%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT263-1 : 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 : n015.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 242.95s 32.98s
% Output : CNFRefutation 242.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 38 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 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 : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_660,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_conjecture_0,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_661,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_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_662,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]) ).
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_663,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_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_664,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_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_665,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_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_670,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_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_671,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]) ).
cnf(c_17215,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_663,c_660]) ).
cnf(c_4589,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_671,c_17215]) ).
cnf(c_4590,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_671,c_661]) ).
cnf(c_17216,plain,
( c_in(c_Tarski_Olub(A,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(A,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ 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(resolve,[status(thm)],[c_670,c_664]) ).
cnf(c_17217,plain,
( c_in(c_Tarski_Olub(A,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),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_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(paramod,[status(thm)],[c_662,c_17216]) ).
cnf(c_17218,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_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(paramod,[status(thm)],[c_662,c_17217]) ).
cnf(c_5011,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_665,c_17218]) ).
cnf(c_17219,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_5011,c_4590]) ).
cnf(c_17214,plain,
$false,
inference(resolve,[status(thm)],[c_4589,c_17219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT263-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 20:25:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2139317 was started by sandbox2 on n015,
% 0.11/0.38 % Fri Sep 25 20:25:12 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 242.95/32.98
% 242.95/32.98 % given #500 (I,wt=9): 990 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # tptp_name(clsrel_Ring__and__Field_Oordered__idom_37) # clausal_fof(1). [assumption].
% 242.95/32.98
% 242.95/32.98 % given #1000 (I,wt=7): 1490 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) # tptp_name(clsarity_Product____Type__Ounit_0) # clausal_fof(1). [assumption].
% 242.95/32.98
% 242.95/32.98 % given #1500 (I,wt=22): 2247 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_uminus(C,A) | B = C # tptp_name(cls_OrderedGroup_Oneg__equal__iff__equal_0) # clausal_fof(1). [assumption].
% 242.95/32.98
% 242.95/32.98 % given #2000 (I,wt=19): 3072 -c_List_Odistinct(c_append(A,B,C),C) | c_List_Odistinct(B,C) # tptp_name(cls_List_Odistinct__append_1) # clausal_fof(1). [assumption].
% 242.95/32.98
% 242.95/32.98 % given #2500 (I,wt=38): 3874 -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_emptyset = B | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [copy(3873),flip(c)].
% 242.95/32.98
% 242.95/32.98 % given #3000 (I,wt=37): 4629 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_minus(C,c_uminus(A,tc_set(B)),tc_set(B)),c_Finite__Set_OFinites,tc_set(B)). [back_rewrite(1657),rewrite([1864(4)])].
% 242.95/32.98
% 242.95/32.98 % SZS status Unsatisfiable for theBenchmark
% 242.95/32.98
% 242.95/32.98 % Proof 1 at 6.67 (+ 0.74) seconds.
% 242.95/32.98 % Length of proof is 12.
% 242.95/32.98 % Level of proof is 2.
% 242.95/32.98 % Maximum clause weight is 40.000.
% 242.95/32.98 % Given clauses 3434.
% 242.95/32.98
% 242.95/32.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------