%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP121-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:32:34 PM UTC 2026
% Result : Unsatisfiable 9.68s 2.04s
% Output : CNFRefutation 12.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 4
% Syntax : Number of formulae : 106 ( 106 unt; 1 def)
% Number of atoms : 106 ( 105 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 137 ( 137 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y,X,Z] : multiply(Y,multiply(multiply(Y,multiply(multiply(Y,Y),multiply(X,Z))),multiply(Z,multiply(Z,Z)))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
multiply(identity,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(a,identity) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2)))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
multiply(identity,identity) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(a,identity) != a,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
sF0_fnc = multiply(a,identity),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f8,plain,
sF0_fnc != a,
inference(definition_folding,[],[f6,f7]) ).
fof(f9,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f10,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1)))) = X0,
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),sF0_fnc)),multiply(identity,multiply(identity,identity)))) = a,
inference(paramodulation,[status(thm)],[f7,f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X1,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X1,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X1,X3))),multiply(X3,multiply(X3,X3))))))) = X2,
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f14,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),multiply(identity,identity))) = X1,
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f17,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),sF0_fnc)),multiply(identity,identity))) = a,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f18,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),sF0_fnc)),identity)) = a,
inference(forward_demodulation,[status(thm)],[f5,f17]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f14]) ).
fof(f20,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,sF0_fnc)),identity)) = a,
inference(paramodulation,[status(thm)],[f5,f18]) ).
fof(f37,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = X0,
inference(paramodulation,[status(thm)],[f5,f19]) ).
fof(f44,plain,
! [X0] : multiply(identity,multiply(multiply(identity,X0),identity)) = multiply(identity,multiply(identity,multiply(X0,identity))),
inference(paramodulation,[status(thm)],[f37,f37]) ).
fof(f61,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1)))))) = multiply(identity,multiply(identity,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f110,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))) = X0,
inference(backward_demodulation,[status(thm)],[f44,f37]) ).
fof(f111,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,sF0_fnc),identity))) = a,
inference(backward_demodulation,[status(thm)],[f44,f20]) ).
fof(f129,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))) = X0,
inference(forward_demodulation,[status(thm)],[f44,f110]) ).
fof(f130,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(sF0_fnc,identity)))) = a,
inference(forward_demodulation,[status(thm)],[f44,f111]) ).
fof(f181,plain,
multiply(identity,multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity))))) = identity,
inference(paramodulation,[status(thm)],[f130,f10]) ).
fof(f235,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f19]) ).
fof(f334,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(identity,identity),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f235]) ).
fof(f335,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f334]) ).
fof(f336,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f335]) ).
fof(f337,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f336]) ).
fof(f338,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(identity,multiply(identity,identity))))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f337]) ).
fof(f339,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(identity,identity)))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f338]) ).
fof(f340,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity))),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f339]) ).
fof(f341,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),identity)),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f340]) ).
fof(f677,plain,
! [X0,X1] : multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X0,identity)),identity)) = multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1))),
inference(paramodulation,[status(thm)],[f10,f341]) ).
fof(f678,plain,
! [X0] : multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)),identity)) = multiply(multiply(identity,X0),identity),
inference(paramodulation,[status(thm)],[f44,f341]) ).
fof(f684,plain,
! [X0,X1,X2] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,identity)),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2))),
inference(paramodulation,[status(thm)],[f4,f341]) ).
fof(f708,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity)) = multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1))),
inference(forward_demodulation,[status(thm)],[f5,f677]) ).
fof(f709,plain,
! [X0,X1] : multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))) = multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1))),
inference(forward_demodulation,[status(thm)],[f44,f708]) ).
fof(f710,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = multiply(multiply(identity,X0),identity),
inference(forward_demodulation,[status(thm)],[f341,f678]) ).
fof(f776,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(identity,multiply(X1,identity)))),identity)) = multiply(identity,X1),
inference(paramodulation,[status(thm)],[f710,f19]) ).
fof(f1391,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(paramodulation,[status(thm)],[f181,f341]) ).
fof(f1401,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f5,f1391]) ).
fof(f1402,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f710,f1401]) ).
fof(f1403,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f710,f1402]) ).
fof(f1404,plain,
multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f5,f1403]) ).
fof(f1405,plain,
multiply(identity,multiply(identity,identity)) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f5,f1404]) ).
fof(f1406,plain,
multiply(identity,identity) = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f5,f1405]) ).
fof(f1407,plain,
identity = multiply(a,multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity)))),
inference(forward_demodulation,[status(thm)],[f5,f1406]) ).
fof(f1485,plain,
multiply(multiply(a,a),multiply(multiply(a,multiply(identity,identity)),identity)) = multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity))),
inference(paramodulation,[status(thm)],[f1407,f341]) ).
