%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG074+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 : n015.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 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 23 unt; 3 def)
% Number of atoms : 166 ( 66 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 162 ( 61 ~; 53 |; 25 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 45 !; 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(op1(U,V),U) != V
& op1(op1(U,V),V) = U
& op1(V,U) != op1(U,V)
& sorti1(V) )
& sorti1(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ? [U] :
( ? [V] :
( op2(op2(U,V),U) != V
& op2(op2(U,V),V) = U
& op2(V,U) != op2(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(op1(sK0_skl,sK1_skl),sK0_skl) != sK1_skl
& op1(op1(sK0_skl,sK1_skl),sK1_skl) = sK0_skl
& op1(sK1_skl,sK0_skl) != op1(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(sK1_skl,sK0_skl) != op1(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
op1(op1(sK0_skl,sK1_skl),sK1_skl) = sK0_skl,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f16,plain,
op1(op1(sK0_skl,sK1_skl),sK0_skl) != sK1_skl,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f17,plain,
! [U] :
( ! [V] :
( op2(op2(U,V),U) = V
| op2(op2(U,V),V) != U
| op2(V,U) = op2(U,V)
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( op2(op2(X0,X1),X0) = X1
| op2(op2(X0,X1),X1) != X0
| op2(X1,X0) = op2(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] :
( sorti1(op1(sK0_skl,X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f28,plain,
! [X0] :
( h(op1(sK0_skl,X0)) = op2(h(sK0_skl),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f12,f22]) ).
fof(f29,plain,
sorti2(h(sK0_skl)),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f30,plain,
! [X0] :
( sorti1(op1(sK1_skl,X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f31,plain,
j(h(sK1_skl)) = sK1_skl,
inference(resolution,[status(thm)],[f13,f25]) ).
fof(f32,plain,
! [X0] :
( h(op1(sK1_skl,X0)) = op2(h(sK1_skl),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f13,f22]) ).
fof(f33,plain,
sorti2(h(sK1_skl)),
inference(resolution,[status(thm)],[f13,f20]) ).
fof(f35,plain,
! [X0] :
( op2(op2(h(sK0_skl),X0),h(sK0_skl)) = X0
| op2(op2(h(sK0_skl),X0),X0) != h(sK0_skl)
| op2(X0,h(sK0_skl)) = op2(h(sK0_skl),X0)
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[f29,f18]) ).
fof(f41,plain,
sorti1(op1(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f26,f13]) ).
fof(f43,plain,
h(op1(sK0_skl,sK1_skl)) = op2(h(sK0_skl),h(sK1_skl)),
inference(resolution,[status(thm)],[f28,f13]) ).
fof(f53,plain,
h(op1(sK1_skl,sK0_skl)) = op2(h(sK1_skl),h(sK0_skl)),
inference(resolution,[status(thm)],[f32,f12]) ).
fof(f57,plain,
! [X0] :
( sorti1(op1(op1(sK0_skl,sK1_skl),X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f41,f8]) ).
fof(f58,plain,
j(h(op1(sK0_skl,sK1_skl))) = op1(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f41,f25]) ).
fof(f59,plain,
! [X0] :
( h(op1(op1(sK0_skl,sK1_skl),X0)) = op2(h(op1(sK0_skl,sK1_skl)),h(X0))
| ~ sorti1(X0) ),
inference(resolution,[status(thm)],[f41,f22]) ).
fof(f71,plain,
sorti1(op1(sK1_skl,sK0_skl)),
inference(resolution,[status(thm)],[f30,f12]) ).
fof(f78,plain,
( op2(op2(h(sK0_skl),h(sK1_skl)),h(sK0_skl)) = h(sK1_skl)
| op2(op2(h(sK0_skl),h(sK1_skl)),h(sK1_skl)) != h(sK0_skl)
| op2(h(sK1_skl),h(sK0_skl)) = op2(h(sK0_skl),h(sK1_skl)) ),
inference(resolution,[status(thm)],[f35,f33]) ).
