%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP707-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 06:44:46 AM UTC 2025
% Result : Unsatisfiable 60.14s 60.87s
% Output : CNFRefutation 60.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 3 RR)
% Number of literals : 73 ( 72 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),a) != mult(a,mult(b,a)),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c06) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
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',c02) ).
cnf(c10,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c11,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c12,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c13,axiom,
mult(mult(X,X),Y) = mult(Y,mult(X,X)),
file('theBenchmark.p',c09) ).
cnf(c14,axiom,
mult(X,mult(X,mult(X,X))) = unit,
file('theBenchmark.p',c08) ).
cnf(c15,plain,
mult(X,mult(X,X)) = ld(X,unit),
inference(equational,[status(thm)],[c9,c14]) ).
cnf(c16,plain,
ld(X,ld(X,unit)) = mult(X,X),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c17,plain,
ld(X,mult(mult(Y,Y),X)) = mult(Y,Y),
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c18,plain,
rd(mult(X,mult(Y,Y)),X) = mult(Y,Y),
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c21,axiom,
mult(X,mult(Y,mult(Y,Z))) = mult(mult(mult(X,Y),Y),Z),
file('theBenchmark.p',c07) ).
cnf(c22,plain,
mult(mult(mult(X,Y),Y),Z) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c21]) ).
cnf(c23,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c24,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c26,plain,
mult(X,mult(X,Y)) = mult(Y,mult(X,X)),
inference(equational,[status(thm)],[c13,c24]) ).
cnf(c28,plain,
mult(X,mult(X,mult(X,Y))) = mult(ld(X,unit),Y),
inference(equational,[status(thm)],[c13,c15,c22]) ).
cnf(c29,plain,
mult(ld(X,unit),X) = unit,
inference(equational,[status(thm)],[c14,c28]) ).
cnf(c31,plain,
ld(ld(X,unit),unit) = X,
inference(equational,[status(thm)],[c9,c29]) ).
cnf(c35,plain,
ld(X,mult(Y,mult(Y,X))) = mult(Y,Y),
inference(equational,[status(thm)],[c17,c24]) ).
cnf(c36,plain,
ld(ld(X,unit),X) = mult(X,X),
inference(equational,[status(thm)],[c1,c14,c15,c35]) ).
cnf(c37,plain,
rd(X,mult(X,X)) = ld(X,unit),
inference(equational,[status(thm)],[c12,c36]) ).
cnf(c38,plain,
rd(X,rd(X,mult(Y,Y))) = mult(Y,Y),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c39,plain,
rd(X,mult(Y,Y)) = ld(mult(Y,Y),X),
inference(equational,[status(thm)],[c11,c38]) ).
cnf(c41,plain,
mult(X,mult(X,rd(Y,X))) = mult(Y,X),
inference(equational,[status(thm)],[c3,c23,c26]) ).
cnf(c42,plain,
mult(X,rd(Y,X)) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c9,c41]) ).
cnf(c43,plain,
rd(mult(X,mult(Y,Y)),Y) = mult(X,Y),
inference(equational,[status(thm)],[c5,c23]) ).
cnf(c44,plain,
mult(X,mult(Y,Y)) = ld(mult(Y,Y),X),
inference(equational,[status(thm)],[c1,c7,c15,c24,c39,c43]) ).
cnf(c45,plain,
mult(X,mult(X,Y)) = ld(mult(X,X),Y),
inference(equational,[status(thm)],[c26,c44]) ).
cnf(c48,plain,
mult(X,ld(mult(X,X),Y)) = mult(ld(X,unit),Y),
inference(equational,[status(thm)],[c15,c22,c24,c45]) ).
cnf(c49,plain,
ld(mult(X,X),mult(Y,X)) = mult(Y,ld(X,unit)),
inference(equational,[status(thm)],[c15,c22,c23,c44]) ).
cnf(c52,plain,
ld(X,ld(mult(X,X),Y)) = mult(X,Y),
inference(equational,[status(thm)],[c9,c26,c44]) ).
cnf(c53,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c9,c24,c45,c48,c52]) ).
cnf(c54,plain,
rd(ld(X,Y),Y) = ld(X,unit),
inference(equational,[status(thm)],[c5,c53]) ).
cnf(c55,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c31,c53]) ).
cnf(c56,plain,
ld(mult(X,X),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c16,c26,c44,c53]) ).
cnf(c59,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c11,c54]) ).
