%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP029-1 : 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 : n007.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 08:41:09 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.60s
% Output : Proof 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 96 ( 76 unt; 0 nHn; 73 RR)
% Number of literals : 150 ( 14 equ; 56 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('GRP002-0.ax',total_function1) ).
cnf(total_function2,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('GRP002-0.ax',total_function2) ).
cnf(associativity1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP002-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP002-0.ax',associativity2) ).
cnf(left_identity,axiom,
product(identity,A,A),
file('theBenchmark.p',left_identity) ).
cnf(left_inverse,axiom,
product(inverse(A),A,identity),
file('theBenchmark.p',left_inverse) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_right_identity(A),A,not_right_identity(A)),
file('theBenchmark.p',prove_there_is_a_right_identity) ).
cnf(equality_6,axiom,
( not_right_identity(Eq_x_0) = not_right_identity(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( product(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ product(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ product(not_right_identity(identity),identity,not_right_identity(identity)),
inference(start,[status(thm),parent(0:0)],[prove_there_is_a_right_identity]) ).
cnf(t2,plain,
( identity != identity
| multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386) != not_right_identity(identity)
| ~ product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386))
| not_right_identity(identity) != not_right_identity(identity)
| product(not_right_identity(identity),identity,not_right_identity(identity)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( identity != identity
| not_right_identity(identity) = not_right_identity(identity) ),
inference(extension,[status(thm),parent(t2:2)],[equality_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ product(inverse(U_323),U_323,identity)
| ~ product(inverse(U_323),U_323,identity)
| identity = identity ),
inference(extension,[status(thm),parent(t4:2)],[total_function2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
product(inverse(U_323),U_323,identity),
inference(extension,[status(thm),parent(t6:2)],[left_inverse]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
product(inverse(U_323),U_323,identity),
inference(extension,[status(thm),parent(t6:3)],[left_inverse]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( ~ product(identity,identity,identity)
| ~ product(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386))
| ~ product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357))
| product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)) ),
inference(extension,[status(thm),parent(t2:3)],[associativity1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( ~ product(identity,identity,identity)
| ~ product(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),identity,multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357))
| ~ product(not_right_identity(identity),identity,multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346))
| product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357)) ),
inference(extension,[status(thm),parent(t12:2)],[associativity1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ product(inverse(U_346),U_346,identity)
| ~ product(multiply(not_right_identity(identity),inverse(U_346)),U_346,multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346))
| ~ product(not_right_identity(identity),inverse(U_346),multiply(not_right_identity(identity),inverse(U_346)))
| product(not_right_identity(identity),identity,multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346)) ),
inference(extension,[status(thm),parent(t14:2)],[associativity1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
product(not_right_identity(identity),inverse(U_346),multiply(not_right_identity(identity),inverse(U_346))),
inference(extension,[status(thm),parent(t16:2)],[total_function1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
product(multiply(not_right_identity(identity),inverse(U_346)),U_346,multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346)),
inference(extension,[status(thm),parent(t16:3)],[total_function1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
product(inverse(U_346),U_346,identity),
inference(extension,[status(thm),parent(t16:4)],[left_inverse]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:4]) ).
cnf(t24,plain,
( ~ product(inverse(U_357),U_357,identity)
| ~ product(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357,multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357))
| ~ product(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357),multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)))
| product(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),identity,multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357)) ),
inference(extension,[status(thm),parent(t14:3)],[associativity1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t14:3]) ).
cnf(t26,plain,
product(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357),multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357))),
inference(extension,[status(thm),parent(t24:2)],[total_function1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
product(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357,multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357)),
inference(extension,[status(thm),parent(t24:3)],[total_function1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
product(inverse(U_357),U_357,identity),
inference(extension,[status(thm),parent(t24:4)],[left_inverse]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:4]) ).
cnf(t32,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t14:4)],[left_identity]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t14:4]) ).
cnf(t34,plain,
( ~ product(identity,identity,identity)
| ~ product(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386))
| ~ product(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),identity,multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375))
| product(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)) ),
inference(extension,[status(thm),parent(t12:3)],[associativity1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t12:3]) ).
cnf(t36,plain,
( ~ product(inverse(U_375),U_375,identity)
| ~ product(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375,multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375))
| ~ product(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375),multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)))
| product(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),identity,multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375)) ),
inference(extension,[status(thm),parent(t34:2)],[associativity1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
product(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375),multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375))),
inference(extension,[status(thm),parent(t36:2)],[total_function1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
product(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375,multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375)),
inference(extension,[status(thm),parent(t36:3)],[total_function1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
product(inverse(U_375),U_375,identity),
inference(extension,[status(thm),parent(t36:4)],[left_inverse]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t36:4]) ).
