? [Xs,Ys,Zs] :
~ ( merge(Xs,Ys) = merge(Ys,Xs)
=> ( merge(Xs,Zs) = merge(Zs,Xs)
=> merge(Ys,Zs) = merge(Zs,Ys) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
! [Xs,Ys,Zs] :
( merge(Ys,Zs) = merge(Zs,Ys)
| merge(Xs,Zs) != merge(Zs,Xs)
| merge(Xs,Ys) != merge(Ys,Xs) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
! [Xs,Ys,Zs] :
( merge(Ys,Zs) = merge(Zs,Ys)
| merge(Xs,Zs) != merge(Zs,Xs)
| merge(Xs,Ys) != merge(Ys,Xs) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
( merge(X1,X2) = merge(X2,X1)
| merge(X0,X2) != merge(X2,X0)
| merge(X0,X1) != merge(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p23,plain,
( merge(cons(X0,X1),X2) = merge(X2,cons(X0,X1))
| X2 != merge(X2,nil)
| cons(X0,X1) != cons(X0,X1) ),
inference(superposition,[status(thm)],[c10,c13]) ).
cnf(p28,plain,
( merge(cons(X1,X2),X0) = merge(X0,cons(X1,X2))
| X0 != merge(X0,nil) ),
inference(equality_resolution,[status(thm)],[p23]) ).
cnf(p29,plain,
( merge(cons(X2,X3),cons(X0,X1)) = merge(cons(X0,X1),cons(X2,X3))
| cons(X0,X1) != cons(X0,X1) ),
inference(superposition,[status(thm)],[c10,p28]) ).
cnf(p30,plain,
merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1)),
inference(equality_resolution,[status(thm)],[p29]) ).
fof(f11,axiom,
! [Z,Xs,Y2,Ys] :
( ~ leqNat(Z,Y2)
=> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f11_nnf,plain,
! [Z,Xs,Y2,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys))
| leqNat(Z,Y2) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Z,Y2,Xs,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys))
| leqNat(Z,Y2) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( merge(cons(X0,X1),cons(X2,X3)) = cons(X2,merge(cons(X0,X1),X3))
| leqNat(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p35,plain,
( merge(cons(X1,X2),cons(X0,X3)) = cons(X1,merge(cons(X0,X3),X2))
| leqNat(X0,X1) ),
inference(superposition,[status(thm)],[p30,c12]) ).
cnf(p38,plain,
( merge(cons(X1,nil),cons(X0,X2)) = cons(X1,cons(X0,X2))
| leqNat(X0,X1) ),
inference(superposition,[status(thm)],[c10,p35]) ).
cnf(p44,plain,
( cons(X1,cons(X0,X2)) = cons(X0,merge(cons(X1,nil),X2))
| leqNat(X1,X0)
| leqNat(X0,X1) ),
inference(superposition,[status(thm)],[p38,c12]) ).
cnf(p627,plain,
( cons(X0,cons(X0,X1)) = cons(X0,merge(cons(X0,nil),X1))
| leqNat(X0,X0) ),
inference(factoring,[status(thm)],[p44]) ).
fof(f1,axiom,
! [X,X2] : tail(cons(X,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(f1_nnf,plain,
! [X,X2] : tail(cons(X,X2)) = X2,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,X2] : tail(cons(X,X2)) = X2,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
tail(cons(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p822,plain,
( cons(X0,X1) = merge(cons(X0,nil),X1)
| leqNat(X0,X0) ),
inference(superposition,[status(thm)],[p627,c1]) ).
fof(f10,axiom,
! [Z,Xs,Y2,Ys] :
( leqNat(Z,Y2)
=> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
fof(f10_nnf,plain,
! [Z,Xs,Y2,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys)))
| ~ leqNat(Z,Y2) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Z,Y2,Xs,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys)))
| ~ leqNat(Z,Y2) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c11,plain,
( merge(cons(X0,X1),cons(X2,X3)) = cons(X0,merge(X1,cons(X2,X3)))
| ~ leqNat(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f5,axiom,
! [Y] : leqNat(z,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(f5_nnf,plain,
! [Y] : leqNat(z,Y),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y] : leqNat(z,Y),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
leqNat(z,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p25,plain,
merge(cons(z,X0),cons(X1,X2)) = cons(z,merge(X0,cons(X1,X2))),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(p94,plain,
merge(cons(X0,X1),cons(z,X2)) = cons(z,merge(X2,cons(X0,X1))),
inference(superposition,[status(thm)],[p25,p30]) ).
