%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP703-12 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:45 AM UTC 2025
% Result : Unsatisfiable 4.72s 4.88s
% Output : CNFRefutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of clauses : 80 ( 80 unt; 0 nHn; 6 RR)
% Number of literals : 80 ( 79 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',f05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',f06) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c4,plain,
rd(X,unit) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c6,plain,
rd(X,X) = unit,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c8,plain,
ld(unit,X) = X,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c9,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c12,axiom,
op_d = ld(X,mult(op_c,X)),
file('theBenchmark.p',f11) ).
cnf(c13,plain,
op_d = op_c,
inference(equational,[status(thm)],[c1,c8,c12]) ).
cnf(c14,plain,
mult(X,op_c) = mult(op_c,X),
inference(equational,[status(thm)],[c7,c12,c13]) ).
cnf(c15,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c16,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c17,plain,
ld(ld(op_c,X),X) = op_c,
inference(equational,[status(thm)],[c7,c12,c13]) ).
cnf(c18,plain,
ld(op_c,X) = rd(X,op_c),
inference(equational,[status(thm)],[c15,c17]) ).
cnf(c20,axiom,
mult(op_c,mult(X,Y)) = mult(mult(op_c,X),Y),
file('theBenchmark.p',f08) ).
cnf(c21,plain,
mult(mult(op_c,X),Y) = mult(op_c,mult(X,Y)),
inference(equational,[status(thm)],[c20]) ).
cnf(c22,axiom,
mult(X,mult(op_c,Y)) = mult(mult(X,op_c),Y),
file('theBenchmark.p',f10) ).
cnf(c23,plain,
mult(mult(X,op_c),Y) = mult(X,mult(op_c,Y)),
inference(equational,[status(thm)],[c22]) ).
cnf(c24,axiom,
mult(X,mult(Y,op_c)) = mult(mult(X,Y),op_c),
file('theBenchmark.p',f09) ).
cnf(c25,plain,
mult(X,mult(Y,op_c)) = mult(op_c,mult(X,Y)),
inference(equational,[status(thm)],[c14,c24]) ).
cnf(c30,plain,
mult(rd(X,X),Y) = Y,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c31,plain,
rd(X,rd(Y,Y)) = X,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c38,plain,
rd(mult(op_c,X),op_c) = X,
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c42,plain,
mult(X,mult(op_c,Y)) = mult(op_c,mult(X,Y)),
inference(equational,[status(thm)],[c14,c21,c23]) ).
cnf(c44,plain,
rd(mult(op_c,mult(X,Y)),Y) = mult(op_c,X),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c45,plain,
mult(op_c,rd(X,Y)) = rd(mult(op_c,X),Y),
inference(equational,[status(thm)],[c3,c44]) ).
cnf(c47,plain,
ld(X,mult(op_c,mult(X,Y))) = mult(Y,op_c),
inference(equational,[status(thm)],[c9,c25]) ).
cnf(c48,plain,
mult(op_c,mult(rd(X,op_c),Y)) = mult(X,Y),
inference(equational,[status(thm)],[c7,c18,c21]) ).
cnf(c49,plain,
mult(rd(X,op_c),Y) = rd(mult(X,Y),op_c),
inference(equational,[status(thm)],[c9,c18,c48]) ).
cnf(c50,plain,
rd(mult(X,mult(op_c,Y)),op_c) = mult(X,Y),
inference(equational,[status(thm)],[c3,c23,c49]) ).
cnf(c51,plain,
mult(X,rd(Y,op_c)) = rd(mult(X,Y),op_c),
inference(equational,[status(thm)],[c7,c18,c50]) ).
cnf(c60,plain,
mult(rd(X,mult(op_c,Y)),Y) = rd(X,op_c),
inference(equational,[status(thm)],[c3,c50]) ).
cnf(c61,plain,
rd(rd(X,op_c),Y) = rd(X,mult(op_c,Y)),
inference(equational,[status(thm)],[c5,c60]) ).
cnf(c62,plain,
rd(X,mult(Y,op_c)) = rd(rd(X,op_c),Y),
inference(equational,[status(thm)],[c14,c61]) ).
