%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN004-4 : 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 : n004.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 08:42:28 AM UTC 2026
% Result : Unsatisfiable 240.36s 245.71s
% Output : Proof 240.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of clauses : 85 ( 57 unt; 0 nHn; 77 RR)
% Number of literals : 131 ( 70 equ; 48 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('HEN002-0.ax',quotient_less_equal1) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('HEN002-0.ax',quotient_less_equal2) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X,Y),X),
file('HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('HEN002-0.ax',quotient_property) ).
cnf(less_equal_and_equal,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('HEN002-0.ax',less_equal_and_equal) ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X) = zero,
file('theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(prove_x_divide_zero_is_x,negated_conjecture,
divide(a,zero) != a,
file('theBenchmark.p',prove_x_divide_zero_is_x) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_4,axiom,
( divide(Eq_x_0,Eq_x_1) = divide(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( less_equal(Eq_y_0,Eq_y_1)
| ~ less_equal(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
divide(a,zero) != a,
inference(start,[status(thm),parent(0:0)],[prove_x_divide_zero_is_x]) ).
cnf(t2,plain,
( ~ less_equal(divide(a,zero),a)
| ~ less_equal(a,divide(a,zero))
| divide(a,zero) = a ),
inference(extension,[status(thm),parent(t1:1)],[less_equal_and_equal]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( divide(a,divide(a,zero)) != zero
| less_equal(a,divide(a,zero)) ),
inference(extension,[status(thm),parent(t2:2)],[quotient_less_equal2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( divide(a,divide(a,zero)) != divide(zero,divide(a,zero))
| divide(zero,divide(a,zero)) != zero
| divide(a,divide(a,zero)) = zero ),
inference(extension,[status(thm),parent(t4:2)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
divide(zero,divide(a,zero)) = zero,
inference(extension,[status(thm),parent(t6:2)],[zero_divide_anything_is_zero]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(l4,lemma,
divide(zero,divide(a,zero)) = zero,
inference(lemma,[status(cth),parent(t6:2),below(t4:2)],[t6:2]) ).
cnf(t10,plain,
( ~ less_equal(divide(a,divide(a,zero)),divide(zero,divide(a,zero)))
| ~ less_equal(divide(zero,divide(a,zero)),divide(a,divide(a,zero)))
| divide(a,divide(a,zero)) = divide(zero,divide(a,zero)) ),
inference(extension,[status(thm),parent(t6:3)],[less_equal_and_equal]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( divide(divide(zero,divide(a,zero)),divide(a,divide(a,zero))) != zero
| less_equal(divide(zero,divide(a,zero)),divide(a,divide(a,zero))) ),
inference(extension,[status(thm),parent(t10:2)],[quotient_less_equal2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( divide(divide(zero,divide(a,zero)),divide(a,divide(a,zero))) != divide(zero,divide(a,divide(a,zero)))
| divide(zero,divide(a,divide(a,zero))) != zero
| divide(divide(zero,divide(a,zero)),divide(a,divide(a,zero))) = zero ),
inference(extension,[status(thm),parent(t12:2)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
divide(zero,divide(a,divide(a,zero))) = zero,
inference(extension,[status(thm),parent(t14:2)],[zero_divide_anything_is_zero]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( divide(zero,divide(a,zero)) != zero
| divide(a,divide(a,zero)) != divide(a,divide(a,zero))
| divide(divide(zero,divide(a,zero)),divide(a,divide(a,zero))) = divide(zero,divide(a,divide(a,zero))) ),
inference(extension,[status(thm),parent(t14:3)],[equality_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
divide(a,divide(a,zero)) = divide(a,divide(a,zero)),
inference(extension,[status(thm),parent(t18:2)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
divide(zero,divide(a,zero)) = zero,
inference(lemma_extension,[status(thm),parent(t18:3)],[l4:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))) != zero
| less_equal(divide(a,divide(a,zero)),divide(zero,divide(a,zero))) ),
inference(extension,[status(thm),parent(t10:3)],[quotient_less_equal2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t10:3]) ).
