%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:06:34 PM UTC 2026
% Result : Unsatisfiable 5.14s 1.38s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 9
% Syntax : Number of formulae : 142 ( 142 unt; 2 def)
% Number of atoms : 142 ( 141 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 219 ( 219 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : multiply(add(X,Y),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : add(X,inverse(X)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : pixley(X,Y,Z) = add(multiply(X,inverse(Y)),add(multiply(X,Z),multiply(inverse(Y),Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : pixley(X,X,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : pixley(X,Y,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
add(multiply(a,b),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : add(X0,inverse(X0)) = n1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),add(multiply(X0,X2),multiply(inverse(X1),X2))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1] : pixley(X0,X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : pixley(X0,X1,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
add(multiply(a,b),b) != b,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,definition,
sF1_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f18,definition,
sF0_fnc = add(sF1_fnc,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f19,plain,
sF0_fnc != b,
inference(definition_folding,[],[f16,f18,f17]) ).
fof(f20,plain,
! [X0,X1,X2] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),multiply(X2,add(X0,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f10,f12]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(X0,add(add(X1,X0),X2)) = add(X0,multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f26,plain,
! [X0,X1,X2] : multiply(X0,add(X1,add(X2,X0))) = add(multiply(X1,X0),X0),
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(multiply(X0,add(X1,X2)),multiply(X2,X0)) = multiply(X2,X0),
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3] : multiply(add(add(X0,X1),X2),add(X1,X3)) = add(add(X1,multiply(X2,X1)),multiply(X3,add(add(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f23,f10]) ).
fof(f37,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),add(X2,multiply(X1,add(X3,X0)))) = add(multiply(X2,multiply(X0,X1)),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f26]) ).
fof(f52,plain,
! [X0,X1,X2] : multiply(add(X0,X1),multiply(X1,add(X2,add(X0,X1)))) = multiply(X1,add(X2,add(X0,X1))),
inference(paramodulation,[status(thm)],[f9,f28]) ).
fof(f56,plain,
! [X0] : multiply(multiply(X0,sF0_fnc),multiply(b,X0)) = multiply(b,X0),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f66,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(multiply(X2,X1),X1)) = multiply(X1,add(X2,add(X0,X1))),
inference(forward_demodulation,[status(thm)],[f26,f52]) ).
fof(f67,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(multiply(X2,X1),X1)) = add(multiply(X2,X1),X1),
inference(forward_demodulation,[status(thm)],[f26,f66]) ).
fof(f163,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X1,X1)) = add(multiply(add(X2,X1),X1),X1),
inference(paramodulation,[status(thm)],[f9,f67]) ).
fof(f164,plain,
! [X0] : multiply(add(X0,b),add(sF1_fnc,b)) = add(multiply(a,b),b),
inference(paramodulation,[status(thm)],[f17,f67]) ).
fof(f186,plain,
! [X0,X1] : multiply(add(X0,X1),add(X1,X1)) = add(X1,X1),
inference(forward_demodulation,[status(thm)],[f9,f163]) ).
fof(f187,plain,
! [X0] : multiply(add(X0,b),sF0_fnc) = add(multiply(a,b),b),
inference(forward_demodulation,[status(thm)],[f18,f164]) ).
fof(f188,plain,
! [X0] : multiply(add(X0,b),sF0_fnc) = add(sF1_fnc,b),
inference(forward_demodulation,[status(thm)],[f17,f187]) ).
fof(f189,plain,
! [X0] : multiply(add(X0,b),sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f18,f188]) ).
fof(f194,plain,
! [X0] : multiply(sF0_fnc,multiply(b,add(X0,b))) = multiply(b,add(X0,b)),
inference(paramodulation,[status(thm)],[f189,f56]) ).
fof(f272,plain,
! [X0,X1] : pixley(X0,X0,X1) = add(multiply(X0,inverse(X0)),multiply(X1,n1)),
inference(paramodulation,[status(thm)],[f11,f20]) ).
