%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG072+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 : n018.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 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 39 unt; 0 def)
% Number of atoms : 223 ( 117 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 219 ( 82 ~; 68 |; 45 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 80 ( 71 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
( ? [V] :
( unit1 = V
& sorti1(V) )
& ! [U] :
( sorti1(U)
=> ( op1(U,unit1) = U
& op1(unit1,U) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( ? [V] :
( unit2 = V
& sorti2(V) )
& ! [U] :
( sorti2(U)
=> ( op2(U,unit2) = U
& op2(unit2,U) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
? [U] :
( ! [V] :
( sorti1(V)
=> ! [W] :
( sorti1(W)
=> ( ( U != unit1
& op1(V,U) = W )
| op1(V,W) != U ) ) )
& sorti1(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ ? [U] :
( ! [V] :
( sorti2(V)
=> ! [W] :
( sorti2(W)
=> ( ( U != unit2
& op2(V,U) = W )
| op2(V,W) != U ) ) )
& sorti2(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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(f10,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)],[f9]) ).
fof(f12,plain,
( ? [V] :
( unit1 = V
& sorti1(V) )
& ! [U] :
( ( op1(U,unit1) = U
& op1(unit1,U) = U )
| ~ sorti1(U) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
( unit1 = sK0_skl
& sorti1(sK0_skl)
& ! [U] :
( ( op1(U,unit1) = U
& op1(unit1,U) = U )
| ~ sorti1(U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(V,sK0_skl)],[f12]) ).
fof(f14,plain,
! [X0] :
( op1(unit1,X0) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( op1(X0,unit1) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
sorti1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
unit1 = sK0_skl,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f19,plain,
( ? [V] :
( unit2 = V
& sorti2(V) )
& ! [U] :
( ( op2(U,unit2) = U
& op2(unit2,U) = U )
| ~ sorti2(U) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
( unit2 = sK1_skl
& sorti2(sK1_skl)
& ! [U] :
( ( op2(U,unit2) = U
& op2(unit2,U) = U )
| ~ sorti2(U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(V,sK1_skl)],[f19]) ).
fof(f22,plain,
! [X0] :
( op2(X0,unit2) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
sorti2(sK1_skl),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,plain,
unit2 = sK1_skl,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f29,plain,
? [U] :
( ! [V] :
( ! [W] :
( ( U != unit1
& op1(V,U) = W )
| op1(V,W) != U
| ~ sorti1(W) )
| ~ sorti1(V) )
& sorti1(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
( ! [V] :
( ! [W] :
( ( sK2_skl != unit1
& op1(V,sK2_skl) = W )
| op1(V,W) != sK2_skl
| ~ sorti1(W) )
| ~ sorti1(V) )
& sorti1(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(U,sK2_skl)],[f29]) ).
fof(f31,plain,
sorti1(sK2_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( op1(X0,sK2_skl) = X1
| op1(X0,X1) != sK2_skl
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( sK2_skl != unit1
| op1(X0,X1) != sK2_skl
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [U] :
( ? [V] :
( ? [W] :
( ( U = unit2
| op2(V,U) != W )
& op2(V,W) = U
& sorti2(W) )
& sorti2(V) )
| ~ sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [U] :
( ( ( U = unit2
| op2(sK3_skl(U),U) != sK4_skl(U) )
& op2(sK3_skl(U),sK4_skl(U)) = U
& sorti2(sK4_skl(U))
& sorti2(sK3_skl(U)) )
| ~ sorti2(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(V,sK3_skl(U)),skolemize(W,sK4_skl(U))],[f34]) ).
fof(f36,plain,
! [X0] :
( sorti2(sK3_skl(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0] :
( sorti2(sK4_skl(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0] :
( op2(sK3_skl(X0),sK4_skl(X0)) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [X0] :
( X0 = unit2
| op2(sK3_skl(X0),X0) != sK4_skl(X0)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f40,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)],[f10]) ).
fof(f41,plain,
! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( j(op2(X0,X1)) = op1(j(X0),j(X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0] :
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f47,plain,
! [X0] :
( op1(X0,sK0_skl) = X0
| ~ sorti1(X0) ),
inference(backward_demodulation,[status(thm)],[f17,f15]) ).
fof(f48,plain,
! [X0] :
( op1(sK0_skl,X0) = X0
| ~ sorti1(X0) ),
inference(backward_demodulation,[status(thm)],[f17,f14]) ).