cnf(t26,plain,
( ~ less_equal(divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),zero)
| ~ less_equal(zero,divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))))
| divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))) = zero ),
inference(extension,[status(thm),parent(t24:2)],[less_equal_and_equal]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( divide(zero,divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero)))) != zero
| less_equal(zero,divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero)))) ),
inference(extension,[status(thm),parent(t26:2)],[quotient_less_equal2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
divide(zero,divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero)))) = zero,
inference(extension,[status(thm),parent(t28:2)],[zero_divide_anything_is_zero]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( divide(divide(a,zero),divide(a,zero)) != zero
| ~ less_equal(divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),divide(divide(a,zero),divide(a,zero)))
| divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))) != divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero)))
| less_equal(divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),zero) ),
inference(extension,[status(thm),parent(t26:3)],[equality_5]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))) = divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),
inference(extension,[status(thm),parent(t32:2)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
less_equal(divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),divide(divide(a,zero),divide(a,zero))),
inference(extension,[status(thm),parent(t32:3)],[quotient_property]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
divide(divide(a,zero),divide(a,zero)) = zero,
inference(extension,[status(thm),parent(t32:4)],[x_divide_x_is_zero]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t32:4]) ).
cnf(t40,plain,
( divide(divide(a,zero),a) != zero
| less_equal(divide(a,zero),a) ),
inference(extension,[status(thm),parent(t2:3)],[quotient_less_equal2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t2:3]) ).
cnf(t42,plain,
( zero != divide(divide(a,zero),a)
| divide(divide(a,zero),a) = zero ),
inference(extension,[status(thm),parent(t40:2)],[equality_2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( zero != divide(divide(a,divide(zero,U_3596)),a)
| divide(divide(a,divide(zero,U_3596)),a) != divide(divide(a,zero),a)
| zero = divide(divide(a,zero),a) ),
inference(extension,[status(thm),parent(t42:2)],[equality_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( divide(a,divide(zero,U_3596)) != divide(a,zero)
| a != a
| divide(divide(a,divide(zero,U_3596)),a) = divide(divide(a,zero),a) ),
inference(extension,[status(thm),parent(t44:2)],[equality_4]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( a != a
| a = a ),
inference(extension,[status(thm),parent(t46:2)],[equality_2]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
a = a,
inference(extension,[status(thm),parent(t48:2)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( a != a
| divide(zero,U_3596) != zero
| divide(a,divide(zero,U_3596)) = divide(a,zero) ),
inference(extension,[status(thm),parent(t46:3)],[equality_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t46:3]) ).
cnf(t54,plain,
divide(zero,U_3596) = zero,
inference(extension,[status(thm),parent(t52:2)],[zero_divide_anything_is_zero]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
( a != a
| a = a ),
inference(extension,[status(thm),parent(t52:3)],[equality_2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
a = a,
inference(extension,[status(thm),parent(t56:2)],[equality_1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( divide(divide(a,divide(zero,U_3596)),a) != zero
| zero = divide(divide(a,divide(zero,U_3596)),a) ),
inference(extension,[status(thm),parent(t44:3)],[equality_2]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t44:3]) ).
cnf(t62,plain,
( ~ less_equal(divide(a,divide(zero,U_3596)),a)
| divide(divide(a,divide(zero,U_3596)),a) = zero ),
inference(extension,[status(thm),parent(t60:2)],[quotient_less_equal1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( a != a
| ~ less_equal(divide(a,divide(zero,U_3596)),a)
| divide(a,divide(zero,U_3596)) != divide(a,divide(zero,U_3596))
| less_equal(divide(a,divide(zero,U_3596)),a) ),
inference(extension,[status(thm),parent(t62:2)],[equality_5]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
divide(a,divide(zero,U_3596)) = divide(a,divide(zero,U_3596)),
inference(extension,[status(thm),parent(t64:2)],[equality_1]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
less_equal(divide(a,divide(zero,U_3596)),a),
inference(extension,[status(thm),parent(t64:3)],[quotient_smaller_than_numerator]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
a = a,
inference(extension,[status(thm),parent(t64:4)],[equality_1]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t64:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-4 : 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
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 19 10:37:49 UTC 2026
% 0.10/5.38 % CPUTime :
% 240.36/245.71 % SZS status Unsatisfiable for theBenchmark
% 240.36/245.71 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------