fof(f1494,plain,
multiply(multiply(a,a),multiply(multiply(a,identity),identity)) = multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity))),
inference(forward_demodulation,[status(thm)],[f5,f1485]) ).
fof(f1495,plain,
multiply(multiply(a,a),multiply(sF0_fnc,identity)) = multiply(multiply(sF0_fnc,identity),multiply(multiply(sF0_fnc,identity),multiply(sF0_fnc,identity))),
inference(forward_demodulation,[status(thm)],[f7,f1494]) ).
fof(f1873,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),multiply(X1,identity)))),
inference(paramodulation,[status(thm)],[f19,f776]) ).
fof(f1905,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))),
inference(forward_demodulation,[status(thm)],[f5,f1873]) ).
fof(f3164,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))),identity)),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity),
inference(paramodulation,[status(thm)],[f1905,f341]) ).
fof(f3270,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X1,identity))),identity))),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity),
inference(forward_demodulation,[status(thm)],[f710,f3164]) ).
fof(f3271,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X1,identity)),identity)))),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity),
inference(forward_demodulation,[status(thm)],[f710,f3270]) ).
fof(f3272,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity))))),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity),
inference(forward_demodulation,[status(thm)],[f710,f3271]) ).
fof(f3273,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,X1),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity),
inference(forward_demodulation,[status(thm)],[f129,f3272]) ).
fof(f3715,plain,
! [X0,X1] : multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),identity)),identity)) = multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),
inference(paramodulation,[status(thm)],[f61,f341]) ).
fof(f3803,plain,
! [X0,X1] : multiply(identity,multiply(X0,X1)) = multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),
inference(forward_demodulation,[status(thm)],[f341,f3715]) ).
fof(f3830,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,multiply(sF0_fnc,identity)))),multiply(multiply(a,a),multiply(sF0_fnc,identity)))) = X0,
inference(paramodulation,[status(thm)],[f1495,f10]) ).
fof(f4010,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,X1),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))),
inference(backward_demodulation,[status(thm)],[f3273,f1905]) ).
fof(f6639,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))) = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))),
inference(paramodulation,[status(thm)],[f129,f709]) ).
fof(f6705,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))) = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[status(thm)],[f710,f6639]) ).
fof(f6706,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[status(thm)],[f5,f6705]) ).
fof(f6707,plain,
! [X0] : multiply(identity,multiply(identity,identity)) = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[status(thm)],[f5,f6706]) ).
fof(f6708,plain,
! [X0] : multiply(identity,identity) = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[status(thm)],[f5,f6707]) ).
fof(f6709,plain,
! [X0] : identity = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[status(thm)],[f5,f6708]) ).
fof(f10665,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X1,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X1,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X1,identity)),identity)))))) = X2,
inference(backward_demodulation,[status(thm)],[f684,f13]) ).
fof(f10768,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),multiply(multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X1,identity)),identity)),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X1,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X1,identity)),identity)))))) = X2,
inference(forward_demodulation,[status(thm)],[f684,f10665]) ).
fof(f10769,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),multiply(multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X1,identity)),identity)),multiply(multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X1,identity)),identity)),multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X1,identity)),identity)))))) = X2,
inference(forward_demodulation,[status(thm)],[f684,f10768]) ).
fof(f14674,plain,
! [X0] : multiply(identity,multiply(identity,X0)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0))))),
inference(paramodulation,[status(thm)],[f5,f3803]) ).
fof(f14860,plain,
! [X0] : multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X0)),identity)),identity)) = multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))),
inference(paramodulation,[status(thm)],[f14674,f341]) ).
fof(f14942,plain,
! [X0] : multiply(identity,X0) = multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))),
inference(forward_demodulation,[status(thm)],[f341,f14860]) ).
fof(f14953,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),multiply(X1,X2))),
inference(backward_demodulation,[status(thm)],[f14942,f9]) ).
fof(f16696,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,identity),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X1,multiply(sF0_fnc,identity)))),multiply(multiply(a,a),multiply(sF0_fnc,identity)))))) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),X1)),
inference(paramodulation,[status(thm)],[f3830,f14953]) ).
fof(f16807,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,identity),X1)) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),X1)),
inference(forward_demodulation,[status(thm)],[f3830,f16696]) ).
fof(f17400,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))) = multiply(X0,multiply(multiply(X0,identity),multiply(X1,X2))),
inference(backward_demodulation,[status(thm)],[f16807,f14953]) ).
fof(f17757,plain,
! [X0,X1,X2] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,multiply(multiply(X0,identity),multiply(X1,X2))),identity)),identity)) = multiply(multiply(X0,X1),multiply(identity,X2)),
inference(paramodulation,[status(thm)],[f17400,f341]) ).
