%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 63 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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; 4 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 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(f6,axiom,
! [X] : and_star(xor(truth,X),X) = falsehood,
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(implies(not(x),not(y)),implies(y,x)) != truth,
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(f20,plain,
! [X0] : and_star(xor(truth,X0),X0) = falsehood,
inference(cnf_transformation,[status(thm)],[f6]) ).
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(implies(not(x),not(y)),implies(y,x)) != truth,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
inference(forward_demodulation,[status(thm)],[f15,f21]) ).
fof(f39,plain,
! [X0] : and_star(X0,xor(truth,X0)) = falsehood,
inference(backward_demodulation,[status(thm)],[f25,f20]) ).
fof(f41,plain,
! [X0,X1] : xor(X0,xor(not(truth),X1)) = xor(not(X0),xor(truth,X1)),
inference(paramodulation,[status(thm)],[f35,f35]) ).
fof(f42,plain,
! [X0] : xor(X0,not(truth)) = xor(not(X0),truth),
inference(paramodulation,[status(thm)],[f15,f35]) ).
fof(f43,plain,
! [X0,X1] : xor(X0,xor(falsehood,X1)) = xor(not(X0),xor(truth,X1)),
inference(forward_demodulation,[status(thm)],[f26,f41]) ).
fof(f44,plain,
! [X0,X1] : xor(X0,xor(falsehood,X1)) = xor(not(not(X0)),X1),
inference(forward_demodulation,[status(thm)],[f35,f43]) ).
fof(f45,plain,
! [X0] : xor(X0,falsehood) = xor(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f26,f42]) ).
fof(f46,plain,
! [X0] : X0 = xor(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f16,f45]) ).
fof(f47,plain,
! [X0,X1] : xor(X0,xor(falsehood,X1)) = xor(X0,X1),
inference(backward_demodulation,[status(thm)],[f48,f44]) ).
fof(f48,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f15,f46]) ).
fof(f50,plain,
! [X0,X1] : implies(X0,xor(truth,X1)) = xor(truth,and_star(X0,xor(not(truth),X1))),
inference(paramodulation,[status(thm)],[f35,f27]) ).
fof(f53,plain,
! [X0,X1] : implies(X0,xor(truth,X1)) = xor(truth,and_star(X0,xor(falsehood,X1))),
inference(forward_demodulation,[status(thm)],[f26,f50]) ).
fof(f58,plain,
truth = not(falsehood),
inference(paramodulation,[status(thm)],[f26,f48]) ).
fof(f72,plain,
! [X0] : implies(X0,xor(truth,truth)) = xor(truth,and_star(X0,not(falsehood))),
inference(paramodulation,[status(thm)],[f15,f53]) ).
fof(f80,plain,
! [X0] : implies(X0,not(truth)) = xor(truth,and_star(X0,not(falsehood))),
inference(forward_demodulation,[status(thm)],[f15,f72]) ).
fof(f81,plain,
! [X0] : implies(X0,falsehood) = xor(truth,and_star(X0,not(falsehood))),
inference(forward_demodulation,[status(thm)],[f26,f80]) ).
fof(f82,plain,
! [X0] : implies(X0,falsehood) = xor(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f58,f81]) ).
fof(f83,plain,
! [X0,X1] : implies(X0,xor(truth,X1)) = implies(and_star(X0,xor(falsehood,X1)),falsehood),
inference(backward_demodulation,[status(thm)],[f90,f53]) ).
fof(f88,plain,
! [X0] : and_star(X0,implies(X0,falsehood)) = falsehood,
inference(backward_demodulation,[status(thm)],[f90,f39]) ).
fof(f90,plain,
! [X0] : implies(X0,falsehood) = xor(truth,X0),
inference(forward_demodulation,[status(thm)],[f18,f82]) ).
fof(f94,plain,
! [X0,X1] : implies(X0,implies(X1,falsehood)) = implies(and_star(X0,xor(falsehood,X1)),falsehood),
inference(forward_demodulation,[status(thm)],[f90,f83]) ).
fof(f99,plain,
! [X0] : implies(xor(falsehood,X0),falsehood) = xor(truth,X0),
inference(paramodulation,[status(thm)],[f47,f90]) ).
fof(f103,plain,
! [X0] : implies(xor(falsehood,X0),falsehood) = implies(X0,falsehood),
inference(forward_demodulation,[status(thm)],[f90,f99]) ).
fof(f110,plain,
! [X0] : and_star(xor(falsehood,X0),implies(X0,falsehood)) = falsehood,
inference(paramodulation,[status(thm)],[f103,f88]) ).
fof(f111,plain,
! [X0] : and_star(implies(X0,falsehood),xor(falsehood,X0)) = falsehood,
inference(forward_demodulation,[status(thm)],[f25,f110]) ).
fof(f242,plain,
! [X0] : implies(X0,falsehood) = xor(X0,truth),
inference(paramodulation,[status(thm)],[f90,f23]) ).
fof(f243,plain,
! [X0] : X0 = xor(falsehood,X0),
inference(paramodulation,[status(thm)],[f16,f23]) ).
fof(f257,plain,
! [X0] : and_star(implies(X0,falsehood),xor(X0,falsehood)) = falsehood,
inference(paramodulation,[status(thm)],[f23,f111]) ).
fof(f285,plain,
! [X0,X1] : implies(X0,implies(X1,falsehood)) = not(and_star(X0,xor(falsehood,X1))),
inference(backward_demodulation,[status(thm)],[f291,f94]) ).
fof(f291,plain,
! [X0] : implies(X0,falsehood) = not(X0),
inference(forward_demodulation,[status(thm)],[f15,f242]) ).
fof(f303,plain,
! [X0] : and_star(not(X0),xor(X0,falsehood)) = falsehood,
inference(forward_demodulation,[status(thm)],[f291,f257]) ).
fof(f304,plain,
! [X0] : and_star(not(X0),X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f16,f303]) ).
fof(f305,plain,
! [X0] : and_star(X0,not(X0)) = falsehood,
inference(forward_demodulation,[status(thm)],[f25,f304]) ).
fof(f335,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and_star(X0,xor(falsehood,X1))),
inference(forward_demodulation,[status(thm)],[f291,f285]) ).
fof(f336,plain,
implies(not(and_star(not(x),y)),implies(y,x)) != truth,
inference(backward_demodulation,[status(thm)],[f337,f28]) ).
fof(f337,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and_star(X0,X1)),
inference(forward_demodulation,[status(thm)],[f243,f335]) ).
fof(f350,plain,
implies(not(and_star(y,not(x))),implies(y,x)) != truth,
inference(forward_demodulation,[status(thm)],[f25,f336]) ).
fof(f434,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,not(X1))),
inference(paramodulation,[status(thm)],[f48,f337]) ).
fof(f438,plain,
implies(implies(y,x),implies(y,x)) != truth,
inference(backward_demodulation,[status(thm)],[f434,f350]) ).
fof(f513,plain,
! [X0] : implies(X0,X0) = not(falsehood),
inference(paramodulation,[status(thm)],[f305,f434]) ).
fof(f528,plain,
truth != truth,
inference(backward_demodulation,[status(thm)],[f529,f438]) ).
fof(f529,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f58,f513]) ).
fof(f543,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:10:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.41/1.64 % Elapsed time: 1.053837 seconds
% 1.41/1.64 % CPU time: 0.181818 seconds
% 1.41/1.64 % Total memory used: 6.576 MB
% 1.41/1.64 % Net memory used: 6.185 MB
%------------------------------------------------------------------------------