cnf(c61,plain,
ld(X,ld(Y,ld(Y,X))) = mult(Y,Y),
inference(equational,[status(thm)],[c9,c26,c45,c56]) ).
cnf(c64,plain,
ld(rd(X,Y),mult(X,Y)) = mult(Y,Y),
inference(equational,[status(thm)],[c35,c41]) ).
cnf(c65,plain,
mult(X,ld(Y,unit)) = rd(X,Y),
inference(equational,[status(thm)],[c12,c39,c49,c64]) ).
cnf(c66,plain,
ld(X,rd(X,Y)) = ld(Y,unit),
inference(equational,[status(thm)],[c9,c65]) ).
cnf(c67,plain,
rd(X,ld(Y,unit)) = mult(X,Y),
inference(equational,[status(thm)],[c31,c65]) ).
cnf(c73,plain,
ld(ld(X,Y),unit) = ld(Y,X),
inference(equational,[status(thm)],[c12,c66]) ).
cnf(c76,plain,
mult(ld(X,ld(X,Y)),X) = rd(Y,X),
inference(equational,[status(thm)],[c1,c7,c15,c23,c24,c43,c44,c56]) ).
cnf(c77,plain,
mult(ld(X,Y),X) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c9,c76]) ).
cnf(c78,plain,
mult(mult(X,Y),X) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c7,c52,c56,c77]) ).
cnf(c79,plain,
rd(ld(X,ld(X,Y)),X) = mult(Y,X),
inference(equational,[status(thm)],[c13,c24,c43,c45,c56]) ).
cnf(c80,plain,
mult(X,mult(Y,X)) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c42,c76,c79]) ).
cnf(c81,plain,
ld(X,ld(X,ld(X,ld(X,Y)))) = Y,
inference(equational,[status(thm)],[c9,c13,c44,c56]) ).
cnf(c82,plain,
ld(X,ld(X,ld(X,Y))) = mult(X,Y),
inference(equational,[status(thm)],[c7,c81]) ).
cnf(c87,plain,
mult(ld(X,ld(X,Y)),Z) = mult(Y,ld(X,ld(X,Z))),
inference(equational,[status(thm)],[c22,c23,c44,c45,c56]) ).
cnf(c88,plain,
ld(ld(X,Y),X) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c9,c37,c39,c56,c61,c73,c82,c87]) ).
cnf(c93,plain,
ld(mult(X,Y),ld(Y,ld(Y,X))) = Y,
inference(equational,[status(thm)],[c9,c23,c44,c56]) ).
cnf(c94,plain,
mult(X,rd(Y,Z)) = rd(X,rd(Z,Y)),
inference(equational,[status(thm)],[c59,c67]) ).
cnf(c95,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c53,c73]) ).
cnf(c96,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c65,c73]) ).
cnf(c98,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c55,c59]) ).
cnf(c104,plain,
rd(X,rd(X,Y)) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c8,c48,c49,c53,c94,c96]) ).
cnf(c106,plain,
ld(mult(X,Y),mult(Y,Y)) = rd(Y,X),
inference(equational,[status(thm)],[c11,c88,c104]) ).
cnf(c113,plain,
ld(ld(X,Y),mult(Y,Y)) = mult(Y,X),
inference(equational,[status(thm)],[c9,c48,c53,c56,c79,c82,c87,c106]) ).
cnf(c114,plain,
ld(rd(X,Y),ld(X,ld(X,Z))) = mult(mult(Y,X),Z),
inference(equational,[status(thm)],[c3,c22,c45,c56,c98]) ).
cnf(c115,plain,
ld(rd(X,Y),ld(X,unit)) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c10,c23,c44,c56,c114]) ).
cnf(c116,plain,
ld(X,ld(ld(Y,X),X)) = rd(Y,X),
inference(equational,[status(thm)],[c53,c55,c66,c78,c93,c94,c95,c104,c114,c115]) ).
cnf(c123,plain,
rd(ld(X,rd(Y,X)),X) = mult(X,Y),
inference(equational,[status(thm)],[c79,c88,c95,c113,c116]) ).
cnf(c124,plain,
rd(ld(X,Y),X) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c3,c78,c123]) ).
cnf(g1,plain,
mult(mult(a,b),a) = mult(a,mult(b,a)),
inference(equational,[status(thm)],[c78,c80,c124]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP707-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:55:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 60.14/60.87 % SZS status Unsatisfiable
% 60.14/60.87 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------