%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP777-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 06:44:52 AM UTC 2025
% Result : Unsatisfiable 63.48s 63.62s
% Output : CNFRefutation 63.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of clauses : 100 ( 100 unt; 0 nHn; 10 RR)
% Number of literals : 100 ( 99 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 223 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
product(X,X) = X,
file('theBenchmark.p',sos06) ).
cnf(c2,axiom,
product(X,difference(X,Y)) = Y,
file('theBenchmark.p',sos02) ).
cnf(c3,axiom,
difference(X,product(X,Y)) = Y,
file('theBenchmark.p',sos01) ).
cnf(c5,axiom,
quotient(product(X,Y),Y) = X,
file('theBenchmark.p',sos03) ).
cnf(c6,plain,
quotient(X,X) = X,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,axiom,
product(quotient(X,Y),Y) = X,
file('theBenchmark.p',sos04) ).
cnf(c8,plain,
difference(quotient(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
quotient(X,difference(Y,X)) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c10,axiom,
bigC(X,Y,Z) = product(product(X,Y),product(Z,X)),
file('theBenchmark.p',sos08) ).
cnf(c11,plain,
product(product(X,Y),product(Z,X)) = bigC(X,Y,Z),
inference(equational,[status(thm)],[c10]) ).
cnf(c13,plain,
product(X,product(Y,X)) = bigC(X,X,Y),
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c14,plain,
product(product(X,Y),X) = bigC(X,Y,X),
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c15,plain,
bigC(X,difference(X,Y),Z) = product(Y,product(Z,X)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c16,plain,
bigC(X,Y,quotient(Z,X)) = product(product(X,Y),Z),
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c17,plain,
difference(X,bigC(X,X,Y)) = product(Y,X),
inference(equational,[status(thm)],[c3,c13]) ).
cnf(c18,plain,
quotient(bigC(X,Y,X),X) = product(X,Y),
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c19,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('theBenchmark.p',sos09) ).
cnf(c22,axiom,
product(product(X,Y),product(Z,W)) = product(product(X,Z),product(Y,W)),
file('theBenchmark.p',sos05) ).
cnf(c23,plain,
bigC(X,Y,Z) = bigC(X,Z,Y),
inference(equational,[status(thm)],[c11,c22]) ).
cnf(c24,plain,
bigC(X,quotient(Y,X),Z) = product(product(X,Z),Y),
inference(equational,[status(thm)],[c16,c23]) ).
cnf(c25,plain,
product(X,quotient(Y,X)) = quotient(product(X,Y),X),
inference(equational,[status(thm)],[c1,c18,c24]) ).
cnf(c26,plain,
bigC(X,Y,difference(X,Z)) = product(Z,product(Y,X)),
inference(equational,[status(thm)],[c15,c23]) ).
cnf(c27,plain,
product(difference(X,Y),X) = difference(X,product(Y,X)),
inference(equational,[status(thm)],[c1,c17,c26]) ).
cnf(c29,plain,
difference(X,bigC(X,Y,X)) = product(Y,X),
inference(equational,[status(thm)],[c17,c23]) ).
cnf(c30,plain,
product(product(X,Y),product(X,Z)) = product(X,product(Y,Z)),
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c31,plain,
product(product(X,Y),product(Z,Y)) = product(product(X,Z),Y),
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c34,plain,
product(product(difference(X,Y),Z),Y) = bigC(difference(X,Y),Z,X),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c35,plain,
product(X,product(Y,quotient(X,Z))) = bigC(quotient(X,Z),Z,Y),
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c40,plain,
product(product(quotient(X,Y),Z),Y) = product(X,product(Z,Y)),
inference(equational,[status(thm)],[c7,c31]) ).
cnf(c41,plain,
product(product(X,quotient(Y,Z)),Z) = product(product(X,Z),Y),
inference(equational,[status(thm)],[c7,c31]) ).
cnf(c42,plain,
product(X,product(Y,difference(X,Z))) = product(product(X,Y),Z),
inference(equational,[status(thm)],[c2,c30]) ).
