%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET851-2 : 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 : n010.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 08:37:08 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 41 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 15 ( 2 sgn 7 !; 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_Osucc__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_0,c_Zorn_Osucc(VAR_3,VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(tc_set(VAR_2))) ),
file('theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
cnf(c_2,plain,
( c_lessequals(A,c_Zorn_Osucc(D,B,C),tc_set(tc_set(C)))
| ~ c_lessequals(A,B,tc_set(tc_set(C))) ),
inference(clausify,[status(thm)],[cls_Zorn_Osucc__trans_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_3,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,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_2) ).
cnf(c_4,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_2]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_5,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_6,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(VAR_0,v_m,tc_set(tc_set(t_a)))
| VAR_0 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,VAR_0,t_a),v_m,tc_set(tc_set(t_a))) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_7,plain,
( ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| A = v_m
| c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_8,plain,
( ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| v_m = A
| c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_10,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_2,c_5]) ).
cnf(c_11,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_15,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| v_m = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_16,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| v_x = v_m ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_12,plain,
v_x = v_m,
inference(resolve,[status(thm)],[c_11,c_17]) ).
cnf(c_18,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(paramod,[status(thm)],[c_12,c_5]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n010.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sat Sep 26 08:22:08 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.39 % Process 2893001 was started by sandbox2 on n010,
% 0.12/5.39 % Sat Sep 26 08:22:08 2026
% 0.12/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/5.39
% 0.12/5.39 % From the command line: assign(max_seconds, 300).
% 0.16/5.40
% 0.16/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.40
% 0.16/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.40 % Length of proof is 12.
% 0.16/5.40 % Level of proof is 4.
% 0.16/5.40 % Maximum clause weight is 26.000.
% 0.16/5.40 % Given clauses 6.
% 0.16/5.40
% 0.16/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------