%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP012-2 : 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 : n010.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 08:41:06 AM UTC 2026
% Result : Unsatisfiable 192.16s 192.44s
% Output : Proof 192.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of clauses : 94 ( 77 unt; 0 nHn; 88 RR)
% Number of literals : 145 ( 14 equ; 53 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('GRP003-0.ax',right_inverse) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('GRP003-0.ax',total_function1) ).
cnf(total_function2,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('GRP003-0.ax',total_function2) ).
cnf(associativity1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity2) ).
cnf(a_multiply_b_is_c,hypothesis,
product(a,b,c),
file('theBenchmark.p',a_multiply_b_is_c) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d),
file('theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
cnf(prove_c_inverse_equals_d,negated_conjecture,
inverse(c) != d,
file('theBenchmark.p',prove_c_inverse_equals_d) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_6,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,
inverse(c) != d,
inference(start,[status(thm),parent(0:0)],[prove_c_inverse_equals_d]) ).
cnf(t2,plain,
( ~ product(inverse(b),inverse(a),inverse(c))
| ~ product(inverse(b),inverse(a),d)
| inverse(c) = d ),
inference(extension,[status(thm),parent(t1:1)],[total_function2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
product(inverse(b),inverse(a),d),
inference(extension,[status(thm),parent(t2:2)],[inverse_b_multiply_inverse_a_is_d]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ product(identity,inverse(a),multiply(b,inverse(c)))
| ~ product(inverse(b),multiply(b,inverse(c)),inverse(c))
| ~ product(inverse(b),identity,inverse(b))
| product(inverse(b),inverse(a),inverse(c)) ),
inference(extension,[status(thm),parent(t2:3)],[associativity2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
product(inverse(b),identity,inverse(b)),
inference(extension,[status(thm),parent(t6:2)],[right_identity]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ product(identity,multiply(b,inverse(c)),multiply(b,inverse(c)))
| ~ product(inverse(b),multiply(b,inverse(c)),inverse(c))
| ~ product(inverse(b),identity,inverse(b))
| product(inverse(b),multiply(b,inverse(c)),inverse(c)) ),
inference(extension,[status(thm),parent(t6:3)],[associativity2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
product(inverse(b),identity,inverse(b)),
inference(extension,[status(thm),parent(t10:2)],[right_identity]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ product(identity,multiply(b,inverse(c)),multiply(b,inverse(c)))
| ~ product(inverse(b),multiply(b,inverse(c)),inverse(c))
| ~ product(inverse(b),identity,inverse(b))
| product(inverse(b),multiply(b,inverse(c)),inverse(c)) ),
inference(extension,[status(thm),parent(t10:3)],[associativity2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
product(inverse(b),identity,inverse(b)),
inference(extension,[status(thm),parent(t14:2)],[right_identity]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ product(b,inverse(c),multiply(b,inverse(c)))
| ~ product(identity,inverse(c),inverse(c))
| ~ product(inverse(b),b,identity)
| product(inverse(b),multiply(b,inverse(c)),inverse(c)) ),
inference(extension,[status(thm),parent(t14:3)],[associativity1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
product(inverse(b),b,identity),
inference(extension,[status(thm),parent(t18:2)],[left_inverse]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
product(identity,inverse(c),inverse(c)),
inference(extension,[status(thm),parent(t18:3)],[left_identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
product(b,inverse(c),multiply(b,inverse(c))),
inference(extension,[status(thm),parent(t18:4)],[total_function1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:4]) ).
cnf(t26,plain,
( multiply(b,inverse(c)) != multiply(b,inverse(c))
| ~ product(identity,multiply(b,inverse(c)),multiply(b,inverse(c)))
| multiply(b,inverse(c)) != multiply(b,inverse(c))
| identity != identity
| product(identity,multiply(b,inverse(c)),multiply(b,inverse(c))) ),
inference(extension,[status(thm),parent(t14:4)],[equality_6]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:4]) ).
cnf(t28,plain,
identity = identity,
inference(extension,[status(thm),parent(t26:2)],[equality_1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
multiply(b,inverse(c)) = multiply(b,inverse(c)),
inference(extension,[status(thm),parent(t26:3)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
product(identity,multiply(b,inverse(c)),multiply(b,inverse(c))),
inference(extension,[status(thm),parent(t26:4)],[left_identity]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:4]) ).
cnf(t34,plain,
multiply(b,inverse(c)) = multiply(b,inverse(c)),
inference(extension,[status(thm),parent(t26:5)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t26:5]) ).
