%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG070+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 : n007.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 0.09s 0.60s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 15 unt; 2 def)
% Number of atoms : 128 ( 46 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 128 ( 45 ~; 38 |; 19 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 45 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> ( op1(U,V) = U
| op1(U,U) != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> ( op2(U,V) = U
| op2(U,U) != 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(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,V) = U
| op1(U,U) != V
| ~ sorti1(V) )
| ~ sorti1(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( op1(X0,X1) = X0
| op1(X0,X0) != X1
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
? [U] :
( ? [V] :
( op2(U,V) != U
& op2(U,U) = V
& sorti2(V) )
& sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( op2(sK0_skl,sK1_skl) != sK0_skl
& op2(sK0_skl,sK0_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,sK0_skl) = sK1_skl,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
op2(sK0_skl,sK1_skl) != sK0_skl,
inference(cnf_transformation,[status(thm)],[f14]) ).
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(f21,plain,
! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( j(op2(X0,X1)) = op1(j(X0),j(X1))
| ~ sorti2(X1)
| ~ sorti2(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,
! [X0] :
( sorti2(op2(sK0_skl,X0))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f33,plain,
sorti1(j(sK1_skl)),
inference(resolution,[status(thm)],[f21,f16]) ).
fof(f34,plain,
sorti1(j(sK0_skl)),
inference(resolution,[status(thm)],[f21,f15]) ).
fof(f41,plain,
! [X0] :
( op1(X0,j(sK1_skl)) = X0
| op1(X0,X0) != j(sK1_skl)
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f33,f12]) ).
fof(f55,plain,
j(op2(sK0_skl,sK0_skl)) = op1(j(sK0_skl),j(sK0_skl)),
inference(resolution,[status(thm)],[f23,f15]) ).
fof(f56,plain,
! [X0] :
( j(op2(sK0_skl,X0)) = op1(j(sK0_skl),j(X0))
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f23,f15]) ).
fof(f62,plain,
j(sK1_skl) = op1(j(sK0_skl),j(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f17,f55]) ).
fof(f87,plain,
h(j(sK0_skl)) = sK0_skl,
inference(resolution,[status(thm)],[f24,f15]) ).
fof(f115,plain,
sorti2(op2(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f29,f16]) ).
fof(f137,plain,
h(j(op2(sK0_skl,sK1_skl))) = op2(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f115,f24]) ).
fof(f260,plain,
j(op2(sK0_skl,sK1_skl)) = op1(j(sK0_skl),j(sK1_skl)),
inference(resolution,[status(thm)],[f56,f16]) ).
fof(f311,plain,
( op1(j(sK0_skl),j(sK1_skl)) = j(sK0_skl)
| op1(j(sK0_skl),j(sK0_skl)) != j(sK1_skl) ),
inference(resolution,[status(thm)],[f41,f34]) ).
fof(f334,definition,
( sQ11_spl
<=> op1(j(sK0_skl),j(sK0_skl)) = j(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( sQ11_spl
| op1(j(sK0_skl),j(sK0_skl)) != j(sK1_skl) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
( sQ12_spl
<=> op1(j(sK0_skl),j(sK1_skl)) = j(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( ~ sQ12_spl
| op1(j(sK0_skl),j(sK1_skl)) = j(sK0_skl) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f311,f334,f337]) ).
fof(f342,plain,
( sQ11_spl
| j(sK1_skl) != j(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f62,f336]) ).
fof(f343,plain,
( sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f342]) ).
fof(f344,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f348,plain,
( ~ sQ12_spl
| j(op2(sK0_skl,sK1_skl)) = j(sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f338,f260]) ).
fof(f363,plain,
( ~ sQ12_spl
| h(j(sK0_skl)) = op2(sK0_skl,sK1_skl) ),
inference(backward_demodulation,[status(thm)],[f348,f137]) ).
fof(f378,plain,
( ~ sQ12_spl
| sK0_skl = op2(sK0_skl,sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f87,f363]) ).
fof(f379,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f18]) ).
fof(f380,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f381,plain,
$false,
inference(sat_refutation,[status(thm)],[f340,f344,f380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG070+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n007.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 12:52:52 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 0.09/0.60 % Refutation found
% 0.09/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.63 % Elapsed time: 0.050300 seconds
% 0.14/0.63 % CPU time: 0.182456 seconds
% 0.14/0.63 % Total memory used: 68.049 MB
% 0.14/0.63 % Net memory used: 67.486 MB
%------------------------------------------------------------------------------