%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG026-7 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 2.13s 2.27s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 3 RR)
% Number of literals : 31 ( 30 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 : 61 ( 0 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(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,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('theBenchmark.p',inverse_product1) ).
cnf(c11,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('theBenchmark.p',inverse_product2) ).
cnf(c12,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('RNG003-0.ax',associativity_for_addition) ).
cnf(c13,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(equational,[status(thm)],[c12]) ).
cnf(c16,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c6,c13]) ).
cnf(c17,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c8,c13]) ).
cnf(c18,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c8,c16]) ).
cnf(c19,plain,
add(additive_inverse(X),add(Y,X)) = Y,
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c20,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG003-0.ax',distribute1) ).
cnf(c21,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('RNG003-0.ax',distribute2) ).
cnf(c23,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c8,c13]) ).
cnf(c24,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c17,c23]) ).
cnf(c25,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c26,plain,
additive_inverse(add(X,additive_inverse(Y))) = add(Y,additive_inverse(X)),
inference(equational,[status(thm)],[c17,c25]) ).
cnf(c27,plain,
add(X,additive_inverse(add(X,Y))) = additive_inverse(Y),
inference(equational,[status(thm)],[c3,c6,c25]) ).
cnf(c28,plain,
additive_inverse(add(additive_inverse(X),Y)) = add(X,additive_inverse(Y)),
inference(equational,[status(thm)],[c17,c27]) ).
cnf(c29,plain,
additive_inverse(add(X,Y)) = add(additive_inverse(Y),additive_inverse(X)),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c32,plain,
add(X,add(Y,add(additive_inverse(X),Z))) = add(Y,Z),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c33,plain,
add(X,add(Y,add(Z,additive_inverse(X)))) = add(Y,Z),
inference(equational,[status(thm)],[c13,c18]) ).
cnf(c35,plain,
add(additive_inverse(X),add(Y,add(Z,X))) = add(Z,Y),
inference(equational,[status(thm)],[c13,c24,c33]) ).
cnf(c39,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('RNG003-0.ax',associator) ).
cnf(c40,plain,
associator(X,Y,Z) = add(additive_inverse(multiply(X,multiply(Y,Z))),multiply(multiply(X,Y),Z)),
inference(equational,[status(thm)],[c6,c16,c17,c35,c39]) ).
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)],[c6,c8,c10,c11,c13,c16,c17,c19,c20,c21,c28,c29,c32,c40]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG026-7 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 16:24:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.13/2.27 % SZS status Unsatisfiable
% 2.13/2.27 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------