%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ROB022-1 : 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 02:06:33 PM UTC 2026
% Result : Unsatisfiable 5.23s 1.39s
% Output : CNFRefutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 89 ( 89 unt; 7 def)
% Number of atoms : 89 ( 88 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 83 ( 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
add(c,negate(c)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
add(c,negate(c)) = c,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF3_fnc = negate(b),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f12,definition,
sF2_fnc = add(a,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f13,definition,
sF1_fnc = negate(sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF6_fnc = negate(a),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f15,definition,
sF5_fnc = add(sF6_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f16,definition,
sF4_fnc = negate(sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f17,definition,
sF0_fnc = add(sF1_fnc,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f18,plain,
sF0_fnc != b,
inference(definition_folding,[],[f10,f17,f16,f15,f14,f13,f12,f11]) ).
fof(f19,plain,
sF2_fnc = add(sF3_fnc,a),
inference(forward_demodulation,[status(thm)],[f6,f12]) ).
fof(f20,plain,
sF0_fnc = add(sF4_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6,f17]) ).
fof(f25,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X1,add(X2,X0)),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f28,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f34,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(forward_demodulation,[status(thm)],[f7,f28]) ).
fof(f39,plain,
! [X0] : add(c,X0) = add(c,add(negate(c),X0)),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f52,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X2,add(X1,X0)),
inference(paramodulation,[status(thm)],[f6,f25]) ).
fof(f109,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(paramodulation,[status(thm)],[f25,f34]) ).
fof(f112,plain,
! [X0] : add(X0,c) = add(c,add(X0,negate(c))),
inference(paramodulation,[status(thm)],[f9,f34]) ).
fof(f181,plain,
! [X0,X1] : negate(add(X0,negate(add(negate(add(X0,X1)),negate(negate(add(X0,negate(X1)))))))) = negate(add(X0,X1)),
inference(paramodulation,[status(thm)],[f8,f8]) ).
fof(f185,plain,
negate(add(negate(sF2_fnc),negate(add(sF3_fnc,negate(a))))) = sF3_fnc,
inference(paramodulation,[status(thm)],[f19,f8]) ).
fof(f191,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X1,negate(X0))))) = X1,
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f193,plain,
! [X0,X1] : negate(add(negate(add(negate(add(X0,X1)),add(X0,negate(X1)))),X0)) = negate(add(X0,X1)),
inference(paramodulation,[status(thm)],[f8,f8]) ).
fof(f194,plain,
negate(add(negate(add(c,c)),negate(c))) = c,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f196,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(negate(X1),X0)))) = X0,
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f204,plain,
negate(add(sF1_fnc,negate(add(sF3_fnc,negate(a))))) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f13,f185]) ).
fof(f205,plain,
negate(add(sF1_fnc,negate(add(sF3_fnc,sF6_fnc)))) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f14,f204]) ).
fof(f206,plain,
negate(add(sF1_fnc,negate(add(sF6_fnc,sF3_fnc)))) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f6,f205]) ).
fof(f207,plain,
negate(add(sF1_fnc,negate(sF5_fnc))) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f15,f206]) ).
fof(f208,plain,
negate(add(sF1_fnc,sF4_fnc)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f16,f207]) ).
fof(f209,plain,
negate(add(sF4_fnc,sF1_fnc)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f6,f208]) ).
fof(f211,plain,
negate(sF0_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f20,f209]) ).
fof(f213,plain,
! [X0,X1] : negate(add(X0,negate(add(negate(add(X0,X1)),add(X0,negate(X1)))))) = negate(add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6,f193]) ).
fof(f214,plain,
! [X0,X1] : negate(add(X0,negate(add(X0,add(negate(add(X0,X1)),negate(X1)))))) = negate(add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f34,f213]) ).
fof(f215,plain,
! [X0,X1] : negate(add(X0,negate(add(X0,add(negate(X1),negate(add(X0,X1))))))) = negate(add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f109,f214]) ).
fof(f216,plain,
negate(add(negate(c),negate(add(c,c)))) = c,
inference(forward_demodulation,[status(thm)],[f6,f194]) ).
fof(f973,plain,
! [X0,X1] : negate(add(X0,negate(add(negate(add(X1,X0)),negate(negate(add(X0,negate(X1)))))))) = negate(add(X0,X1)),
inference(paramodulation,[status(thm)],[f6,f181]) ).
fof(f1043,plain,
negate(add(negate(c),negate(add(negate(add(negate(c),add(c,c))),negate(c))))) = negate(add(negate(c),add(c,c))),
inference(paramodulation,[status(thm)],[f216,f181]) ).
