%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ANA039-2 : 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 : n001.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 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 37 ( 22 unt; 0 nHn; 34 RR)
% Number of literals : 60 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Oabs__ge__self_0,axiom,
( c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
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__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_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0,axiom,
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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__right__mono_0) ).
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_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(t1,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_2]) ).
cnf(t2,plain,
( ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(extension,[status(thm),parent(t1:1)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
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_a)
| class_Orderings_Oorder(t_a) ),
inference(extension,[status(thm),parent(t2:2)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
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_a),
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(t8,plain,
c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(extension,[status(thm),parent(t2:3)],[cls_conjecture_0]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(extension,[status(thm),parent(t2:4)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:4]) ).
cnf(t12,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(extension,[status(thm),parent(t10:2)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(extension,[status(thm),parent(t12:2)],[tfree_tcs]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
inference(extension,[status(thm),parent(t10:3)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(extension,[status(thm),parent(t16:2)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
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_a),
inference(extension,[status(thm),parent(t18:2)],[tfree_tcs]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(extension,[status(thm),parent(t10:4)],[cls_OrderedGroup_Oabs__ge__self_0]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t10:4]) ).
cnf(t24,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(extension,[status(thm),parent(t22:2)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(extension,[status(thm),parent(t24:2)],[tfree_tcs]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 12:07:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------