%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:13:55 AM UTC 2026
% Result : Unsatisfiable 126.79s 127.08s
% Output : Proof 126.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 46 ( 39 unt; 0 nHn; 40 RR)
% Number of literals : 74 ( 0 equ; 30 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 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 : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('BOO002-0.ax',closure_of_multiplication) ).
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(multiplicative_identity2,axiom,
product(X,multiplicative_identity,X),
file('BOO002-0.ax',multiplicative_identity2) ).
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_inverse2,axiom,
sum(X,inverse(X),multiplicative_identity),
file('BOO002-0.ax',additive_inverse2) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('BOO002-0.ax',multiplicative_inverse1) ).
cnf(prove_both_equalities,negated_conjecture,
~ product(x,x,x),
file('theBenchmark.p',prove_both_equalities) ).
cnf(t1,plain,
~ product(x,x,x),
inference(start,[status(thm),parent(0:0)],[prove_both_equalities]) ).
cnf(t2,plain,
( ~ sum(x,additive_identity,x)
| ~ product(x,x,multiply(x,x))
| ~ sum(multiply(x,x),additive_identity,x)
| ~ sum(x,additive_identity,x)
| product(x,x,x) ),
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(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ product(x,multiplicative_identity,x)
| ~ product(x,multiplicative_identity,x)
| ~ sum(x,additive_identity,x)
| sum(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(x,additive_identity,x),
inference(extension,[status(thm),parent(t4:2)],[additive_identity2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
product(x,multiplicative_identity,x),
inference(extension,[status(thm),parent(t4:3)],[multiplicative_identity2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
product(x,multiplicative_identity,x),
inference(extension,[status(thm),parent(t4:4)],[multiplicative_identity2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
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(l2,lemma,
sum(x,additive_identity,x),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t14,plain,
( ~ product(inverse(x),x,additive_identity)
| ~ sum(x,inverse(x),multiplicative_identity)
| ~ product(multiplicative_identity,x,x)
| ~ product(x,x,multiply(x,x))
| sum(multiply(x,x),additive_identity,x) ),
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(x,x,multiply(x,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(multiplicative_identity,x,x),
inference(extension,[status(thm),parent(t14:3)],[multiplicative_identity1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
sum(x,inverse(x),multiplicative_identity),
inference(extension,[status(thm),parent(t14:4)],[additive_inverse2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
product(inverse(x),x,additive_identity),
inference(extension,[status(thm),parent(t14:5)],[multiplicative_inverse1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:5]) ).
cnf(t24,plain,
( ~ sum(x,additive_identity,x)
| ~ product(x,x,multiply(x,x))
| ~ sum(multiply(x,x),additive_identity,multiply(x,x))
| ~ sum(x,additive_identity,x)
| product(x,x,multiply(x,x)) ),
inference(extension,[status(thm),parent(t2:4)],[distributivity7]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:4]) ).
cnf(t26,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t24:2)],[additive_identity2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
sum(multiply(x,x),additive_identity,multiply(x,x)),
inference(extension,[status(thm),parent(t24:3)],[additive_identity2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
product(x,x,multiply(x,x)),
inference(extension,[status(thm),parent(t24:4)],[closure_of_multiplication]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:4]) ).
cnf(t32,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t24:5)],[additive_identity2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t24:5]) ).
cnf(t34,plain,
sum(x,additive_identity,x),
inference(lemma_extension,[status(thm),parent(t2:5)],[l2:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:37:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 126.79/127.08 % SZS status Unsatisfiable for theBenchmark
% 126.79/127.08 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------