%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 90 ( 90 unt; 2 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 108 ( 108 !; 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(f13,axiom,
! [X,Y] : and_star(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] : and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] : and_star(X,Y) = and_star(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,
and_star(xor(truth,x),x) != falsehood,
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(f30,plain,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0,X1,X2] : and_star(and_star(X0,X1),X2) = and_star(X0,and_star(X1,X2)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
and_star(xor(truth,x),x) != falsehood,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF1_fnc = xor(truth,x),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f36,definition,
sF0_fnc = and_star(sF1_fnc,x),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f37,plain,
sF0_fnc != falsehood,
inference(definition_folding,[],[f34,f36,f35]) ).
fof(f39,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f40,plain,
! [X0,X1] : implies(implies(implies(implies(X0,X1),X1),X0),truth) = truth,
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f46,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f39]) ).
fof(f49,plain,
sF1_fnc = xor(x,truth),
inference(paramodulation,[status(thm)],[f35,f29]) ).
fof(f61,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f46]) ).
fof(f70,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f61]) ).
fof(f93,plain,
! [X0] : xor(X0,truth) = or(and(X0,falsehood),and(not(X0),truth)),
inference(paramodulation,[status(thm)],[f33,f28]) ).
fof(f126,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(backward_demodulation,[status(thm)],[f22,f21]) ).
fof(f128,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f70,f22]) ).
fof(f129,plain,
! [X0] : or(truth,X0) = implies(falsehood,X0),
inference(paramodulation,[status(thm)],[f33,f22]) ).
fof(f141,plain,
! [X0] : or(not(X0),X0) = truth,
inference(paramodulation,[status(thm)],[f24,f128]) ).
fof(f159,plain,
! [X0] : implies(X0,X0) = implies(implies(X0,truth),truth),
inference(paramodulation,[status(thm)],[f18,f20]) ).
fof(f178,plain,
! [X0] : truth = implies(implies(X0,truth),truth),
inference(forward_demodulation,[status(thm)],[f70,f159]) ).
fof(f214,plain,
! [X0] : and(X0,not(X0)) = not(truth),
inference(paramodulation,[status(thm)],[f128,f25]) ).
fof(f227,plain,
! [X0] : and(X0,not(X0)) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f214]) ).
fof(f233,plain,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
inference(backward_demodulation,[status(thm)],[f235,f25]) ).
fof(f235,plain,
! [X0,X1] : and_star(X0,X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f30]) ).
fof(f244,plain,
! [X0] : and_star(X0,not(X0)) = falsehood,
inference(forward_demodulation,[status(thm)],[f235,f227]) ).
fof(f270,plain,
! [X0] : and_star(and_star(X0,sF1_fnc),x) = and_star(X0,sF0_fnc),
inference(paramodulation,[status(thm)],[f36,f31]) ).
fof(f282,plain,
! [X0] : implies(truth,implies(X0,not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f141,f126]) ).
fof(f299,plain,
! [X0] : implies(X0,not(not(X0))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f282]) ).
fof(f330,plain,
not(not(truth)) = truth,
inference(paramodulation,[status(thm)],[f18,f299]) ).
fof(f336,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(paramodulation,[status(thm)],[f299,f20]) ).
fof(f342,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f33,f330]) ).
fof(f346,plain,
! [X0] : implies(or(not(X0),X0),X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f22,f336]) ).
fof(f347,plain,
! [X0] : implies(truth,X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f141,f346]) ).
fof(f348,plain,
! [X0] : X0 = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f18,f347]) ).
fof(f349,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f18,f348]) ).
fof(f364,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f342,f22]) ).
fof(f367,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f364]) ).
fof(f377,plain,
! [X0,X1] : or(not(X0),X1) = implies(X0,X1),
inference(paramodulation,[status(thm)],[f349,f22]) ).
fof(f381,plain,
! [X0] : or(X0,falsehood) = X0,
inference(paramodulation,[status(thm)],[f24,f367]) ).
