%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET833-1 : 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 : n013.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 08:37:04 AM UTC 2026
% Result : Unsatisfiable 21.31s 3.40s
% Output : CNFRefutation 21.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_3,axiom,
~ c_in(v_x,v_V,t_a),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_1443,plain,
~ c_in(v_x,v_V,t_a),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
c_in(v_x,v_Z,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1444,plain,
c_in(v_x,v_Z,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(v_Z,v_V,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1445,plain,
c_lessequals(v_Z,v_V,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Set_OsubsetD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(c_1650,plain,
( c_in(A,D,C)
| ~ c_lessequals(B,D,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetD_0]) ).
cnf(c_2236,plain,
( c_in(v_x,A,t_a)
| ~ c_lessequals(v_Z,A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_1650,c_1444]) ).
cnf(c_2237,plain,
c_in(v_x,v_V,t_a),
inference(resolve,[status(thm)],[c_2236,c_1445]) ).
cnf(c_2235,plain,
$false,
inference(resolve,[status(thm)],[c_1443,c_2237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET833-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.58 % Computer : n013.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Sat Sep 26 08:19:08 UTC 2026
% 0.12/0.59 % CPUTime :
% 0.12/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.59 % Process 2315283 was started by sandbox on n013,
% 0.12/0.59 % Sat Sep 26 08:19:08 2026
% 0.12/0.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.62
% 0.12/0.62 % From the command line: assign(max_seconds, 300).
% 21.31/3.40
% 21.31/3.40 % given #500 (I,wt=9): 1500 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # tptp_name(clsrel_Ring__and__Field_Oordered__idom_41) # clausal_fof(1). [assumption].
% 21.31/3.40
% 21.31/3.40 % SZS status Unsatisfiable for theBenchmark
% 21.31/3.40
% 21.31/3.40 % Proof 1 at 2.67 (+ 0.07) seconds.
% 21.31/3.40 % Length of proof is 5.
% 21.31/3.40 % Level of proof is 1.
% 21.31/3.40 % Maximum clause weight is 23.000.
% 21.31/3.40 % Given clauses 647.
% 21.31/3.40
% 21.31/3.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------