%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:06:56 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 62 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : or(X,Y) = or(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : and(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] : xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
not(x) != xor(x,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
not(x) != xor(x,truth),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
not(x) != xor(truth,x),
inference(paramodulation,[status(thm)],[f29,f34]) ).
fof(f48,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f60,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f48]) ).
fof(f64,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f60]) ).
fof(f75,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f64]) ).
fof(f225,plain,
! [X0] : xor(truth,X0) = or(and(truth,not(X0)),and(falsehood,X0)),
inference(paramodulation,[status(thm)],[f33,f28]) ).
fof(f274,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(backward_demodulation,[status(thm)],[f22,f21]) ).
fof(f277,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f75,f22]) ).
fof(f298,plain,
! [X0] : or(not(X0),X0) = truth,
inference(paramodulation,[status(thm)],[f24,f277]) ).
fof(f421,plain,
! [X0] : implies(truth,implies(X0,not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f298,f274]) ).
fof(f426,plain,
! [X0] : implies(or(X0,falsehood),implies(truth,X0)) = truth,
inference(paramodulation,[status(thm)],[f33,f274]) ).
fof(f441,plain,
! [X0] : implies(X0,not(not(X0))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f421]) ).
fof(f443,plain,
! [X0] : implies(or(X0,falsehood),X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f426]) ).
fof(f450,plain,
implies(truth,not(falsehood)) = truth,
inference(paramodulation,[status(thm)],[f298,f443]) ).
fof(f459,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f18,f450]) ).
fof(f470,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f459,f22]) ).
fof(f475,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f470]) ).
fof(f485,plain,
! [X0] : or(X0,falsehood) = X0,
inference(paramodulation,[status(thm)],[f24,f475]) ).
fof(f800,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(paramodulation,[status(thm)],[f441,f20]) ).
fof(f820,plain,
! [X0] : implies(or(not(X0),X0),X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f22,f800]) ).
fof(f821,plain,
! [X0] : implies(truth,X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f298,f820]) ).
fof(f822,plain,
! [X0] : X0 = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f18,f821]) ).
fof(f823,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f18,f822]) ).
fof(f845,plain,
! [X0,X1] : or(not(X0),X1) = implies(X0,X1),
inference(paramodulation,[status(thm)],[f823,f22]) ).
fof(f887,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(backward_demodulation,[status(thm)],[f845,f25]) ).
fof(f891,plain,
! [X0] : not(X0) = implies(X0,falsehood),
inference(paramodulation,[status(thm)],[f485,f845]) ).
fof(f919,plain,
! [X0] : not(implies(X0,falsehood)) = implies(implies(falsehood,X0),X0),
inference(paramodulation,[status(thm)],[f20,f891]) ).
fof(f946,plain,
! [X0] : not(not(X0)) = implies(implies(falsehood,X0),X0),
inference(forward_demodulation,[status(thm)],[f891,f919]) ).
fof(f947,plain,
! [X0] : X0 = implies(implies(falsehood,X0),X0),
inference(forward_demodulation,[status(thm)],[f823,f946]) ).
fof(f996,plain,
! [X0] : implies(falsehood,X0) = truth,
inference(paramodulation,[status(thm)],[f947,f60]) ).
fof(f1067,plain,
! [X0] : and(falsehood,X0) = not(truth),
inference(paramodulation,[status(thm)],[f996,f887]) ).
fof(f1071,plain,
! [X0] : and(truth,X0) = not(not(X0)),
inference(paramodulation,[status(thm)],[f18,f887]) ).
fof(f1087,plain,
! [X0] : and(falsehood,X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f1067]) ).
fof(f1090,plain,
! [X0] : and(truth,X0) = X0,
inference(forward_demodulation,[status(thm)],[f823,f1071]) ).
fof(f2063,plain,
! [X0] : xor(truth,X0) = or(not(X0),and(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f1090,f225]) ).
fof(f2064,plain,
! [X0] : xor(truth,X0) = implies(X0,and(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f845,f2063]) ).
fof(f2065,plain,
! [X0] : xor(truth,X0) = implies(X0,falsehood),
inference(forward_demodulation,[status(thm)],[f1087,f2064]) ).
fof(f2066,plain,
not(x) != not(x),
inference(backward_demodulation,[status(thm)],[f2067,f42]) ).
fof(f2067,plain,
! [X0] : xor(truth,X0) = not(X0),
inference(forward_demodulation,[status(thm)],[f891,f2065]) ).
fof(f2076,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 00:10:21 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.52 % Elapsed time: 0.080644 seconds
% 0.17/0.52 % CPU time: 0.388180 seconds
% 0.17/0.52 % Total memory used: 15.168 MB
% 0.17/0.52 % Net memory used: 14.840 MB
%------------------------------------------------------------------------------