%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n009.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 08:13:58 AM UTC 2026
% Result : Unsatisfiable 124.56s 124.86s
% Output : Proof 124.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 27 unt; 0 nHn; 27 RR)
% Number of literals : 53 ( 4 equ; 22 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('BOO002-0.ax',closure_of_addition) ).
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(distributivity5,axiom,
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('BOO002-0.ax',distributivity5) ).
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(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(multiplicative_inverse2,axiom,
product(X,inverse(X),additive_identity),
file('BOO002-0.ax',multiplicative_inverse2) ).
cnf(multiplication_is_well_defined,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('BOO002-0.ax',multiplication_is_well_defined) ).
cnf(prove_inverse_is_an_involution,negated_conjecture,
inverse(inverse(x)) != x,
file('theBenchmark.p',prove_inverse_is_an_involution) ).
cnf(t1,plain,
inverse(inverse(x)) != x,
inference(start,[status(thm),parent(0:0)],[prove_inverse_is_an_involution]) ).
cnf(t2,plain,
( ~ product(multiplicative_identity,add(x,inverse(inverse(x))),x)
| ~ product(multiplicative_identity,add(x,inverse(inverse(x))),inverse(inverse(x)))
| inverse(inverse(x)) = x ),
inference(extension,[status(thm),parent(t1:1)],[multiplication_is_well_defined]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(x,inverse(inverse(x)),add(x,inverse(inverse(x))))
| ~ product(inverse(x),x,additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity)
| product(multiplicative_identity,add(x,inverse(inverse(x))),inverse(inverse(x))) ),
inference(extension,[status(thm),parent(t2:2)],[distributivity7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sum(inverse(x),inverse(inverse(x)),multiplicative_identity),
inference(extension,[status(thm),parent(t4:2)],[additive_inverse2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sum(additive_identity,inverse(inverse(x)),inverse(inverse(x))),
inference(extension,[status(thm),parent(t4:3)],[additive_identity1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
product(inverse(x),x,additive_identity),
inference(extension,[status(thm),parent(t4:4)],[multiplicative_inverse1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
sum(x,inverse(inverse(x)),add(x,inverse(inverse(x)))),
inference(extension,[status(thm),parent(t4:5)],[closure_of_addition]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:5]) ).
cnf(t14,plain,
( ~ sum(x,inverse(inverse(x)),add(x,inverse(inverse(x))))
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ sum(x,additive_identity,x)
| ~ sum(x,inverse(x),multiplicative_identity)
| product(multiplicative_identity,add(x,inverse(inverse(x))),x) ),
inference(extension,[status(thm),parent(t2:3)],[distributivity5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
sum(x,inverse(x),multiplicative_identity),
inference(extension,[status(thm),parent(t14:2)],[additive_inverse2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t14:3)],[additive_identity2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
product(inverse(x),inverse(inverse(x)),additive_identity),
inference(extension,[status(thm),parent(t14:4)],[multiplicative_inverse2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
sum(x,inverse(inverse(x)),add(x,inverse(inverse(x)))),
inference(extension,[status(thm),parent(t14:5)],[closure_of_addition]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:35:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 124.56/124.86 % SZS status Unsatisfiable for theBenchmark
% 124.56/124.86 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------