%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN011-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n020.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 08:42:32 AM UTC 2026
% Result : Unsatisfiable 8.45s 8.72s
% Output : Proof 8.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 43 ( 28 unt; 0 nHn; 39 RR)
% Number of literals : 65 ( 48 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X,Y),X) = zero,
file('HEN003-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_property,axiom,
divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
file('HEN003-0.ax',quotient_property) ).
cnf(divide_and_equal,axiom,
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
file('HEN003-0.ax',divide_and_equal) ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(transitivity_of_divide_to_zero,axiom,
( divide(X,Z) = zero
| divide(Y,Z) != zero
| divide(X,Y) != zero ),
file('theBenchmark.p',transitivity_of_divide_to_zero) ).
cnf(property_of_divide1,axiom,
( divide(divide(X,Z),Y) = zero
| divide(divide(X,Y),Z) != zero ),
file('theBenchmark.p',property_of_divide1) ).
cnf(property_of_divide2,axiom,
( divide(divide(Z,Y),divide(Z,X)) = zero
| divide(X,Y) != zero ),
file('theBenchmark.p',property_of_divide2) ).
cnf(prove_this,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
cnf(t1,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(start,[status(thm),parent(0:0)],[prove_this]) ).
cnf(t2,plain,
( divide(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b)))) != zero
| divide(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) != zero
| divide(divide(identity,a),divide(identity,divide(identity,b))) = divide(divide(identity,b),divide(identity,divide(identity,a))) ),
inference(extension,[status(thm),parent(t1:1)],[divide_and_equal]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( divide(divide(divide(identity,b),a),divide(divide(identity,b),divide(identity,divide(identity,a)))) != zero
| divide(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),a)) != zero
| divide(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) = zero ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_of_divide_to_zero]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( divide(divide(divide(identity,a),divide(divide(identity,b),a)),divide(identity,divide(identity,b))) != zero
| divide(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),a)) = zero ),
inference(extension,[status(thm),parent(t4:2)],[property_of_divide1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( divide(divide(divide(identity,divide(identity,b)),a),divide(identity,divide(identity,b))) != zero
| divide(divide(divide(identity,a),divide(divide(identity,b),a)),divide(divide(identity,divide(identity,b)),a)) != zero
| divide(divide(divide(identity,a),divide(divide(identity,b),a)),divide(identity,divide(identity,b))) = zero ),
inference(extension,[status(thm),parent(t6:2)],[transitivity_of_divide_to_zero]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
divide(divide(divide(identity,a),divide(divide(identity,b),a)),divide(divide(identity,divide(identity,b)),a)) = zero,
inference(extension,[status(thm),parent(t8:2)],[quotient_property]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
divide(divide(divide(identity,divide(identity,b)),a),divide(identity,divide(identity,b))) = zero,
inference(extension,[status(thm),parent(t8:3)],[quotient_smaller_than_numerator]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( divide(divide(identity,divide(identity,a)),a) != zero
| divide(divide(divide(identity,b),a),divide(divide(identity,b),divide(identity,divide(identity,a)))) = zero ),
inference(extension,[status(thm),parent(t4:3)],[property_of_divide2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:3]) ).
cnf(t16,plain,
( divide(divide(identity,a),divide(identity,a)) != zero
| divide(divide(identity,divide(identity,a)),a) = zero ),
inference(extension,[status(thm),parent(t14:2)],[property_of_divide1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
divide(divide(identity,a),divide(identity,a)) = zero,
inference(extension,[status(thm),parent(t16:2)],[x_divide_x_is_zero]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( divide(divide(divide(identity,a),b),divide(divide(identity,a),divide(identity,divide(identity,b)))) != zero
| divide(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),b)) != zero
| divide(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b)))) = zero ),
inference(extension,[status(thm),parent(t2:3)],[transitivity_of_divide_to_zero]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
cnf(t22,plain,
( divide(divide(divide(identity,b),divide(divide(identity,a),b)),divide(identity,divide(identity,a))) != zero
| divide(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),b)) = zero ),
inference(extension,[status(thm),parent(t20:2)],[property_of_divide1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( divide(divide(divide(identity,divide(identity,a)),b),divide(identity,divide(identity,a))) != zero
| divide(divide(divide(identity,b),divide(divide(identity,a),b)),divide(divide(identity,divide(identity,a)),b)) != zero
| divide(divide(divide(identity,b),divide(divide(identity,a),b)),divide(identity,divide(identity,a))) = zero ),
inference(extension,[status(thm),parent(t22:2)],[transitivity_of_divide_to_zero]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
divide(divide(divide(identity,b),divide(divide(identity,a),b)),divide(divide(identity,divide(identity,a)),b)) = zero,
inference(extension,[status(thm),parent(t24:2)],[quotient_property]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
divide(divide(divide(identity,divide(identity,a)),b),divide(identity,divide(identity,a))) = zero,
inference(extension,[status(thm),parent(t24:3)],[quotient_smaller_than_numerator]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
( divide(divide(identity,divide(identity,b)),b) != zero
| divide(divide(divide(identity,a),b),divide(divide(identity,a),divide(identity,divide(identity,b)))) = zero ),
inference(extension,[status(thm),parent(t20:3)],[property_of_divide2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t20:3]) ).
cnf(t32,plain,
( divide(divide(identity,b),divide(identity,b)) != zero
| divide(divide(identity,divide(identity,b)),b) = zero ),
inference(extension,[status(thm),parent(t30:2)],[property_of_divide1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
divide(divide(identity,b),divide(identity,b)) = zero,
inference(extension,[status(thm),parent(t32:2)],[x_divide_x_is_zero]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN011-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_NUE 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
% 0.09/0.36 % Computer : n020.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Sep 19 10:43:32 UTC 2026
% 0.13/0.36 % CPUTime :
% 8.45/8.72 % SZS status Unsatisfiable for theBenchmark
% 8.45/8.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------