fof(f273,plain,
! [X0] : multiply(n1,add(inverse(X0),inverse(X0))) = add(inverse(X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f11,f186]) ).
fof(f276,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,n1)) = add(multiply(X1,inverse(X0)),inverse(X0)),
inference(paramodulation,[status(thm)],[f11,f26]) ).
fof(f277,plain,
! [X0,X1] : multiply(inverse(X0),add(n1,X1)) = add(inverse(X0),multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f11,f23]) ).
fof(f278,plain,
! [X0] : multiply(n1,inverse(X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f280,plain,
! [X0,X1] : X0 = add(multiply(X1,inverse(X1)),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f13,f272]) ).
fof(f294,plain,
! [X0] : X0 = add(inverse(n1),multiply(X0,n1)),
inference(paramodulation,[status(thm)],[f278,f280]) ).
fof(f296,plain,
! [X0] : multiply(X0,add(multiply(X0,n1),multiply(X0,n1))) = add(multiply(X0,n1),multiply(X0,n1)),
inference(paramodulation,[status(thm)],[f280,f186]) ).
fof(f299,plain,
! [X0,X1] : multiply(multiply(X0,n1),add(X1,X0)) = add(multiply(X1,multiply(X0,n1)),multiply(X0,n1)),
inference(paramodulation,[status(thm)],[f280,f26]) ).
fof(f301,plain,
! [X0] : multiply(X0,multiply(X0,n1)) = multiply(X0,n1),
inference(paramodulation,[status(thm)],[f280,f9]) ).
fof(f302,plain,
! [X0] : multiply(X0,multiply(n1,add(X0,X0))) = add(multiply(X0,n1),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f10,f296]) ).
fof(f303,plain,
! [X0] : multiply(X0,multiply(n1,add(X0,X0))) = multiply(n1,add(X0,X0)),
inference(forward_demodulation,[status(thm)],[f10,f302]) ).
fof(f306,plain,
! [X0] : add(X0,n1) = add(inverse(n1),n1),
inference(paramodulation,[status(thm)],[f9,f294]) ).
fof(f320,plain,
! [X0,X1] : multiply(add(X0,multiply(X1,n1)),add(multiply(X1,n1),multiply(X1,n1))) = add(multiply(X1,multiply(X1,n1)),multiply(X1,n1)),
inference(paramodulation,[status(thm)],[f301,f67]) ).
fof(f325,plain,
! [X0] : add(multiply(X0,n1),multiply(X0,n1)) = add(multiply(X0,multiply(X0,n1)),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f186,f320]) ).
fof(f326,plain,
! [X0] : multiply(n1,add(X0,X0)) = add(multiply(X0,multiply(X0,n1)),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f10,f325]) ).
fof(f327,plain,
! [X0] : multiply(n1,add(X0,X0)) = multiply(multiply(X0,n1),add(X0,X0)),
inference(forward_demodulation,[status(thm)],[f299,f326]) ).
fof(f329,plain,
! [X0,X1] : add(X0,n1) = add(X1,n1),
inference(paramodulation,[status(thm)],[f306,f306]) ).
fof(f350,plain,
! [X0,X1] : multiply(X0,add(X1,n1)) = add(X0,multiply(n1,X0)),
inference(paramodulation,[status(thm)],[f329,f23]) ).
fof(f843,plain,
! [X0,X1] : multiply(multiply(n1,add(X0,X0)),add(X1,X0)) = add(multiply(X1,multiply(n1,add(X0,X0))),multiply(n1,add(X0,X0))),
inference(paramodulation,[status(thm)],[f303,f10]) ).
fof(f865,plain,
! [X0,X1] : multiply(n1,add(multiply(X0,X1),multiply(X0,X1))) = multiply(multiply(multiply(X0,X1),n1),multiply(X1,add(X0,X0))),
inference(paramodulation,[status(thm)],[f10,f327]) ).
