%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 03:13:29 PM UTC 2026
% Result : Theorem 0.29s 0.61s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 15 unt; 1 def)
% Number of atoms : 81 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 41 ~; 30 |; 9 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 106 ( 104 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Z,Xs,N] : index(cons(Z,Xs),suc(N)) = index(Xs,N),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Z,F,X2,Tx] :
( tc(X,app(F,X2,Tx),Z)
<=> ( tc(X,X2,Tx)
& tc(X,F,arr(Tx,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,E,Tx2,T1] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Z,X3,Tx3] :
( index(X,X3) = just(Tx3)
=> ( tc(X,var(X3),Z)
<=> Tx3 = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
? [E] : tc(nil,E,arr(arr(a,arr(a,b)),arr(a,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ? [E] : tc(nil,E,arr(arr(a,arr(a,b)),arr(a,b))),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f58,plain,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f59,plain,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f60,plain,
! [X,Z,F,X2,Tx] :
( ( ~ tc(X,X2,Tx)
| ~ tc(X,F,arr(Tx,Z))
| tc(X,app(F,X2,Tx),Z) )
& ( ( tc(X,X2,Tx)
& tc(X,F,arr(Tx,Z)) )
| ~ tc(X,app(F,X2,Tx),Z) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f61,plain,
( ! [X,Z,F,X2,Tx] :
( ~ tc(X,X2,Tx)
| ~ tc(X,F,arr(Tx,Z))
| tc(X,app(F,X2,Tx),Z) )
& ! [X,Z,F,X2,Tx] :
( ( tc(X,X2,Tx)
& tc(X,F,arr(Tx,Z)) )
| ~ tc(X,app(F,X2,Tx),Z) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4] :
( ~ tc(X0,X2,X3)
| ~ tc(X0,X1,arr(X3,X4))
| tc(X0,app(X1,X2,X3),X4) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f68,plain,
! [X,E,Tx2,T1] :
( ( ~ tc(cons(Tx2,X),E,T1)
| tc(X,lam(E),arr(Tx2,T1)) )
& ( tc(cons(Tx2,X),E,T1)
| ~ tc(X,lam(E),arr(Tx2,T1)) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( ! [X,E,Tx2,T1] :
( ~ tc(cons(Tx2,X),E,T1)
| tc(X,lam(E),arr(Tx2,T1)) )
& ! [X,E,Tx2,T1] :
( tc(cons(Tx2,X),E,T1)
| ~ tc(X,lam(E),arr(Tx2,T1)) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,plain,
! [X,Z,X3,Tx3] :
( ( tc(X,var(X3),Z)
<=> Tx3 = Z )
| index(X,X3) != just(Tx3) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f76,plain,
! [X,Z,X3,Tx3] :
( ( ( Tx3 != Z
| tc(X,var(X3),Z) )
& ( Tx3 = Z
| ~ tc(X,var(X3),Z) ) )
| index(X,X3) != just(Tx3) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
! [X,X3,Tx3] :
( ( ! [Z] :
( Tx3 != Z
| tc(X,var(X3),Z) )
& ! [Z] :
( Tx3 = Z
| ~ tc(X,var(X3),Z) ) )
| index(X,X3) != just(Tx3) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| tc(X0,var(X1),X3)
| index(X0,X1) != just(X2) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f80,plain,
! [E] : ~ tc(nil,E,arr(arr(a,arr(a,b)),arr(a,b))),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( tc(X0,var(X1),X2)
| index(X0,X1) != just(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(resolution,[status(thm)],[f82,f58]) ).
fof(f90,plain,
! [X0] : ~ tc(cons(arr(a,arr(a,b)),nil),X0,arr(a,b)),
inference(resolution,[status(thm)],[f71,f81]) ).
fof(f92,plain,
! [X0] : ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,b),
inference(resolution,[status(thm)],[f90,f71]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,X1)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X1,b)) ),
inference(resolution,[status(thm)],[f64,f92]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( tc(cons(X3,X0),var(suc(X1)),X2)
| index(X0,X1) != just(X2) ),
inference(paramodulation,[status(thm)],[f59,f82]) ).
fof(f130,plain,
! [X0,X1,X2] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(resolution,[status(thm)],[f105,f58]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,arr(X3,arr(X1,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,X1) ),
inference(resolution,[status(thm)],[f94,f64]) ).
fof(f210,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[status(thm)],[f147,f130]) ).
fof(f213,definition,
! [X0] :
( sQ5_spl
<=> ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f214,plain,
! [X0] :
( ~ sQ5_spl
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
sQ5_spl,
inference(split_clause,[status(thm)],[f210,f213]) ).
fof(f249,plain,
( ~ sQ5_spl
| $false ),
inference(resolution,[status(thm)],[f214,f83]) ).
fof(f251,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f252,plain,
$false,
inference(sat_refutation,[status(thm)],[f216,f251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n006.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 10:36:00 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 0.29/0.61 % Refutation found
% 0.29/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.29/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.66 % Elapsed time: 0.190589 seconds
% 0.29/0.66 % CPU time: 1.175261 seconds
% 0.29/0.66 % Total memory used: 88.129 MB
% 0.29/0.66 % Net memory used: 86.017 MB
%------------------------------------------------------------------------------