%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP003-2 : 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 : n026.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 08:41:05 AM UTC 2026
% Result : Unsatisfiable 6.34s 6.70s
% Output : Proof 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 33 ( 27 unt; 0 nHn; 30 RR)
% Number of literals : 51 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('GRP005-0.ax',left_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('GRP005-0.ax',left_inverse) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('GRP005-0.ax',total_function1) ).
cnf(associativity1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP005-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP005-0.ax',associativity2) ).
cnf(prove_right_identity,negated_conjecture,
~ product(a,identity,a),
file('theBenchmark.p',prove_right_identity) ).
cnf(t1,plain,
~ product(a,identity,a),
inference(start,[status(thm),parent(0:0)],[prove_right_identity]) ).
cnf(t2,plain,
( ~ product(identity,identity,multiply(inverse(a),a))
| ~ product(inverse(inverse(a)),multiply(inverse(a),a),a)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,identity,a) ),
inference(extension,[status(thm),parent(t1:1)],[associativity2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| ~ product(inverse(inverse(a)),inverse(a),identity)
| product(inverse(inverse(a)),identity,a) ),
inference(extension,[status(thm),parent(t2:2)],[associativity1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
product(inverse(inverse(a)),inverse(a),identity),
inference(extension,[status(thm),parent(t4:2)],[left_inverse]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
product(identity,a,a),
inference(extension,[status(thm),parent(t4:3)],[left_identity]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
product(inverse(a),a,identity),
inference(extension,[status(thm),parent(t4:4)],[left_inverse]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
( ~ product(inverse(a),a,multiply(inverse(a),a))
| ~ product(identity,a,a)
| ~ product(inverse(inverse(a)),inverse(a),identity)
| product(inverse(inverse(a)),multiply(inverse(a),a),a) ),
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(inverse(inverse(a)),inverse(a),identity),
inference(extension,[status(thm),parent(t12:2)],[left_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
product(identity,a,a),
inference(extension,[status(thm),parent(t12:3)],[left_identity]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
product(inverse(a),a,multiply(inverse(a),a)),
inference(extension,[status(thm),parent(t12:4)],[total_function1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
( ~ product(inverse(a),a,identity)
| ~ product(inverse(a),a,multiply(inverse(a),a))
| ~ product(identity,inverse(a),inverse(a))
| product(identity,identity,multiply(inverse(a),a)) ),
inference(extension,[status(thm),parent(t2:4)],[associativity1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:4]) ).
cnf(t22,plain,
product(identity,inverse(a),inverse(a)),
inference(extension,[status(thm),parent(t20:2)],[left_identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
product(inverse(a),a,multiply(inverse(a),a)),
inference(extension,[status(thm),parent(t20:3)],[total_function1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
product(inverse(a),a,identity),
inference(extension,[status(thm),parent(t20:4)],[left_inverse]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_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
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 19 08:34:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 6.34/6.70 % SZS status Unsatisfiable for theBenchmark
% 6.34/6.70 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------