%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET852-2 : 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 : n016.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 0.10s 5.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 42 ( 12 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 33 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Zorn_OUnion__lemma0_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Union(VAR_2,VAR_3),VAR_0,tc_set(VAR_3))
| c_lessequals(VAR_1,c_Union(VAR_2,VAR_3),tc_set(VAR_3))
| c_in(c_Zorn_OUnion__lemma0__1(VAR_0,VAR_1,VAR_2,VAR_3),VAR_2,tc_set(VAR_3)) ),
file('theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
cnf(c_1,plain,
( c_lessequals(c_Union(C,D),A,tc_set(D))
| c_lessequals(B,c_Union(C,D),tc_set(D))
| c_in(c_Zorn_OUnion__lemma0__1(A,B,C,D),C,tc_set(D)) ),
inference(clausify,[status(thm)],[cls_Zorn_OUnion__lemma0_0]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(VAR_0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),VAR_0,tc_set(tc_set(t_a))) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_2,plain,
( ~ c_in(A,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),A,tc_set(tc_set(t_a))) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_3,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(B,A,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(B,A,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),B,tc_set(tc_set(t_a)))
| c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_Zorn_OUnion__lemma0_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Union(VAR_2,VAR_3),VAR_1,tc_set(VAR_3))
| c_lessequals(VAR_0,c_Union(VAR_2,VAR_3),tc_set(VAR_3))
| ~ c_lessequals(VAR_0,c_Zorn_OUnion__lemma0__1(VAR_1,VAR_0,VAR_2,VAR_3),tc_set(VAR_3)) ),
file('theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
cnf(c_4,plain,
( c_lessequals(c_Union(C,D),B,tc_set(D))
| c_lessequals(A,c_Union(C,D),tc_set(D))
| ~ c_lessequals(A,c_Zorn_OUnion__lemma0__1(B,A,C,D),tc_set(D)) ),
inference(clausify,[status(thm)],[cls_Zorn_OUnion__lemma0_2]) ).
fof(cls_Zorn_OUnion__lemma0_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Union(VAR_2,VAR_3),VAR_0,tc_set(VAR_3))
| c_lessequals(VAR_1,c_Union(VAR_2,VAR_3),tc_set(VAR_3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(VAR_0,VAR_1,VAR_2,VAR_3),VAR_0,tc_set(VAR_3)) ),
file('theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
cnf(c_5,plain,
( c_lessequals(c_Union(C,D),A,tc_set(D))
| c_lessequals(B,c_Union(C,D),tc_set(D))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(A,B,C,D),A,tc_set(D)) ),
inference(clausify,[status(thm)],[cls_Zorn_OUnion__lemma0_1]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_6,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_7,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_16,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,A,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_17,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,A,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,A,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_11,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,A,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7,c_18]) ).
cnf(c_19,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(A,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_13,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_19,c_7]) ).
cnf(c_20,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.38 % Computer : n016.cluster.edu
% 0.07/5.38 % Model : x86_64 x86_64
% 0.07/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.38 % Memory : 8046.5625MB
% 0.07/5.38 % OS : Linux 6.8.0-71-generic
% 0.07/5.38 % CPULimit : 300
% 0.07/5.38 % WCLimit : 300
% 0.07/5.38 % DateTime : Sat Sep 26 08:26:20 UTC 2026
% 0.07/5.38 % CPUTime :
% 0.07/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/5.39 % Process 417567 was started by sandbox on n016,
% 0.07/5.39 % Sat Sep 26 08:26:20 2026
% 0.07/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/5.39
% 0.07/5.39 % From the command line: assign(max_seconds, 300).
% 0.10/5.40
% 0.10/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.40
% 0.10/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.40 % Length of proof is 10.
% 0.10/5.40 % Level of proof is 3.
% 0.10/5.40 % Maximum clause weight is 43.000.
% 0.10/5.40 % Given clauses 9.
% 0.10/5.40
% 0.10/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------