%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV254-2 : 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 : n004.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 09:03:06 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 24 unt; 0 nHn; 29 RR)
% Number of literals : 51 ( 32 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
cnf(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat),
file('theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
cnf(cls_Set_Oempty__not__insert_0,axiom,
c_emptyset != c_insert(V_a,V_A,T_a),
file('theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(V_U,v_x(V_U),tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
v_x(V_U) = v_nat,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(clsarity_nat_3,axiom,
class_Orderings_Oorder(tc_nat),
file('theBenchmark.p',clsarity_nat_3) ).
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,
( c_SetInterval_OatLeastLessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_OatLeastLessThan(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(t1,plain,
c_emptyset != c_insert(v_nat,c_emptyset,tc_nat),
inference(start,[status(thm),parent(0:0)],[cls_Set_Oempty__not__insert_0]) ).
cnf(t2,plain,
( c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) != c_insert(v_nat,c_emptyset,tc_nat)
| c_emptyset != c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat)
| c_emptyset = c_insert(v_nat,c_emptyset,tc_nat) ),
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_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) != c_emptyset
| c_emptyset = c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) ),
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,
( ~ c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) = c_emptyset ),
inference(extension,[status(thm),parent(t4:2)],[cls_SetInterval_OatLeastLessThan__empty_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
class_Orderings_Oorder(tc_nat),
inference(extension,[status(thm),parent(t6:2)],[clsarity_nat_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat),
inference(extension,[status(thm),parent(t6:3)],[cls_conjecture_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) != c_insert(v_nat,c_emptyset,tc_nat)
| c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) != c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat)
| c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) = c_insert(v_nat,c_emptyset,tc_nat) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( c_Suc(v_nat) != c_Suc(v_nat)
| tc_nat != tc_nat
| v_x(c_Suc(v_nat)) != v_nat
| c_SetInterval_OatLeastLessThan(v_x(c_Suc(v_nat)),c_Suc(v_nat),tc_nat) = c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) ),
inference(extension,[status(thm),parent(t12:2)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
v_x(c_Suc(v_nat)) = v_nat,
inference(extension,[status(thm),parent(t14:2)],[cls_conjecture_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
tc_nat = tc_nat,
inference(extension,[status(thm),parent(t14:3)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
c_Suc(v_nat) = c_Suc(v_nat),
inference(extension,[status(thm),parent(t14:4)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_insert(v_nat,c_emptyset,tc_nat),
inference(extension,[status(thm),parent(t12:3)],[cls_SetInterval_OatLeastLessThan__singleton_0]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t12:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV254-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 03:13:04 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------