fof(f50,plain,
! [X0] :
( op2(X0,sK1_skl) = X0
| ~ sorti2(X0) ),
inference(backward_demodulation,[status(thm)],[f24,f22]) ).
fof(f53,plain,
! [X0,X1] :
( sK2_skl != sK0_skl
| op1(X0,X1) != sK2_skl
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f33]) ).
fof(f54,plain,
! [X0] :
( X0 = sK1_skl
| op2(sK3_skl(X0),X0) != sK4_skl(X0)
| ~ sorti2(X0) ),
inference(forward_demodulation,[status(thm)],[f24,f39]) ).
fof(f56,plain,
j(h(sK0_skl)) = sK0_skl,
inference(resolution,[status(thm)],[f16,f46]) ).
fof(f57,plain,
! [X0] :
( h(op1(sK0_skl,X0)) = op2(h(sK0_skl),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f16,f43]) ).
fof(f58,plain,
sorti2(h(sK0_skl)),
inference(resolution,[status(thm)],[f16,f41]) ).
fof(f68,plain,
h(j(sK1_skl)) = sK1_skl,
inference(resolution,[status(thm)],[f23,f45]) ).
fof(f69,plain,
sorti1(j(sK1_skl)),
inference(resolution,[status(thm)],[f23,f42]) ).
fof(f72,plain,
j(h(sK2_skl)) = sK2_skl,
inference(resolution,[status(thm)],[f31,f46]) ).
fof(f74,plain,
sorti2(h(sK2_skl)),
inference(resolution,[status(thm)],[f31,f41]) ).
fof(f89,plain,
sorti2(sK3_skl(h(sK2_skl))),
inference(resolution,[status(thm)],[f36,f74]) ).
fof(f92,plain,
sorti2(sK4_skl(h(sK2_skl))),
inference(resolution,[status(thm)],[f37,f74]) ).
fof(f98,plain,
! [X0] :
( sK2_skl != sK0_skl
| op1(sK2_skl,X0) != sK2_skl
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f53,f31]) ).
fof(f101,plain,
op2(sK3_skl(h(sK2_skl)),sK4_skl(h(sK2_skl))) = h(sK2_skl),
inference(resolution,[status(thm)],[f38,f74]) ).
fof(f106,plain,
! [X0] :
( j(op2(sK3_skl(h(sK2_skl)),X0)) = op1(j(sK3_skl(h(sK2_skl))),j(X0))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f89,f44]) ).
fof(f108,plain,
h(j(sK3_skl(h(sK2_skl)))) = sK3_skl(h(sK2_skl)),
inference(resolution,[status(thm)],[f89,f45]) ).
fof(f109,plain,
sorti1(j(sK3_skl(h(sK2_skl)))),
inference(resolution,[status(thm)],[f89,f42]) ).
fof(f117,plain,
h(op1(sK0_skl,j(sK1_skl))) = op2(h(sK0_skl),h(j(sK1_skl))),
inference(resolution,[status(thm)],[f57,f69]) ).
fof(f120,plain,
h(op1(sK0_skl,j(sK1_skl))) = op2(h(sK0_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f68,f117]) ).
fof(f126,plain,
h(j(sK4_skl(h(sK2_skl)))) = sK4_skl(h(sK2_skl)),
inference(resolution,[status(thm)],[f92,f45]) ).
fof(f127,plain,
sorti1(j(sK4_skl(h(sK2_skl)))),
inference(resolution,[status(thm)],[f92,f42]) ).
fof(f137,plain,
! [X0] :
( op1(j(sK3_skl(h(sK2_skl))),sK2_skl) = X0
| op1(j(sK3_skl(h(sK2_skl))),X0) != sK2_skl
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f109,f32]) ).
fof(f141,plain,
! [X0] :
( h(op1(j(sK3_skl(h(sK2_skl))),X0)) = op2(h(j(sK3_skl(h(sK2_skl)))),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f109,f43]) ).
fof(f144,plain,
! [X0] :
( h(op1(j(sK3_skl(h(sK2_skl))),X0)) = op2(sK3_skl(h(sK2_skl)),h(X0))
| ~ sorti1(X0) ),
inference(forward_demodulation,[status(thm)],[f108,f141]) ).
fof(f200,plain,
op1(sK2_skl,sK0_skl) = sK2_skl,
inference(resolution,[status(thm)],[f47,f31]) ).
fof(f211,plain,
op1(sK0_skl,j(sK1_skl)) = j(sK1_skl),
inference(resolution,[status(thm)],[f48,f69]) ).
