%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n005.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 08:12:52 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 46 ( 30 unt; 0 nHn; 42 RR)
% Number of literals : 76 ( 33 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_lb(V_U),v_f(V_U),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_4,axiom,
( c_plus(Eq_x_0,Eq_x_1,Eq_x_2) = c_plus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_uminus(Eq_x_0,Eq_x_1) = c_uminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( v_f(Eq_x_0) = v_f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_lessequals(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_lessequals(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,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_2]) ).
cnf(t2,plain,
( c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b) != c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b)
| t_b != t_b
| ~ c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
| c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) != c_0
| c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t1:1)],[equality_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0 ),
inference(extension,[status(thm),parent(t2:2)],[cls_OrderedGroup_Oright__minus_0]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__group__add(t_b) ),
inference(extension,[status(thm),parent(t4:2)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t6:2)],[tfree_tcs]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ c_lessequals(v_lb(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:3)],[cls_OrderedGroup_Oadd__le__cancel__right_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(extension,[status(thm),parent(t10:2)],[clsrel_Ring__and__Field_Oordered__idom_37]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t12:2)],[tfree_tcs]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
c_lessequals(v_lb(v_x),v_f(v_x),t_b),
inference(extension,[status(thm),parent(t10:3)],[cls_conjecture_0]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:4]) ).
cnf(l9,lemma,
t_b = t_b,
inference(lemma,[status(cth),parent(t2:4),below(t1:1)],[t2:4]) ).
cnf(t20,plain,
( c_uminus(v_lb(v_x),t_b) != c_uminus(v_lb(v_x),t_b)
| t_b != t_b
| v_f(v_x) != v_f(v_x)
| c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:5)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:5]) ).
cnf(t22,plain,
( v_x != v_x
| v_f(v_x) = v_f(v_x) ),
inference(extension,[status(thm),parent(t20:2)],[equality_7]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
v_x = v_x,
inference(extension,[status(thm),parent(t22:2)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
t_b = t_b,
inference(lemma_extension,[status(thm),parent(t20:3)],[l9:1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:3]) ).
cnf(t28,plain,
( t_b != t_b
| v_lb(v_x) != v_lb(v_x)
| c_uminus(v_lb(v_x),t_b) = c_uminus(v_lb(v_x),t_b) ),
inference(extension,[status(thm),parent(t20:4)],[equality_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t20:4]) ).
cnf(t30,plain,
v_lb(v_x) = v_lb(v_x),
inference(extension,[status(thm),parent(t28:2)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
t_b = t_b,
inference(lemma_extension,[status(thm),parent(t28:3)],[l9:1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.09/0.36 % Computer : n005.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
% 0.09/0.36 % DateTime : Sun Sep 20 11:39:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------