cnf(c63,plain,
ld(rd(X,Y),mult(op_c,X)) = mult(Y,op_c),
inference(equational,[status(thm)],[c3,c47]) ).
cnf(c64,plain,
ld(rd(unit,X),op_c) = mult(X,op_c),
inference(equational,[status(thm)],[c1,c63]) ).
cnf(c65,plain,
ld(rd(unit,X),op_c) = mult(op_c,X),
inference(equational,[status(thm)],[c38,c44,c64]) ).
cnf(c66,plain,
rd(unit,X) = rd(rd(op_c,op_c),X),
inference(equational,[status(thm)],[c15,c62,c64]) ).
cnf(c67,plain,
mult(op_c,X) = mult(Y,ld(rd(Y,op_c),X)),
inference(equational,[status(thm)],[c7,c48]) ).
cnf(c68,plain,
ld(X,mult(op_c,Y)) = ld(rd(X,op_c),Y),
inference(equational,[status(thm)],[c9,c67]) ).
cnf(c69,plain,
ld(rd(X,op_c),unit) = ld(X,op_c),
inference(equational,[status(thm)],[c1,c68]) ).
cnf(c71,plain,
ld(X,unit) = ld(mult(X,op_c),op_c),
inference(equational,[status(thm)],[c5,c69]) ).
cnf(c73,plain,
mult(X,op_c) = ld(rd(rd(op_c,op_c),X),op_c),
inference(equational,[status(thm)],[c18,c38,c47,c65,c66]) ).
cnf(c74,plain,
ld(rd(X,op_c),mult(X,Y)) = ld(rd(rd(op_c,op_c),Y),op_c),
inference(equational,[status(thm)],[c47,c48,c73]) ).
cnf(c76,plain,
mult(op_c,X) = ld(rd(rd(op_c,op_c),X),op_c),
inference(equational,[status(thm)],[c14,c47,c68,c74]) ).
cnf(c77,plain,
ld(X,ld(rd(rd(op_c,op_c),mult(X,Y)),op_c)) = ld(rd(rd(op_c,op_c),Y),op_c),
inference(equational,[status(thm)],[c38,c44,c47,c76]) ).
cnf(c87,axiom,
op_e = mult(mult(rd(op_c,mult(X,Y)),Y),X),
file('theBenchmark.p',f12) ).
cnf(c88,plain,
op_e = op_c,
inference(equational,[status(thm)],[c7,c15,c23,c73,c76,c87]) ).
cnf(c89,plain,
mult(rd(op_c,mult(X,Y)),Y) = rd(op_c,X),
inference(equational,[status(thm)],[c5,c87,c88]) ).
cnf(c90,plain,
rd(op_c,mult(X,Y)) = rd(rd(op_c,X),Y),
inference(equational,[status(thm)],[c5,c89]) ).
cnf(c91,plain,
mult(rd(op_c,X),Y) = rd(op_c,rd(X,Y)),
inference(equational,[status(thm)],[c3,c89]) ).
cnf(c92,plain,
rd(op_c,rd(op_c,X)) = X,
inference(equational,[status(thm)],[c30,c91]) ).
cnf(c93,plain,
ld(X,op_c) = rd(op_c,X),
inference(equational,[status(thm)],[c15,c92]) ).
cnf(c94,plain,
mult(X,rd(op_c,X)) = op_c,
inference(equational,[status(thm)],[c3,c92]) ).
cnf(c95,plain,
rd(rd(op_c,op_c),X) = rd(rd(op_c,X),op_c),
inference(equational,[status(thm)],[c15,c47,c76,c77,c90]) ).
cnf(c97,axiom,
op_f = mult(X,mult(Y,ld(mult(X,Y),op_c))),
file('theBenchmark.p',f13) ).
cnf(c98,plain,
op_f = mult(X,mult(Y,rd(rd(op_c,X),Y))),
inference(equational,[status(thm)],[c90,c93,c97]) ).
