%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA020-2 : 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 : n018.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 08:12:55 AM UTC 2026
% Result : Unsatisfiable 224.06s 224.36s
% Output : Proof 224.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of clauses : 157 ( 100 unt; 0 nHn; 155 RR)
% Number of literals : 247 ( 124 equ; 92 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
v_f(c_0) = c_0,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_less(c_0,v_c,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_3,negated_conjecture,
v_x = c_0,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( c_HOL_Oabs(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
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_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_Omult__nonneg__nonneg_0,axiom,
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
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_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(equality_13,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_4]) ).
cnf(t2,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| c_HOL_Oabs(v_f(c_0),t_a) != c_HOL_Oabs(v_f(v_x),t_a)
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) != c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| t_a != t_a
| c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
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_a != t_a
| t_a = 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,
t_a = t_a,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) != c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( t_a != t_a
| c_HOL_Oabs(v_h(v_x),t_a) != c_HOL_Oabs(v_h(v_x),t_a)
| v_c != v_c
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t8:2)],[equality_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( v_c != v_c
| v_c = v_c ),
inference(extension,[status(thm),parent(t10:2)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
v_c = v_c,
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_HOL_Oabs(v_h(v_x),t_a) != c_HOL_Oabs(v_h(v_x),t_a)
| c_HOL_Oabs(v_h(v_x),t_a) = c_HOL_Oabs(v_h(v_x),t_a) ),
inference(extension,[status(thm),parent(t10:3)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
( v_h(v_x) != v_h(v_x)
| t_a != t_a
| c_HOL_Oabs(v_h(v_x),t_a) = c_HOL_Oabs(v_h(v_x),t_a) ),
inference(extension,[status(thm),parent(t16:2)],[equality_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t18:2)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t20:2)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( v_h(v_x) != v_h(v_x)
| v_h(v_x) = v_h(v_x) ),
inference(extension,[status(thm),parent(t18:3)],[equality_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:3]) ).
cnf(t26,plain,
v_h(v_x) = v_h(v_x),
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_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t10:4)],[equality_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t10:4]) ).
cnf(t30,plain,
t_a = t_a,
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_HOL_Oabs(v_f(v_x),t_a) != c_HOL_Oabs(v_f(c_0),t_a)
| c_HOL_Oabs(v_f(c_0),t_a) = c_HOL_Oabs(v_f(v_x),t_a) ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t2:4]) ).
cnf(t34,plain,
( v_f(v_x) != v_f(c_0)
| t_a != t_a
| c_HOL_Oabs(v_f(v_x),t_a) = c_HOL_Oabs(v_f(c_0),t_a) ),
inference(extension,[status(thm),parent(t32:2)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t34:2)],[equality_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t36:2)],[equality_1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( v_f(c_0) != v_f(v_x)
| v_f(v_x) = v_f(c_0) ),
inference(extension,[status(thm),parent(t34:3)],[equality_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t34:3]) ).
cnf(t42,plain,
( c_0 != v_x
| v_f(c_0) = v_f(v_x) ),
inference(extension,[status(thm),parent(t40:2)],[equality_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( v_x != c_0
| c_0 = v_x ),
inference(extension,[status(thm),parent(t42:2)],[equality_2]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
v_x = c_0,
inference(extension,[status(thm),parent(t44:2)],[cls_conjecture_3]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( ~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| c_HOL_Oabs(c_0,t_a) != c_HOL_Oabs(v_f(c_0),t_a)
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) != c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| t_a != t_a
| c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(extension,[status(thm),parent(t2:5)],[equality_9]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t2:5]) ).
cnf(t50,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t48:2)],[equality_2]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t50:2)],[equality_1]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) != c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t48:3)],[equality_2]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t48:3]) ).
cnf(t56,plain,
( t_a != t_a
| c_HOL_Oabs(v_h(v_x),t_a) != c_HOL_Oabs(v_h(v_x),t_a)
| v_c != v_c
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t54:2)],[equality_7]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( v_c != v_c
| v_c = v_c ),
inference(extension,[status(thm),parent(t56:2)],[equality_2]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
v_c = v_c,
inference(extension,[status(thm),parent(t58:2)],[equality_1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( c_HOL_Oabs(v_h(v_x),t_a) != c_HOL_Oabs(v_h(v_x),t_a)
| c_HOL_Oabs(v_h(v_x),t_a) = c_HOL_Oabs(v_h(v_x),t_a) ),
inference(extension,[status(thm),parent(t56:3)],[equality_2]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t56:3]) ).
cnf(t64,plain,
( v_h(v_x) != v_h(v_x)
| t_a != t_a
| c_HOL_Oabs(v_h(v_x),t_a) = c_HOL_Oabs(v_h(v_x),t_a) ),
inference(extension,[status(thm),parent(t62:2)],[equality_5]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t64:2)],[equality_1]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
v_h(v_x) = v_h(v_x),
inference(extension,[status(thm),parent(t64:3)],[equality_1]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t56:4)],[equality_2]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t56:4]) ).
cnf(t72,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t70:2)],[equality_1]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
( c_HOL_Oabs(v_f(c_0),t_a) != c_HOL_Oabs(c_0,t_a)
| c_HOL_Oabs(c_0,t_a) = c_HOL_Oabs(v_f(c_0),t_a) ),
inference(extension,[status(thm),parent(t48:4)],[equality_2]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t48:4]) ).
