%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.03s 0.35s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 98 ( 98 unt; 0 def)
% Number of atoms : 98 ( 97 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 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,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
uu = f(u,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
f(a,v) != f(b,v),
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,
n2 = f(n1,n1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
n3 = f(n2,n1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
u = f(n2,n2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
u1 = f(u,n1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
u2 = f(u,n2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
u3 = f(u,n3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
uu = f(u,u),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
a = f(f(n3,n2),u2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
b = f(u1,u3),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
v = f(uu,uu),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
f(a,v) != f(b,v),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] : f(f(n3,n2),f(u2,X0)) = f(a,f(f(n3,n2),X0)),
inference(paramodulation,[status(thm)],[f21,f13]) ).
fof(f34,plain,
! [X0] : f(uu,f(X0,uu)) = f(f(uu,X0),v),
inference(paramodulation,[status(thm)],[f23,f13]) ).
fof(f41,plain,
! [X0] : f(f(n3,n2),f(u2,f(n3,X0))) = f(a,f(n3,f(n2,X0))),
inference(paramodulation,[status(thm)],[f13,f28]) ).
fof(f230,plain,
! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),n2),
inference(paramodulation,[status(thm)],[f14,f13]) ).
fof(f231,plain,
! [X0] : f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(paramodulation,[status(thm)],[f14,f13]) ).
fof(f236,plain,
! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f241,plain,
! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(paramodulation,[status(thm)],[f16,f13]) ).
fof(f246,plain,
! [X0] : f(u,f(n1,X0)) = f(u1,f(u,X0)),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f250,plain,
! [X0] : f(u,f(X0,n2)) = f(f(u,X0),u2),
inference(paramodulation,[status(thm)],[f18,f13]) ).
fof(f251,plain,
! [X0] : f(u,f(n2,X0)) = f(u2,f(u,X0)),
inference(paramodulation,[status(thm)],[f18,f13]) ).
fof(f260,plain,
! [X0] : f(u,f(X0,u)) = f(f(u,X0),uu),
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f261,plain,
! [X0] : f(u,f(u,X0)) = f(uu,f(u,X0)),
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f264,plain,
f(n1,n2) = f(n2,f(n1,n1)),
inference(paramodulation,[status(thm)],[f14,f231]) ).
fof(f271,plain,
f(n1,n2) = f(n2,n2),
inference(forward_demodulation,[status(thm)],[f14,f264]) ).
fof(f272,plain,
f(n1,n2) = u,
inference(forward_demodulation,[status(thm)],[f16,f271]) ).
fof(f276,plain,
f(n1,u) = f(n2,f(n1,n2)),
inference(paramodulation,[status(thm)],[f272,f231]) ).
fof(f281,plain,
f(n1,u) = f(n2,u),
inference(forward_demodulation,[status(thm)],[f272,f276]) ).
fof(f290,plain,
f(n2,f(n1,n2)) = f(n3,u),
inference(paramodulation,[status(thm)],[f16,f236]) ).
fof(f297,plain,
f(n2,u) = f(n3,u),
inference(forward_demodulation,[status(thm)],[f272,f290]) ).
fof(f311,plain,
f(n2,f(n2,n2)) = f(u,u),
inference(paramodulation,[status(thm)],[f16,f241]) ).
fof(f318,plain,
f(n2,u) = f(u,u),
inference(forward_demodulation,[status(thm)],[f16,f311]) ).
fof(f319,plain,
f(n2,u) = uu,
inference(forward_demodulation,[status(thm)],[f20,f318]) ).
fof(f325,plain,
uu = f(n3,u),
inference(backward_demodulation,[status(thm)],[f319,f297]) ).
fof(f326,plain,
f(n1,u) = uu,
inference(backward_demodulation,[status(thm)],[f319,f281]) ).
fof(f327,plain,
f(n2,f(n2,u)) = f(u,uu),
inference(paramodulation,[status(thm)],[f319,f241]) ).
fof(f328,plain,
f(n2,f(n1,u)) = f(n3,uu),
inference(paramodulation,[status(thm)],[f319,f236]) ).
fof(f333,plain,
f(n2,uu) = f(u,uu),
inference(forward_demodulation,[status(thm)],[f319,f327]) ).
fof(f340,plain,
f(n1,uu) = f(n2,f(n1,u)),
inference(paramodulation,[status(thm)],[f326,f231]) ).
fof(f345,plain,
f(n1,uu) = f(n2,uu),
inference(forward_demodulation,[status(thm)],[f326,f340]) ).
fof(f535,plain,
f(n1,n3) = f(f(n1,n2),n2),
inference(paramodulation,[status(thm)],[f15,f230]) ).
fof(f551,plain,
f(n1,n3) = f(u,n2),
inference(forward_demodulation,[status(thm)],[f272,f535]) ).
fof(f552,plain,
f(n1,n3) = u2,
inference(forward_demodulation,[status(thm)],[f18,f551]) ).
fof(f701,plain,
f(n2,uu) = f(n3,uu),
inference(forward_demodulation,[status(thm)],[f326,f328]) ).
fof(f815,plain,
f(u,f(n1,n3)) = f(u1,u3),
inference(paramodulation,[status(thm)],[f19,f246]) ).
fof(f834,plain,
f(u,u2) = f(u1,u3),
inference(forward_demodulation,[status(thm)],[f552,f815]) ).
fof(f835,plain,
f(u,u2) = b,
inference(forward_demodulation,[status(thm)],[f22,f834]) ).
fof(f842,plain,
f(u,u2) = f(f(u,u),u2),
inference(paramodulation,[status(thm)],[f18,f250]) ).
fof(f860,plain,
f(u,u2) = f(uu,u2),
inference(forward_demodulation,[status(thm)],[f20,f842]) ).