cnf(t36,plain,
( ~ product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity)
| ~ product(inverse(inverse(multiply(b,inverse(c)))),identity,multiply(b,inverse(c)))
| ~ product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity)
| product(identity,multiply(b,inverse(c)),multiply(b,inverse(c))) ),
inference(extension,[status(thm),parent(t10:4)],[associativity2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t10:4]) ).
cnf(t38,plain,
product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity),
inference(extension,[status(thm),parent(t36:2)],[left_inverse]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( ~ product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity)
| ~ product(identity,multiply(b,inverse(c)),multiply(b,inverse(c)))
| ~ product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity)
| product(inverse(inverse(multiply(b,inverse(c)))),identity,multiply(b,inverse(c))) ),
inference(extension,[status(thm),parent(t36:3)],[associativity1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity),
inference(extension,[status(thm),parent(t40:2)],[left_inverse]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
product(identity,multiply(b,inverse(c)),multiply(b,inverse(c))),
inference(extension,[status(thm),parent(t40:3)],[left_identity]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity),
inference(extension,[status(thm),parent(t40:4)],[left_inverse]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t40:4]) ).
cnf(t48,plain,
product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity),
inference(extension,[status(thm),parent(t36:4)],[left_inverse]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t36:4]) ).
cnf(t50,plain,
( ~ product(identity,multiply(b,inverse(c)),inverse(a))
| ~ product(identity,multiply(b,inverse(c)),multiply(b,inverse(c)))
| ~ product(identity,identity,identity)
| product(identity,inverse(a),multiply(b,inverse(c))) ),
inference(extension,[status(thm),parent(t6:4)],[associativity1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t6:4]) ).
cnf(t52,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t50:2)],[right_identity]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( ~ product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity)
| ~ product(inverse(inverse(multiply(b,inverse(c)))),identity,multiply(b,inverse(c)))
| ~ product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity)
| product(identity,multiply(b,inverse(c)),multiply(b,inverse(c))) ),
inference(extension,[status(thm),parent(t50:3)],[associativity2]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity),
inference(extension,[status(thm),parent(t54:2)],[left_inverse]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( ~ product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity)
| ~ product(identity,multiply(b,inverse(c)),multiply(b,inverse(c)))
| ~ product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity)
| product(inverse(inverse(multiply(b,inverse(c)))),identity,multiply(b,inverse(c))) ),
inference(extension,[status(thm),parent(t54:3)],[associativity1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
product(inverse(inverse(multiply(b,inverse(c)))),inverse(multiply(b,inverse(c))),identity),
inference(extension,[status(thm),parent(t58:2)],[left_inverse]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
product(identity,multiply(b,inverse(c)),multiply(b,inverse(c))),
inference(extension,[status(thm),parent(t58:3)],[left_identity]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t58:3]) ).
cnf(t64,plain,
product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity),
inference(extension,[status(thm),parent(t58:4)],[left_inverse]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t58:4]) ).
cnf(t66,plain,
product(inverse(multiply(b,inverse(c))),multiply(b,inverse(c)),identity),
inference(extension,[status(thm),parent(t54:4)],[left_inverse]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t54:4]) ).
cnf(t68,plain,
( ~ product(a,multiply(b,inverse(c)),identity)
| ~ product(inverse(a),identity,inverse(a))
| ~ product(inverse(a),a,identity)
| product(identity,multiply(b,inverse(c)),inverse(a)) ),
inference(extension,[status(thm),parent(t50:4)],[associativity2]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t50:4]) ).
cnf(t70,plain,
product(inverse(a),a,identity),
inference(extension,[status(thm),parent(t68:2)],[left_inverse]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
product(inverse(a),identity,inverse(a)),
inference(extension,[status(thm),parent(t68:3)],[right_identity]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t68:3]) ).
cnf(t74,plain,
( ~ product(b,inverse(c),multiply(b,inverse(c)))
| ~ product(c,inverse(c),identity)
| ~ product(a,b,c)
| product(a,multiply(b,inverse(c)),identity) ),
inference(extension,[status(thm),parent(t68:4)],[associativity1]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t68:4]) ).
cnf(t76,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t74:2)],[a_multiply_b_is_c]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
product(c,inverse(c),identity),
inference(extension,[status(thm),parent(t74:3)],[right_inverse]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t74:3]) ).
cnf(t80,plain,
product(b,inverse(c),multiply(b,inverse(c))),
inference(extension,[status(thm),parent(t74:4)],[total_function1]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t74:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 08:30:53 UTC 2026
% 0.09/0.35 % CPUTime :
% 192.16/192.44 % SZS status Unsatisfiable for theBenchmark
% 192.16/192.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------