%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG178+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 : n014.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 11:48:47 AM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 101 ( 33 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 96 ( 31 ~; 24 |; 17 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 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 : 48 ( 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> op1(U,op1(U,V)) = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> op2(U,op2(U,V)) = V ) ),
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(f9,plain,
! [U] :
( ! [V] :
( sorti2(op2(U,V))
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [U] :
( ! [V] :
( op1(U,op1(U,V)) = V
| ~ sorti1(V) )
| ~ sorti1(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
? [U] :
( ? [V] :
( op2(U,op2(U,V)) != V
& sorti2(V) )
& sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( op2(sK0_skl,op2(sK0_skl,sK1_skl)) != sK1_skl
& sorti2(sK1_skl)
& sorti2(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f13]) ).
fof(f15,plain,
sorti2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
sorti2(sK1_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
op2(sK0_skl,op2(sK0_skl,sK1_skl)) != sK1_skl,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,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] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( j(op2(X0,X1)) = op1(j(X0),j(X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [X0] :
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f25,plain,
! [X0] :
( sorti2(op2(sK0_skl,X0))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f15,f10]) ).
fof(f27,plain,
sorti1(j(sK1_skl)),
inference(resolution,[status(thm)],[f20,f16]) ).
fof(f28,plain,
sorti1(j(sK0_skl)),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f29,plain,
! [X0] :
( j(op2(X0,sK1_skl)) = op1(j(X0),j(sK1_skl))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f22,f16]) ).
fof(f31,plain,
h(j(sK1_skl)) = sK1_skl,
inference(resolution,[status(thm)],[f23,f16]) ).
fof(f36,plain,
! [X0] :
( op1(X0,op1(X0,j(sK1_skl))) = j(sK1_skl)
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f27,f12]) ).
fof(f40,plain,
sorti2(op2(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f25,f16]) ).
fof(f52,plain,
j(op2(sK0_skl,sK1_skl)) = op1(j(sK0_skl),j(sK1_skl)),
inference(resolution,[status(thm)],[f29,f15]) ).
fof(f61,plain,
op1(j(sK0_skl),op1(j(sK0_skl),j(sK1_skl))) = j(sK1_skl),
inference(resolution,[status(thm)],[f36,f28]) ).
fof(f63,plain,
op1(j(sK0_skl),j(op2(sK0_skl,sK1_skl))) = j(sK1_skl),
inference(forward_demodulation,[status(thm)],[f52,f61]) ).
fof(f72,plain,
sorti2(op2(sK0_skl,op2(sK0_skl,sK1_skl))),
inference(resolution,[status(thm)],[f40,f25]) ).
fof(f74,plain,
! [X0] :
( j(op2(X0,op2(sK0_skl,sK1_skl))) = op1(j(X0),j(op2(sK0_skl,sK1_skl)))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f40,f22]) ).
fof(f167,plain,
h(j(op2(sK0_skl,op2(sK0_skl,sK1_skl)))) = op2(sK0_skl,op2(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f72,f23]) ).
fof(f178,plain,
j(op2(sK0_skl,op2(sK0_skl,sK1_skl))) = op1(j(sK0_skl),j(op2(sK0_skl,sK1_skl))),
inference(resolution,[status(thm)],[f74,f15]) ).
fof(f182,plain,
h(j(sK1_skl)) = op2(sK0_skl,op2(sK0_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f185,f167]) ).
fof(f185,plain,
j(op2(sK0_skl,op2(sK0_skl,sK1_skl))) = j(sK1_skl),
inference(forward_demodulation,[status(thm)],[f63,f178]) ).
fof(f187,plain,
sK1_skl = op2(sK0_skl,op2(sK0_skl,sK1_skl)),
inference(forward_demodulation,[status(thm)],[f31,f182]) ).
fof(f188,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f187,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:00:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.059508 seconds
% 0.15/0.43 % CPU time: 0.252858 seconds
% 0.15/0.43 % Total memory used: 47.403 MB
% 0.15/0.43 % Net memory used: 46.848 MB
%------------------------------------------------------------------------------