%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.24s 0.58s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 23 unt; 0 def)
% Number of atoms : 137 ( 56 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 133 ( 49 ~; 39 |; 23 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 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 : 58 ( 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( op1(U,op1(V,U)) = V
& op1(V,op1(V,U)) != U
& sorti1(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( op2(U,op2(V,U)) = V
& op2(V,op2(V,U)) != U
& sorti2(V) ) ),
file('/export/starexec/sandbox/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/sandbox/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,
! [U] :
( ? [V] :
( op1(U,op1(V,U)) = V
& op1(V,op1(V,U)) != U
& sorti1(V) )
| ~ sorti1(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [U] :
( ( op1(U,op1(sK0_skl(U),U)) = sK0_skl(U)
& op1(sK0_skl(U),op1(sK0_skl(U),U)) != U
& sorti1(sK0_skl(U)) )
| ~ sorti1(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(V,sK0_skl(U))],[f11]) ).
fof(f13,plain,
! [X0] :
( sorti1(sK0_skl(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( op1(sK0_skl(X0),op1(sK0_skl(X0),X0)) != X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0] :
( op1(X0,op1(sK0_skl(X0),X0)) = sK0_skl(X0)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
? [U] :
( ! [V] :
( op2(U,op2(V,U)) != V
| op2(V,op2(V,U)) = U
| ~ sorti2(V) )
& sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
( ! [V] :
( op2(sK1_skl,op2(V,sK1_skl)) != V
| op2(V,op2(V,sK1_skl)) = sK1_skl
| ~ sorti2(V) )
& sorti2(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(U,sK1_skl)],[f16]) ).
fof(f18,plain,
sorti2(sK1_skl),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0] :
( op2(sK1_skl,op2(X0,sK1_skl)) != X0
| op2(X0,op2(X0,sK1_skl)) = sK1_skl
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,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(f21,plain,
! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( j(op2(X0,X1)) = op1(j(X0),j(X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f25,plain,
! [X0] :
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f26,plain,
! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f29,plain,
h(j(sK1_skl)) = sK1_skl,
inference(resolution,[status(thm)],[f18,f25]) ).
fof(f30,plain,
sorti1(j(sK1_skl)),
inference(resolution,[status(thm)],[f18,f22]) ).
fof(f33,plain,
! [X0] :
( h(op1(j(sK1_skl),X0)) = op2(h(j(sK1_skl)),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f30,f23]) ).
fof(f37,plain,
sorti1(sK0_skl(j(sK1_skl))),
inference(resolution,[status(thm)],[f13,f30]) ).
fof(f40,plain,
! [X0] :
( sorti1(op1(sK0_skl(j(sK1_skl)),X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f37,f8]) ).
fof(f41,plain,
j(h(sK0_skl(j(sK1_skl)))) = sK0_skl(j(sK1_skl)),
inference(resolution,[status(thm)],[f37,f26]) ).
fof(f42,plain,
! [X0] :
( h(op1(sK0_skl(j(sK1_skl)),X0)) = op2(h(sK0_skl(j(sK1_skl))),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f37,f23]) ).
fof(f43,plain,
sorti2(h(sK0_skl(j(sK1_skl)))),
inference(resolution,[status(thm)],[f37,f21]) ).
fof(f46,plain,
! [X0] :
( j(op2(h(sK0_skl(j(sK1_skl))),X0)) = op1(j(h(sK0_skl(j(sK1_skl)))),j(X0))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f43,f24]) ).
fof(f57,plain,
sorti1(op1(sK0_skl(j(sK1_skl)),j(sK1_skl))),
inference(resolution,[status(thm)],[f40,f30]) ).
fof(f67,plain,
op1(sK0_skl(j(sK1_skl)),op1(sK0_skl(j(sK1_skl)),j(sK1_skl))) != j(sK1_skl),
inference(resolution,[status(thm)],[f14,f30]) ).
fof(f71,plain,
op1(j(sK1_skl),op1(sK0_skl(j(sK1_skl)),j(sK1_skl))) = sK0_skl(j(sK1_skl)),
inference(resolution,[status(thm)],[f15,f30]) ).
fof(f72,plain,
( op2(sK1_skl,op2(h(sK0_skl(j(sK1_skl))),sK1_skl)) != h(sK0_skl(j(sK1_skl)))
| op2(h(sK0_skl(j(sK1_skl))),op2(h(sK0_skl(j(sK1_skl))),sK1_skl)) = sK1_skl ),
inference(resolution,[status(thm)],[f19,f43]) ).
