%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 03:13:25 PM UTC 2026
% Result : Theorem 0.22s 21.03s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 23 unt; 3 def)
% Number of atoms : 159 ( 111 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 160 ( 79 ~; 72 |; 0 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 190 ( 184 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,X2] : head(cons(X,X2)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,X2] : tail(cons(X,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : z != s(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y] : leqNat(z,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Z] : ~ leqNat(s(Z),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Y] : merge(nil,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Z,Xs,Y2,Ys] :
( leqNat(Z,Y2)
=> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Z,Xs,Y2,Ys] :
( ~ leqNat(Z,Y2)
=> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
? [Xs,Ys,Zs] :
~ ( merge(Xs,Ys) = merge(Ys,Xs)
=> ( merge(Xs,Zs) = merge(Zs,Xs)
=> merge(Ys,Zs) = merge(Zs,Ys) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ? [Xs,Ys,Zs] :
~ ( merge(Xs,Ys) = merge(Ys,Xs)
=> ( merge(Xs,Zs) = merge(Zs,Xs)
=> merge(Ys,Zs) = merge(Zs,Ys) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] : head(cons(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1] : tail(cons(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : z != s(X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0] : leqNat(z,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0] : ~ leqNat(s(X0),z),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : merge(nil,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0,X1] : merge(cons(X0,X1),nil) = cons(X0,X1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [Z,Xs,Y2,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys)))
| ~ leqNat(Z,Y2) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [Z,Y2] :
( ! [Xs,Ys] : merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys)))
| ~ leqNat(Z,Y2) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( merge(cons(X0,X2),cons(X1,X3)) = cons(X0,merge(X2,cons(X1,X3)))
| ~ leqNat(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [Z,Xs,Y2,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys))
| leqNat(Z,Y2) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
! [Z,Y2] :
( ! [Xs,Ys] : merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys))
| leqNat(Z,Y2) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( merge(cons(X0,X2),cons(X1,X3)) = cons(X1,merge(cons(X0,X2),X3))
| leqNat(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [Xs,Ys,Zs] :
( merge(Ys,Zs) = merge(Zs,Ys)
| merge(Xs,Zs) != merge(Zs,Xs)
| merge(Xs,Ys) != merge(Ys,Xs) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
! [Xs,Ys] :
( ! [Zs] :
( merge(Ys,Zs) = merge(Zs,Ys)
| merge(Xs,Zs) != merge(Zs,Xs) )
| merge(Xs,Ys) != merge(Ys,Xs) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( merge(X1,X2) = merge(X2,X1)
| merge(X0,X2) != merge(X2,X0)
| merge(X0,X1) != merge(X1,X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( merge(X1,nil) = merge(nil,X1)
| merge(X0,nil) != X0
| merge(X0,X1) != merge(X1,X0) ),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f39,plain,
! [X0,X1] :
( merge(X0,X1) = merge(X1,X0)
| X1 != merge(X1,nil)
| merge(nil,X0) != merge(X0,nil) ),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f40,plain,
! [X0,X1] :
( merge(X1,nil) = X1
| merge(X0,nil) != X0
| merge(X0,X1) != merge(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f26,f38]) ).
fof(f41,plain,
! [X0,X1] :
( merge(X0,X1) = merge(X1,X0)
| X1 != merge(X1,nil)
| X0 != merge(X0,nil) ),
inference(forward_demodulation,[status(thm)],[f26,f39]) ).
fof(f43,plain,
! [X0] :
( merge(nil,nil) = nil
| merge(X0,nil) != X0
| merge(X0,nil) != X0 ),
inference(paramodulation,[status(thm)],[f26,f40]) ).
fof(f48,definition,
( sQ1_spl
<=> merge(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f52,definition,
! [X0] :
( sQ2_spl
<=> ( merge(X0,nil) != X0
| merge(X0,nil) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f53,plain,
! [X0] :
( ~ sQ2_spl
| merge(X0,nil) != X0
| merge(X0,nil) != X0 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f43,f52,f48]) ).
fof(f56,plain,
! [X0] :
( ~ sQ2_spl
| merge(X0,nil) != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f53]) ).
fof(f57,plain,
( ~ sQ2_spl
| $false ),
inference(resolution,[status(thm)],[f56,f26]) ).
