%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 69 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 114 ( 114 !; 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(f5,axiom,
! [X] : and_star(X,falsehood) = 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(f8,axiom,
! [X,Y] : and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X),
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(x,y),y) != implies(implies(y,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(f19,plain,
! [X0] : and_star(X0,falsehood) = falsehood,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1] : and_star(xor(and_star(xor(truth,X0),X1),truth),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(x,y),y) != implies(implies(y,x),x),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
inference(forward_demodulation,[status(thm)],[f15,f21]) ).
fof(f35,plain,
! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
inference(forward_demodulation,[status(thm)],[f15,f22]) ).
fof(f36,plain,
! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f15,f35]) ).
fof(f37,plain,
! [X0,X1,X2] : implies(X0,and_star(X1,xor(truth,X2))) = xor(truth,and_star(X0,implies(X1,X2))),
inference(paramodulation,[status(thm)],[f27,f27]) ).
fof(f40,plain,
! [X0] : implies(X0,truth) = xor(truth,and_star(X0,not(truth))),
inference(paramodulation,[status(thm)],[f15,f27]) ).
fof(f41,plain,
! [X0] : implies(X0,truth) = xor(truth,and_star(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f26,f40]) ).
fof(f42,plain,
! [X0] : implies(X0,truth) = xor(truth,falsehood),
inference(forward_demodulation,[status(thm)],[f19,f41]) ).
fof(f43,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f16,f42]) ).
fof(f44,plain,
! [X0,X1] : implies(X0,and_star(X1,xor(truth,truth))) = xor(truth,and_star(X0,truth)),
inference(paramodulation,[status(thm)],[f43,f37]) ).
fof(f45,plain,
! [X0,X1] : implies(X0,and_star(X1,not(truth))) = xor(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f15,f44]) ).
fof(f46,plain,
! [X0,X1] : implies(X0,and_star(X1,falsehood)) = xor(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f26,f45]) ).
fof(f47,plain,
! [X0] : implies(X0,falsehood) = xor(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f19,f46]) ).
fof(f48,plain,
! [X0,X1,X2] : implies(X0,and_star(X1,xor(truth,X2))) = implies(and_star(X0,implies(X1,X2)),falsehood),
inference(backward_demodulation,[status(thm)],[f53,f37]) ).
fof(f49,plain,
! [X0,X1] : implies(X0,X1) = implies(and_star(X0,xor(truth,X1)),falsehood),
inference(backward_demodulation,[status(thm)],[f53,f27]) ).
fof(f50,plain,
! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),X0)),X0),
inference(backward_demodulation,[status(thm)],[f53,f36]) ).
fof(f51,plain,
! [X0,X1] : xor(X0,implies(X1,falsehood)) = xor(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f53,f34]) ).
fof(f53,plain,
! [X0] : implies(X0,falsehood) = xor(truth,X0),
inference(forward_demodulation,[status(thm)],[f18,f47]) ).
fof(f54,plain,
! [X0,X1,X2] : implies(X0,and_star(X1,implies(X2,falsehood))) = implies(and_star(X0,implies(X1,X2)),falsehood),
inference(forward_demodulation,[status(thm)],[f53,f48]) ).
fof(f55,plain,
! [X0,X1] : implies(X0,X1) = implies(and_star(X0,implies(X1,falsehood)),falsehood),
inference(forward_demodulation,[status(thm)],[f53,f49]) ).
fof(f56,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,implies(falsehood,falsehood))),
inference(forward_demodulation,[status(thm)],[f54,f55]) ).
fof(f57,plain,
! [X0,X1] : and_star(not(and_star(implies(X0,falsehood),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),X0)),X0),
inference(forward_demodulation,[status(thm)],[f53,f50]) ).
fof(f89,plain,
! [X0] : not(X0) = xor(truth,X0),
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f100,plain,
! [X0] : implies(X0,falsehood) = not(X0),
inference(backward_demodulation,[status(thm)],[f89,f53]) ).
fof(f101,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,not(falsehood))),
inference(backward_demodulation,[status(thm)],[f100,f56]) ).
fof(f102,plain,
! [X0,X1] : and_star(not(and_star(implies(X0,falsehood),X1)),X1) = and_star(not(and_star(not(X1),X0)),X0),
inference(backward_demodulation,[status(thm)],[f100,f57]) ).
fof(f106,plain,
! [X0,X1,X2] : implies(X0,and_star(X1,implies(X2,falsehood))) = not(and_star(X0,implies(X1,X2))),
inference(backward_demodulation,[status(thm)],[f100,f54]) ).
fof(f108,plain,
! [X0,X1] : xor(X0,not(X1)) = xor(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f100,f51]) ).
fof(f109,plain,
! [X0,X1] : and_star(not(and_star(not(X0),X1)),X1) = and_star(not(and_star(not(X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f100,f102]) ).
fof(f115,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,implies(X1,falsehood))),
inference(backward_demodulation,[status(thm)],[f116,f101]) ).
fof(f116,plain,
! [X0,X1,X2] : implies(X0,and_star(X1,not(X2))) = not(and_star(X0,implies(X1,X2))),
inference(forward_demodulation,[status(thm)],[f100,f106]) ).
fof(f118,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f100,f115]) ).
fof(f236,plain,
! [X0] : xor(X0,not(truth)) = not(not(X0)),
inference(paramodulation,[status(thm)],[f15,f108]) ).
fof(f246,plain,
! [X0] : xor(X0,falsehood) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f26,f236]) ).
fof(f250,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f16,f246]) ).
fof(f271,plain,
! [X0,X1] : implies(not(and_star(not(X0),not(X1))),X1) = not(and_star(not(and_star(not(not(X1)),X0)),X0)),
inference(paramodulation,[status(thm)],[f109,f118]) ).
fof(f275,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(not(X1),X0)),
inference(paramodulation,[status(thm)],[f25,f118]) ).
fof(f282,plain,
! [X0,X1] : and_star(X0,not(X1)) = not(implies(X0,X1)),
inference(paramodulation,[status(thm)],[f118,f250]) ).
fof(f287,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = not(and_star(not(and_star(not(not(X1)),X0)),X0)),
inference(forward_demodulation,[status(thm)],[f118,f271]) ).
fof(f288,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = not(and_star(not(and_star(X1,X0)),X0)),
inference(forward_demodulation,[status(thm)],[f250,f287]) ).
fof(f294,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = implies(X0,and_star(X1,X0)),
inference(backward_demodulation,[status(thm)],[f275,f288]) ).
fof(f448,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and_star(X1,X0)),
inference(paramodulation,[status(thm)],[f250,f275]) ).
fof(f510,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(not(X0),and_star(X1,not(X0))),
inference(paramodulation,[status(thm)],[f250,f294]) ).
fof(f538,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(not(X0),not(implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f282,f510]) ).
fof(f539,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = not(and_star(implies(X1,X0),not(X0))),
inference(forward_demodulation,[status(thm)],[f448,f538]) ).
fof(f540,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = not(not(implies(implies(X1,X0),X0))),
inference(forward_demodulation,[status(thm)],[f282,f539]) ).
fof(f542,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f250,f540]) ).
fof(f543,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f28,f542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n020.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 00:09:17 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.53 % Refutation found
% 0.19/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.59/1.77 % Elapsed time: 1.079704 seconds
% 1.59/1.77 % CPU time: 0.312913 seconds
% 1.59/1.77 % Total memory used: 8.036 MB
% 1.59/1.77 % Net memory used: 7.732 MB
%------------------------------------------------------------------------------