%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:04:40 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.63s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 86 ( 86 unt; 1 def)
% Number of atoms : 86 ( 85 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : add(X,additive_inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : add(X,add(Y,Z)) = add(add(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] : multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
! [X] : multiply(X,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0] : multiply(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
multiply(a,b) = c,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
multiply(b,a) != c,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,definition,
sF0_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f26,plain,
sF0_fnc != c,
inference(definition_folding,[],[f24,f25]) ).
fof(f32,plain,
! [X0,X1] : multiply(X0,multiply(X0,X1)) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f63,plain,
multiply(b,sF0_fnc) = multiply(b,a),
inference(paramodulation,[status(thm)],[f25,f32]) ).
fof(f65,plain,
multiply(a,c) = multiply(a,b),
inference(paramodulation,[status(thm)],[f23,f32]) ).
fof(f83,plain,
multiply(b,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f25,f63]) ).
fof(f85,plain,
multiply(a,c) = c,
inference(forward_demodulation,[status(thm)],[f23,f65]) ).
fof(f167,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f177,plain,
! [X0] : multiply(b,add(X0,sF0_fnc)) = add(multiply(b,X0),sF0_fnc),
inference(paramodulation,[status(thm)],[f83,f20]) ).
fof(f180,plain,
! [X0] : multiply(b,add(X0,a)) = add(multiply(b,X0),sF0_fnc),
inference(paramodulation,[status(thm)],[f25,f20]) ).
fof(f181,plain,
! [X0] : multiply(a,add(X0,c)) = add(multiply(a,X0),c),
inference(paramodulation,[status(thm)],[f85,f20]) ).
fof(f183,plain,
! [X0] : multiply(a,add(X0,b)) = add(multiply(a,X0),c),
inference(paramodulation,[status(thm)],[f23,f20]) ).
fof(f224,plain,
! [X0] : multiply(b,add(X0,sF0_fnc)) = add(sF0_fnc,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f18,f177]) ).
fof(f227,plain,
! [X0] : multiply(b,add(X0,sF0_fnc)) = multiply(b,add(X0,a)),
inference(backward_demodulation,[status(thm)],[f228,f224]) ).
fof(f228,plain,
! [X0] : multiply(b,add(X0,a)) = add(sF0_fnc,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f18,f180]) ).
fof(f229,plain,
! [X0] : multiply(a,add(X0,c)) = add(c,multiply(a,X0)),
inference(forward_demodulation,[status(thm)],[f18,f181]) ).
fof(f231,plain,
! [X0] : multiply(a,add(X0,c)) = multiply(a,add(X0,b)),
inference(backward_demodulation,[status(thm)],[f232,f229]) ).
fof(f232,plain,
! [X0] : multiply(a,add(X0,b)) = add(c,multiply(a,X0)),
inference(forward_demodulation,[status(thm)],[f18,f183]) ).
fof(f258,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f21]) ).
fof(f387,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f395,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f405,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f13,f395]) ).
fof(f409,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f16,f405]) ).
fof(f411,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f18,f405]) ).
fof(f419,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f14,f409]) ).
fof(f429,plain,
! [X0,X1,X2] : add(X0,add(X1,add(X2,additive_inverse(add(X0,X1))))) = X2,
inference(paramodulation,[status(thm)],[f17,f411]) ).
fof(f462,plain,
multiply(b,add(b,sF0_fnc)) = add(b,sF0_fnc),
inference(paramodulation,[status(thm)],[f83,f167]) ).
fof(f466,plain,
multiply(a,add(a,c)) = add(a,c),
inference(paramodulation,[status(thm)],[f85,f167]) ).
fof(f471,plain,
! [X0] : multiply(X0,add(X0,X0)) = add(X0,X0),
inference(paramodulation,[status(thm)],[f22,f167]) ).
fof(f508,plain,
multiply(b,add(b,a)) = add(b,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f227,f462]) ).
fof(f509,plain,
multiply(b,add(a,b)) = add(b,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f18,f508]) ).
fof(f512,plain,
multiply(a,add(a,b)) = add(a,c),
inference(forward_demodulation,[status(thm)],[f231,f466]) ).
fof(f537,plain,
! [X0,X1] : multiply(add(X0,X1),add(X0,X0)) = add(add(X0,X0),multiply(X1,add(X0,X0))),
inference(paramodulation,[status(thm)],[f471,f21]) ).
fof(f567,plain,
! [X0,X1] : multiply(add(X0,X1),add(X0,X0)) = add(X0,add(X0,multiply(X1,add(X0,X0)))),
inference(forward_demodulation,[status(thm)],[f17,f537]) ).
fof(f659,plain,
! [X0,X1] : add(X0,additive_identity) = add(X1,additive_inverse(add(additive_inverse(X0),X1))),
inference(paramodulation,[status(thm)],[f387,f405]) ).
fof(f679,plain,
! [X0,X1] : X0 = add(X1,additive_inverse(add(additive_inverse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f14,f659]) ).
fof(f695,plain,
! [X0,X1] : X0 = add(X1,additive_inverse(add(X1,additive_inverse(X0)))),
inference(paramodulation,[status(thm)],[f18,f679]) ).