fof(f448,plain,
! [X0] : and_star(truth,X0) = not(or(falsehood,not(X0))),
inference(paramodulation,[status(thm)],[f33,f233]) ).
fof(f452,plain,
! [X0] : and_star(X0,truth) = not(or(not(X0),falsehood)),
inference(paramodulation,[status(thm)],[f33,f233]) ).
fof(f466,plain,
! [X0] : and_star(truth,X0) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f367,f448]) ).
fof(f467,plain,
! [X0] : and_star(truth,X0) = X0,
inference(forward_demodulation,[status(thm)],[f349,f466]) ).
fof(f468,plain,
! [X0] : and_star(X0,truth) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f381,f452]) ).
fof(f469,plain,
! [X0] : and_star(X0,truth) = X0,
inference(forward_demodulation,[status(thm)],[f349,f468]) ).
fof(f476,plain,
! [X0] : and_star(x,and_star(X0,sF1_fnc)) = and_star(X0,sF0_fnc),
inference(paramodulation,[status(thm)],[f32,f270]) ).
fof(f668,plain,
! [X0,X1] : and_star(X0,X1) = not(implies(X0,not(X1))),
inference(backward_demodulation,[status(thm)],[f377,f233]) ).
fof(f1038,plain,
and_star(x,sF1_fnc) = and_star(truth,sF0_fnc),
inference(paramodulation,[status(thm)],[f467,f476]) ).
fof(f1046,plain,
and_star(x,sF1_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f467,f1038]) ).
fof(f1410,plain,
! [X0] : implies(implies(truth,X0),truth) = truth,
inference(paramodulation,[status(thm)],[f178,f40]) ).
fof(f1442,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f18,f1410]) ).
fof(f1477,plain,
! [X0] : or(X0,truth) = truth,
inference(paramodulation,[status(thm)],[f22,f1442]) ).
fof(f1540,plain,
! [X0] : or(truth,X0) = truth,
inference(paramodulation,[status(thm)],[f24,f1477]) ).
fof(f1585,plain,
! [X0] : truth = implies(falsehood,X0),
inference(backward_demodulation,[status(thm)],[f1540,f129]) ).
fof(f1608,plain,
! [X0] : and_star(falsehood,X0) = not(truth),
inference(paramodulation,[status(thm)],[f1585,f668]) ).
fof(f1626,plain,
! [X0] : and_star(falsehood,X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f1608]) ).
fof(f1663,plain,
! [X0] : and_star(X0,falsehood) = falsehood,
inference(paramodulation,[status(thm)],[f32,f1626]) ).
fof(f2039,plain,
! [X0] : xor(X0,truth) = or(and_star(X0,falsehood),and(not(X0),truth)),
inference(forward_demodulation,[status(thm)],[f235,f93]) ).
fof(f2040,plain,
! [X0] : xor(X0,truth) = or(falsehood,and(not(X0),truth)),
inference(forward_demodulation,[status(thm)],[f1663,f2039]) ).
fof(f2041,plain,
! [X0] : xor(X0,truth) = and(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f367,f2040]) ).
fof(f2042,plain,
! [X0] : xor(X0,truth) = and_star(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f235,f2041]) ).
fof(f2043,plain,
sF1_fnc = not(x),
inference(backward_demodulation,[status(thm)],[f2044,f49]) ).
fof(f2044,plain,
! [X0] : xor(X0,truth) = not(X0),
inference(forward_demodulation,[status(thm)],[f469,f2042]) ).
fof(f2060,plain,
and_star(x,sF1_fnc) = falsehood,
inference(paramodulation,[status(thm)],[f2043,f244]) ).
fof(f2063,plain,
sF0_fnc = falsehood,
inference(forward_demodulation,[status(thm)],[f1046,f2060]) ).
fof(f2064,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2063,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n015.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 00:10:51 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.052895 seconds
% 0.13/0.40 % CPU time: 0.214720 seconds
% 0.13/0.40 % Total memory used: 10.133 MB
% 0.13/0.40 % Net memory used: 9.914 MB
%------------------------------------------------------------------------------