%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG073+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 : n009.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 11:48:01 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 19 unt; 0 def)
% Number of atoms : 140 ( 61 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 153 ( 58 ~; 50 |; 25 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
? [U] :
( ? [V] :
( op1(U,V) != U
& op1(V,V) = U
& op1(U,U) = V
& sorti1(V) )
& sorti1(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ? [U] :
( ? [V] :
( op2(U,V) != U
& op2(V,V) = U
& op2(U,U) = V
& sorti2(V) )
& 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(f7,plain,
! [U] :
( ! [V] :
( sorti1(op1(U,V))
| ~ sorti1(V) )
| ~ sorti1(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
( op1(sK0_skl,sK1_skl) != sK0_skl
& op1(sK1_skl,sK1_skl) = sK0_skl
& op1(sK0_skl,sK0_skl) = sK1_skl
& sorti1(sK1_skl)
& sorti1(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f3]) ).
fof(f12,plain,
sorti1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
sorti1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f14,plain,
op1(sK0_skl,sK0_skl) = sK1_skl,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
op1(sK1_skl,sK1_skl) = sK0_skl,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f16,plain,
op1(sK0_skl,sK1_skl) != sK0_skl,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f17,plain,
! [U] :
( ! [V] :
( op2(U,V) = U
| op2(V,V) != U
| op2(U,U) != V
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
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(f22,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f25,plain,
! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,plain,
! [X0] :
( op2(X0,op2(X0,X0)) = X0
| op2(op2(X0,X0),op2(X0,X0)) != X0
| ~ sorti2(op2(X0,X0))
| ~ sorti2(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f27,plain,
! [X0] :
( sorti1(op1(sK0_skl,X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f28,plain,
j(h(sK0_skl)) = sK0_skl,
inference(resolution,[status(thm)],[f12,f25]) ).
fof(f29,plain,
! [X0] :
( h(op1(sK0_skl,X0)) = op2(h(sK0_skl),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f12,f22]) ).
fof(f30,plain,
sorti2(h(sK0_skl)),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f33,plain,
sorti1(op1(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f13,f27]) ).
fof(f36,plain,
! [X0] :
( h(op1(sK1_skl,X0)) = op2(h(sK1_skl),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f13,f22]) ).
fof(f37,plain,
sorti2(h(sK1_skl)),
inference(resolution,[status(thm)],[f13,f20]) ).
fof(f50,plain,
h(op1(sK0_skl,sK1_skl)) = op2(h(sK0_skl),h(sK1_skl)),
inference(resolution,[status(thm)],[f29,f13]) ).
fof(f51,plain,
h(op1(sK0_skl,sK0_skl)) = op2(h(sK0_skl),h(sK0_skl)),
inference(resolution,[status(thm)],[f29,f12]) ).
fof(f52,plain,
h(sK1_skl) = op2(h(sK0_skl),h(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f14,f51]) ).
fof(f53,plain,
( op2(h(sK0_skl),op2(h(sK0_skl),h(sK0_skl))) = h(sK0_skl)
| op2(op2(h(sK0_skl),h(sK0_skl)),op2(h(sK0_skl),h(sK0_skl))) != h(sK0_skl)
| ~ sorti2(h(sK1_skl))
| ~ sorti2(h(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f52,f26]) ).
fof(f54,plain,
( op2(h(sK0_skl),op2(h(sK0_skl),h(sK0_skl))) = h(sK0_skl)
| op2(h(sK1_skl),op2(h(sK0_skl),h(sK0_skl))) != h(sK0_skl)
| ~ sorti2(h(sK1_skl))
| ~ sorti2(h(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f52,f53]) ).
fof(f55,plain,
( op2(h(sK0_skl),op2(h(sK0_skl),h(sK0_skl))) = h(sK0_skl)
| op2(h(sK1_skl),h(sK1_skl)) != h(sK0_skl)
| ~ sorti2(h(sK1_skl))
| ~ sorti2(h(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f52,f54]) ).
fof(f56,plain,
( op2(h(sK0_skl),h(sK1_skl)) = h(sK0_skl)
| op2(h(sK1_skl),h(sK1_skl)) != h(sK0_skl)
| ~ sorti2(h(sK1_skl))
| ~ sorti2(h(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f52,f55]) ).
fof(f57,plain,
( h(op1(sK0_skl,sK1_skl)) = h(sK0_skl)
| op2(h(sK1_skl),h(sK1_skl)) != h(sK0_skl)
| ~ sorti2(h(sK1_skl))
| ~ sorti2(h(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f50,f56]) ).
fof(f58,plain,
( h(op1(sK0_skl,sK1_skl)) = h(sK0_skl)
| op2(h(sK1_skl),h(sK1_skl)) != h(sK0_skl)
| ~ sorti2(h(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f30]) ).
fof(f59,plain,
h(op1(sK1_skl,sK1_skl)) = op2(h(sK1_skl),h(sK1_skl)),
inference(resolution,[status(thm)],[f36,f13]) ).
fof(f61,plain,
( h(op1(sK0_skl,sK1_skl)) = h(sK0_skl)
| h(sK0_skl) != h(sK0_skl)
| ~ sorti2(h(sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f62,f58]) ).
fof(f62,plain,
h(sK0_skl) = op2(h(sK1_skl),h(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f15,f59]) ).
fof(f63,plain,
( h(op1(sK0_skl,sK1_skl)) = h(sK0_skl)
| ~ sorti2(h(sK1_skl)) ),
inference(trivial_equality_resolution,[status(thm)],[f61]) ).
fof(f65,plain,
h(op1(sK0_skl,sK1_skl)) = h(sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f63,f37]) ).
fof(f103,plain,
j(h(op1(sK0_skl,sK1_skl))) = op1(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f33,f25]) ).
fof(f110,plain,
j(h(sK0_skl)) = op1(sK0_skl,sK1_skl),
inference(forward_demodulation,[status(thm)],[f65,f103]) ).
fof(f111,plain,
sK0_skl = op1(sK0_skl,sK1_skl),
inference(forward_demodulation,[status(thm)],[f28,f110]) ).
fof(f112,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f111,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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 12:55:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.048637 seconds
% 0.13/0.41 % CPU time: 0.158519 seconds
% 0.13/0.41 % Total memory used: 60.970 MB
% 0.13/0.41 % Net memory used: 60.493 MB
%------------------------------------------------------------------------------