%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT263-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:49:55 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 40 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(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(c_3,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(clausify,[status(thm)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]) ).
fof(cls_Tarski_OCL_Olub__in__lattice_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Tarski_Olub(VAR_2,VAR_0,VAR_1),c_Tarski_Opotype_Opset(VAR_0,VAR_1,tc_Product__Type_Ounit),VAR_1)
| ~ c_lessequals(VAR_2,c_Tarski_Opotype_Opset(VAR_0,VAR_1,tc_Product__Type_Ounit),tc_set(VAR_1))
| ~ c_in(VAR_0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(VAR_1,tc_Product__Type_Ounit))
| ~ c_in(VAR_0,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(VAR_1,tc_Product__Type_Ounit)) ),
file('theBenchmark.p',cls_Tarski_OCL_Olub__in__lattice_0) ).
cnf(c_4,plain,
( c_in(c_Tarski_Olub(C,A,B),c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),B)
| ~ c_lessequals(C,c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),tc_set(B))
| ~ c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_in(A,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit)) ),
inference(clausify,[status(thm)],[cls_Tarski_OCL_Olub__in__lattice_0]) ).
fof(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
cnf(c_5,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(clausify,[status(thm)],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0]) ).
fof(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
cnf(c_6,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(clausify,[status(thm)],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0]) ).
fof(cls_Tarski_Oglb__dual__lub_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Tarski_Oglb(VAR_0,VAR_1,VAR_2) = c_Tarski_Olub(VAR_0,c_Tarski_Odual(VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
cnf(c_7,plain,
c_Tarski_Oglb(A,B,C) = c_Tarski_Olub(A,c_Tarski_Odual(B,C),C),
inference(clausify,[status(thm)],[cls_Tarski_Oglb__dual__lub_0]) ).
fof(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,axiom,
! [VAR_0,VAR_1] : c_Tarski_Opotype_Opset(c_Tarski_Odual(VAR_0,VAR_1),VAR_1,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(VAR_0,VAR_1,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
cnf(c_8,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),
inference(clausify,[status(thm)],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0]) ).
cnf(c_14,plain,
~ c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_A,t_a),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_9,plain,
~ c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(paramod,[status(thm)],[c_3,c_14]) ).
cnf(c_10,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_15,plain,
( c_in(c_Tarski_Olub(C,c_Tarski_Odual(A,B),B),c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit),B)
| ~ c_lessequals(C,c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),tc_set(B))
| ~ c_in(c_Tarski_Odual(A,B),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(A,B),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit)) ),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_11,plain,
( c_in(c_Tarski_Olub(C,c_Tarski_Odual(A,B),B),c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),B)
| ~ c_lessequals(C,c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),tc_set(B))
| ~ c_in(c_Tarski_Odual(A,B),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(A,B),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit)) ),
inference(paramod,[status(thm)],[c_8,c_15]) ).
cnf(c_16,plain,
( c_in(c_Tarski_Olub(A,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(A,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(resolve,[status(thm)],[c_11,c_5]) ).
cnf(c_17,plain,
( c_in(c_Tarski_Olub(A,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(A,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_12,plain,
c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(resolve,[status(thm)],[c_17,c_10]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT263-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n016.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Fri Sep 25 20:26:44 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 3212571 was started by sandbox on n016,
% 0.20/0.45 % Fri Sep 25 20:26:44 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.45
% 0.20/0.45 % From the command line: assign(max_seconds, 300).
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.47
% 0.20/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.47 % Length of proof is 13.
% 0.20/0.47 % Level of proof is 3.
% 0.20/0.47 % Maximum clause weight is 36.000.
% 0.20/0.47 % Given clauses 9.
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------