fof(f17952,plain,
! [X0,X1,X2] : multiply(multiply(X0,identity),multiply(X1,X2)) = multiply(multiply(X0,X1),multiply(identity,X2)),
inference(forward_demodulation,[status(thm)],[f341,f17757]) ).
fof(f18136,plain,
! [X0,X1] : multiply(sF0_fnc,multiply(X0,X1)) = multiply(multiply(a,X0),multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f7,f17952]) ).
fof(f18209,plain,
! [X0,X1] : multiply(multiply(X0,identity),multiply(X1,identity)) = multiply(multiply(X0,X1),identity),
inference(paramodulation,[status(thm)],[f5,f17952]) ).
fof(f18847,plain,
! [X0] : multiply(sF0_fnc,multiply(X0,identity)) = multiply(multiply(a,X0),identity),
inference(paramodulation,[status(thm)],[f5,f18136]) ).
fof(f19301,plain,
! [X0] : identity = multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),multiply(X0,identity)),identity))),
inference(backward_demodulation,[status(thm)],[f18209,f6709]) ).
fof(f19426,plain,
! [X0] : identity = multiply(X0,multiply(multiply(multiply(X0,identity),multiply(multiply(X0,identity),multiply(X0,identity))),identity)),
inference(forward_demodulation,[status(thm)],[f18209,f19301]) ).
fof(f19427,plain,
! [X0] : identity = multiply(X0,multiply(multiply(multiply(X0,identity),multiply(multiply(X0,X0),identity)),identity)),
inference(forward_demodulation,[status(thm)],[f18209,f19426]) ).
fof(f19428,plain,
! [X0] : identity = multiply(X0,multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity)),
inference(forward_demodulation,[status(thm)],[f18209,f19427]) ).
fof(f20657,plain,
identity = multiply(a,multiply(multiply(sF0_fnc,multiply(multiply(a,a),identity)),identity)),
inference(paramodulation,[status(thm)],[f18847,f19428]) ).
fof(f20704,plain,
identity = multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,multiply(a,identity))),identity)),
inference(forward_demodulation,[status(thm)],[f18847,f20657]) ).
fof(f20705,plain,
identity = multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),
inference(forward_demodulation,[status(thm)],[f7,f20704]) ).
fof(f20960,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),identity)),multiply(multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),identity)),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(paramodulation,[status(thm)],[f20705,f10769]) ).
fof(f20973,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(multiply(a,a),multiply(sF0_fnc,multiply(multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity),identity))),multiply(multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),identity)),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f18847,f20960]) ).
fof(f20974,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(multiply(a,a),identity),multiply(multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),identity)),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f19428,f20973]) ).
fof(f20975,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,multiply(a,identity)),multiply(multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),identity)),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f18847,f20974]) ).
fof(f20976,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity)),identity)),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f7,f20975]) ).
fof(f20977,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(multiply(a,a),multiply(sF0_fnc,multiply(multiply(multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)),identity),identity))),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f18847,f20976]) ).
fof(f20978,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(multiply(a,a),identity),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f19428,f20977]) ).
fof(f20979,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(sF0_fnc,multiply(a,identity)),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f18847,f20978]) ).
fof(f20980,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(a,a),multiply(identity,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f7,f20979]) ).
fof(f20981,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(sF0_fnc,sF0_fnc),multiply(sF0_fnc,multiply(a,identity)))))) = a,
inference(forward_demodulation,[status(thm)],[f18136,f20980]) ).
fof(f20982,plain,
! [X0] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(sF0_fnc,multiply(sF0_fnc,sF0_fnc)))),multiply(multiply(sF0_fnc,sF0_fnc),multiply(multiply(sF0_fnc,sF0_fnc),multiply(sF0_fnc,sF0_fnc))))) = a,
inference(forward_demodulation,[status(thm)],[f7,f20981]) ).
fof(f20983,plain,
! [X0] : multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,multiply(sF0_fnc,identity)),identity))) = a,
inference(forward_demodulation,[status(thm)],[f684,f20982]) ).
fof(f20984,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(sF0_fnc,identity),identity)))) = a,
inference(forward_demodulation,[status(thm)],[f4010,f20983]) ).
fof(f20985,plain,
sF0_fnc = a,
inference(forward_demodulation,[status(thm)],[f129,f20984]) ).
fof(f20986,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20985,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP121-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.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 : Sun Sep 20 19:57:55 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 9.68/2.04 % Refutation found
% 9.68/2.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.68/2.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/2.14 % Elapsed time: 1.775361 seconds
% 0.39/2.14 % CPU time: 13.410725 seconds
% 0.39/2.14 % Total memory used: 270.088 MB
% 0.39/2.14 % Net memory used: 257.333 MB
%------------------------------------------------------------------------------