%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET841-2 : 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 : n020.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 08:37:06 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.54s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 17 unt; 0 def)
% Number of atoms : 36 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_Osubset__refl_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,VAR_0,tc_set(VAR_1)),
file('theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(c_1,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_0]) ).
fof(cls_Zorn_OTFin__subsetD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| ~ c_lessequals(VAR_0,VAR_3,tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_3,c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_0,c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(VAR_2))) ),
file('theBenchmark.p',cls_Zorn_OTFin__subsetD_0) ).
cnf(c_2,plain,
( A = D
| c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| ~ c_lessequals(A,D,tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) ),
inference(clausify,[status(thm)],[cls_Zorn_OTFin__subsetD_0]) ).
fof(cls_conjecture_0,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_4,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_5,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(copy,[status(thm)],[c_4]) ).
fof(cls_conjecture_2,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_6,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_7,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_8,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_9,plain,
( v_x = v_m
| c_lessequals(c_Zorn_Osucc(A,v_x,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(A,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(A,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_12,plain,
( v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_13,plain,
( v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_3,c_12]) ).
cnf(c_10,plain,
v_x = v_m,
inference(resolve,[status(thm)],[c_8,c_13]) ).
cnf(c_14,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(paramod,[status(thm)],[c_10,c_8]) ).
cnf(c_15,plain,
~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))),
inference(paramod,[status(thm)],[c_5,c_14]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET841-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n020.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sat Sep 26 08:21:34 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.52 % Process 1071935 was started by sandbox on n020,
% 0.10/0.52 % Sat Sep 26 08:21:34 2026
% 0.10/0.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.53
% 0.10/0.53 % From the command line: assign(max_seconds, 300).
% 0.10/0.54
% 0.10/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.54
% 0.10/0.54 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.54 % Length of proof is 11.
% 0.10/0.54 % Level of proof is 3.
% 0.10/0.54 % Maximum clause weight is 34.000.
% 0.10/0.54 % Given clauses 8.
% 0.10/0.54
% 0.10/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------