%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA024-2 : 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 : n006.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 0.20s 5.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 22 unt; 0 nHn; 31 RR)
% Number of literals : 54 ( 15 equ; 22 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Ocompare__rls__10_0,axiom,
( V_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_k(V_U),v_f(V_U),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_0,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_7,axiom,
( v_f(Eq_x_0) = v_f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_3]) ).
cnf(t2,plain,
( ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(extension,[status(thm),parent(t1:1)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(extension,[status(thm),parent(t2:2)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
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),
inference(extension,[status(thm),parent(t4:2)],[tfree_tcs]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l2,lemma,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t8,plain,
( v_f(v_x) != v_f(v_x)
| t_b != t_b
| ~ c_lessequals(v_k(v_x),v_f(v_x),t_b)
| v_k(v_x) != c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b)
| c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(extension,[status(thm),parent(t2:3)],[equality_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| v_k(v_x) = c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) ),
inference(extension,[status(thm),parent(t8:2)],[cls_OrderedGroup_Ocompare__rls__10_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| class_OrderedGroup_Oab__group__add(t_b) ),
inference(extension,[status(thm),parent(t10:2)],[clsrel_OrderedGroup_Opordered__ab__group__add_0]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(lemma_extension,[status(thm),parent(t12:2)],[l2:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(extension,[status(thm),parent(t8:3)],[cls_conjecture_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:3]) ).
cnf(t18,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t8:4)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t8:4]) ).
cnf(t20,plain,
( v_x != v_x
| v_f(v_x) = v_f(v_x) ),
inference(extension,[status(thm),parent(t8:5)],[equality_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t8:5]) ).
cnf(t22,plain,
v_x = v_x,
inference(extension,[status(thm),parent(t20:2)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.47 % Computer : n006.cluster.edu
% 0.16/5.47 % Model : x86_64 x86_64
% 0.16/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.47 % Memory : 8046.5625MB
% 0.16/5.47 % OS : Linux 6.8.0-71-generic
% 0.16/5.47 % CPULimit : 300
% 0.16/5.47 % WCLimit : 300
% 0.16/5.47 % DateTime : Sun Sep 20 11:47:49 UTC 2026
% 0.16/5.48 % CPUTime :
% 0.20/5.53 % SZS status Unsatisfiable for theBenchmark
% 0.20/5.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------