fof(f875,plain,
! [X0,X1] : multiply(add(X0,X0),add(X1,multiply(X0,n1))) = add(multiply(X1,add(X0,X0)),multiply(n1,add(X0,X0))),
inference(paramodulation,[status(thm)],[f327,f10]) ).
fof(f877,plain,
! [X0,X1] : multiply(n1,multiply(X0,add(X1,X1))) = multiply(multiply(multiply(X1,X0),n1),multiply(X0,add(X1,X1))),
inference(forward_demodulation,[status(thm)],[f10,f865]) ).
fof(f893,plain,
! [X0,X1] : multiply(add(X0,X0),add(X1,multiply(X0,n1))) = multiply(add(X0,X0),add(X1,n1)),
inference(forward_demodulation,[status(thm)],[f10,f875]) ).
fof(f902,plain,
! [X0] : multiply(inverse(X0),add(inverse(X0),inverse(X0))) = multiply(n1,add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f273,f303]) ).
fof(f908,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f273,f10]) ).
fof(f910,plain,
! [X0] : multiply(inverse(X0),add(inverse(X0),inverse(X0))) = add(inverse(X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f273,f902]) ).
fof(f931,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f273,f350]) ).
fof(f932,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,n1)) = add(inverse(X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f278,f350]) ).
fof(f1503,plain,
! [X0] : pixley(inverse(X0),X0,inverse(X0)) = add(multiply(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f910,f20]) ).
fof(f1510,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,inverse(X0))) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f910,f10]) ).
fof(f1514,plain,
! [X0] : inverse(X0) = add(multiply(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f15,f1503]) ).
fof(f1523,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,inverse(X0))) = multiply(add(inverse(X0),inverse(X0)),add(X1,n1)),
inference(forward_demodulation,[status(thm)],[f908,f1510]) ).
fof(f1556,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = add(multiply(multiply(inverse(X0),inverse(X0)),inverse(X0)),inverse(X0)),
inference(paramodulation,[status(thm)],[f1514,f26]) ).
fof(f1560,plain,
! [X0] : multiply(inverse(X0),add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0)))) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f1514,f186]) ).
fof(f1561,plain,
! [X0,X1] : multiply(inverse(X0),add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0)))) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f1514,f67]) ).
fof(f1563,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,inverse(X0))) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f1514,f26]) ).
fof(f1568,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = multiply(inverse(X0),add(multiply(inverse(X0),inverse(X0)),n1)),
inference(forward_demodulation,[status(thm)],[f276,f1556]) ).
fof(f1569,plain,
! [X0] : inverse(X0) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(backward_demodulation,[status(thm)],[f1574,f1514]) ).
fof(f1574,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = add(inverse(X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f932,f1568]) ).
fof(f1578,plain,
! [X0] : add(inverse(X0),multiply(add(inverse(X0),inverse(X0)),inverse(X0))) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f23,f1560]) ).
fof(f1579,plain,
! [X0] : multiply(inverse(X0),add(n1,add(inverse(X0),inverse(X0)))) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f277,f1578]) ).
fof(f1580,plain,
! [X0] : add(multiply(n1,inverse(X0)),inverse(X0)) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f26,f1579]) ).
fof(f1583,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = multiply(inverse(X0),add(n1,n1)),
inference(backward_demodulation,[status(thm)],[f1584,f931]) ).
fof(f1584,plain,
! [X0] : multiply(inverse(X0),add(n1,n1)) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f276,f1580]) ).
fof(f1585,plain,
! [X0,X1] : add(multiply(multiply(X0,add(inverse(X1),inverse(X1))),inverse(X1)),inverse(X1)) = add(multiply(X0,add(inverse(X1),inverse(X1))),add(inverse(X1),inverse(X1))),
inference(forward_demodulation,[status(thm)],[f26,f1561]) ).
fof(f1586,plain,
! [X0,X1] : multiply(inverse(X0),add(multiply(X1,add(inverse(X0),inverse(X0))),n1)) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f276,f1585]) ).