cnf(t44,plain,
( ~ product(inverse(U_386),U_386,identity)
| ~ product(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386))
| ~ product(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386),multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)))
| product(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)) ),
inference(extension,[status(thm),parent(t34:3)],[associativity1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t34:3]) ).
cnf(t46,plain,
product(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386),multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386))),
inference(extension,[status(thm),parent(t44:2)],[total_function1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
product(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)),
inference(extension,[status(thm),parent(t44:3)],[total_function1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
product(inverse(U_386),U_386,identity),
inference(extension,[status(thm),parent(t44:4)],[left_inverse]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t44:4]) ).
cnf(t52,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t34:4)],[left_identity]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t34:4]) ).
cnf(t54,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t12:4)],[left_identity]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t12:4]) ).
cnf(l6,lemma,
product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)),
inference(lemma,[status(cth),parent(t2:3),below(t1:1)],[t2:3]) ).
cnf(t56,plain,
( ~ product(identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386),not_right_identity(identity))
| ~ product(identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386),multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386))
| multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386) = not_right_identity(identity) ),
inference(extension,[status(thm),parent(t2:4)],[total_function2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t2:4]) ).
cnf(t58,plain,
product(identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386),multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)),
inference(extension,[status(thm),parent(t56:2)],[left_identity]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( ~ product(inverse(not_right_identity(identity)),multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386),identity)
| ~ product(inverse(inverse(not_right_identity(identity))),identity,not_right_identity(identity))
| ~ product(inverse(inverse(not_right_identity(identity))),inverse(not_right_identity(identity)),identity)
| product(identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386),not_right_identity(identity)) ),
inference(extension,[status(thm),parent(t56:3)],[associativity2]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
cnf(t62,plain,
product(inverse(inverse(not_right_identity(identity))),inverse(not_right_identity(identity)),identity),
inference(extension,[status(thm),parent(t60:2)],[left_inverse]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( ~ product(inverse(not_right_identity(identity)),not_right_identity(identity),identity)
| ~ product(identity,not_right_identity(identity),not_right_identity(identity))
| ~ product(inverse(inverse(not_right_identity(identity))),inverse(not_right_identity(identity)),identity)
| product(inverse(inverse(not_right_identity(identity))),identity,not_right_identity(identity)) ),
inference(extension,[status(thm),parent(t60:3)],[associativity1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t60:3]) ).
cnf(t66,plain,
product(inverse(inverse(not_right_identity(identity))),inverse(not_right_identity(identity)),identity),
inference(extension,[status(thm),parent(t64:2)],[left_inverse]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
product(identity,not_right_identity(identity),not_right_identity(identity)),
inference(extension,[status(thm),parent(t64:3)],[left_identity]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
product(inverse(not_right_identity(identity)),not_right_identity(identity),identity),
inference(extension,[status(thm),parent(t64:4)],[left_inverse]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t64:4]) ).
cnf(t72,plain,
( ~ product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386))
| ~ product(identity,identity,identity)
| ~ product(inverse(not_right_identity(identity)),not_right_identity(identity),identity)
| product(inverse(not_right_identity(identity)),multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386),identity) ),
inference(extension,[status(thm),parent(t60:4)],[associativity1]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t60:4]) ).
cnf(t74,plain,
product(inverse(not_right_identity(identity)),not_right_identity(identity),identity),
inference(extension,[status(thm),parent(t72:2)],[left_inverse]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t72:3)],[left_identity]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t72:3]) ).
cnf(t78,plain,
product(not_right_identity(identity),identity,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(not_right_identity(identity),inverse(U_346)),U_346),inverse(U_357)),U_357),inverse(U_375)),U_375),inverse(U_386)),U_386)),
inference(lemma_extension,[status(thm),parent(t72:4)],[l6:1]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t72:4]) ).
cnf(t80,plain,
( ~ product(inverse(U_422),U_422,identity)
| ~ product(inverse(U_422),U_422,identity)
| identity = identity ),
inference(extension,[status(thm),parent(t2:5)],[total_function2]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t2:5]) ).
cnf(t82,plain,
product(inverse(U_422),U_422,identity),
inference(extension,[status(thm),parent(t80:2)],[left_inverse]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t80:2]) ).
cnf(l40,lemma,
product(inverse(U_422),U_422,identity),
inference(lemma,[status(cth),parent(t80:2),below(t2:5)],[t80:2]) ).
cnf(t84,plain,
product(inverse(U_422),U_422,identity),
inference(lemma_extension,[status(thm),parent(t80:3)],[l40:1]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t80:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP029-1 : 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
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 08:32:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.30/0.60 % SZS status Unsatisfiable for theBenchmark
% 0.30/0.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------