%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN008-1 : 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 : 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 08:42:30 AM UTC 2026
% Result : Unsatisfiable 256.67s 257.12s
% Output : Proof 256.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of clauses : 86 ( 62 unt; 0 nHn; 83 RR)
% Number of literals : 138 ( 37 equ; 54 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('HEN001-0.ax',quotient_less_equal) ).
cnf(less_equal_quotient,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('HEN001-0.ax',less_equal_quotient) ).
cnf(quotient_property,axiom,
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('HEN001-0.ax',quotient_property) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X),
file('HEN001-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('HEN001-0.ax',less_equal_and_equal) ).
cnf(closure,axiom,
quotient(X,Y,divide(X,Y)),
file('HEN001-0.ax',closure) ).
cnf(well_defined,axiom,
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('HEN001-0.ax',well_defined) ).
cnf(aLEb,hypothesis,
less_equal(a,b),
file('theBenchmark.p',aLEb) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc),
file('theBenchmark.p',aQc) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc),
file('theBenchmark.p',bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc),
file('theBenchmark.p',prove_aQcLEbQc) ).
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_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_6,axiom,
( quotient(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ quotient(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ less_equal(aQc,bQc),
inference(start,[status(thm),parent(0:0)],[prove_aQcLEbQc]) ).
cnf(t2,plain,
( ~ quotient(aQc,bQc,zero)
| less_equal(aQc,bQc) ),
inference(extension,[status(thm),parent(t1:1)],[less_equal_quotient]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( divide(a,c) != aQc
| divide(divide(a,c),bQc) != zero
| ~ quotient(divide(a,c),bQc,divide(divide(a,c),bQc))
| bQc != bQc
| quotient(aQc,bQc,zero) ),
inference(extension,[status(thm),parent(t2:2)],[equality_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
bQc = bQc,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
quotient(divide(a,c),bQc,divide(divide(a,c),bQc)),
inference(extension,[status(thm),parent(t4:3)],[closure]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( zero != divide(divide(a,c),bQc)
| divide(divide(a,c),bQc) = zero ),
inference(extension,[status(thm),parent(t4:4)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
( ~ less_equal(zero,divide(divide(a,c),bQc))
| ~ less_equal(divide(divide(a,c),bQc),zero)
| zero = divide(divide(a,c),bQc) ),
inference(extension,[status(thm),parent(t10:2)],[less_equal_and_equal]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ quotient(a,b,zero)
| ~ quotient(zero,c,zero)
| ~ quotient(a,c,divide(a,c))
| ~ quotient(divide(a,c),divide(b,c),divide(divide(a,c),bQc))
| ~ quotient(b,c,divide(b,c))
| less_equal(divide(divide(a,c),bQc),zero) ),
inference(extension,[status(thm),parent(t12:2)],[quotient_property]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
quotient(b,c,divide(b,c)),
inference(extension,[status(thm),parent(t14:2)],[closure]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( divide(a,c) != divide(a,c)
| divide(divide(a,c),divide(b,c)) != divide(divide(a,c),bQc)
| ~ quotient(divide(a,c),divide(b,c),divide(divide(a,c),divide(b,c)))
| divide(b,c) != divide(b,c)
| quotient(divide(a,c),divide(b,c),divide(divide(a,c),bQc)) ),
inference(extension,[status(thm),parent(t14:3)],[equality_6]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
divide(b,c) = divide(b,c),
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,
quotient(divide(a,c),divide(b,c),divide(divide(a,c),divide(b,c))),
inference(extension,[status(thm),parent(t18:3)],[closure]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( divide(b,c) != bQc
| divide(a,c) != divide(a,c)
| divide(divide(a,c),divide(b,c)) = divide(divide(a,c),bQc) ),
inference(extension,[status(thm),parent(t18:4)],[equality_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:4]) ).