fof(f59,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f99,plain,
! [X0,X1,X2] :
( merge(X0,cons(X1,X2)) = merge(cons(X1,X2),X0)
| X0 != merge(X0,nil) ),
inference(resolution,[status(thm)],[f27,f41]) ).
fof(f106,plain,
! [X0,X1,X2] :
( merge(X2,nil) = merge(nil,X2)
| cons(X0,X1) != merge(nil,cons(X0,X1))
| merge(cons(X0,X1),X2) != merge(X2,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f27,f36]) ).
fof(f124,plain,
! [X0,X1,X2] :
( merge(X2,nil) = merge(nil,X2)
| cons(X0,X1) != cons(X0,X1)
| merge(cons(X0,X1),X2) != merge(X2,cons(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f26,f106]) ).
fof(f125,plain,
! [X0,X1,X2] :
( merge(X2,nil) = X2
| cons(X0,X1) != cons(X0,X1)
| merge(cons(X0,X1),X2) != merge(X2,cons(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f26,f124]) ).
fof(f126,plain,
! [X0,X1,X2] :
( merge(X2,nil) = X2
| merge(cons(X0,X1),X2) != merge(X2,cons(X0,X1)) ),
inference(trivial_equality_resolution,[status(thm)],[f125]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( merge(X1,cons(X2,X3)) = merge(cons(X2,X3),X1)
| merge(X0,X1) != merge(X1,X0)
| X0 != merge(X0,nil) ),
inference(resolution,[status(thm)],[f99,f36]) ).
fof(f164,plain,
! [X0,X1,X2] : merge(cons(z,X0),cons(X1,X2)) = cons(z,merge(X0,cons(X1,X2))),
inference(resolution,[status(thm)],[f30,f20]) ).
fof(f172,plain,
! [X0,X1,X2] : tail(merge(cons(z,X0),cons(X1,X2))) = merge(X0,cons(X1,X2)),
inference(paramodulation,[status(thm)],[f164,f16]) ).
fof(f173,plain,
! [X0,X1,X2] : head(merge(cons(z,X0),cons(X1,X2))) = z,
inference(paramodulation,[status(thm)],[f164,f15]) ).
fof(f182,plain,
! [X0,X1,X2] : merge(cons(s(X0),X1),cons(z,X2)) = cons(z,merge(cons(s(X0),X1),X2)),
inference(resolution,[status(thm)],[f33,f21]) ).
fof(f183,plain,
! [X0,X1,X2,X3,X4,X5] :
( merge(cons(X0,X4),cons(X2,X5)) = cons(X0,merge(X4,cons(X2,X5)))
| merge(cons(X0,X1),cons(X2,X3)) = cons(X2,merge(cons(X0,X1),X3)) ),
inference(resolution,[status(thm)],[f33,f30]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1))
| merge(nil,cons(X0,X1)) != cons(X0,X1)
| nil != merge(nil,nil) ),
inference(paramodulation,[status(thm)],[f27,f132]) ).
fof(f208,definition,
! [X0,X1,X2,X3] :
( sQ17_spl
<=> ( merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1))
| merge(nil,cons(X0,X1)) != cons(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1))
| merge(nil,cons(X0,X1)) != cons(X0,X1) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( sQ17_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f195,f48,f208]) ).
fof(f214,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1))
| cons(X0,X1) != cons(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f26,f209]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1)) ),
inference(trivial_equality_resolution,[status(thm)],[f214]) ).
fof(f584,plain,
! [X0,X1,X2,X3,X4] : head(merge(merge(cons(z,X0),cons(X1,X2)),cons(X3,X4))) = z,
inference(paramodulation,[status(thm)],[f164,f173]) ).
fof(f671,plain,
! [X0,X1,X2] : tail(merge(cons(s(X0),X1),cons(z,X2))) = merge(cons(s(X0),X1),X2),
inference(paramodulation,[status(thm)],[f182,f16]) ).
fof(f1046,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| tail(merge(cons(X0,X1),cons(z,X2))) = merge(X2,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f215,f172]) ).
fof(f2000,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ17_spl
| head(merge(merge(cons(X0,X1),cons(z,X2)),cons(X3,X4))) = z ),
inference(paramodulation,[status(thm)],[f215,f584]) ).
fof(f3435,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| merge(X0,cons(s(X1),X2)) = merge(cons(s(X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f1046,f671]) ).