fof(f919,plain,
b = f(uu,u2),
inference(forward_demodulation,[status(thm)],[f835,f860]) ).
fof(f1078,plain,
! [X0] : f(n2,f(n2,X0)) = f(u2,f(u,X0)),
inference(forward_demodulation,[status(thm)],[f241,f251]) ).
fof(f1086,plain,
f(n2,f(n2,u)) = f(u2,uu),
inference(paramodulation,[status(thm)],[f20,f1078]) ).
fof(f1101,plain,
f(n2,uu) = f(u2,uu),
inference(forward_demodulation,[status(thm)],[f319,f1086]) ).
fof(f1146,plain,
f(u,uu) = f(f(u,u),uu),
inference(paramodulation,[status(thm)],[f20,f260]) ).
fof(f1166,plain,
f(n2,uu) = f(f(u,u),uu),
inference(forward_demodulation,[status(thm)],[f333,f1146]) ).
fof(f1167,plain,
f(n2,uu) = f(uu,uu),
inference(forward_demodulation,[status(thm)],[f20,f1166]) ).
fof(f1168,plain,
f(n2,uu) = v,
inference(forward_demodulation,[status(thm)],[f23,f1167]) ).
fof(f1184,plain,
v = f(n3,uu),
inference(backward_demodulation,[status(thm)],[f1168,f701]) ).
fof(f1185,plain,
f(n1,uu) = v,
inference(backward_demodulation,[status(thm)],[f1168,f345]) ).
fof(f1186,plain,
v = f(u,uu),
inference(backward_demodulation,[status(thm)],[f1168,f333]) ).
fof(f1187,plain,
f(n2,f(n2,uu)) = f(u,v),
inference(paramodulation,[status(thm)],[f1168,f241]) ).
fof(f1188,plain,
f(n2,f(n1,uu)) = f(n3,v),
inference(paramodulation,[status(thm)],[f1168,f236]) ).
fof(f1194,plain,
! [X0] : f(n2,f(X0,uu)) = f(f(n2,X0),v),
inference(paramodulation,[status(thm)],[f1168,f13]) ).
fof(f1196,plain,
f(n2,v) = f(u,v),
inference(forward_demodulation,[status(thm)],[f1168,f1187]) ).
fof(f1213,plain,
! [X0] : f(n3,f(X0,uu)) = f(f(n3,X0),v),
inference(paramodulation,[status(thm)],[f1184,f13]) ).
fof(f1257,plain,
f(u,f(u,uu)) = f(uu,v),
inference(paramodulation,[status(thm)],[f1186,f261]) ).
fof(f1282,plain,
f(u,v) = f(uu,v),
inference(forward_demodulation,[status(thm)],[f1186,f1257]) ).
fof(f1309,plain,
v = f(u2,uu),
inference(forward_demodulation,[status(thm)],[f1168,f1101]) ).
fof(f1310,plain,
f(uu,v) = f(f(uu,u2),v),
inference(paramodulation,[status(thm)],[f1309,f34]) ).
fof(f1317,plain,
f(uu,v) = f(b,v),
inference(forward_demodulation,[status(thm)],[f919,f1310]) ).
fof(f1386,plain,
f(a,v) != f(uu,v),
inference(backward_demodulation,[status(thm)],[f1317,f24]) ).
fof(f1503,plain,
f(a,v) != f(n2,v),
inference(backward_demodulation,[status(thm)],[f1508,f1386]) ).
fof(f1508,plain,
f(n2,v) = f(uu,v),
inference(forward_demodulation,[status(thm)],[f1196,f1282]) ).
fof(f1700,plain,
! [X0] : f(f(n3,n2),f(u2,f(n3,X0))) = f(a,f(n2,f(n1,X0))),
inference(forward_demodulation,[status(thm)],[f236,f41]) ).
fof(f1703,plain,
f(f(n3,n2),f(u2,uu)) = f(a,f(n2,f(n1,u))),
inference(paramodulation,[status(thm)],[f325,f1700]) ).
fof(f1719,plain,
f(f(n3,n2),v) = f(a,f(n2,f(n1,u))),
inference(forward_demodulation,[status(thm)],[f1309,f1703]) ).
fof(f1720,plain,
f(f(n3,n2),v) = f(a,f(n2,uu)),
inference(forward_demodulation,[status(thm)],[f326,f1719]) ).
fof(f1721,plain,
f(f(n3,n2),v) = f(a,v),
inference(forward_demodulation,[status(thm)],[f1168,f1720]) ).
fof(f1803,plain,
f(n2,v) = f(n3,v),
inference(forward_demodulation,[status(thm)],[f1185,f1188]) ).
fof(f4161,plain,
f(n2,f(n1,uu)) = f(f(n3,n2),v),
inference(paramodulation,[status(thm)],[f236,f1213]) ).
fof(f4192,plain,
f(f(n2,n1),v) = f(f(n3,n2),v),
inference(forward_demodulation,[status(thm)],[f1194,f4161]) ).
fof(f4193,plain,
f(n3,v) = f(f(n3,n2),v),
inference(forward_demodulation,[status(thm)],[f15,f4192]) ).
fof(f4194,plain,
f(n2,v) = f(f(n3,n2),v),
inference(forward_demodulation,[status(thm)],[f1803,f4193]) ).
fof(f4195,plain,
f(n2,v) = f(a,v),
inference(forward_demodulation,[status(thm)],[f1721,f4194]) ).
fof(f4196,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4195,f1503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 01:16:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.35 % Refutation found
% 0.03/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.36 % Elapsed time: 0.063832 seconds
% 0.03/0.36 % CPU time: 0.407503 seconds
% 0.03/0.36 % Total memory used: 40.368 MB
% 0.03/0.36 % Net memory used: 40.073 MB
%------------------------------------------------------------------------------