%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA043-2 : 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 : n008.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 08:12:58 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.57s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of clauses : 69 ( 42 unt; 0 nHn; 65 RR)
% Number of literals : 115 ( 51 equ; 48 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
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_OrderedGroup_Omult__left__commute_0,axiom,
( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Omult__left__commute_0) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
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_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,
( v_f(Eq_x_0) = v_f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_HOL_Oabs(Eq_x_0,Eq_x_1) = c_HOL_Oabs(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,
( c_times(Eq_x_0,Eq_x_1,Eq_x_2) = c_times(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_10,axiom,
( v_l(Eq_x_0,Eq_x_1) = v_l(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_1]) ).
cnf(t2,plain,
( c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) != c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| t_b != t_b
| ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b) != c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t1:1)],[equality_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b) != c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b)
| t_b != t_b
| c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b) != c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b)
| c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b) = c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:2)],[equality_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( t_b != t_b
| v_l(v_x(v_c),v_xa(v_c)) != v_l(v_x(v_c),v_xa(v_c))
| c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b) = c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( v_xa(v_c) != v_xa(v_c)
| v_x(v_c) != v_x(v_c)
| v_l(v_x(v_c),v_xa(v_c)) = v_l(v_x(v_c),v_xa(v_c)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
v_x(v_c) = v_x(v_c),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
v_xa(v_c) = v_xa(v_c),
inference(extension,[status(thm),parent(t8:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( t_b != t_b
| t_b = t_b ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( t_b != t_b
| t_b = t_b ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:3]) ).
cnf(t20,plain,
t_b = t_b,
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,
( t_b != t_b
| v_f(v_k(v_x(v_c),v_xa(v_c))) != v_f(v_k(v_x(v_c),v_xa(v_c)))
| c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b) = c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b) ),
inference(extension,[status(thm),parent(t4:4)],[equality_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t4:4]) ).
cnf(t24,plain,
( v_k(v_x(v_c),v_xa(v_c)) != v_k(v_x(v_c),v_xa(v_c))
| v_f(v_k(v_x(v_c),v_xa(v_c))) = v_f(v_k(v_x(v_c),v_xa(v_c))) ),
inference(extension,[status(thm),parent(t22:2)],[equality_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
v_k(v_x(v_c),v_xa(v_c)) = v_k(v_x(v_c),v_xa(v_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,
( t_b != 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 = t_b,
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,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:3)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t2:3]) ).
cnf(t34,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(extension,[status(thm),parent(t32:2)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t34:2)],[tfree_tcs]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ),
inference(extension,[status(thm),parent(t32:3)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t32:3]) ).
cnf(t40,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(extension,[status(thm),parent(t38:2)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t40:2)],[tfree_tcs]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),
inference(extension,[status(thm),parent(t32:4)],[cls_conjecture_0]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t32:4]) ).
cnf(t46,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t2:4]) ).
cnf(t48,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:5)],[cls_OrderedGroup_Omult__left__commute_0]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t2:5]) ).
cnf(t50,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(extension,[status(thm),parent(t48:2)],[clsrel_Ring__and__Field_Oordered__idom_17]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t50:2)],[tfree_tcs]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA043-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n008.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Sun Sep 20 11:59:38 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.23/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------