%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA018-2 : 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 : n020.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 08:12:54 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.66s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 42 unt; 0 nHn; 64 RR)
% Number of literals : 112 ( 30 equ; 46 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_Orderings_Oorder__less__imp__le_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_LOrder_Ojoin__semilorder_1,axiom,
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
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(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_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_8,axiom,
( v_x(Eq_x_0) = v_x(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_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_4]) ).
cnf(t2,plain,
( c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b)
| t_b != t_b
| ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b)
| c_HOL_Oabs(v_x(v_xa),t_b) != c_HOL_Oabs(v_x(v_xa),t_b)
| c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),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,
( t_b != t_b
| v_x(v_xa) != v_x(v_xa)
| c_HOL_Oabs(v_x(v_xa),t_b) = c_HOL_Oabs(v_x(v_xa),t_b) ),
inference(extension,[status(thm),parent(t2:2)],[equality_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( v_xa != v_xa
| v_x(v_xa) = v_x(v_xa) ),
inference(extension,[status(thm),parent(t4:2)],[equality_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( v_xa != v_xa
| v_xa = v_xa ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
v_xa = v_xa,
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,
( t_b != t_b
| t_b = t_b ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:3)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( ~ class_LOrder_Ojoin__semilorder(t_b)
| class_Orderings_Oorder(t_b) ),
inference(extension,[status(thm),parent(t16:2)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
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)
| class_LOrder_Ojoin__semilorder(t_b) ),
inference(extension,[status(thm),parent(t18:2)],[clsrel_Ring__and__Field_Oordered__idom_35]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t20:2)],[tfree_tcs]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(l9,lemma,
class_Orderings_Oorder(t_b),
inference(lemma,[status(cth),parent(t16:2),below(t2:3)],[t16:2]) ).
cnf(t24,plain,
c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),t_b),
inference(extension,[status(thm),parent(t16:3)],[cls_conjecture_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
cnf(t26,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t16:4)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t16:4]) ).
cnf(t28,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(extension,[status(thm),parent(t26:2)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t28:2)],[tfree_tcs]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( ~ c_less(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(extension,[status(thm),parent(t26:3)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
class_Orderings_Oorder(t_b),
inference(lemma_extension,[status(thm),parent(t32:2)],[l9:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
c_less(c_0,v_ca,t_b),
inference(extension,[status(thm),parent(t32:3)],[cls_conjecture_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(extension,[status(thm),parent(t26:4)],[cls_conjecture_1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t26:4]) ).
cnf(t40,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t2:4]) ).
cnf(t42,plain,
( c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b) != c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b)
| c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) = c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b) ),
inference(extension,[status(thm),parent(t2:5)],[equality_2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t2:5]) ).
cnf(t44,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b) = c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) ),
inference(extension,[status(thm),parent(t42:2)],[cls_OrderedGroup_Omult__ac__1_0]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(extension,[status(thm),parent(t44:2)],[clsrel_Ring__and__Field_Oordered__idom_21]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(extension,[status(thm),parent(t46:2)],[tfree_tcs]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n020.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sun Sep 20 11:46:17 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.13/0.66 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------