%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 03:13:23 PM UTC 2026
% Result : Theorem 0.02s 0.52s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 27 unt; 0 def)
% Number of atoms : 148 ( 103 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 67 ~; 76 |; 2 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 179 ( 171 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,X2] : head(cons(X,X2)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,X2] : nil != cons(X,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : s(X) != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Y,Xs] : length(cons(Y,Xs)) = s(length(Xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Z,Y2] :
( x2(s(Z),s(Y2))
<=> x2(Z,Y2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X2] : x2(z,s(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Y] : x(nil,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Y,Z,Xs] : x(cons(Z,Xs),Y) = cons(Z,x(Xs,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Z,X2,X3] : rotate(s(Z),cons(X2,X3)) = rotate(Z,x(X3,cons(X2,nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Y] : rotate(z,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
? [N,M,Ys,Xs] :
~ ( x2(N,length(Xs))
=> ( x2(M,length(Ys))
=> ( Xs = Ys
=> ( rotate(s(z),Xs) != Xs
=> ( rotate(N,Xs) = rotate(M,Ys)
=> N = M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ? [N,M,Ys,Xs] :
~ ( x2(N,length(Xs))
=> ( x2(M,length(Ys))
=> ( Xs = Ys
=> ( rotate(s(z),Xs) != Xs
=> ( rotate(N,Xs) = rotate(M,Ys)
=> N = M ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : head(cons(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0,X1] : nil != cons(X0,X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0] : s(X0) != z,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [Z,Y2] :
( ( ~ x2(Z,Y2)
| x2(s(Z),s(Y2)) )
& ( x2(Z,Y2)
| ~ x2(s(Z),s(Y2)) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
( ! [Z,Y2] :
( ~ x2(Z,Y2)
| x2(s(Z),s(Y2)) )
& ! [Z,Y2] :
( x2(Z,Y2)
| ~ x2(s(Z),s(Y2)) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( ~ x2(X0,X1)
| x2(s(X0),s(X1)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0] : x2(z,s(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
! [X0] : x(nil,X0) = X0,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
! [X0,X1,X2] : x(cons(X0,X1),X2) = cons(X0,x(X1,X2)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
! [X0,X1,X2] : rotate(s(X0),cons(X1,X2)) = rotate(X0,x(X2,cons(X1,nil))),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0] : rotate(z,X0) = X0,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
! [N,M,Ys,Xs] :
( N = M
| rotate(N,Xs) != rotate(M,Ys)
| rotate(s(z),Xs) = Xs
| Xs != Ys
| ~ x2(M,length(Ys))
| ~ x2(N,length(Xs)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f39,plain,
! [N,Xs] :
( ! [M,Ys] :
( N = M
| rotate(N,Xs) != rotate(M,Ys)
| rotate(s(z),Xs) = Xs
| Xs != Ys
| ~ x2(M,length(Ys)) )
| ~ x2(N,length(Xs)) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| rotate(X0,X1) != rotate(X2,X3)
| rotate(s(z),X1) = X1
| X1 != X3
| ~ x2(X2,length(X3))
| ~ x2(X0,length(X1)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( X0 = X2
| rotate(X0,X1) != rotate(X2,X1)
| rotate(s(z),X1) = X1
| ~ x2(X2,length(X1))
| ~ x2(X0,length(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| rotate(X0,cons(X3,X1)) != rotate(X2,cons(X3,X1))
| rotate(s(z),cons(X3,X1)) = cons(X3,X1)
| ~ x2(X2,length(cons(X3,X1)))
| ~ x2(X0,s(length(X1))) ),
inference(paramodulation,[status(thm)],[f25,f41]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| rotate(X0,cons(X3,X1)) != rotate(X2,cons(X3,X1))
| rotate(s(z),cons(X3,X1)) = cons(X3,X1)
| ~ x2(X2,s(length(X1)))
| ~ x2(X0,s(length(X1))) ),
inference(forward_demodulation,[status(thm)],[f25,f44]) ).
fof(f46,plain,
! [X0] : x2(s(z),s(s(X0))),
inference(resolution,[status(thm)],[f29,f31]) ).
fof(f47,plain,
! [X0,X1] : rotate(s(z),cons(X0,X1)) = x(X1,cons(X0,nil)),
inference(paramodulation,[status(thm)],[f37,f36]) ).
