%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP035-3 : 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 : n013.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 08:41:11 AM UTC 2026
% Result : Unsatisfiable 17.66s 22.99s
% Output : Proof 17.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 62 ( 52 unt; 0 nHn; 58 RR)
% Number of literals : 92 ( 0 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 13 ( 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(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity2) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('theBenchmark.p',b_is_in_subgroup) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('theBenchmark.p',a_times_b_is_c) ).
cnf(prove_c_is_in_subgroup,negated_conjecture,
~ subgroup_member(c),
file('theBenchmark.p',prove_c_is_in_subgroup) ).
cnf(t1,plain,
~ subgroup_member(c),
inference(start,[status(thm),parent(0:0)],[prove_c_is_in_subgroup]) ).
cnf(t2,plain,
( ~ subgroup_member(inverse(b))
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(a)
| subgroup_member(c) ),
inference(extension,[status(thm),parent(t1:1)],[closure_of_product_and_inverse]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
subgroup_member(a),
inference(extension,[status(thm),parent(t2:2)],[a_is_in_subgroup]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ product(inverse(b),inverse(inverse(b)),identity)
| ~ product(c,identity,c)
| ~ product(c,inverse(b),a)
| product(a,inverse(inverse(b)),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(b,inverse(b),identity)
| ~ product(a,identity,a)
| ~ product(a,b,c)
| product(c,inverse(b),a) ),
inference(extension,[status(thm),parent(t6:2)],[associativity2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t8:2)],[a_times_b_is_c]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
product(a,identity,a),
inference(extension,[status(thm),parent(t8:3)],[right_identity]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
product(b,inverse(b),identity),
inference(extension,[status(thm),parent(t8:4)],[right_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
cnf(t16,plain,
( ~ product(b,identity,b)
| ~ product(a,b,c)
| ~ product(a,b,c)
| product(c,identity,c) ),
inference(extension,[status(thm),parent(t6:3)],[associativity2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:3]) ).
cnf(t18,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t16:2)],[a_times_b_is_c]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t16:3)],[a_times_b_is_c]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
product(b,identity,b),
inference(extension,[status(thm),parent(t16:4)],[right_identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:4]) ).
cnf(t24,plain,
( ~ product(identity,inverse(inverse(b)),inverse(inverse(b)))
| ~ product(inverse(b),inverse(inverse(b)),identity)
| ~ product(inverse(b),identity,inverse(b))
| product(inverse(b),inverse(inverse(b)),identity) ),
inference(extension,[status(thm),parent(t6:4)],[associativity2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t6:4]) ).
cnf(t26,plain,
product(inverse(b),identity,inverse(b)),
inference(extension,[status(thm),parent(t24:2)],[right_identity]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
product(inverse(b),inverse(inverse(b)),identity),
inference(extension,[status(thm),parent(t24:3)],[right_inverse]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
product(identity,inverse(inverse(b)),inverse(inverse(b))),
inference(extension,[status(thm),parent(t24:4)],[left_identity]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:4]) ).
cnf(t32,plain,
( ~ subgroup_member(b)
| ~ product(identity,inverse(b),inverse(b))
| ~ subgroup_member(identity)
| subgroup_member(inverse(b)) ),
inference(extension,[status(thm),parent(t2:4)],[closure_of_product_and_inverse]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t2:4]) ).
cnf(t34,plain,
( ~ subgroup_member(b)
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) ),
inference(extension,[status(thm),parent(t32:2)],[closure_of_product_and_inverse]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
subgroup_member(b),
inference(extension,[status(thm),parent(t34:2)],[b_is_in_subgroup]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(l18,lemma,
subgroup_member(b),
inference(lemma,[status(cth),parent(t34:2),below(t32:2)],[t34:2]) ).
cnf(t38,plain,
product(b,inverse(b),identity),
inference(extension,[status(thm),parent(t34:3)],[right_inverse]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
subgroup_member(b),
inference(lemma_extension,[status(thm),parent(t34:4)],[l18:1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t34:4]) ).
cnf(t42,plain,
( ~ product(inverse(inverse(b)),inverse(b),identity)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(identity,inverse(b),inverse(b)) ),
inference(extension,[status(thm),parent(t32:3)],[associativity2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t32:3]) ).
cnf(t44,plain,
product(inverse(b),inverse(inverse(b)),identity),
inference(extension,[status(thm),parent(t42:2)],[right_inverse]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
product(inverse(b),identity,inverse(b)),
inference(extension,[status(thm),parent(t42:3)],[right_identity]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
product(inverse(inverse(b)),inverse(b),identity),
inference(extension,[status(thm),parent(t42:4)],[left_inverse]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t42:4]) ).
cnf(t50,plain,
subgroup_member(b),
inference(extension,[status(thm),parent(t32:4)],[b_is_in_subgroup]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t32:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP035-3 : 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
% 0.11/5.39 % Computer : n013.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 19 08:34:26 UTC 2026
% 0.11/5.39 % CPUTime :
% 17.66/22.99 % SZS status Unsatisfiable for theBenchmark
% 17.66/22.99 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------