fof(f1048,plain,
! [X0] : negate(add(negate(add(X0,add(negate(c),negate(add(c,c))))),negate(add(X0,c)))) = X0,
inference(paramodulation,[status(thm)],[f216,f8]) ).
fof(f1049,plain,
negate(add(negate(c),negate(add(negate(c),negate(add(negate(c),add(c,c))))))) = negate(add(negate(c),add(c,c))),
inference(forward_demodulation,[status(thm)],[f6,f1043]) ).
fof(f1050,plain,
negate(add(negate(c),negate(add(negate(c),negate(add(c,add(c,negate(c)))))))) = negate(add(negate(c),add(c,c))),
inference(forward_demodulation,[status(thm)],[f52,f1049]) ).
fof(f1051,plain,
negate(add(negate(c),negate(add(negate(c),negate(add(c,c)))))) = negate(add(negate(c),add(c,c))),
inference(forward_demodulation,[status(thm)],[f112,f1050]) ).
fof(f1052,plain,
negate(add(negate(c),c)) = negate(add(negate(c),add(c,c))),
inference(forward_demodulation,[status(thm)],[f216,f1051]) ).
fof(f1053,plain,
negate(add(c,negate(c))) = negate(add(negate(c),add(c,c))),
inference(forward_demodulation,[status(thm)],[f6,f1052]) ).
fof(f1054,plain,
negate(c) = negate(add(negate(c),add(c,c))),
inference(forward_demodulation,[status(thm)],[f9,f1053]) ).
fof(f1055,plain,
negate(c) = negate(add(c,add(c,negate(c)))),
inference(forward_demodulation,[status(thm)],[f52,f1054]) ).
fof(f1058,plain,
negate(c) = negate(add(c,c)),
inference(forward_demodulation,[status(thm)],[f112,f1055]) ).
fof(f1069,plain,
! [X0] : negate(add(negate(add(X0,c)),negate(add(X0,add(negate(c),negate(add(c,c))))))) = X0,
inference(forward_demodulation,[status(thm)],[f6,f1048]) ).
fof(f1070,plain,
! [X0] : negate(add(negate(add(X0,c)),negate(add(X0,add(negate(c),negate(c)))))) = X0,
inference(forward_demodulation,[status(thm)],[f1058,f1069]) ).
fof(f1302,plain,
! [X0] : negate(add(negate(add(c,X0)),negate(add(add(negate(c),X0),negate(c))))) = add(negate(c),X0),
inference(paramodulation,[status(thm)],[f39,f191]) ).
fof(f1303,plain,
! [X0] : negate(add(negate(add(X0,c)),negate(add(add(X0,negate(c)),negate(c))))) = add(X0,negate(c)),
inference(paramodulation,[status(thm)],[f112,f191]) ).
fof(f1335,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(negate(X0),X1)))) = X1,
inference(paramodulation,[status(thm)],[f6,f191]) ).
fof(f1355,plain,
! [X0,X1] : negate(add(X0,negate(add(negate(add(X1,X0)),negate(negate(add(X0,negate(X1)))))))) = negate(add(X1,X0)),
inference(paramodulation,[status(thm)],[f191,f8]) ).
fof(f1374,plain,
! [X0] : negate(add(negate(add(c,X0)),negate(add(negate(c),add(X0,negate(c)))))) = add(negate(c),X0),
inference(forward_demodulation,[status(thm)],[f7,f1302]) ).
fof(f1375,plain,
! [X0] : negate(add(negate(add(X0,c)),negate(add(X0,add(negate(c),negate(c)))))) = add(X0,negate(c)),
inference(forward_demodulation,[status(thm)],[f7,f1303]) ).
fof(f1381,plain,
! [X0] : negate(add(negate(add(c,X0)),negate(add(negate(c),X0)))) = add(negate(c),X0),
inference(backward_demodulation,[status(thm)],[f1389,f1374]) ).
fof(f1389,plain,
! [X0] : X0 = add(X0,negate(c)),
inference(forward_demodulation,[status(thm)],[f1070,f1375]) ).
fof(f1460,plain,
! [X0,X1] : negate(add(X0,X1)) = negate(add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f973,f1355]) ).
fof(f1476,plain,
! [X0] : X0 = add(negate(c),X0),
inference(forward_demodulation,[status(thm)],[f1335,f1381]) ).