fof(f48,plain,
! [X0,X1,X2,X3] : rotate(s(X0),cons(X1,cons(X2,X3))) = rotate(X0,cons(X2,x(X3,cons(X1,nil)))),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X2
| rotate(X0,cons(X4,cons(X3,X1))) != rotate(X2,cons(X4,cons(X3,X1)))
| rotate(s(z),cons(X4,cons(X3,X1))) = cons(X4,cons(X3,X1))
| ~ x2(X2,s(length(cons(X3,X1))))
| ~ x2(X0,s(s(length(X1)))) ),
inference(paramodulation,[status(thm)],[f25,f45]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X2
| rotate(X0,cons(X3,cons(X4,X1))) != rotate(X2,cons(X3,cons(X4,X1)))
| rotate(s(z),cons(X3,cons(X4,X1))) = cons(X3,cons(X4,X1))
| ~ x2(X2,s(s(length(X1))))
| ~ x2(X0,s(s(length(X1)))) ),
inference(forward_demodulation,[status(thm)],[f25,f52]) ).
fof(f61,plain,
! [X0] : x2(s(s(z)),s(s(s(X0)))),
inference(resolution,[status(thm)],[f46,f29]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X2
| rotate(X0,cons(X4,cons(X3,X1))) != rotate(X2,cons(X4,cons(X3,X1)))
| x(cons(X3,X1),cons(X4,nil)) = cons(X4,cons(X3,X1))
| ~ x2(X2,s(s(length(X1))))
| ~ x2(X0,s(s(length(X1)))) ),
inference(forward_demodulation,[status(thm)],[f47,f55]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X2
| rotate(X0,cons(X4,cons(X3,X1))) != rotate(X2,cons(X4,cons(X3,X1)))
| cons(X3,x(X1,cons(X4,nil))) = cons(X4,cons(X3,X1))
| ~ x2(X2,s(s(length(X1))))
| ~ x2(X0,s(s(length(X1)))) ),
inference(forward_demodulation,[status(thm)],[f34,f73]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( z = X0
| rotate(z,cons(X3,cons(X2,X1))) != rotate(X0,cons(X3,cons(X2,X1)))
| cons(X2,x(X1,cons(X3,nil))) = cons(X3,cons(X2,X1))
| ~ x2(X0,s(s(length(X1)))) ),
inference(resolution,[status(thm)],[f74,f31]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( z = X0
| cons(X3,cons(X2,X1)) != rotate(X0,cons(X3,cons(X2,X1)))
| cons(X2,x(X1,cons(X3,nil))) = cons(X3,cons(X2,X1))
| ~ x2(X0,s(s(length(X1)))) ),
inference(forward_demodulation,[status(thm)],[f37,f76]) ).
fof(f94,plain,
! [X0,X1,X2] : rotate(s(s(z)),cons(X0,cons(X1,X2))) = x(x(X2,cons(X0,nil)),cons(X1,nil)),
inference(paramodulation,[status(thm)],[f47,f48]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4] :
( z = X0
| cons(X4,cons(X2,cons(X3,X1))) != rotate(X0,cons(X4,cons(X2,cons(X3,X1))))
| cons(X2,x(cons(X3,X1),cons(X4,nil))) = cons(X4,cons(X2,cons(X3,X1)))
| ~ x2(X0,s(s(s(length(X1))))) ),
inference(paramodulation,[status(thm)],[f25,f81]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( z = X0
| cons(X4,cons(X2,cons(X3,X1))) != rotate(X0,cons(X4,cons(X2,cons(X3,X1))))
| cons(X2,cons(X3,x(X1,cons(X4,nil)))) = cons(X4,cons(X2,cons(X3,X1)))
| ~ x2(X0,s(s(s(length(X1))))) ),
inference(forward_demodulation,[status(thm)],[f34,f118]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( z = s(s(z))
| cons(X3,cons(X0,cons(X1,X2))) != rotate(s(s(z)),cons(X3,cons(X0,cons(X1,X2))))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f121,f61]) ).
fof(f305,plain,
! [X0,X1,X2,X3] :
( z = s(s(z))
| cons(X3,cons(X0,cons(X1,X2))) != x(x(cons(X1,X2),cons(X3,nil)),cons(X0,nil))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f94,f300]) ).
fof(f306,plain,
! [X0,X1,X2,X3] :
( z = s(s(z))
| cons(X3,cons(X0,cons(X1,X2))) != x(cons(X1,x(X2,cons(X3,nil))),cons(X0,nil))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f34,f305]) ).
