%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP540-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 : n006.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 08:41:57 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 21 unt; 0 nHn; 29 RR)
% Number of literals : 47 ( 35 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,B),divide(divide(A,C),B)) = C,
file('theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('theBenchmark.p',multiply) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_5,axiom,
( multiply(Eq_x_0,Eq_x_1) = multiply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
multiply(a,b) != multiply(b,a),
inference(start,[status(thm),parent(0:0)],[prove_these_axioms_4]) ).
cnf(t2,plain,
( multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) != multiply(b,a)
| multiply(a,b) != multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a)))
| multiply(a,b) = multiply(b,a) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( b != divide(divide(b,a),divide(divide(b,b),a))
| a != divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a)))
| multiply(a,b) = multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))) != a
| a = divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))) = a,
inference(extension,[status(thm),parent(t6:2)],[single_axiom]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( divide(divide(b,a),divide(divide(b,b),a)) != b
| b = divide(divide(b,a),divide(divide(b,b),a)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
divide(divide(b,a),divide(divide(b,b),a)) = b,
inference(extension,[status(thm),parent(t10:2)],[single_axiom]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( divide(b,divide(divide(b,b),a)) != multiply(b,a)
| multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) != divide(b,divide(divide(b,b),a))
| multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) = multiply(b,a) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( divide(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a)))) != divide(b,divide(divide(b,b),a))
| multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) != divide(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))))
| multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) = divide(b,divide(divide(b,b),a)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
multiply(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a))) = divide(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a)))),
inference(extension,[status(thm),parent(t16:2)],[multiply]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
divide(divide(divide(b,divide(divide(b,b),a)),divide(divide(b,a),divide(divide(b,b),a))),divide(divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a))),divide(divide(b,a),divide(divide(b,b),a)))) = divide(b,divide(divide(b,b),a)),
inference(extension,[status(thm),parent(t16:3)],[single_axiom]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( multiply(b,a) != divide(b,divide(divide(b,b),a))
| divide(b,divide(divide(b,b),a)) = multiply(b,a) ),
inference(extension,[status(thm),parent(t14:3)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:3]) ).
cnf(t24,plain,
multiply(b,a) = divide(b,divide(divide(b,b),a)),
inference(extension,[status(thm),parent(t22:2)],[multiply]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP540-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ 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
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 19 09:41:12 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------