%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG018+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 11:47:46 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 90 ( 30 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 91 ( 30 ~; 22 |; 19 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
? [U] :
( ! [V] :
( sorti1(V)
=> op1(V,V) = U )
& sorti1(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ? [U] :
( ! [V] :
( sorti2(V)
=> op2(V,V) = U )
& sorti2(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f11,plain,
? [U] :
( ! [V] :
( op1(V,V) = U
| ~ sorti1(V) )
& sorti1(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
( ! [V] :
( op1(V,V) = sK0_skl
| ~ sorti1(V) )
& sorti1(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl)],[f11]) ).
fof(f13,plain,
sorti1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( op1(X0,X0) = sK0_skl
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [U] :
( ? [V] :
( op2(V,V) != U
& sorti2(V) )
| ~ sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [U] :
( ( op2(sK1_skl(U),sK1_skl(U)) != U
& sorti2(sK1_skl(U)) )
| ~ sorti2(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(V,sK1_skl(U))],[f15]) ).
fof(f17,plain,
! [X0] :
( sorti2(sK1_skl(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( op2(sK1_skl(X0),sK1_skl(X0)) != X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [Y] :
( ! [Z] :
( j(op2(Y,Z)) = op1(j(Y),j(Z))
| ~ sorti2(Z) )
| ~ sorti2(Y) )
& ! [W] :
( ! [X] :
( h(op1(W,X)) = op2(h(W),h(X))
| ~ sorti1(X) )
| ~ sorti1(W) )
& ! [V] :
( sorti1(j(V))
| ~ sorti2(V) )
& ! [U] :
( sorti2(h(U))
| ~ sorti1(U) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,plain,
! [X0] :
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f29,plain,
sorti2(h(sK0_skl)),
inference(resolution,[status(thm)],[f13,f20]) ).
fof(f40,plain,
sorti2(sK1_skl(h(sK0_skl))),
inference(resolution,[status(thm)],[f17,f29]) ).
fof(f51,plain,
h(j(sK1_skl(h(sK0_skl)))) = sK1_skl(h(sK0_skl)),
inference(resolution,[status(thm)],[f40,f24]) ).
fof(f52,plain,
sorti1(j(sK1_skl(h(sK0_skl)))),
inference(resolution,[status(thm)],[f40,f21]) ).
fof(f63,plain,
op1(j(sK1_skl(h(sK0_skl))),j(sK1_skl(h(sK0_skl)))) = sK0_skl,
inference(resolution,[status(thm)],[f52,f14]) ).
fof(f67,plain,
! [X0] :
( h(op1(j(sK1_skl(h(sK0_skl))),X0)) = op2(h(j(sK1_skl(h(sK0_skl)))),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f52,f22]) ).
fof(f72,plain,
op2(sK1_skl(h(sK0_skl)),sK1_skl(h(sK0_skl))) != h(sK0_skl),
inference(resolution,[status(thm)],[f18,f29]) ).
fof(f487,plain,
! [X0] :
( h(op1(j(sK1_skl(h(sK0_skl))),X0)) = op2(sK1_skl(h(sK0_skl)),h(X0))
| ~ sorti1(X0) ),
inference(forward_demodulation,[status(thm)],[f51,f67]) ).
fof(f498,plain,
h(op1(j(sK1_skl(h(sK0_skl))),j(sK1_skl(h(sK0_skl))))) = op2(sK1_skl(h(sK0_skl)),h(j(sK1_skl(h(sK0_skl))))),
inference(resolution,[status(thm)],[f487,f52]) ).
fof(f502,plain,
h(sK0_skl) = op2(sK1_skl(h(sK0_skl)),h(j(sK1_skl(h(sK0_skl))))),
inference(forward_demodulation,[status(thm)],[f63,f498]) ).
fof(f503,plain,
h(sK0_skl) = op2(sK1_skl(h(sK0_skl)),sK1_skl(h(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f51,f502]) ).
fof(f504,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f503,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG018+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 12:53:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.053120 seconds
% 0.09/0.43 % CPU time: 0.186641 seconds
% 0.09/0.43 % Total memory used: 45.624 MB
% 0.09/0.43 % Net memory used: 45.132 MB
%------------------------------------------------------------------------------