%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET855-1 : 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 : n001.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 08:37:09 AM UTC 2026
% Result : Unsatisfiable 20.98s 8.29s
% Output : CNFRefutation 20.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1158,plain,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_1159,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
v_n != c_Union(v_Y,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_1160,plain,
v_n != c_Union(v_Y,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_Set_Osubset__antisym_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_0
| ~ c_lessequals(VAR_1,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(c_1671,plain,
( B = A
| ~ c_lessequals(B,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
cnf(c_2143,plain,
( v_n = c_Union(v_Y,tc_set(t_a))
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_1671,c_1159]) ).
cnf(c_2144,plain,
v_n = c_Union(v_Y,tc_set(t_a)),
inference(resolve,[status(thm)],[c_1158,c_2143]) ).
cnf(c_2142,plain,
$false,
inference(resolve,[status(thm)],[c_1160,c_2144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET855-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.44 % Computer : n001.cluster.edu
% 0.19/5.44 % Model : x86_64 x86_64
% 0.19/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.44 % Memory : 8046.5625MB
% 0.19/5.44 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sat Sep 26 08:28:03 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.45 % Process 1367334 was started by sandbox2 on n001,
% 0.19/5.45 % Sat Sep 26 08:28:03 2026
% 0.19/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.48
% 0.19/5.48 % From the command line: assign(max_seconds, 300).
% 20.98/8.29
% 20.98/8.29 % given #500 (I,wt=16): 1440 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(94,b,81,a)].
% 20.98/8.29
% 20.98/8.29 % SZS status Unsatisfiable for theBenchmark
% 20.98/8.29
% 20.98/8.29 % Proof 1 at 2.69 (+ 0.07) seconds.
% 20.98/8.29 % Length of proof is 5.
% 20.98/8.29 % Level of proof is 1.
% 20.98/8.29 % Maximum clause weight is 17.000.
% 20.98/8.29 % Given clauses 728.
% 20.98/8.29
% 20.98/8.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------