%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT277-2 : 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 : n005.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 08:48:01 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 60 ( 43 unt; 0 nHn; 59 RR)
% Number of literals : 96 ( 51 equ; 38 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_x,v_A,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Relation_OreflD_0,axiom,
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_Relation_OreflD_0) ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
cnf(cls_Tarski_OPartialOrder__iff_0,axiom,
( c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
file('theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
cnf(cls_Tarski_Ocl_A_58_APartialOrder_0,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_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_4,axiom,
( c_Pair(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Pair(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_in(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_in(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_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_1]) ).
cnf(t2,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| tc_prod(t_a,t_a) != tc_prod(t_a,t_a)
| ~ c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_Pair(v_x,v_x,t_a,t_a) != c_Pair(v_x,v_x,t_a,t_a)
| c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(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,
( v_x != v_x
| t_a != t_a
| t_a != t_a
| v_x != v_x
| c_Pair(v_x,v_x,t_a,t_a) = c_Pair(v_x,v_x,t_a,t_a) ),
inference(extension,[status(thm),parent(t2:2)],[equality_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( v_x != v_x
| v_x = v_x ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
v_x = v_x,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( t_a != t_a
| t_a = t_a ),
inference(extension,[status(thm),parent(t4:4)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:4]) ).
cnf(t16,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( v_x != v_x
| v_x = v_x ),
inference(extension,[status(thm),parent(t4:5)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:5]) ).
cnf(t20,plain,
v_x = v_x,
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_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(extension,[status(thm),parent(t2:3)],[cls_Relation_OreflD_0]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
cnf(t24,plain,
( ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(extension,[status(thm),parent(t22:2)],[cls_Tarski_OPartialOrder__iff_0]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(extension,[status(thm),parent(t24:2)],[cls_Tarski_Ocl_A_58_APartialOrder_0]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( v_A != c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)
| t_a != t_a
| ~ c_in(v_x,v_A,t_a)
| v_x != v_x
| c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(extension,[status(thm),parent(t22:3)],[equality_9]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
v_x = v_x,
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_in(v_x,v_A,t_a),
inference(extension,[status(thm),parent(t28:3)],[cls_conjecture_0]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t28:4)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(extension,[status(thm),parent(t28:5)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:5]) ).
cnf(t38,plain,
( t_a != t_a
| t_a != t_a
| tc_prod(t_a,t_a) = tc_prod(t_a,t_a) ),
inference(extension,[status(thm),parent(t2:4)],[equality_5]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t2:4]) ).
cnf(t40,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t38:2)],[equality_1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(l20,lemma,
t_a = t_a,
inference(lemma,[status(cth),parent(t38:2),below(t2:4)],[t38:2]) ).
cnf(t42,plain,
t_a = t_a,
inference(lemma_extension,[status(thm),parent(t38:3)],[l20:1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
( v_r != c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r ),
inference(extension,[status(thm),parent(t2:5)],[equality_2]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t2:5]) ).
cnf(t46,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(extension,[status(thm),parent(t44:2)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT277-2 : 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
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 13:00:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------