%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA016-2 : 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 08:12:54 AM UTC 2026
% Result : Unsatisfiable 260.56s 260.89s
% Output : Proof 260.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of clauses : 70 ( 40 unt; 2 nHn; 66 RR)
% Number of literals : 112 ( 55 equ; 44 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
v_c != c_0,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_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_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(cls_Ring__and__Field_Oright__inverse_0,axiom,
( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
cnf(clsrel_Ring__and__Field_Ofield_12,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
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_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_4,axiom,
( v_g(Eq_x_0) = v_g(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_9,axiom,
( class_OrderedGroup_Osemigroup__mult(Eq_y_0)
| ~ class_OrderedGroup_Osemigroup__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_2]) ).
cnf(t2,plain,
( c_times(c_1,v_g(v_x),t_a) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)
| v_g(v_x) != c_times(c_1,v_g(v_x),t_a)
| v_g(v_x) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( c_times(c_1,v_g(v_x),t_a) != v_g(v_x)
| v_g(v_x) = c_times(c_1,v_g(v_x),t_a) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ class_OrderedGroup_Omonoid__mult(t_a)
| c_times(c_1,v_g(v_x),t_a) = v_g(v_x) ),
inference(extension,[status(thm),parent(t4:2)],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) ),
inference(extension,[status(thm),parent(t6:2)],[clsrel_Ring__and__Field_Ofield_12]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(extension,[status(thm),parent(t8:2)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(extension,[status(thm),parent(t10:2)],[tfree_tcs]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)
| c_times(c_1,v_g(v_x),t_a) != c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a)
| c_times(c_1,v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( v_g(v_x) != v_g(v_x)
| c_1 != c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a)
| t_a != t_a
| c_times(c_1,v_g(v_x),t_a) = c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) ),
inference(extension,[status(thm),parent(t14:2)],[equality_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t16:2)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
t_a = t_a,
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,
( c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) != c_1
| c_1 = c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) ),
inference(extension,[status(thm),parent(t16:3)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| v_c = c_0
| c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_1 ),
inference(extension,[status(thm),parent(t22:2)],[cls_Ring__and__Field_Oright__inverse_0]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( v_c != v_c
| v_c = c_0
| v_c != c_0 ),
inference(extension,[status(thm),parent(t24:2)],[equality_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
v_c != c_0,
inference(extension,[status(thm),parent(t26:2)],[cls_conjecture_0]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
v_c = v_c,
inference(extension,[status(thm),parent(t26:3)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(extension,[status(thm),parent(t24:3)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t24:3]) ).
cnf(t34,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(extension,[status(thm),parent(t32:2)],[tfree_tcs]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( v_g(v_x) != v_g(v_x)
| v_g(v_x) = v_g(v_x) ),
inference(extension,[status(thm),parent(t16:4)],[equality_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t16:4]) ).
cnf(t38,plain,
( v_x != v_x
| v_g(v_x) = v_g(v_x) ),
inference(extension,[status(thm),parent(t36:2)],[equality_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( v_x != v_x
| v_x = v_x ),
inference(extension,[status(thm),parent(t38:2)],[equality_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
v_x = v_x,
inference(extension,[status(thm),parent(t40:2)],[equality_1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t14:3)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t14:3]) ).
cnf(t46,plain,
( t_a != t_a
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| class_OrderedGroup_Osemigroup__mult(t_a) ),
inference(extension,[status(thm),parent(t44:2)],[equality_9]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| class_OrderedGroup_Osemigroup__mult(t_a) ),
inference(extension,[status(thm),parent(t46:2)],[clsrel_Ring__and__Field_Ofield_21]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(extension,[status(thm),parent(t48:2)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(extension,[status(thm),parent(t50:2)],[tfree_tcs]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t46:3)],[equality_1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t46:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n011.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 11:40:25 UTC 2026
% 0.20/0.46 % CPUTime :
% 260.56/260.89 % SZS status Unsatisfiable for theBenchmark
% 260.56/260.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------