cnf(p161,plain,
cons(z,merge(X0,cons(z,X1))) = cons(z,merge(X1,cons(z,X0))),
inference(superposition,[status(thm)],[p94,p25]) ).
cnf(p224,plain,
merge(X0,cons(z,X1)) = merge(X1,cons(z,X0)),
inference(superposition,[status(thm)],[p161,c1]) ).
fof(f8,axiom,
! [Y] : merge(nil,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(f8_nnf,plain,
! [Y] : merge(nil,Y) = Y,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Y] : merge(nil,Y) = Y,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
merge(nil,X0) = X0,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p248,plain,
merge(X0,cons(z,nil)) = cons(z,X0),
inference(superposition,[status(thm)],[p224,c9]) ).
cnf(p915,plain,
( cons(X0,cons(z,nil)) = cons(z,cons(X0,nil))
| leqNat(X0,X0) ),
inference(superposition,[status(thm)],[p822,p248]) ).
fof(f0,axiom,
! [X,X2] : head(cons(X,X2)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f0_nnf,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
head(cons(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p961,plain,
( z = X0
| leqNat(X0,X0) ),
inference(superposition,[status(thm)],[p915,c0]) ).
fof(f7,axiom,
! [Z,M] :
( leqNat(s(Z),s(M))
<=> leqNat(Z,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(f7_nnf,plain,
! [Z,M] :
( ( ~ leqNat(Z,M)
| leqNat(s(Z),s(M)) )
& ( leqNat(Z,M)
| ~ leqNat(s(Z),s(M)) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Z,M] :
( ( ~ leqNat(Z,M)
| leqNat(s(Z),s(M)) )
& ( leqNat(Z,M)
| ~ leqNat(s(Z),s(M)) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( leqNat(X0,X1)
| ~ leqNat(s(X0),s(X1)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p1024,plain,
( leqNat(X0,X0)
| z = s(X0) ),
inference(resolution,[status(thm)],[p961,c7]) ).
fof(f4,axiom,
! [X] : z != s(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f4_nnf,plain,
! [X] : z != s(X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : z != s(X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
z != s(X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p1034,plain,
leqNat(X0,X0),
inference(resolution,[status(thm)],[p1024,c4]) ).
cnf(p1074,plain,
merge(cons(X0,X1),cons(X0,X2)) = cons(X0,merge(X1,cons(X0,X2))),
inference(resolution,[status(thm)],[p1034,c11]) ).
cnf(p1098,plain,
cons(X0,merge(X1,cons(X0,X2))) = cons(X0,merge(X2,cons(X0,X1))),
inference(superposition,[status(thm)],[p1074,p30]) ).
cnf(p1120,plain,
merge(X0,cons(X1,X2)) = merge(X2,cons(X1,X0)),
inference(superposition,[status(thm)],[p1098,c1]) ).
cnf(p1220,plain,
merge(cons(X0,X1),cons(X2,X3)) = merge(X1,cons(X0,cons(X2,X3))),
inference(superposition,[status(thm)],[p1120,p30]) ).
cnf(p1213,plain,
merge(X0,cons(X1,nil)) = cons(X1,X0),
inference(superposition,[status(thm)],[p1120,c9]) ).
cnf(p1478,plain,
merge(X0,cons(X1,cons(X2,nil))) = cons(X2,cons(X1,X0)),
inference(superposition,[status(thm)],[p1220,p1213]) ).
cnf(p1508,plain,
cons(X0,cons(X1,nil)) = cons(X1,cons(X0,nil)),
inference(superposition,[status(thm)],[p1478,c9]) ).
cnf(p1535,plain,
X0 = X1,
inference(superposition,[status(thm)],[p1508,c0]) ).
cnf(p1536,plain,
$false,
inference(resolution,[status(thm)],[p1535,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 % Computer : n001.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Thu Sep 24 23:41:42 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.40/3.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.40/3.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------