%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX220+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 : n020.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 03:13:28 PM UTC 2026
% Result : Theorem 0.22s 0.91s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 17 unt; 2 def)
% Number of atoms : 93 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 48 ~; 34 |; 9 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 118 ( 116 !; 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(b,c)),arr(b,arr(a,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ? [E] : tc(nil,E,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
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(b,c)),arr(b,arr(a,c)))),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
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(f96,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(resolution,[status(thm)],[f82,f58]) ).
fof(f97,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(f122,plain,
! [X0,X1,X2] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(resolution,[status(thm)],[f97,f58]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4] :
( tc(cons(X3,cons(X4,X0)),var(suc(suc(X1))),X2)
| index(X0,X1) != just(X2) ),
inference(paramodulation,[status(thm)],[f59,f97]) ).
fof(f126,plain,
! [X0] : ~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))),
inference(resolution,[status(thm)],[f81,f71]) ).
fof(f143,plain,
! [X0] : ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c)),
inference(resolution,[status(thm)],[f126,f71]) ).
fof(f145,plain,
! [X0,X1,X2,X3] : tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(resolution,[status(thm)],[f123,f58]) ).
fof(f157,plain,
! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c),
inference(resolution,[status(thm)],[f143,f71]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,X1)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X1,c)) ),
inference(resolution,[status(thm)],[f157,f64]) ).
fof(f665,plain,
! [X0,X1,X2,X3,X4] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,arr(X3,arr(X1,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,X1) ),
inference(resolution,[status(thm)],[f160,f64]) ).
fof(f1118,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
inference(resolution,[status(thm)],[f665,f145]) ).
fof(f1121,definition,
! [X0] :
( sQ37_spl
<=> ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1122,plain,
! [X0] :
( ~ sQ37_spl
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
inference(component_clause,[status(thm)],[f1121]) ).
fof(f1124,definition,
! [X1] :
( sQ38_spl
<=> ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1125,plain,
! [X0] :
( ~ sQ38_spl
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,a) ),
inference(component_clause,[status(thm)],[f1124]) ).
fof(f1127,plain,
( sQ38_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1118,f1121,f1124]) ).
fof(f1128,plain,
( ~ sQ37_spl
| $false ),
inference(resolution,[status(thm)],[f1122,f122]) ).
fof(f1130,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f1128]) ).
fof(f1131,plain,
( ~ sQ38_spl
| $false ),
inference(resolution,[status(thm)],[f1125,f96]) ).
fof(f1133,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f1131]) ).
fof(f1134,plain,
$false,
inference(sat_refutation,[status(thm)],[f1127,f1130,f1133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX220+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n020.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 10:36:32 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.22/0.91 % Refutation found
% 0.22/0.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.98 % Elapsed time: 0.613992 seconds
% 0.22/0.98 % CPU time: 4.402104 seconds
% 0.22/0.98 % Total memory used: 126.434 MB
% 0.22/0.98 % Net memory used: 118.555 MB
%------------------------------------------------------------------------------