fof(f1588,plain,
! [X0,X1] : add(inverse(X0),inverse(X0)) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f932,f1586]) ).
fof(f1589,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = add(multiply(X1,add(inverse(X0),inverse(X0))),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f1523,f1563]) ).
fof(f1591,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,inverse(X0))) = add(inverse(X0),inverse(X0)),
inference(backward_demodulation,[status(thm)],[f1593,f1523]) ).
fof(f1593,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = add(inverse(X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f1588,f1589]) ).
fof(f1597,plain,
! [X0] : multiply(inverse(X0),add(n1,n1)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f1569,f1584]) ).
fof(f1606,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f1597,f1583]) ).
fof(f1612,plain,
! [X0] : inverse(X0) = add(inverse(X0),inverse(X0)),
inference(backward_demodulation,[status(thm)],[f1606,f1593]) ).
fof(f1614,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,n1)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f1612,f932]) ).
fof(f1622,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,inverse(X0))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f1612,f1591]) ).
fof(f1686,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,inverse(X0))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f1612,f1622]) ).
fof(f1927,plain,
! [X0] : multiply(inverse(X0),n1) = inverse(X0),
inference(paramodulation,[status(thm)],[f11,f1686]) ).
fof(f2010,plain,
! [X0] : inverse(X0) = add(inverse(n1),inverse(X0)),
inference(paramodulation,[status(thm)],[f1927,f294]) ).
fof(f2033,plain,
inverse(inverse(n1)) = n1,
inference(paramodulation,[status(thm)],[f11,f2010]) ).
fof(f2321,plain,
! [X0,X1,X2] : multiply(multiply(X0,add(X1,X0)),add(X2,add(X0,X0))) = add(multiply(X2,multiply(X0,add(X1,X0))),multiply(X0,add(X1,X0))),
inference(paramodulation,[status(thm)],[f186,f37]) ).
fof(f2737,plain,
! [X0,X1] : multiply(add(X0,multiply(b,add(X1,b))),add(multiply(b,add(X1,b)),multiply(b,add(X1,b)))) = add(multiply(sF0_fnc,multiply(b,add(X1,b))),multiply(b,add(X1,b))),
inference(paramodulation,[status(thm)],[f194,f67]) ).
fof(f2739,plain,
! [X0,X1] : multiply(multiply(b,add(X0,b)),add(X1,sF0_fnc)) = add(multiply(X1,multiply(b,add(X0,b))),multiply(b,add(X0,b))),
inference(paramodulation,[status(thm)],[f194,f10]) ).
fof(f2756,plain,
! [X0] : add(multiply(b,add(X0,b)),multiply(b,add(X0,b))) = add(multiply(sF0_fnc,multiply(b,add(X0,b))),multiply(b,add(X0,b))),
inference(forward_demodulation,[status(thm)],[f186,f2737]) ).
fof(f2757,plain,
! [X0] : multiply(add(X0,b),add(b,b)) = add(multiply(sF0_fnc,multiply(b,add(X0,b))),multiply(b,add(X0,b))),
inference(forward_demodulation,[status(thm)],[f10,f2756]) ).
fof(f2758,plain,
! [X0] : add(b,b) = add(multiply(sF0_fnc,multiply(b,add(X0,b))),multiply(b,add(X0,b))),
inference(forward_demodulation,[status(thm)],[f186,f2757]) ).
fof(f2759,plain,
! [X0] : add(b,b) = multiply(multiply(b,add(X0,b)),add(sF0_fnc,add(b,b))),
inference(forward_demodulation,[status(thm)],[f2321,f2758]) ).
fof(f2761,plain,
! [X0] : add(b,b) = multiply(multiply(b,add(X0,b)),add(sF0_fnc,sF0_fnc)),
inference(backward_demodulation,[status(thm)],[f2762,f2759]) ).
fof(f2762,plain,
! [X0,X1] : multiply(multiply(b,add(X0,b)),add(X1,sF0_fnc)) = multiply(multiply(b,add(X0,b)),add(X1,add(b,b))),
inference(forward_demodulation,[status(thm)],[f2321,f2739]) ).
