%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:06:57 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 33 unt; 1 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : not(X) = xor(X,truth),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : xor(X,falsehood) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : and_star(X,truth) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] : xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : and_star(X,Y) = and_star(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
implies(truth,x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : not(X0) = xor(X0,truth),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : xor(X0,falsehood) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0] : and_star(X0,truth) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(truth,X1))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
implies(truth,x) != x,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f29,definition,
sF0_fnc = implies(truth,x),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f30,plain,
sF0_fnc != x,
inference(definition_folding,[],[f28,f29]) ).
fof(f246,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f15,f21]) ).
fof(f260,plain,
! [X0] : not(X0) = xor(truth,X0),
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f291,plain,
! [X0] : X0 = and_star(truth,X0),
inference(paramodulation,[status(thm)],[f18,f25]) ).
fof(f592,plain,
! [X0] : xor(X0,not(truth)) = xor(not(X0),truth),
inference(paramodulation,[status(thm)],[f15,f246]) ).
fof(f609,plain,
! [X0] : xor(X0,falsehood) = xor(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f26,f592]) ).
fof(f610,plain,
! [X0] : X0 = xor(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f16,f609]) ).
fof(f611,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f15,f610]) ).
fof(f768,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,xor(truth,X1))),
inference(backward_demodulation,[status(thm)],[f260,f27]) ).
fof(f790,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f260,f768]) ).
fof(f802,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(paramodulation,[status(thm)],[f291,f790]) ).
fof(f816,plain,
! [X0] : implies(truth,X0) = X0,
inference(forward_demodulation,[status(thm)],[f611,f802]) ).
fof(f1018,plain,
sF0_fnc = x,
inference(backward_demodulation,[status(thm)],[f816,f29]) ).
fof(f1025,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1018,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:13:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.050584 seconds
% 0.13/0.41 % CPU time: 0.051587 seconds
% 0.13/0.41 % Total memory used: 1.703 MB
% 0.13/0.41 % Net memory used: 1.639 MB
%------------------------------------------------------------------------------