fof(f222,plain,
h(j(sK1_skl)) = op2(h(sK0_skl),sK1_skl),
inference(backward_demodulation,[status(thm)],[f211,f120]) ).
fof(f231,plain,
sK1_skl = op2(h(sK0_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f68,f222]) ).
fof(f239,plain,
op2(h(sK0_skl),sK1_skl) = h(sK0_skl),
inference(resolution,[status(thm)],[f50,f58]) ).
fof(f247,plain,
j(sK1_skl) = sK0_skl,
inference(backward_demodulation,[status(thm)],[f288,f56]) ).
fof(f288,plain,
sK1_skl = h(sK0_skl),
inference(forward_demodulation,[status(thm)],[f231,f239]) ).
fof(f353,plain,
( sK2_skl != sK0_skl
| op1(sK2_skl,sK0_skl) != sK2_skl ),
inference(resolution,[status(thm)],[f98,f16]) ).
fof(f354,plain,
( sK2_skl != sK0_skl
| sK2_skl != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f200,f353]) ).
fof(f355,plain,
sK2_skl != sK0_skl,
inference(trivial_equality_resolution,[status(thm)],[f354]) ).
fof(f359,plain,
( h(sK2_skl) = sK1_skl
| op2(sK3_skl(h(sK2_skl)),h(sK2_skl)) != sK4_skl(h(sK2_skl)) ),
inference(resolution,[status(thm)],[f54,f74]) ).
fof(f399,plain,
j(op2(sK3_skl(h(sK2_skl)),sK4_skl(h(sK2_skl)))) = op1(j(sK3_skl(h(sK2_skl))),j(sK4_skl(h(sK2_skl)))),
inference(resolution,[status(thm)],[f106,f92]) ).
fof(f404,plain,
j(h(sK2_skl)) = op1(j(sK3_skl(h(sK2_skl))),j(sK4_skl(h(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f101,f399]) ).
fof(f405,plain,
sK2_skl = op1(j(sK3_skl(h(sK2_skl))),j(sK4_skl(h(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f72,f404]) ).
fof(f419,plain,
h(op1(j(sK3_skl(h(sK2_skl))),sK2_skl)) = op2(sK3_skl(h(sK2_skl)),h(sK2_skl)),
inference(resolution,[status(thm)],[f144,f31]) ).
fof(f640,plain,
( op1(j(sK3_skl(h(sK2_skl))),sK2_skl) = j(sK4_skl(h(sK2_skl)))
| op1(j(sK3_skl(h(sK2_skl))),j(sK4_skl(h(sK2_skl)))) != sK2_skl ),
inference(resolution,[status(thm)],[f137,f127]) ).
fof(f646,plain,
( op1(j(sK3_skl(h(sK2_skl))),sK2_skl) = j(sK4_skl(h(sK2_skl)))
| sK2_skl != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f405,f640]) ).
fof(f649,plain,
h(j(sK4_skl(h(sK2_skl)))) = op2(sK3_skl(h(sK2_skl)),h(sK2_skl)),
inference(backward_demodulation,[status(thm)],[f651,f419]) ).
fof(f651,plain,
op1(j(sK3_skl(h(sK2_skl))),sK2_skl) = j(sK4_skl(h(sK2_skl))),
inference(trivial_equality_resolution,[status(thm)],[f646]) ).
fof(f658,plain,
( h(sK2_skl) = sK1_skl
| sK4_skl(h(sK2_skl)) != sK4_skl(h(sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f659,f359]) ).
fof(f659,plain,
sK4_skl(h(sK2_skl)) = op2(sK3_skl(h(sK2_skl)),h(sK2_skl)),
inference(forward_demodulation,[status(thm)],[f126,f649]) ).
fof(f678,plain,
j(sK1_skl) = sK2_skl,
inference(backward_demodulation,[status(thm)],[f756,f72]) ).
fof(f756,plain,
h(sK2_skl) = sK1_skl,
inference(trivial_equality_resolution,[status(thm)],[f658]) ).
fof(f767,plain,
sK0_skl = sK2_skl,
inference(forward_demodulation,[status(thm)],[f247,f678]) ).
fof(f768,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f767,f355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG072+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 12:57:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.102882 seconds
% 0.14/0.48 % CPU time: 0.562129 seconds
% 0.14/0.48 % Total memory used: 78.314 MB
% 0.14/0.48 % Net memory used: 77.699 MB
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