fof(f1504,plain,
! [X0] : negate(add(negate(X0),negate(add(negate(c),negate(X0))))) = negate(c),
inference(paramodulation,[status(thm)],[f1389,f191]) ).
fof(f1525,plain,
! [X0] : negate(add(negate(X0),negate(negate(X0)))) = negate(c),
inference(forward_demodulation,[status(thm)],[f1476,f1504]) ).
fof(f2207,plain,
! [X0] : negate(negate(add(negate(c),add(negate(X0),negate(add(negate(c),X0)))))) = negate(add(negate(c),X0)),
inference(paramodulation,[status(thm)],[f1476,f215]) ).
fof(f2286,plain,
! [X0] : negate(negate(add(negate(X0),negate(add(negate(c),X0))))) = negate(add(negate(c),X0)),
inference(forward_demodulation,[status(thm)],[f1476,f2207]) ).
fof(f2287,plain,
! [X0] : negate(negate(add(negate(X0),negate(X0)))) = negate(add(negate(c),X0)),
inference(forward_demodulation,[status(thm)],[f1476,f2286]) ).
fof(f2288,plain,
! [X0] : negate(negate(add(negate(X0),negate(X0)))) = negate(X0),
inference(forward_demodulation,[status(thm)],[f1476,f2287]) ).
fof(f2402,plain,
! [X0,X1] : negate(negate(add(X0,negate(add(negate(add(X1,X0)),negate(add(X0,negate(X1)))))))) = negate(add(negate(add(X1,X0)),negate(add(X0,negate(X1))))),
inference(paramodulation,[status(thm)],[f191,f2288]) ).
fof(f2453,plain,
! [X0,X1] : negate(negate(add(X0,X0))) = negate(add(negate(add(X1,X0)),negate(add(X0,negate(X1))))),
inference(forward_demodulation,[status(thm)],[f191,f2402]) ).
fof(f2459,plain,
! [X0] : negate(negate(add(X0,X0))) = X0,
inference(forward_demodulation,[status(thm)],[f191,f2453]) ).
fof(f2580,plain,
! [X0] : negate(add(X0,negate(negate(negate(add(X0,X0)))))) = negate(c),
inference(paramodulation,[status(thm)],[f2459,f1525]) ).
fof(f2638,plain,
! [X0] : negate(add(X0,negate(X0))) = negate(c),
inference(forward_demodulation,[status(thm)],[f2459,f2580]) ).
fof(f2764,plain,
! [X0] : negate(add(negate(c),negate(add(X0,negate(negate(X0)))))) = X0,
inference(paramodulation,[status(thm)],[f2638,f8]) ).
fof(f2811,plain,
! [X0] : negate(negate(add(X0,negate(negate(X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f1476,f2764]) ).
fof(f2968,plain,
! [X0] : negate(add(negate(add(negate(negate(X0)),X0)),negate(c))) = negate(negate(X0)),
inference(paramodulation,[status(thm)],[f2638,f196]) ).
fof(f3097,plain,
! [X0] : negate(add(negate(c),negate(add(negate(negate(X0)),X0)))) = negate(negate(X0)),
inference(forward_demodulation,[status(thm)],[f1460,f2968]) ).
fof(f3098,plain,
! [X0] : negate(negate(add(negate(negate(X0)),X0))) = negate(negate(X0)),
inference(forward_demodulation,[status(thm)],[f1476,f3097]) ).
fof(f3099,plain,
! [X0] : negate(negate(add(X0,negate(negate(X0))))) = negate(negate(X0)),
inference(forward_demodulation,[status(thm)],[f1460,f3098]) ).
fof(f3195,plain,
! [X0] : X0 = negate(negate(X0)),
inference(forward_demodulation,[status(thm)],[f2811,f3099]) ).
fof(f3562,plain,
sF0_fnc = negate(sF3_fnc),
inference(paramodulation,[status(thm)],[f211,f3195]) ).
fof(f3581,plain,
b = negate(sF3_fnc),
inference(paramodulation,[status(thm)],[f11,f3195]) ).
fof(f3715,plain,
b = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f3562,f3581]) ).
fof(f3716,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3715,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:26:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 5.23/1.39 % Refutation found
% 5.23/1.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.23/1.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.27/2.63 % Elapsed time: 2.043282 seconds
% 12.27/2.63 % CPU time: 6.256086 seconds
% 12.27/2.63 % Total memory used: 51.333 MB
% 12.27/2.63 % Net memory used: 49.950 MB
%------------------------------------------------------------------------------