%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT281-1 : 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 : n011.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 07:50:00 AM UTC 2026
% Result : Unsatisfiable 75.11s 11.46s
% Output : CNFRefutation 75.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 33 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 16 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Relation_Otrans__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(c_Pair(VAR_4,VAR_3,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_4,VAR_2,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_2,VAR_3,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_Relation_Otrans(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_Relation_Otrans__def_0) ).
cnf(c_718,plain,
( c_in(c_Pair(E,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(E,C,B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_Relation_Otrans(A,B) ),
inference(clausify,[status(thm)],[cls_Relation_Otrans__def_0]) ).
fof(cls_Tarski_OPartialOrder__iff_2,axiom,
! [VAR_0,VAR_1] :
( c_Relation_Otrans(c_Tarski_Opotype_Oorder(VAR_0,VAR_1,tc_Product__Type_Ounit),VAR_1)
| ~ c_in(VAR_0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(VAR_1,tc_Product__Type_Ounit)) ),
file('theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).
cnf(c_726,plain,
( c_Relation_Otrans(c_Tarski_Opotype_Oorder(A,B,tc_Product__Type_Ounit),B)
| ~ c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit)) ),
inference(clausify,[status(thm)],[cls_Tarski_OPartialOrder__iff_2]) ).
fof(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(c_728,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(clausify,[status(thm)],[cls_Tarski_Ocl_A_58_APartialOrder_0]) ).
fof(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(c_729,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(clausify,[status(thm)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]) ).
fof(cls_conjecture_0,axiom,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_730,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_731,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(paramod,[status(thm)],[c_729,c_730]) ).
fof(cls_conjecture_1,axiom,
c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_732,plain,
c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_733,plain,
c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(paramod,[status(thm)],[c_729,c_732]) ).
fof(cls_conjecture_2,axiom,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_734,plain,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_735,plain,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(paramod,[status(thm)],[c_729,c_734]) ).
cnf(c_4732,plain,
c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(resolve,[status(thm)],[c_728,c_726]) ).
cnf(c_15941,plain,
( c_in(c_Pair(v_a,A,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_b,A,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(resolve,[status(thm)],[c_731,c_718]) ).
cnf(c_4735,plain,
( c_in(c_Pair(v_a,A,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_b,A,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_4732,c_15941]) ).
cnf(c_15942,plain,
c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_4735,c_733]) ).
cnf(c_15940,plain,
$false,
inference(resolve,[status(thm)],[c_735,c_15942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT281-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 20:23:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2800535 was started by sandbox2 on n011,
% 0.09/0.37 % Fri Sep 25 20:23:58 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.44
% 0.09/0.44 % From the command line: assign(max_seconds, 300).
% 75.11/11.46
% 75.11/11.46 % given #500 (I,wt=19): 821 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(60,a,8,a)].
% 75.11/11.46
% 75.11/11.46 % given #1000 (I,wt=23): 1523 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | c_emptyset = B. [copy(1522),flip(e)].
% 75.11/11.46
% 75.11/11.46 % given #1500 (I,wt=2): 2079 class_Divides_Odiv(tc_nat) # tptp_name(clsarity_nat_44) # clausal_fof(1). [assumption].
% 75.11/11.46
% 75.11/11.46 % given #2000 (I,wt=17): 2835 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A) # tptp_name(cls_OrderedGroup_Oneg__meet__eq__join_0) # clausal_fof(1). [assumption].
% 75.11/11.46
% 75.11/11.46 % given #2500 (I,wt=5): 3661 c_List_Odistinct(c_List_Oupt(A,B),tc_nat) # tptp_name(cls_List_Odistinct__upt_0) # clausal_fof(1). [assumption].
% 75.11/11.46
% 75.11/11.46 % given #3000 (I,wt=18): 4438 -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | -c_less(c_0,c_0,A) | c_less(c_HOL_Oinverse(c_0,A),c_HOL_Oinverse(B,A),A). [factor(2623,b,c)].
% 75.11/11.46
% 75.11/11.46 % SZS status Unsatisfiable for theBenchmark
% 75.11/11.46
% 75.11/11.46 % Proof 1 at 8.09 (+ 0.79) seconds.
% 75.11/11.46 % Length of proof is 13.
% 75.11/11.46 % Level of proof is 3.
% 75.11/11.46 % Maximum clause weight is 33.000.
% 75.11/11.46 % Given clauses 3228.
% 75.11/11.46
% 75.11/11.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------