%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT278-1 : 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 : n014.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 07:49:59 AM UTC 2026
% Result : Unsatisfiable 25.86s 9.18s
% Output : CNFRefutation 25.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 12 unt; 0 def)
% Number of atoms : 16 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_2234,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_OPartialOrder__iff_0,axiom,
! [VAR_0,VAR_1] :
( c_Relation_Orefl(c_Tarski_Opotype_Opset(VAR_0,VAR_1,tc_Product__Type_Ounit),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_0) ).
cnf(c_2235,plain,
( c_Relation_Orefl(c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),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_0]) ).
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_2239,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_2240,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_Relation_Orefl(v_A,v_r,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2241,plain,
~ c_Relation_Orefl(v_A,v_r,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_7274,plain,
~ c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_r,t_a),
inference(paramod,[status(thm)],[c_2234,c_2241]) ).
cnf(c_2242,plain,
~ 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(paramod,[status(thm)],[c_2240,c_7274]) ).
cnf(c_7275,plain,
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(resolve,[status(thm)],[c_2239,c_2235]) ).
cnf(c_7273,plain,
$false,
inference(resolve,[status(thm)],[c_2242,c_7275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT278-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n014.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 20:23:38 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1021431 was started by sandbox2 on n014,
% 0.10/5.38 % Fri Sep 25 20:23:38 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.46
% 0.14/5.46 % From the command line: assign(max_seconds, 300).
% 25.86/9.18
% 25.86/9.18 % given #500 (I,wt=3): 1402 c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) # tptp_name(cls_Wellfounded__Relations_Otrans__less__than_0) # clausal_fof(1). [assumption].
% 25.86/9.18
% 25.86/9.18 % given #1000 (I,wt=4): 1902 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # tptp_name(clsrel_Ring__and__Field_Oordered__field_35) # clausal_fof(1). [assumption].
% 25.86/9.18
% 25.86/9.18 % SZS status Unsatisfiable for theBenchmark
% 25.86/9.18
% 25.86/9.18 % Proof 1 at 3.52 (+ 0.14) seconds.
% 25.86/9.18 % Length of proof is 7.
% 25.86/9.18 % Level of proof is 2.
% 25.86/9.18 % Maximum clause weight is 16.000.
% 25.86/9.18 % Given clauses 1337.
% 25.86/9.18
% 25.86/9.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------