%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:13:56 AM UTC 2026
% Result : Unsatisfiable 147.77s 153.26s
% Output : Proof 147.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 50 ( 41 unt; 0 nHn; 39 RR)
% Number of literals : 80 ( 0 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('BOO002-0.ax',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('BOO002-0.ax',commutativity_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('BOO002-0.ax',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X),
file('BOO002-0.ax',additive_identity2) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('BOO002-0.ax',multiplicative_identity1) ).
cnf(distributivity3,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('BOO002-0.ax',distributivity3) ).
cnf(distributivity7,axiom,
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('BOO002-0.ax',distributivity7) ).
cnf(distributivity8,axiom,
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('BOO002-0.ax',distributivity8) ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity),
file('BOO002-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('BOO002-0.ax',multiplicative_inverse1) ).
cnf(multiplicative_inverse2,axiom,
product(X,inverse(X),additive_identity),
file('BOO002-0.ax',multiplicative_inverse2) ).
cnf(prove_equations,negated_conjecture,
~ product(x,additive_identity,additive_identity),
file('theBenchmark.p',prove_equations) ).
cnf(t1,plain,
~ product(x,additive_identity,additive_identity),
inference(start,[status(thm),parent(0:0)],[prove_equations]) ).
cnf(t2,plain,
( ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(multiply(inverse(additive_identity),x),additive_identity,multiply(additive_identity,multiply(inverse(additive_identity),x)))
| ~ sum(multiply(additive_identity,multiply(inverse(additive_identity),x)),additive_identity,additive_identity)
| ~ sum(multiply(inverse(additive_identity),x),additive_identity,x)
| product(x,additive_identity,additive_identity) ),
inference(extension,[status(thm),parent(t1:1)],[distributivity7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(x,additive_identity,x)
| ~ product(inverse(additive_identity),x,multiply(inverse(additive_identity),x))
| ~ product(multiplicative_identity,x,x)
| ~ sum(inverse(additive_identity),additive_identity,multiplicative_identity)
| sum(multiply(inverse(additive_identity),x),additive_identity,x) ),
inference(extension,[status(thm),parent(t2:2)],[distributivity8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sum(inverse(additive_identity),additive_identity,multiplicative_identity),
inference(extension,[status(thm),parent(t4:2)],[additive_inverse1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
product(multiplicative_identity,x,x),
inference(extension,[status(thm),parent(t4:3)],[multiplicative_identity1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
product(inverse(additive_identity),x,multiply(inverse(additive_identity),x)),
inference(extension,[status(thm),parent(t4:4)],[closure_of_multiplication]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t4:5)],[additive_identity2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:5]) ).
cnf(t14,plain,
( ~ product(inverse(multiply(inverse(additive_identity),x)),multiply(inverse(additive_identity),x),additive_identity)
| ~ sum(additive_identity,inverse(multiply(inverse(additive_identity),x)),inverse(multiply(inverse(additive_identity),x)))
| ~ product(inverse(multiply(inverse(additive_identity),x)),multiply(inverse(additive_identity),x),additive_identity)
| ~ product(additive_identity,multiply(inverse(additive_identity),x),multiply(additive_identity,multiply(inverse(additive_identity),x)))
| sum(multiply(additive_identity,multiply(inverse(additive_identity),x)),additive_identity,additive_identity) ),
inference(extension,[status(thm),parent(t2:3)],[distributivity3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
product(additive_identity,multiply(inverse(additive_identity),x),multiply(additive_identity,multiply(inverse(additive_identity),x))),
inference(extension,[status(thm),parent(t14:2)],[closure_of_multiplication]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
product(inverse(multiply(inverse(additive_identity),x)),multiply(inverse(additive_identity),x),additive_identity),
inference(extension,[status(thm),parent(t14:3)],[multiplicative_inverse1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(l9,lemma,
product(inverse(multiply(inverse(additive_identity),x)),multiply(inverse(additive_identity),x),additive_identity),
inference(lemma,[status(cth),parent(t14:3),below(t2:3)],[t14:3]) ).
cnf(t20,plain,
sum(additive_identity,inverse(multiply(inverse(additive_identity),x)),inverse(multiply(inverse(additive_identity),x))),
inference(extension,[status(thm),parent(t14:4)],[additive_identity1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
product(inverse(multiply(inverse(additive_identity),x)),multiply(inverse(additive_identity),x),additive_identity),
inference(lemma_extension,[status(thm),parent(t14:5)],[l9:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:5]) ).
cnf(t24,plain,
( ~ product(additive_identity,multiply(inverse(additive_identity),x),multiply(additive_identity,multiply(inverse(additive_identity),x)))
| product(multiply(inverse(additive_identity),x),additive_identity,multiply(additive_identity,multiply(inverse(additive_identity),x))) ),
inference(extension,[status(thm),parent(t2:4)],[commutativity_of_multiplication]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:4]) ).
cnf(t26,plain,
product(additive_identity,multiply(inverse(additive_identity),x),multiply(additive_identity,multiply(inverse(additive_identity),x))),
inference(extension,[status(thm),parent(t24:2)],[closure_of_multiplication]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ sum(inverse(U_1326),additive_identity,inverse(U_1326))
| ~ product(U_1326,inverse(U_1326),additive_identity)
| ~ product(U_1326,inverse(U_1326),additive_identity)
| ~ sum(U_1326,additive_identity,U_1326)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(extension,[status(thm),parent(t2:5)],[distributivity8]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:5]) ).
cnf(t30,plain,
sum(U_1326,additive_identity,U_1326),
inference(extension,[status(thm),parent(t28:2)],[additive_identity2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
product(U_1326,inverse(U_1326),additive_identity),
inference(extension,[status(thm),parent(t28:3)],[multiplicative_inverse2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
product(U_1326,inverse(U_1326),additive_identity),
inference(extension,[status(thm),parent(t28:4)],[multiplicative_inverse2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
sum(inverse(U_1326),additive_identity,inverse(U_1326)),
inference(extension,[status(thm),parent(t28:5)],[additive_identity2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.53 % Computer : n018.cluster.edu
% 0.13/5.53 % Model : x86_64 x86_64
% 0.13/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.53 % Memory : 8046.5625MB
% 0.13/5.53 % OS : Linux 6.8.0-71-generic
% 0.13/5.53 % CPULimit : 300
% 0.13/5.53 % WCLimit : 300
% 0.13/5.53 % DateTime : Sun Sep 20 13:33:18 UTC 2026
% 0.13/5.54 % CPUTime :
% 147.77/153.26 % SZS status Unsatisfiable for theBenchmark
% 147.77/153.26 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------