fof(f307,plain,
! [X0,X1,X2,X3] :
( z = s(s(z))
| cons(X3,cons(X0,cons(X1,X2))) != cons(X1,x(x(X2,cons(X3,nil)),cons(X0,nil)))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f34,f306]) ).
fof(f308,plain,
! [X0,X1,X2,X3] :
( cons(X3,cons(X0,cons(X1,X2))) != cons(X1,x(x(X2,cons(X3,nil)),cons(X0,nil)))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f23]) ).
fof(f719,plain,
! [X0,X1,X2,X3,X4] :
( cons(X4,cons(X0,cons(X1,cons(X2,X3)))) != cons(X1,x(cons(X2,x(X3,cons(X4,nil))),cons(X0,nil)))
| cons(X0,cons(X1,x(cons(X2,X3),cons(X4,nil)))) = cons(X4,cons(X0,cons(X1,cons(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f34,f308]) ).
fof(f726,plain,
! [X0,X1,X2,X3,X4] :
( cons(X4,cons(X0,cons(X1,cons(X2,X3)))) != cons(X1,x(cons(X2,x(X3,cons(X4,nil))),cons(X0,nil)))
| cons(X0,cons(X1,cons(X2,x(X3,cons(X4,nil))))) = cons(X4,cons(X0,cons(X1,cons(X2,X3)))) ),
inference(forward_demodulation,[status(thm)],[f34,f719]) ).
fof(f727,plain,
! [X0,X1,X2,X3,X4] :
( cons(X4,cons(X0,cons(X1,cons(X2,X3)))) != cons(X1,cons(X2,x(x(X3,cons(X4,nil)),cons(X0,nil))))
| cons(X0,cons(X1,cons(X2,x(X3,cons(X4,nil))))) = cons(X4,cons(X0,cons(X1,cons(X2,X3)))) ),
inference(forward_demodulation,[status(thm)],[f34,f726]) ).
fof(f1397,plain,
! [X0,X1,X2,X3] :
( cons(X3,cons(X0,cons(X1,cons(X2,nil)))) != cons(X1,cons(X2,x(cons(X3,nil),cons(X0,nil))))
| cons(X0,cons(X1,cons(X2,x(nil,cons(X3,nil))))) = cons(X3,cons(X0,cons(X1,cons(X2,nil)))) ),
inference(paramodulation,[status(thm)],[f33,f727]) ).
fof(f1405,plain,
! [X0,X1,X2,X3] :
( cons(X3,cons(X0,cons(X1,cons(X2,nil)))) != cons(X1,cons(X2,x(cons(X3,nil),cons(X0,nil))))
| cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,cons(X2,nil)))) ),
inference(forward_demodulation,[status(thm)],[f33,f1397]) ).
fof(f1406,plain,
! [X0,X1,X2,X3] :
( cons(X3,cons(X0,cons(X1,cons(X2,nil)))) != cons(X1,cons(X2,cons(X3,x(nil,cons(X0,nil)))))
| cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,cons(X2,nil)))) ),
inference(forward_demodulation,[status(thm)],[f34,f1405]) ).
fof(f1407,plain,
! [X0,X1,X2,X3] :
( cons(X3,cons(X0,cons(X1,cons(X2,nil)))) != cons(X1,cons(X2,cons(X3,cons(X0,nil))))
| cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,cons(X2,nil)))) ),
inference(forward_demodulation,[status(thm)],[f33,f1406]) ).
fof(f1408,plain,
! [X0,X1] : cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))),
inference(equality_resolution,[status(thm)],[f1407]) ).
fof(f1457,plain,
! [X0,X1] : head(cons(X0,cons(X1,cons(X0,cons(X1,nil))))) = X1,
inference(paramodulation,[status(thm)],[f1408,f19]) ).
fof(f1937,plain,
! [X0,X1] : X0 = X1,
inference(forward_demodulation,[status(thm)],[f19,f1457]) ).
fof(f2388,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f21,f1937]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 10:34:52 UTC 2026
% 0.02/0.35 % CPUTime :
% 0.02/0.36 % Drodi V4.1.1
% 0.02/0.52 % Refutation found
% 0.02/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.91/0.56 % Elapsed time: 0.187156 seconds
% 0.91/0.56 % CPU time: 1.196037 seconds
% 0.91/0.56 % Total memory used: 138.312 MB
% 0.91/0.56 % Net memory used: 137.495 MB
%------------------------------------------------------------------------------