cnf(c43,plain,
product(X,product(difference(X,Y),Z)) = product(Y,product(X,Z)),
inference(equational,[status(thm)],[c2,c30]) ).
cnf(c49,plain,
product(product(X,difference(Y,Z)),Z) = product(product(X,Y),difference(Y,Z)),
inference(equational,[status(thm)],[c2,c31]) ).
cnf(c51,plain,
product(product(quotient(X,Y),Z),X) = product(quotient(X,Y),product(Z,Y)),
inference(equational,[status(thm)],[c7,c30]) ).
cnf(c52,plain,
difference(X,product(Y,product(X,Z))) = product(difference(X,Y),Z),
inference(equational,[status(thm)],[c3,c43]) ).
cnf(c54,plain,
quotient(product(X,product(Y,Z)),Z) = product(quotient(X,Z),Y),
inference(equational,[status(thm)],[c5,c40]) ).
cnf(c55,plain,
difference(X,product(product(X,Y),Z)) = product(Y,difference(X,Z)),
inference(equational,[status(thm)],[c3,c42]) ).
cnf(c56,plain,
quotient(product(product(X,Y),Z),Y) = product(X,quotient(Z,Y)),
inference(equational,[status(thm)],[c5,c41]) ).
cnf(c64,plain,
product(product(X,Y),difference(Y,X)) = bigC(X,X,difference(Y,X)),
inference(equational,[status(thm)],[c14,c23,c49]) ).
cnf(c65,plain,
product(c,difference(a,product(c,b))) = b,
inference(equational,[status(thm)],[c3,c19,c55]) ).
cnf(c66,plain,
difference(a,product(c,b)) = difference(c,b),
inference(equational,[status(thm)],[c3,c65]) ).
cnf(c78,plain,
bigC(product(X,Y),Y,product(X,Y)) = product(bigC(X,Y,X),Y),
inference(equational,[status(thm)],[c14,c31]) ).
cnf(c81,plain,
product(difference(X,Y),difference(X,Z)) = difference(X,product(Y,Z)),
inference(equational,[status(thm)],[c2,c52]) ).
cnf(c84,plain,
product(X,difference(Y,difference(X,Y))) = product(difference(X,Y),Y),
inference(equational,[status(thm)],[c17,c55,c64]) ).
cnf(c94,plain,
product(product(X,quotient(Y,Z)),product(W,Z)) = product(product(X,W),Y),
inference(equational,[status(thm)],[c7,c22]) ).
cnf(c100,plain,
product(product(X,Y),product(Z,difference(Y,W))) = product(product(X,Z),W),
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c115,plain,
product(X,difference(Y,product(Z,Y))) = difference(Y,bigC(Y,X,Z)),
inference(equational,[status(thm)],[c11,c55]) ).
cnf(c116,plain,
product(quotient(product(X,Y),X),Z) = quotient(bigC(X,Y,Z),X),
inference(equational,[status(thm)],[c11,c54]) ).
cnf(c117,plain,
quotient(product(X,product(Y,Z)),product(X,Z)) = product(X,Y),
inference(equational,[status(thm)],[c5,c30]) ).
cnf(c118,plain,
quotient(product(X,Y),product(X,Z)) = product(X,quotient(Y,Z)),
inference(equational,[status(thm)],[c7,c117]) ).
cnf(c119,plain,
product(X,quotient(X,Y)) = quotient(X,product(X,Y)),
inference(equational,[status(thm)],[c1,c118]) ).
cnf(c123,plain,
quotient(X,product(X,difference(Y,X))) = product(X,Y),
inference(equational,[status(thm)],[c9,c119]) ).
cnf(c124,plain,
product(X,difference(Y,X)) = difference(product(X,Y),X),
inference(equational,[status(thm)],[c8,c123]) ).
cnf(c127,plain,
product(quotient(X,product(X,Y)),Z) = bigC(X,X,quotient(Z,Y)),
inference(equational,[status(thm)],[c13,c54,c118]) ).