fof(f80,definition,
( sQ0_spl
<=> op2(h(sK1_skl),h(sK0_skl)) = op2(h(sK0_skl),h(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| op2(h(sK1_skl),h(sK0_skl)) = op2(h(sK0_skl),h(sK1_skl)) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> op2(op2(h(sK0_skl),h(sK1_skl)),h(sK1_skl)) = h(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( sQ1_spl
| op2(op2(h(sK0_skl),h(sK1_skl)),h(sK1_skl)) != h(sK0_skl) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ2_spl
<=> op2(op2(h(sK0_skl),h(sK1_skl)),h(sK0_skl)) = h(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ2_spl
| op2(op2(h(sK0_skl),h(sK1_skl)),h(sK0_skl)) = h(sK1_skl) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f80,f83,f86]) ).
fof(f97,plain,
( ~ sQ2_spl
| op2(h(op1(sK0_skl,sK1_skl)),h(sK0_skl)) = h(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f43,f87]) ).
fof(f115,plain,
j(h(op1(sK1_skl,sK0_skl))) = op1(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f71,f25]) ).
fof(f165,plain,
( sQ1_spl
| op2(h(op1(sK0_skl,sK1_skl)),h(sK1_skl)) != h(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f43,f85]) ).
fof(f166,plain,
( ~ sQ0_spl
| op2(h(sK1_skl),h(sK0_skl)) = h(op1(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f43,f81]) ).
fof(f169,plain,
( ~ sQ0_spl
| j(h(op1(sK0_skl,sK1_skl))) = op1(sK1_skl,sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f172,f115]) ).
fof(f172,plain,
( ~ sQ0_spl
| h(op1(sK1_skl,sK0_skl)) = h(op1(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f166,f53]) ).
fof(f176,plain,
( ~ sQ0_spl
| op1(sK0_skl,sK1_skl) = op1(sK1_skl,sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f58,f169]) ).
fof(f177,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f14]) ).
fof(f178,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f383,plain,
sorti1(op1(op1(sK0_skl,sK1_skl),sK0_skl)),
inference(resolution,[status(thm)],[f57,f12]) ).
fof(f389,plain,
h(op1(op1(sK0_skl,sK1_skl),sK1_skl)) = op2(h(op1(sK0_skl,sK1_skl)),h(sK1_skl)),
inference(resolution,[status(thm)],[f59,f13]) ).
fof(f390,plain,
h(op1(op1(sK0_skl,sK1_skl),sK0_skl)) = op2(h(op1(sK0_skl,sK1_skl)),h(sK0_skl)),
inference(resolution,[status(thm)],[f59,f12]) ).
fof(f391,plain,
h(sK0_skl) = op2(h(op1(sK0_skl,sK1_skl)),h(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f15,f389]) ).
fof(f396,plain,
( sQ1_spl
| h(sK0_skl) != h(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f391,f165]) ).
fof(f397,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f396]) ).
fof(f398,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f406,plain,
( ~ sQ2_spl
| h(op1(op1(sK0_skl,sK1_skl),sK0_skl)) = h(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f390,f97]) ).
fof(f568,plain,
j(h(op1(op1(sK0_skl,sK1_skl),sK0_skl))) = op1(op1(sK0_skl,sK1_skl),sK0_skl),
inference(resolution,[status(thm)],[f383,f25]) ).
fof(f581,plain,
( ~ sQ2_spl
| j(h(sK1_skl)) = op1(op1(sK0_skl,sK1_skl),sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f406,f568]) ).
fof(f582,plain,
( ~ sQ2_spl
| sK1_skl = op1(op1(sK0_skl,sK1_skl),sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f31,f581]) ).
fof(f583,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f16]) ).
fof(f584,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f585,plain,
$false,
inference(sat_refutation,[status(thm)],[f89,f178,f398,f584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG074+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 12:58:37 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.49 % Refutation found
% 0.13/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.133116 seconds
% 0.13/0.50 % CPU time: 0.748628 seconds
% 0.13/0.50 % Total memory used: 123.836 MB
% 0.13/0.50 % Net memory used: 122.862 MB
%------------------------------------------------------------------------------