%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LDA004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:24:38 PM UTC 2026
% Result : Unsatisfiable 35.51s 5.26s
% Output : CNFRefutation 20.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 98 ( 91 unt; 0 def)
% Number of atoms : 109 ( 66 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 25 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : left(X,f(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( left(X,Z)
| ~ left(Y,Z)
| ~ left(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ left(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1,X2] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1] : left(X0,f(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X,Z] :
( left(X,Z)
| ! [Y] :
( ~ left(Y,Z)
| ~ left(X,Y) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( left(X0,X2)
| ~ left(X1,X2)
| ~ left(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
n2 = f(n1,n1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
n3 = f(n2,n1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
u = f(n2,n2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
u1 = f(u,n1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
u2 = f(u,n2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
u3 = f(u,n3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
a = f(f(n3,n2),u2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f24,plain,
b = f(u1,u3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f25,plain,
~ left(a,b),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0] :
( ~ left(X0,b)
| ~ left(a,X0) ),
inference(resolution,[status(thm)],[f16,f25]) ).
fof(f29,plain,
! [X0,X1] :
( ~ left(X1,X0)
| ~ left(a,X1)
| ~ left(X0,b) ),
inference(resolution,[status(thm)],[f27,f16]) ).
fof(f69,plain,
! [X0] : f(u,f(n3,X0)) = f(u3,f(u,X0)),
inference(paramodulation,[status(thm)],[f22,f13]) ).
fof(f71,plain,
! [X0] : f(u,f(n1,X0)) = f(u1,f(u,X0)),
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f72,plain,
! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f73,plain,
! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(paramodulation,[status(thm)],[f18,f13]) ).
fof(f74,plain,
! [X0] : f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f79,plain,
! [X0] : f(u,f(X0,n2)) = f(f(u,X0),u2),
inference(paramodulation,[status(thm)],[f21,f13]) ).
fof(f80,plain,
! [X0] : f(u,f(X0,n1)) = f(f(u,X0),u1),
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f81,plain,
! [X0] : f(n2,f(X0,n2)) = f(f(n2,X0),u),
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f83,plain,
! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),n2),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f85,plain,
! [X0,X1,X2,X3] : f(f(X0,X1),f(X2,f(X0,X3))) = f(f(f(X0,X1),X2),f(X0,f(X1,X3))),
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f87,plain,
! [X0,X1,X2] : left(f(X0,X1),f(X0,f(X1,X2))),
inference(paramodulation,[status(thm)],[f13,f14]) ).
fof(f97,plain,
f(u,f(n1,n2)) = f(u1,u2),
inference(paramodulation,[status(thm)],[f21,f71]) ).
fof(f98,plain,
f(u,f(n1,n1)) = f(u1,u1),
inference(paramodulation,[status(thm)],[f20,f71]) ).
fof(f103,plain,
f(u,n2) = f(u1,u1),
inference(forward_demodulation,[status(thm)],[f17,f98]) ).
fof(f104,plain,
u2 = f(u1,u1),
inference(forward_demodulation,[status(thm)],[f21,f103]) ).
fof(f138,plain,
! [X0,X1,X2,X3] : left(f(X0,f(X1,X2)),f(f(X0,X1),f(f(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f13,f87]) ).
fof(f143,plain,
! [X0,X1,X2] : left(f(f(X0,X1),X0),f(X0,f(X1,X2))),
inference(paramodulation,[status(thm)],[f13,f87]) ).
fof(f145,plain,
! [X0,X1] : left(f(X0,u3),f(X0,f(u,f(n3,X1)))),
inference(paramodulation,[status(thm)],[f69,f87]) ).
fof(f196,plain,
! [X0] : f(u1,f(X0,u1)) = f(f(u1,X0),u2),
inference(paramodulation,[status(thm)],[f104,f13]) ).
fof(f220,plain,
f(n2,f(n2,n2)) = f(u,u),
inference(paramodulation,[status(thm)],[f19,f72]) ).
fof(f221,plain,
f(n2,f(n2,n1)) = f(u,n3),
inference(paramodulation,[status(thm)],[f18,f72]) ).
