%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT269-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 07:49:57 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 30 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0,axiom,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
file('theBenchmark.p',cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0) ).
cnf(c_2,plain,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
inference(clausify,[status(thm)],[cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0]) ).
fof(cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1] :
( c_Tarski_Ointerval(v_r,VAR_1,VAR_0,t_a) = c_emptyset
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,VAR_1,VAR_0,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,VAR_1,VAR_0,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(VAR_1,v_A,t_a)
| ~ c_in(VAR_0,v_A,t_a) ),
file('theBenchmark.p',cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
cnf(c_3,plain,
( c_Tarski_Ointerval(v_r,B,A,t_a) = c_emptyset
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,B,A,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,B,A,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(B,v_A,t_a)
| ~ c_in(A,v_A,t_a) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0]) ).
fof(cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0,axiom,
v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),
file('theBenchmark.p',cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0) ).
cnf(c_4,plain,
v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),
inference(clausify,[status(thm)],[cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0]) ).
fof(cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0,axiom,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
file('theBenchmark.p',cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0) ).
cnf(c_5,plain,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
inference(clausify,[status(thm)],[cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0]) ).
fof(cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0,axiom,
! [VAR_0] :
( c_Tarski_Ointerval(v_r,VAR_0,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset
| ~ c_in(VAR_0,v_A,t_a) ),
file('theBenchmark.p',cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0) ).
cnf(c_6,plain,
( c_Tarski_Ointerval(v_r,A,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset
| ~ c_in(A,v_A,t_a) ),
inference(clausify,[status(thm)],[cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0]) ).
cnf(c_18,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_8,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(paramod,[status(thm)],[c_4,c_18]) ).
cnf(c_9,plain,
( c_Tarski_Ointerval(v_r,A,c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,A,c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,A,c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(A,v_A,t_a) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_13,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset,
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_19,plain,
( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_20,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset,
inference(resolve,[status(thm)],[c_8,c_19]) ).
cnf(c_17,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT269-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 : Fri Sep 25 20:22:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 108855 was started by sandbox2 on n005,
% 0.10/0.37 % Fri Sep 25 20:22:18 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 10.
% 0.10/0.38 % Level of proof is 2.
% 0.10/0.38 % Maximum clause weight is 39.000.
% 0.10/0.38 % Given clauses 8.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------