fof(f2983,plain,
multiply(n1,n1) = inverse(inverse(n1)),
inference(paramodulation,[status(thm)],[f2033,f1927]) ).
fof(f2987,plain,
! [X0] : multiply(n1,add(X0,n1)) = inverse(inverse(n1)),
inference(paramodulation,[status(thm)],[f2033,f1614]) ).
fof(f3012,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = add(multiply(X0,inverse(inverse(n1))),multiply(X1,add(X0,n1))),
inference(paramodulation,[status(thm)],[f2033,f20]) ).
fof(f3028,plain,
multiply(n1,n1) = n1,
inference(forward_demodulation,[status(thm)],[f2033,f2983]) ).
fof(f3034,plain,
add(n1,multiply(n1,n1)) = inverse(inverse(n1)),
inference(forward_demodulation,[status(thm)],[f350,f2987]) ).
fof(f3035,plain,
add(n1,n1) = inverse(inverse(n1)),
inference(forward_demodulation,[status(thm)],[f3028,f3034]) ).
fof(f3046,plain,
add(n1,n1) = n1,
inference(forward_demodulation,[status(thm)],[f2033,f3035]) ).
fof(f3088,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = add(multiply(X0,n1),multiply(X1,add(X0,n1))),
inference(forward_demodulation,[status(thm)],[f2033,f3012]) ).
fof(f3168,plain,
! [X0] : add(X0,n1) = n1,
inference(paramodulation,[status(thm)],[f329,f3046]) ).
fof(f3222,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = add(multiply(X0,n1),multiply(X1,n1)),
inference(backward_demodulation,[status(thm)],[f3168,f3088]) ).
fof(f3266,plain,
! [X0,X1] : multiply(add(X0,X0),add(X1,multiply(X0,n1))) = multiply(add(X0,X0),n1),
inference(backward_demodulation,[status(thm)],[f3168,f893]) ).
fof(f3352,plain,
! [X0] : pixley(X0,inverse(n1),X0) = multiply(multiply(X0,n1),add(X0,X0)),
inference(backward_demodulation,[status(thm)],[f3370,f327]) ).
fof(f3368,plain,
! [X0,X1] : multiply(multiply(n1,add(X0,X0)),add(X1,X0)) = add(multiply(X1,multiply(n1,add(X0,X0))),pixley(X0,inverse(n1),X0)),
inference(backward_demodulation,[status(thm)],[f3370,f843]) ).
fof(f3370,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = multiply(n1,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f10,f3222]) ).
fof(f3474,plain,
! [X0] : X0 = multiply(multiply(X0,n1),add(X0,X0)),
inference(forward_demodulation,[status(thm)],[f15,f3352]) ).
fof(f3537,plain,
! [X0,X1] : multiply(pixley(X0,inverse(n1),X0),add(X1,X0)) = add(multiply(X1,multiply(n1,add(X0,X0))),pixley(X0,inverse(n1),X0)),
inference(forward_demodulation,[status(thm)],[f3370,f3368]) ).
fof(f3538,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X1,multiply(n1,add(X0,X0))),pixley(X0,inverse(n1),X0)),
inference(forward_demodulation,[status(thm)],[f15,f3537]) ).
fof(f3539,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X1,pixley(X0,inverse(n1),X0)),pixley(X0,inverse(n1),X0)),
inference(forward_demodulation,[status(thm)],[f3370,f3538]) ).
fof(f3540,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X1,X0),pixley(X0,inverse(n1),X0)),
inference(forward_demodulation,[status(thm)],[f15,f3539]) ).
fof(f3545,plain,
! [X0] : add(b,b) = multiply(add(multiply(X0,b),b),add(sF0_fnc,sF0_fnc)),
inference(backward_demodulation,[status(thm)],[f3560,f2761]) ).
fof(f3560,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f15,f3540]) ).
