%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA045-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n011.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 08:12:59 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 44 ( 27 unt; 0 nHn; 42 RR)
% Number of literals : 70 ( 28 equ; 28 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
( V_c = c_times(c_1,V_c,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
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_8,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_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_0]) ).
cnf(t2,plain,
( c_HOL_Oabs(v_g(v_x(c_1)),t_b) != c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b)
| t_b != t_b
| ~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b)
| c_0 != c_0
| c_lessequals(c_0,c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t1:1)],[equality_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( c_times(c_1,c_0,t_b) != c_0
| c_0 != c_times(c_1,c_0,t_b)
| c_0 = c_0 ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
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)
| c_0 = c_times(c_1,c_0,t_b) ),
inference(extension,[status(thm),parent(t4:2)],[cls_Ring__and__Field_Omult__cancel__right1_2]) ).
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_0 != c_times(c_1,c_0,t_b)
| c_times(c_1,c_0,t_b) = c_0 ),
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,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| c_0 = c_times(c_1,c_0,t_b) ),
inference(extension,[status(thm),parent(t10:2)],[cls_Ring__and__Field_Omult__cancel__right1_2]) ).
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,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:3)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(extension,[status(thm),parent(t16:2)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t18:2)],[tfree_tcs]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( c_times(c_1,t_b,t_b) != t_b
| t_b != c_times(c_1,t_b,t_b)
| t_b = t_b ),
inference(extension,[status(thm),parent(t2:4)],[equality_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:4]) ).
cnf(t24,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| t_b = c_times(c_1,t_b,t_b) ),
inference(extension,[status(thm),parent(t22:2)],[cls_Ring__and__Field_Omult__cancel__right1_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t24:2)],[tfree_tcs]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(l12,lemma,
t_b = c_times(c_1,t_b,t_b),
inference(lemma,[status(cth),parent(t22:2),below(t2:4)],[t22:2]) ).
cnf(t28,plain,
( t_b != c_times(c_1,t_b,t_b)
| c_times(c_1,t_b,t_b) = t_b ),
inference(extension,[status(thm),parent(t22:3)],[equality_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
t_b = c_times(c_1,t_b,t_b),
inference(lemma_extension,[status(thm),parent(t28:2)],[l12:1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| c_HOL_Oabs(v_g(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:5)],[cls_Ring__and__Field_Omult__cancel__right1_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t2:5]) ).
cnf(t34,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t32:2)],[tfree_tcs]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA045-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n011.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 20 12:00:40 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.18/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------