cnf(t76,plain,
( v_f(c_0) != c_0
| t_a != t_a
| c_HOL_Oabs(v_f(c_0),t_a) = c_HOL_Oabs(c_0,t_a) ),
inference(extension,[status(thm),parent(t74:2)],[equality_5]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t76:2)],[equality_2]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t78:2)],[equality_1]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t78:2]) ).
cnf(t82,plain,
v_f(c_0) = c_0,
inference(extension,[status(thm),parent(t76:3)],[cls_conjecture_0]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t76:3]) ).
cnf(t84,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| c_0 != c_HOL_Oabs(c_0,t_a)
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) != c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| t_a != t_a
| c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(extension,[status(thm),parent(t48:5)],[equality_9]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t48:5]) ).
cnf(t86,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t84:2)],[equality_2]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t84:2]) ).
cnf(t88,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t86:2)],[equality_1]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t86:2]) ).
cnf(l43,lemma,
t_a = t_a,
inference(lemma,[status(cth),parent(t84:2),below(t48:5)],[t84:2]) ).
cnf(t90,plain,
( c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) != c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t84:3)],[equality_2]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t84:3]) ).
cnf(t92,plain,
( t_a != t_a
| c_HOL_Oabs(v_h(v_x),t_a) != c_HOL_Oabs(v_h(v_x),t_a)
| v_c != v_c
| c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t90:2)],[equality_7]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t90:2]) ).
cnf(t94,plain,
( v_c != v_c
| v_c = v_c ),
inference(extension,[status(thm),parent(t92:2)],[equality_2]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t92:2]) ).
cnf(t96,plain,
v_c = v_c,
inference(extension,[status(thm),parent(t94:2)],[equality_1]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t94:2]) ).
cnf(t98,plain,
( c_HOL_Oabs(v_h(v_x),t_a) != c_HOL_Oabs(v_h(v_x),t_a)
| c_HOL_Oabs(v_h(v_x),t_a) = c_HOL_Oabs(v_h(v_x),t_a) ),
inference(extension,[status(thm),parent(t92:3)],[equality_2]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t92:3]) ).
cnf(t100,plain,
c_HOL_Oabs(v_h(v_x),t_a) = c_HOL_Oabs(v_h(v_x),t_a),
inference(extension,[status(thm),parent(t98:2)],[equality_1]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t98:2]) ).
cnf(t102,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t92:4)],[equality_2]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t92:4]) ).
cnf(t104,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t102:2)],[equality_1]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t102:2]) ).
cnf(t106,plain,
( c_HOL_Oabs(c_0,t_a) != c_0
| c_0 = c_HOL_Oabs(c_0,t_a) ),
inference(extension,[status(thm),parent(t84:4)],[equality_2]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t84:4]) ).
cnf(t108,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_HOL_Oabs(c_0,t_a) = c_0 ),
inference(extension,[status(thm),parent(t106:2)],[cls_OrderedGroup_Oabs__eq__0_1]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t106:2]) ).
cnf(t110,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(extension,[status(thm),parent(t108:2)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t108:2]) ).
cnf(t112,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(extension,[status(thm),parent(t110:2)],[tfree_tcs]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t110:2]) ).
cnf(t114,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(extension,[status(thm),parent(t84:5)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t84:5]) ).
cnf(t116,plain,
( ~ class_Orderings_Oorder(t_a)
| ~ c_less(c_0,v_c,t_a)
| c_lessequals(c_0,v_c,t_a) ),
inference(extension,[status(thm),parent(t114:2)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t114:2]) ).
cnf(t118,plain,
c_less(c_0,v_c,t_a),
inference(extension,[status(thm),parent(t116:2)],[cls_conjecture_1]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t116:2]) ).
cnf(t120,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) ),
inference(extension,[status(thm),parent(t116:3)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t116:3]) ).
cnf(t122,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(extension,[status(thm),parent(t120:2)],[tfree_tcs]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t120:2]) ).
cnf(t124,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t114:3)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t114:3]) ).
cnf(t126,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(extension,[status(thm),parent(t124:2)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t124:2]) ).
cnf(t128,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(extension,[status(thm),parent(t126:2)],[tfree_tcs]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t126:2]) ).
cnf(t130,plain,
( t_a != t_a
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(extension,[status(thm),parent(t114:4)],[equality_13]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t114:4]) ).
cnf(t132,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(extension,[status(thm),parent(t130:2)],[clsrel_Ring__and__Field_Oordered__idom_40]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t130:2]) ).
cnf(t134,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(extension,[status(thm),parent(t132:2)],[tfree_tcs]) ).
cnf(t135,plain,
$false,
inference(connection,[status(thm),parent(t134:1)],[t134:1,t132:2]) ).
cnf(t136,plain,
t_a = t_a,
inference(lemma_extension,[status(thm),parent(t130:3)],[l43:1]) ).
cnf(t137,plain,
$false,
inference(connection,[status(thm),parent(t136:1)],[t136:1,t130:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA020-2 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n018.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 11:45:13 UTC 2026
% 0.11/0.36 % CPUTime :
% 224.06/224.36 % SZS status Unsatisfiable for theBenchmark
% 224.06/224.36 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------