cnf(c128,plain,
difference(product(X,Y),product(X,product(Y,Z))) = product(X,Z),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c129,plain,
difference(product(X,Y),product(X,Z)) = product(X,difference(Y,Z)),
inference(equational,[status(thm)],[c2,c128]) ).
cnf(c130,plain,
product(X,difference(difference(X,Y),Z)) = difference(Y,product(X,Z)),
inference(equational,[status(thm)],[c2,c129]) ).
cnf(c131,plain,
product(X,difference(Y,difference(X,Z))) = difference(product(X,Y),Z),
inference(equational,[status(thm)],[c2,c129]) ).
cnf(c132,plain,
product(difference(X,Y),Y) = difference(product(X,Y),Y),
inference(equational,[status(thm)],[c84,c131]) ).
cnf(c141,plain,
difference(product(X,Y),product(product(X,Z),Y)) = product(Z,Y),
inference(equational,[status(thm)],[c3,c31]) ).
cnf(c143,plain,
difference(product(X,Y),product(Z,Y)) = product(difference(X,Z),Y),
inference(equational,[status(thm)],[c2,c141]) ).
cnf(c144,plain,
difference(X,product(Y,difference(Z,X))) = difference(Z,product(Y,X)),
inference(equational,[status(thm)],[c2,c81,c143]) ).
cnf(c146,plain,
product(difference(X,quotient(Y,Z)),Z) = difference(product(X,Z),Y),
inference(equational,[status(thm)],[c7,c143]) ).
cnf(c147,plain,
product(a,difference(product(c,b),b)) = product(c,product(c,b)),
inference(equational,[status(thm)],[c19,c129,c141]) ).
cnf(c148,plain,
product(X,difference(product(Y,Z),Z)) = bigC(Z,difference(Y,X),Z),
inference(equational,[status(thm)],[c14,c55,c143]) ).
cnf(c153,plain,
quotient(product(product(X,Y),Z),product(Y,Z)) = product(X,Z),
inference(equational,[status(thm)],[c5,c31]) ).
cnf(c154,plain,
quotient(product(X,Y),product(Z,Y)) = product(quotient(X,Z),Y),
inference(equational,[status(thm)],[c7,c153]) ).
cnf(c161,plain,
product(quotient(X,quotient(Y,Z)),Z) = quotient(product(X,Z),Y),
inference(equational,[status(thm)],[c7,c154]) ).
cnf(c172,plain,
bigC(X,X,difference(Y,X)) = difference(bigC(X,X,Y),X),
inference(equational,[status(thm)],[c13,c124,c132]) ).
cnf(c173,plain,
product(product(X,Y),bigC(Y,Y,X)) = product(bigC(X,Y,X),Y),
inference(equational,[status(thm)],[c13,c23,c78]) ).
cnf(c176,plain,
difference(bigC(X,X,Y),X) = product(product(X,Y),difference(Y,X)),
inference(equational,[status(thm)],[c1,c2,c15,c23,c34,c81,c132,c148,c172,c173]) ).
cnf(c178,plain,
product(X,difference(difference(Y,X),Y)) = difference(product(X,Y),Y),
inference(equational,[status(thm)],[c1,c2,c26,c176]) ).
cnf(c179,plain,
difference(difference(X,Y),X) = difference(X,difference(Y,X)),
inference(equational,[status(thm)],[c1,c2,c130,c131,c178]) ).
cnf(c225,plain,
product(product(X,c),product(c,b)) = product(product(X,a),b),
inference(equational,[status(thm)],[c31,c100,c147]) ).
cnf(c226,plain,
bigC(b,c,c) = bigC(b,a,b),
inference(equational,[status(thm)],[c11,c14,c225]) ).
cnf(c227,axiom,
product(product(product(X,Y),Y),product(Y,product(Y,X))) = Y,
file('theBenchmark.p',sos07) ).