fof(f231,plain,
f(n2,u) = f(u,u),
inference(forward_demodulation,[status(thm)],[f19,f220]) ).
fof(f232,plain,
f(n2,n3) = f(u,n3),
inference(forward_demodulation,[status(thm)],[f18,f221]) ).
fof(f235,plain,
f(n2,n3) = u3,
inference(forward_demodulation,[status(thm)],[f22,f232]) ).
fof(f240,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(paramodulation,[status(thm)],[f18,f73]) ).
fof(f248,plain,
f(n2,n2) = f(n3,n3),
inference(forward_demodulation,[status(thm)],[f17,f240]) ).
fof(f250,plain,
u = f(n3,n3),
inference(forward_demodulation,[status(thm)],[f19,f248]) ).
fof(f255,plain,
f(n1,n2) = f(n2,f(n1,n1)),
inference(paramodulation,[status(thm)],[f17,f74]) ).
fof(f264,plain,
f(n1,n2) = f(n2,n2),
inference(forward_demodulation,[status(thm)],[f17,f255]) ).
fof(f267,plain,
f(u,u) = f(u1,u2),
inference(backward_demodulation,[status(thm)],[f268,f97]) ).
fof(f268,plain,
f(n1,n2) = u,
inference(forward_demodulation,[status(thm)],[f19,f264]) ).
fof(f272,plain,
f(n2,u) = f(u1,u2),
inference(forward_demodulation,[status(thm)],[f231,f267]) ).
fof(f343,plain,
! [X0] : left(f(f(X0,u),X0),f(X0,u2)),
inference(paramodulation,[status(thm)],[f21,f143]) ).
fof(f430,plain,
! [X0] : f(n3,f(X0,n3)) = f(f(n3,X0),u),
inference(paramodulation,[status(thm)],[f250,f13]) ).
fof(f452,plain,
! [X0] : f(n1,f(n2,X0)) = f(u,f(n1,X0)),
inference(paramodulation,[status(thm)],[f268,f13]) ).
fof(f949,plain,
f(u,f(u,n2)) = f(f(n2,u),u2),
inference(paramodulation,[status(thm)],[f231,f79]) ).
fof(f975,plain,
f(u,u2) = f(f(n2,u),u2),
inference(forward_demodulation,[status(thm)],[f21,f949]) ).
fof(f1197,plain,
f(u,f(n2,n1)) = f(u2,u1),
inference(paramodulation,[status(thm)],[f21,f80]) ).
fof(f1198,plain,
f(u,f(n1,n1)) = f(u1,u1),
inference(paramodulation,[status(thm)],[f20,f80]) ).
fof(f1219,plain,
f(n2,f(n2,n1)) = f(u2,u1),
inference(forward_demodulation,[status(thm)],[f72,f1197]) ).
fof(f1220,plain,
f(n2,n3) = f(u2,u1),
inference(forward_demodulation,[status(thm)],[f18,f1219]) ).
fof(f1224,plain,
u3 = f(u2,u1),
inference(forward_demodulation,[status(thm)],[f235,f1220]) ).
fof(f1225,plain,
f(n1,f(n2,n1)) = f(u1,u1),
inference(forward_demodulation,[status(thm)],[f452,f1198]) ).
fof(f1226,plain,
f(n1,n3) = f(u1,u1),
inference(forward_demodulation,[status(thm)],[f18,f1225]) ).
fof(f1233,plain,
f(n1,n3) = u2,
inference(forward_demodulation,[status(thm)],[f104,f1226]) ).
fof(f1406,plain,
! [X0] : left(f(X0,u2),f(X0,u3)),
inference(paramodulation,[status(thm)],[f1224,f87]) ).
fof(f1486,plain,
left(a,f(f(n3,n2),u3)),
inference(paramodulation,[status(thm)],[f23,f1406]) ).
fof(f1552,plain,
f(n1,f(n3,n1)) = f(u2,n2),
inference(paramodulation,[status(thm)],[f1233,f83]) ).
fof(f2059,plain,
! [X0] :
( ~ left(f(f(n3,n2),u3),X0)
| ~ left(X0,b) ),
inference(resolution,[status(thm)],[f1486,f29]) ).
