%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 08:41:07 AM UTC 2026
% Result : Unsatisfiable 3.14s 3.48s
% Output : Proof 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 25 unt; 0 nHn; 28 RR)
% Number of literals : 45 ( 0 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
product(X,identity,X),
file('GRP003-0.ax',right_identity) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('GRP003-0.ax',total_function1) ).
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(squareness,hypothesis,
product(A,A,identity),
file('theBenchmark.p',squareness) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('theBenchmark.p',a_times_b_is_c) ).
cnf(inverse_a_times_inverse_b_is_d,hypothesis,
product(inverse(a),inverse(b),d),
file('theBenchmark.p',inverse_a_times_inverse_b_is_d) ).
cnf(inverses_have_property,hypothesis,
( product(A,C,B)
| ~ product(inverse(A),inverse(B),C) ),
file('theBenchmark.p',inverses_have_property) ).
cnf(prove_c_times_d_is_identity,negated_conjecture,
~ product(c,d,identity),
file('theBenchmark.p',prove_c_times_d_is_identity) ).
cnf(t1,plain,
~ product(c,d,identity),
inference(start,[status(thm),parent(0:0)],[prove_c_times_d_is_identity]) ).
cnf(t2,plain,
( ~ product(a,d,b)
| ~ product(multiply(c,a),b,identity)
| ~ product(multiply(c,a),a,c)
| product(c,d,identity) ),
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(a,a,identity)
| ~ product(c,identity,c)
| ~ product(c,a,multiply(c,a))
| product(multiply(c,a),a,c) ),
inference(extension,[status(thm),parent(t2:2)],[associativity2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
product(c,a,multiply(c,a)),
inference(extension,[status(thm),parent(t4:2)],[total_function1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
product(c,identity,c),
inference(extension,[status(thm),parent(t4:3)],[right_identity]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
product(a,a,identity),
inference(extension,[status(thm),parent(t4:4)],[squareness]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
( ~ product(a,b,c)
| ~ product(c,c,identity)
| ~ product(c,a,multiply(c,a))
| product(multiply(c,a),b,identity) ),
inference(extension,[status(thm),parent(t2:3)],[associativity2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
product(c,a,multiply(c,a)),
inference(extension,[status(thm),parent(t12:2)],[total_function1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
product(c,c,identity),
inference(extension,[status(thm),parent(t12:3)],[squareness]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t12:4)],[a_times_b_is_c]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
( ~ product(inverse(a),inverse(b),d)
| product(a,d,b) ),
inference(extension,[status(thm),parent(t2:4)],[inverses_have_property]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:4]) ).
cnf(t22,plain,
product(inverse(a),inverse(b),d),
inference(extension,[status(thm),parent(t20:2)],[inverse_a_times_inverse_b_is_d]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % 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 : n026.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 : Sat Sep 19 08:33:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 3.14/3.48 % SZS status Unsatisfiable for theBenchmark
% 3.14/3.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------