%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET835-1 : 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 : 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 08:37:05 AM UTC 2026
% Result : Unsatisfiable 12.10s 3.41s
% Output : CNFRefutation 12.10s
% 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_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_630,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]) ).
fof(cls_conjecture_0,axiom,
c_lessequals(v_Y,v_X,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1202,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_2,axiom,
c_in(v_x,v_Y,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1204,plain,
c_in(v_x,v_Y,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_in(v_x,v_X,t_a),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_1205,plain,
~ c_in(v_x,v_X,t_a),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_2161,plain,
( c_in(A,v_X,t_a)
| ~ c_in(A,v_Y,t_a) ),
inference(resolve,[status(thm)],[c_1202,c_630]) ).
cnf(c_3196,plain,
c_in(v_x,v_X,t_a),
inference(resolve,[status(thm)],[c_2161,c_1204]) ).
cnf(c_3195,plain,
$false,
inference(resolve,[status(thm)],[c_1205,c_3196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET835-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % 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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:19:59 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 24703 was started by sandbox on n011,
% 0.09/0.37 % Sat Sep 26 08:19:59 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 12.10/3.41
% 12.10/3.41 % given #500 (I,wt=9): 1058 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # tptp_name(clsrel_Ring__and__Field_Oordered__idom_9) # clausal_fof(1). [assumption].
% 12.10/3.41
% 12.10/3.41 % given #1000 (I,wt=22): 1558 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(98,b,79,a)].
% 12.10/3.41
% 12.10/3.41 % SZS status Unsatisfiable for theBenchmark
% 12.10/3.41
% 12.10/3.41 % Proof 1 at 1.68 (+ 0.07) seconds.
% 12.10/3.41 % Length of proof is 6.
% 12.10/3.41 % Level of proof is 2.
% 12.10/3.41 % Maximum clause weight is 23.000.
% 12.10/3.41 % Given clauses 1338.
% 12.10/3.41
% 12.10/3.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------