fof(f3444,plain,
! [X0] :
( ~ sQ17_spl
| merge(X0,nil) = X0 ),
inference(resolution,[status(thm)],[f3435,f126]) ).
fof(f3717,plain,
! [X0,X1] :
( ~ sQ17_spl
| merge(X0,X1) = merge(X1,X0)
| X1 != X1
| X0 != merge(X0,nil) ),
inference(backward_demodulation,[status(thm)],[f3444,f41]) ).
fof(f3737,plain,
! [X0,X1] :
( ~ sQ17_spl
| merge(X0,X1) = merge(X1,X0)
| X1 != X1
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f3444,f3717]) ).
fof(f3738,plain,
! [X0,X1] :
( ~ sQ17_spl
| merge(X0,X1) = merge(X1,X0) ),
inference(trivial_equality_resolution,[status(thm)],[f3737]) ).
fof(f3798,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ17_spl
| merge(cons(X0,X4),cons(X2,X5)) = cons(X0,merge(X4,cons(X2,X5)))
| merge(cons(X0,X1),cons(X2,X3)) = cons(X2,merge(X3,cons(X0,X1))) ),
inference(paramodulation,[status(thm)],[f3738,f183]) ).
fof(f4825,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| cons(X0,merge(X2,cons(X0,X1))) = merge(cons(X0,X2),cons(X0,X1))
| merge(cons(X0,X1),cons(X0,X2)) != merge(cons(X0,X2),cons(X0,X1)) ),
inference(equality_factoring,[status(thm)],[f3798]) ).
fof(f4865,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| cons(X0,merge(X1,cons(X0,X2))) = merge(cons(X0,X1),cons(X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4825,f3738]) ).
fof(f5179,plain,
! [X0,X1] :
( ~ sQ17_spl
| cons(X0,cons(X0,X1)) = merge(cons(X0,nil),cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f26,f4865]) ).
fof(f5275,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| tail(merge(cons(X0,X1),cons(X0,X2))) = merge(X1,cons(X0,X2)) ),
inference(paramodulation,[status(thm)],[f4865,f16]) ).
fof(f5461,plain,
! [X0,X1] :
( ~ sQ17_spl
| cons(X0,cons(X0,X1)) = merge(cons(X0,X1),cons(X0,nil)) ),
inference(paramodulation,[status(thm)],[f3738,f5179]) ).
fof(f5982,plain,
! [X0,X1] :
( ~ sQ17_spl
| tail(cons(X0,cons(X0,X1))) = merge(X1,cons(X0,nil)) ),
inference(paramodulation,[status(thm)],[f5461,f5275]) ).
fof(f6021,plain,
! [X0,X1] :
( ~ sQ17_spl
| cons(X0,X1) = merge(X1,cons(X0,nil)) ),
inference(forward_demodulation,[status(thm)],[f16,f5982]) ).
fof(f6057,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| head(cons(X0,merge(cons(X1,X2),cons(z,X3)))) = z ),
inference(paramodulation,[status(thm)],[f6021,f2000]) ).
fof(f6101,plain,
! [X0] :
( ~ sQ17_spl
| X0 = z ),
inference(forward_demodulation,[status(thm)],[f15,f6057]) ).
fof(f6116,plain,
( ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f6101]) ).
fof(f6156,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f6116]) ).
fof(f6157,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f59,f211,f6156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/20.47 % Computer : n006.cluster.edu
% 0.17/20.47 % Model : x86_64 x86_64
% 0.17/20.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/20.47 % Memory : 8046.5625MB
% 0.17/20.47 % OS : Linux 6.8.0-71-generic
% 0.17/20.47 % CPULimit : 300
% 0.17/20.47 % WCLimit : 300
% 0.17/20.47 % DateTime : Mon Sep 21 10:32:35 UTC 2026
% 0.17/20.47 % CPUTime :
% 0.17/20.48 % Drodi V4.1.1
% 0.22/21.03 % Refutation found
% 0.22/21.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/21.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/21.06 % Elapsed time: 0.569744 seconds
% 0.22/21.06 % CPU time: 4.297633 seconds
% 0.22/21.06 % Total memory used: 154.664 MB
% 0.22/21.06 % Net memory used: 152.879 MB
%------------------------------------------------------------------------------