fof(f86,plain,
j(h(op1(sK0_skl(j(sK1_skl)),j(sK1_skl)))) = op1(sK0_skl(j(sK1_skl)),j(sK1_skl)),
inference(resolution,[status(thm)],[f57,f26]) ).
fof(f88,plain,
sorti2(h(op1(sK0_skl(j(sK1_skl)),j(sK1_skl)))),
inference(resolution,[status(thm)],[f57,f21]) ).
fof(f125,plain,
! [X0] :
( h(op1(j(sK1_skl),X0)) = op2(sK1_skl,h(X0))
| ~ sorti1(X0) ),
inference(forward_demodulation,[status(thm)],[f29,f33]) ).
fof(f127,plain,
h(op1(j(sK1_skl),op1(sK0_skl(j(sK1_skl)),j(sK1_skl)))) = op2(sK1_skl,h(op1(sK0_skl(j(sK1_skl)),j(sK1_skl)))),
inference(resolution,[status(thm)],[f125,f57]) ).
fof(f134,plain,
h(op1(sK0_skl(j(sK1_skl)),j(sK1_skl))) = op2(h(sK0_skl(j(sK1_skl))),h(j(sK1_skl))),
inference(resolution,[status(thm)],[f42,f30]) ).
fof(f135,plain,
h(op1(sK0_skl(j(sK1_skl)),j(sK1_skl))) = op2(h(sK0_skl(j(sK1_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f29,f134]) ).
fof(f136,plain,
sorti2(op2(h(sK0_skl(j(sK1_skl))),sK1_skl)),
inference(backward_demodulation,[status(thm)],[f135,f88]) ).
fof(f139,plain,
j(op2(h(sK0_skl(j(sK1_skl))),sK1_skl)) = op1(sK0_skl(j(sK1_skl)),j(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f135,f86]) ).
fof(f141,plain,
h(sK0_skl(j(sK1_skl))) = op2(sK1_skl,h(op1(sK0_skl(j(sK1_skl)),j(sK1_skl)))),
inference(forward_demodulation,[status(thm)],[f71,f127]) ).
fof(f142,plain,
h(sK0_skl(j(sK1_skl))) = op2(sK1_skl,op2(h(sK0_skl(j(sK1_skl))),sK1_skl)),
inference(forward_demodulation,[status(thm)],[f135,f141]) ).
fof(f188,plain,
( h(sK0_skl(j(sK1_skl))) != h(sK0_skl(j(sK1_skl)))
| op2(h(sK0_skl(j(sK1_skl))),op2(h(sK0_skl(j(sK1_skl))),sK1_skl)) = sK1_skl ),
inference(forward_demodulation,[status(thm)],[f142,f72]) ).
fof(f190,plain,
op2(h(sK0_skl(j(sK1_skl))),op2(h(sK0_skl(j(sK1_skl))),sK1_skl)) = sK1_skl,
inference(trivial_equality_resolution,[status(thm)],[f188]) ).
fof(f440,plain,
! [X0] :
( j(op2(h(sK0_skl(j(sK1_skl))),X0)) = op1(sK0_skl(j(sK1_skl)),j(X0))
| ~ sorti2(X0) ),
inference(forward_demodulation,[status(thm)],[f41,f46]) ).
fof(f443,plain,
j(op2(h(sK0_skl(j(sK1_skl))),op2(h(sK0_skl(j(sK1_skl))),sK1_skl))) = op1(sK0_skl(j(sK1_skl)),j(op2(h(sK0_skl(j(sK1_skl))),sK1_skl))),
inference(resolution,[status(thm)],[f440,f136]) ).
fof(f452,plain,
j(sK1_skl) = op1(sK0_skl(j(sK1_skl)),j(op2(h(sK0_skl(j(sK1_skl))),sK1_skl))),
inference(forward_demodulation,[status(thm)],[f190,f443]) ).
fof(f453,plain,
j(sK1_skl) = op1(sK0_skl(j(sK1_skl)),op1(sK0_skl(j(sK1_skl)),j(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f139,f452]) ).
fof(f454,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f453,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n019.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 12:55:06 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.24/0.58 % Refutation found
% 0.24/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.62 % Elapsed time: 0.163137 seconds
% 0.24/0.62 % CPU time: 0.927115 seconds
% 0.24/0.62 % Total memory used: 62.875 MB
% 0.24/0.62 % Net memory used: 62.199 MB
%------------------------------------------------------------------------------