fof(f3855,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(multiply(X0,X1),n1),multiply(X1,add(X0,X0))),
inference(paramodulation,[status(thm)],[f10,f3474]) ).
fof(f3859,plain,
! [X0,X1] : multiply(add(add(X0,X1),add(X0,X1)),add(X1,multiply(add(X0,X1),n1))) = add(add(X1,multiply(add(X0,X1),X1)),add(X0,X1)),
inference(paramodulation,[status(thm)],[f3474,f34]) ).
fof(f3873,plain,
! [X0,X1] : multiply(multiply(add(X0,X0),add(X1,multiply(X0,n1))),X0) = multiply(multiply(X0,n1),add(X0,X0)),
inference(paramodulation,[status(thm)],[f3474,f28]) ).
fof(f3884,plain,
! [X0,X1] : multiply(n1,multiply(X0,add(X1,X1))) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f3855,f877]) ).
fof(f3890,plain,
! [X0,X1] : multiply(add(add(X0,X1),add(X0,X1)),n1) = add(add(X1,multiply(add(X0,X1),X1)),add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f3266,f3859]) ).
fof(f3891,plain,
! [X0,X1] : multiply(add(add(X0,X1),add(X0,X1)),n1) = add(add(X1,X1),add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f9,f3890]) ).
fof(f3917,plain,
! [X0] : multiply(multiply(add(X0,X0),n1),X0) = multiply(multiply(X0,n1),add(X0,X0)),
inference(forward_demodulation,[status(thm)],[f3266,f3873]) ).
fof(f3918,plain,
! [X0] : multiply(multiply(add(X0,X0),n1),X0) = X0,
inference(forward_demodulation,[status(thm)],[f3474,f3917]) ).
fof(f4772,plain,
! [X0] : multiply(n1,add(X0,X0)) = multiply(X0,multiply(add(add(X0,X0),add(X0,X0)),n1)),
inference(paramodulation,[status(thm)],[f3918,f3884]) ).
fof(f4804,plain,
! [X0] : pixley(X0,inverse(n1),X0) = multiply(X0,multiply(add(add(X0,X0),add(X0,X0)),n1)),
inference(forward_demodulation,[status(thm)],[f3370,f4772]) ).
fof(f4805,plain,
! [X0] : X0 = multiply(X0,multiply(add(add(X0,X0),add(X0,X0)),n1)),
inference(forward_demodulation,[status(thm)],[f15,f4804]) ).
fof(f4806,plain,
! [X0] : X0 = multiply(X0,add(add(X0,X0),add(X0,X0))),
inference(forward_demodulation,[status(thm)],[f3891,f4805]) ).
fof(f4807,plain,
! [X0] : X0 = add(X0,multiply(add(X0,X0),X0)),
inference(forward_demodulation,[status(thm)],[f23,f4806]) ).
fof(f4820,plain,
! [X0] : add(b,b) = multiply(add(multiply(X0,b),b),sF0_fnc),
inference(backward_demodulation,[status(thm)],[f4960,f3545]) ).
fof(f4960,plain,
! [X0] : X0 = add(X0,X0),
inference(forward_demodulation,[status(thm)],[f9,f4807]) ).
fof(f5240,plain,
! [X0] : b = multiply(add(multiply(X0,b),b),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f4960,f4820]) ).
fof(f5241,plain,
b = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f189,f5240]) ).
fof(f5242,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5241,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.59 % Computer : n016.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Mon Sep 21 13:53:39 UTC 2026
% 0.11/0.60 % CPUTime :
% 0.11/0.62 % Drodi V4.1.1
% 5.14/1.38 % Refutation found
% 5.14/1.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.14/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.94/1.44 % Elapsed time: 0.810656 seconds
% 2.94/1.44 % CPU time: 5.826237 seconds
% 2.94/1.44 % Total memory used: 176.606 MB
% 2.94/1.44 % Net memory used: 172.045 MB
%------------------------------------------------------------------------------