%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG026-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 07:42:46 AM UTC 2025
% Result : Unsatisfiable 8.50s 8.68s
% Output : CNFRefutation 8.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 3 RR)
% Number of literals : 43 ( 42 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 99 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('theBenchmark.p',prove_teichmuller_identity) ).
cnf(c1,axiom,
add(additive_identity,X) = X,
file('RNG003-0.ax',left_additive_identity) ).
cnf(c2,axiom,
add(X,additive_identity) = X,
file('RNG003-0.ax',right_additive_identity) ).
cnf(c3,axiom,
additive_inverse(additive_inverse(X)) = X,
file('RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(c4,axiom,
multiply(additive_identity,X) = additive_identity,
file('RNG003-0.ax',left_multiplicative_zero) ).
cnf(c5,axiom,
multiply(X,additive_identity) = additive_identity,
file('RNG003-0.ax',right_multiplicative_zero) ).
cnf(c6,axiom,
add(X,Y) = add(Y,X),
file('RNG003-0.ax',commutativity_for_addition) ).
cnf(c7,axiom,
add(additive_inverse(X),X) = additive_identity,
file('RNG003-0.ax',left_additive_inverse) ).
cnf(c8,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c10,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('RNG003-0.ax',associativity_for_addition) ).
cnf(c11,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(equational,[status(thm)],[c10]) ).
cnf(c14,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c15,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c8,c11]) ).
cnf(c16,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c8,c14]) ).
cnf(c18,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG003-0.ax',distribute1) ).
cnf(c19,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('RNG003-0.ax',distribute2) ).
cnf(c21,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c20]) ).
cnf(c24,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c25,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c15,c24]) ).
cnf(c26,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c3,c25]) ).
cnf(c27,plain,
additive_inverse(add(X,additive_inverse(Y))) = add(Y,additive_inverse(X)),
inference(equational,[status(thm)],[c15,c26]) ).
cnf(c30,plain,
additive_inverse(add(X,Y)) = add(additive_inverse(Y),additive_inverse(X)),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c48,plain,
add(multiply(add(X,Y),Z),W) = add(multiply(X,Z),add(multiply(Y,Z),W)),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c53,plain,
add(multiply(X,add(Y,Z)),W) = add(multiply(X,Y),add(multiply(X,Z),W)),
inference(equational,[status(thm)],[c11,c19]) ).
cnf(c56,plain,
add(multiply(X,Y),add(multiply(X,additive_inverse(Y)),Z)) = Z,
inference(equational,[status(thm)],[c1,c5,c8,c53]) ).
cnf(c57,plain,
additive_inverse(multiply(X,Y)) = multiply(X,additive_inverse(Y)),
inference(equational,[status(thm)],[c16,c56]) ).
cnf(c60,plain,
add(multiply(X,Y),add(multiply(additive_inverse(X),Y),Z)) = Z,
inference(equational,[status(thm)],[c1,c4,c8,c48]) ).
cnf(c61,plain,
multiply(X,additive_inverse(Y)) = multiply(additive_inverse(X),Y),
inference(equational,[status(thm)],[c16,c57,c60]) ).
cnf(c62,plain,
multiply(additive_inverse(X),additive_inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c15,c24,c30,c57,c60]) ).
cnf(c63,plain,
multiply(multiply(X,additive_inverse(Y)),Z) = multiply(multiply(X,Y),additive_inverse(Z)),
inference(equational,[status(thm)],[c57,c61]) ).
cnf(c65,plain,
multiply(X,multiply(Y,additive_inverse(Z))) = multiply(additive_inverse(X),multiply(Y,Z)),
inference(equational,[status(thm)],[c57,c61]) ).
cnf(c66,plain,
multiply(multiply(additive_inverse(X),Y),Z) = multiply(multiply(X,Y),additive_inverse(Z)),
inference(equational,[status(thm)],[c61,c63]) ).
cnf(c69,plain,
multiply(X,multiply(additive_inverse(Y),Z)) = multiply(additive_inverse(X),multiply(Y,Z)),
inference(equational,[status(thm)],[c61,c65]) ).
cnf(c73,plain,
multiply(additive_inverse(X),multiply(Y,additive_inverse(Z))) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c57,c62]) ).
cnf(c77,plain,
multiply(multiply(additive_inverse(X),Y),additive_inverse(Z)) = multiply(multiply(X,Y),Z),
inference(equational,[status(thm)],[c3,c61,c63]) ).
cnf(c78,plain,
multiply(additive_inverse(X),multiply(additive_inverse(Y),Z)) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c61,c73]) ).
cnf(c90,plain,
add(multiply(X,Y),add(multiply(Z,Y),W)) = add(W,multiply(add(X,Z),Y)),
inference(equational,[status(thm)],[c6,c48]) ).
cnf(c148,plain,
add(X,multiply(add(Y,Z),W)) = add(multiply(Z,W),add(X,multiply(Y,W))),
inference(equational,[status(thm)],[c6,c11,c90]) ).
cnf(c169,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('RNG003-0.ax',associator) ).
cnf(c170,plain,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,additive_inverse(Z)))),
inference(equational,[status(thm)],[c57,c169]) ).
cnf(g1,plain,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = additive_identity,
inference(equational,[status(thm)],[c2,c4,c6,c8,c11,c14,c21,c30,c48,c53,c57,c60,c61,c66,c69,c77,c78,c148,c170]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG026-6 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.32 % Computer : n014.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 16:24:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 8.50/8.68 % SZS status Unsatisfiable
% 8.50/8.68 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------