fof(f2823,plain,
left(f(f(f(n2,u),u),f(n2,u)),f(u,u2)),
inference(paramodulation,[status(thm)],[f975,f343]) ).
fof(f2852,plain,
left(f(f(n2,f(u,n2)),f(n2,u)),f(u,u2)),
inference(forward_demodulation,[status(thm)],[f81,f2823]) ).
fof(f2853,plain,
left(f(n2,f(f(u,n2),u)),f(u,u2)),
inference(forward_demodulation,[status(thm)],[f13,f2852]) ).
fof(f2854,plain,
left(f(n2,f(u2,u)),f(u,u2)),
inference(forward_demodulation,[status(thm)],[f21,f2853]) ).
fof(f3660,plain,
! [X0] : ~ left(f(f(n3,n2),f(u,f(n3,X0))),b),
inference(resolution,[status(thm)],[f2059,f145]) ).
fof(f5843,plain,
f(u1,f(u2,u1)) = f(f(n2,u),u2),
inference(paramodulation,[status(thm)],[f272,f196]) ).
fof(f5880,plain,
f(u1,u3) = f(f(n2,u),u2),
inference(forward_demodulation,[status(thm)],[f1224,f5843]) ).
fof(f5881,plain,
b = f(f(n2,u),u2),
inference(forward_demodulation,[status(thm)],[f24,f5880]) ).
fof(f5911,plain,
left(f(n2,f(u2,u)),b),
inference(backward_demodulation,[status(thm)],[f5919,f2854]) ).
fof(f5919,plain,
b = f(u,u2),
inference(forward_demodulation,[status(thm)],[f975,f5881]) ).
fof(f14580,plain,
! [X0,X1] : f(f(n3,X0),f(u,f(n3,X1))) = f(f(n3,f(X0,n3)),f(n3,f(X0,X1))),
inference(paramodulation,[status(thm)],[f430,f85]) ).
fof(f14753,plain,
! [X0,X1] : f(f(n3,X0),f(u,f(n3,X1))) = f(n3,f(f(X0,n3),f(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13,f14580]) ).
fof(f14757,plain,
! [X0] : ~ left(f(n3,f(n2,f(n3,X0))),b),
inference(backward_demodulation,[status(thm)],[f14760,f3660]) ).
fof(f14760,plain,
! [X0,X1] : f(f(n3,X0),f(u,f(n3,X1))) = f(n3,f(X0,f(n3,X1))),
inference(forward_demodulation,[status(thm)],[f13,f14753]) ).
fof(f14803,plain,
! [X0] : ~ left(f(n2,f(n1,f(n3,X0))),b),
inference(forward_demodulation,[status(thm)],[f73,f14757]) ).
fof(f14807,plain,
~ left(f(n2,f(u2,n2)),b),
inference(paramodulation,[status(thm)],[f1552,f14803]) ).
fof(f14817,plain,
! [X0] :
( ~ left(X0,b)
| ~ left(f(n2,f(u2,n2)),X0) ),
inference(resolution,[status(thm)],[f14807,f16]) ).
fof(f16004,plain,
! [X0] : ~ left(f(f(n2,u2),f(f(n2,n2),X0)),b),
inference(resolution,[status(thm)],[f14817,f138]) ).
fof(f16009,plain,
! [X0] : ~ left(f(f(n2,u2),f(u,X0)),b),
inference(forward_demodulation,[status(thm)],[f19,f16004]) ).
fof(f16013,plain,
~ left(f(f(n2,u2),f(n2,u)),b),
inference(paramodulation,[status(thm)],[f231,f16009]) ).
fof(f16026,plain,
~ left(f(n2,f(u2,u)),b),
inference(forward_demodulation,[status(thm)],[f13,f16013]) ).
fof(f16027,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16026,f5911]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LDA004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 01:14:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 35.51/5.26 % Refutation found
% 35.51/5.26 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 35.51/5.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.46/5.42 % Elapsed time: 5.026673 seconds
% 7.46/5.42 % CPU time: 39.271220 seconds
% 7.46/5.42 % Total memory used: 568.856 MB
% 7.46/5.42 % Net memory used: 562.422 MB
%------------------------------------------------------------------------------