fof(f697,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(paramodulation,[status(thm)],[f419,f679]) ).
fof(f738,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X1,X0))),
inference(paramodulation,[status(thm)],[f419,f695]) ).
fof(f1303,plain,
! [X0,X1,X2] : multiply(add(add(X0,X1),X2),add(X0,X1)) = add(X0,add(X1,multiply(X2,add(X0,X1)))),
inference(paramodulation,[status(thm)],[f17,f258]) ).
fof(f1320,plain,
multiply(add(add(a,b),b),add(a,b)) = add(add(a,b),add(b,sF0_fnc)),
inference(paramodulation,[status(thm)],[f509,f258]) ).
fof(f1331,plain,
! [X0] : multiply(add(add(X0,X0),X0),add(X0,X0)) = add(add(X0,X0),add(X0,X0)),
inference(paramodulation,[status(thm)],[f471,f258]) ).
fof(f1357,plain,
! [X0,X1] : multiply(add(X0,X1),add(X0,X0)) = multiply(add(X0,add(X0,X1)),add(X0,X0)),
inference(backward_demodulation,[status(thm)],[f1359,f567]) ).
fof(f1359,plain,
! [X0,X1,X2] : multiply(add(X0,add(X1,X2)),add(X0,X1)) = add(X0,add(X1,multiply(X2,add(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f17,f1303]) ).
fof(f1396,plain,
multiply(add(a,add(b,b)),add(a,b)) = add(add(a,b),add(b,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f17,f1320]) ).
fof(f1397,plain,
multiply(add(a,add(b,b)),add(a,b)) = add(a,add(b,add(b,sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f17,f1396]) ).
fof(f1428,plain,
! [X0] : multiply(add(X0,add(X0,X0)),add(X0,X0)) = add(add(X0,X0),add(X0,X0)),
inference(forward_demodulation,[status(thm)],[f17,f1331]) ).
fof(f1429,plain,
! [X0] : multiply(add(X0,add(X0,X0)),add(X0,X0)) = add(X0,add(X0,add(X0,X0))),
inference(forward_demodulation,[status(thm)],[f17,f1428]) ).
fof(f1464,plain,
! [X0] : multiply(add(X0,X0),add(X0,X0)) = add(X0,add(X0,add(X0,X0))),
inference(backward_demodulation,[status(thm)],[f1357,f1429]) ).
fof(f1467,plain,
! [X0] : add(X0,X0) = add(X0,add(X0,add(X0,X0))),
inference(forward_demodulation,[status(thm)],[f22,f1464]) ).
fof(f1481,plain,
! [X0] : additive_inverse(X0) = add(add(X0,add(X0,X0)),additive_inverse(add(X0,X0))),
inference(paramodulation,[status(thm)],[f1467,f697]) ).
fof(f1512,plain,
! [X0] : additive_inverse(X0) = add(X0,add(add(X0,X0),additive_inverse(add(X0,X0)))),
inference(forward_demodulation,[status(thm)],[f17,f1481]) ).
fof(f1513,plain,
! [X0] : additive_inverse(X0) = add(X0,add(X0,add(X0,additive_inverse(add(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f17,f1512]) ).
fof(f1514,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,add(X1,X0)),
inference(backward_demodulation,[status(thm)],[f1545,f738]) ).
fof(f1520,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(backward_demodulation,[status(thm)],[f1545,f16]) ).
fof(f1545,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[status(thm)],[f429,f1513]) ).
fof(f1555,plain,
multiply(add(a,add(b,b)),add(a,b)) = add(a,sF0_fnc),
inference(backward_demodulation,[status(thm)],[f1574,f1397]) ).
fof(f1574,plain,
! [X0,X1] : X0 = add(X1,add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1545,f1514]) ).
fof(f1665,plain,
multiply(add(a,additive_identity),add(a,b)) = add(a,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f1520,f1555]) ).
fof(f1666,plain,
multiply(a,add(a,b)) = add(a,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f14,f1665]) ).
fof(f1670,plain,
add(a,c) = add(a,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f512,f1666]) ).
fof(f1981,plain,
sF0_fnc = add(a,add(a,c)),
inference(paramodulation,[status(thm)],[f1670,f1574]) ).
fof(f1984,plain,
sF0_fnc = c,
inference(forward_demodulation,[status(thm)],[f1574,f1981]) ).
fof(f1985,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1984,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.35 % Computer : n005.cluster.edu
% 0.09/5.35 % Model : x86_64 x86_64
% 0.09/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.35 % Memory : 8046.5625MB
% 0.09/5.35 % OS : Linux 6.8.0-71-generic
% 0.09/5.35 % CPULimit : 300
% 0.09/5.35 % WCLimit : 300
% 0.09/5.35 % DateTime : Mon Sep 21 04:10:53 UTC 2026
% 0.09/5.35 % CPUTime :
% 0.09/5.36 % Drodi V4.1.1
% 0.12/5.63 % Refutation found
% 0.12/5.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.66 % Elapsed time: 0.288124 seconds
% 0.12/5.66 % CPU time: 2.151815 seconds
% 0.12/5.66 % Total memory used: 38.048 MB
% 0.12/5.66 % Net memory used: 37.001 MB
%------------------------------------------------------------------------------