cnf(t26,plain,
divide(a,c) = divide(a,c),
inference(extension,[status(thm),parent(t24:2)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ quotient(b,c,bQc)
| ~ quotient(b,c,divide(b,c))
| divide(b,c) = bQc ),
inference(extension,[status(thm),parent(t24:3)],[well_defined]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
quotient(b,c,divide(b,c)),
inference(extension,[status(thm),parent(t28:2)],[closure]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
quotient(b,c,bQc),
inference(extension,[status(thm),parent(t28:3)],[bQc]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
divide(a,c) = divide(a,c),
inference(extension,[status(thm),parent(t18:5)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t18:5]) ).
cnf(t36,plain,
quotient(a,c,divide(a,c)),
inference(extension,[status(thm),parent(t14:4)],[closure]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t14:4]) ).
cnf(t38,plain,
( ~ less_equal(zero,c)
| quotient(zero,c,zero) ),
inference(extension,[status(thm),parent(t14:5)],[quotient_less_equal]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t14:5]) ).
cnf(t40,plain,
less_equal(zero,c),
inference(extension,[status(thm),parent(t38:2)],[zero_is_smallest]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( ~ less_equal(a,b)
| quotient(a,b,zero) ),
inference(extension,[status(thm),parent(t14:6)],[quotient_less_equal]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t14:6]) ).
cnf(t44,plain,
less_equal(a,b),
inference(extension,[status(thm),parent(t42:2)],[aLEb]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( ~ quotient(zero,divide(divide(a,c),bQc),zero)
| less_equal(zero,divide(divide(a,c),bQc)) ),
inference(extension,[status(thm),parent(t12:3)],[less_equal_quotient]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t12:3]) ).
cnf(t48,plain,
( zero != zero
| divide(zero,divide(divide(a,c),bQc)) != zero
| ~ quotient(zero,divide(divide(a,c),bQc),divide(zero,divide(divide(a,c),bQc)))
| divide(divide(a,c),bQc) != divide(divide(a,c),bQc)
| quotient(zero,divide(divide(a,c),bQc),zero) ),
inference(extension,[status(thm),parent(t46:2)],[equality_6]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
divide(divide(a,c),bQc) = divide(divide(a,c),bQc),
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,
quotient(zero,divide(divide(a,c),bQc),divide(zero,divide(divide(a,c),bQc))),
inference(extension,[status(thm),parent(t48:3)],[closure]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).
cnf(t54,plain,
( ~ quotient(zero,divide(divide(a,c),bQc),zero)
| ~ quotient(zero,divide(divide(a,c),bQc),divide(zero,divide(divide(a,c),bQc)))
| divide(zero,divide(divide(a,c),bQc)) = zero ),
inference(extension,[status(thm),parent(t48:4)],[well_defined]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t48:4]) ).
cnf(t56,plain,
quotient(zero,divide(divide(a,c),bQc),divide(zero,divide(divide(a,c),bQc))),
inference(extension,[status(thm),parent(t54:2)],[closure]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( ~ less_equal(zero,divide(divide(a,c),bQc))
| quotient(zero,divide(divide(a,c),bQc),zero) ),
inference(extension,[status(thm),parent(t54:3)],[quotient_less_equal]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
less_equal(zero,divide(divide(a,c),bQc)),
inference(extension,[status(thm),parent(t58:2)],[zero_is_smallest]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
zero = zero,
inference(extension,[status(thm),parent(t48:5)],[equality_1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t48:5]) ).
cnf(t64,plain,
( aQc != divide(a,c)
| divide(a,c) = aQc ),
inference(extension,[status(thm),parent(t4:5)],[equality_2]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t4:5]) ).
cnf(t66,plain,
( ~ quotient(a,c,divide(a,c))
| ~ quotient(a,c,aQc)
| aQc = divide(a,c) ),
inference(extension,[status(thm),parent(t64:2)],[well_defined]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
quotient(a,c,aQc),
inference(extension,[status(thm),parent(t66:2)],[aQc]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
quotient(a,c,divide(a,c)),
inference(extension,[status(thm),parent(t66:3)],[closure]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t66:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n004.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sat Sep 19 10:40:05 UTC 2026
% 0.10/0.58 % CPUTime :
% 256.67/257.12 % SZS status Unsatisfiable for theBenchmark
% 256.67/257.12 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------