cnf(c99,plain,
op_f = op_c,
inference(equational,[status(thm)],[c2,c4,c94,c98]) ).
cnf(c100,plain,
mult(X,rd(rd(op_c,Y),X)) = rd(op_c,Y),
inference(equational,[status(thm)],[c9,c93,c98,c99]) ).
cnf(c101,plain,
mult(X,rd(Y,X)) = Y,
inference(equational,[status(thm)],[c15,c92,c93,c100]) ).
cnf(c102,plain,
ld(X,Y) = rd(Y,X),
inference(equational,[status(thm)],[c9,c101]) ).
cnf(c103,plain,
mult(X,Y) = mult(Y,X),
inference(equational,[status(thm)],[c5,c101]) ).
cnf(c104,plain,
rd(X,rd(X,Y)) = Y,
inference(equational,[status(thm)],[c5,c101]) ).
cnf(c107,plain,
rd(rd(op_c,X),Y) = rd(rd(op_c,Y),X),
inference(equational,[status(thm)],[c90,c103]) ).
cnf(c108,plain,
mult(X,rd(op_c,Y)) = rd(op_c,rd(Y,X)),
inference(equational,[status(thm)],[c91,c103]) ).
cnf(c111,plain,
rd(X,rd(op_c,rd(rd(op_c,op_c),Y))) = rd(rd(X,op_c),Y),
inference(equational,[status(thm)],[c14,c62,c76,c93]) ).
cnf(c120,plain,
rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(op_c,op_c),mult(X,Y))) = rd(op_c,rd(rd(rd(op_c,op_c),rd(op_c,rd(rd(op_c,op_c),Y))),X)),
inference(equational,[status(thm)],[c23,c25,c45,c76,c93,c108,c111]) ).
cnf(c121,plain,
mult(X,rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(op_c,op_c),Y))) = rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(rd(op_c,op_c),Y),X)),
inference(equational,[status(thm)],[c23,c25,c45,c73,c76,c93,c108]) ).
cnf(c123,plain,
rd(op_c,rd(rd(rd(op_c,op_c),rd(op_c,rd(rd(op_c,op_c),X))),Y)) = rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(rd(op_c,op_c),X),Y)),
inference(equational,[status(thm)],[c21,c23,c25,c45,c76,c93,c108,c120]) ).
cnf(c124,plain,
rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(rd(op_c,op_c),X),Y)) = rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(rd(op_c,op_c),Y),X)),
inference(equational,[status(thm)],[c23,c45,c76,c91,c93,c108,c111,c121,c123]) ).
cnf(c130,plain,
rd(rd(op_c,X),rd(Y,X)) = rd(op_c,Y),
inference(equational,[status(thm)],[c3,c90,c107]) ).
cnf(c135,plain,
rd(X,op_c) = rd(rd(op_c,op_c),rd(op_c,X)),
inference(equational,[status(thm)],[c16,c66,c71,c91,c102]) ).
cnf(c140,plain,
mult(X,Y) = rd(op_c,rd(rd(op_c,X),Y)),
inference(equational,[status(thm)],[c7,c18,c42,c45,c51,c76,c90,c92,c93,c95,c130,c135]) ).
cnf(c162,plain,
rd(rd(rd(op_c,rd(rd(op_c,op_c),op_c)),rd(rd(op_c,X),Y)),rd(op_c,rd(rd(op_c,op_c),X))) = Y,
inference(equational,[status(thm)],[c9,c21,c45,c76,c93,c102,c140]) ).
cnf(c170,plain,
rd(rd(rd(op_c,op_c),X),Y) = rd(rd(rd(op_c,op_c),Y),X),
inference(equational,[status(thm)],[c31,c92,c104,c124,c130,c162]) ).
cnf(g1,plain,
mult(x2,mult(op_e,x3)) = mult(mult(x2,op_e),x3),
inference(equational,[status(thm)],[c73,c76,c88,c91,c93,c108,c170]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP703-12 : TPTP v9.0.0. Released v8.1.0.
% 0.02/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:54:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.72/4.88 % SZS status Unsatisfiable
% 4.72/4.88 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------