cnf(c228,plain,
quotient(X,product(X,product(X,Y))) = product(product(Y,X),X),
inference(equational,[status(thm)],[c5,c227]) ).
cnf(c229,plain,
difference(product(product(X,Y),Y),Y) = product(Y,product(Y,X)),
inference(equational,[status(thm)],[c3,c227]) ).
cnf(c230,plain,
quotient(product(X,product(X,Y)),X) = difference(product(Y,X),X),
inference(equational,[status(thm)],[c7,c25,c229]) ).
cnf(c232,plain,
difference(X,product(product(Y,X),X)) = quotient(X,product(X,Y)),
inference(equational,[status(thm)],[c2,c27,c228]) ).
cnf(c241,plain,
quotient(X,quotient(X,product(X,Y))) = difference(product(X,Y),X),
inference(equational,[status(thm)],[c51,c52,c119,c146,c232]) ).
cnf(c246,plain,
quotient(bigC(X,Y,Y),X) = quotient(Y,product(Y,X)),
inference(equational,[status(thm)],[c6,c56,c116,c154,c227,c232,c241]) ).
cnf(c247,plain,
bigC(X,X,Y) = bigC(Y,X,X),
inference(equational,[status(thm)],[c6,c7,c127,c246]) ).
cnf(c248,plain,
bigC(X,Y,Y) = bigC(Y,X,Y),
inference(equational,[status(thm)],[c23,c247]) ).
cnf(c261,plain,
difference(X,bigC(X,Y,Y)) = difference(product(X,Y),Y),
inference(equational,[status(thm)],[c27,c115,c129,c161,c230,c241]) ).
cnf(c262,plain,
difference(product(b,c),c) = product(a,b),
inference(equational,[status(thm)],[c29,c226,c261]) ).
cnf(c357,plain,
difference(X,difference(product(X,Y),Y)) = difference(Y,difference(X,Y)),
inference(equational,[status(thm)],[c1,c132,c144]) ).
cnf(c358,plain,
difference(c,difference(b,c)) = difference(b,product(a,b)),
inference(equational,[status(thm)],[c262,c357]) ).
cnf(c390,plain,
product(X,quotient(product(Y,X),Y)) = product(Y,X),
inference(equational,[status(thm)],[c1,c16,c25,c35,c247]) ).
cnf(c391,plain,
bigC(X,Y,Z) = bigC(Y,Z,X),
inference(equational,[status(thm)],[c11,c94,c390]) ).
cnf(c393,plain,
bigC(X,Y,Z) = bigC(Z,Y,X),
inference(equational,[status(thm)],[c23,c391]) ).
cnf(c447,plain,
difference(product(X,Y),product(product(X,Z),W)) = product(Z,difference(Y,W)),
inference(equational,[status(thm)],[c3,c100]) ).
cnf(c449,plain,
difference(product(X,Y),bigC(X,Z,X)) = product(Z,difference(Y,X)),
inference(equational,[status(thm)],[c14,c447]) ).
cnf(c451,plain,
difference(b,bigC(c,X,c)) = difference(b,bigC(a,X,b)),
inference(equational,[status(thm)],[c65,c66,c115,c179,c358,c393,c449]) ).
cnf(c452,plain,
bigC(c,X,c) = bigC(a,X,b),
inference(equational,[status(thm)],[c2,c451]) ).
cnf(c453,plain,
bigC(a,X,b) = bigC(X,c,c),
inference(equational,[status(thm)],[c248,c452]) ).
cnf(c456,plain,
bigC(X,c,c) = bigC(X,a,b),
inference(equational,[status(thm)],[c23,c391,c453]) ).
cnf(g1,plain,
bigC(a,b,x0) = bigC(c,c,x0),
inference(equational,[status(thm)],[c23,c248,c391,c456]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP777-10 : TPTP v9.0.0. Released v8.1.0.
% 0.07/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 09:05:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 63.48/63.62 % SZS status Unsatisfiable
% 63.48/63.62 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------