%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET845-2 : 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 08:37:07 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 32 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_OUnion__upper_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,c_Union(VAR_1,VAR_2),tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUnion__upper_0) ).
cnf(c_1,plain,
( c_lessequals(A,c_Union(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUnion__upper_0]) ).
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_2,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]) ).
fof(cls_Zorn_OAbrial__axiom1_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_lessequals(VAR_0,c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),tc_set(tc_set(VAR_2))),
file('theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(c_3,plain,
c_lessequals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))),
inference(clausify,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]) ).
fof(cls_Zorn_OTFin_OsuccI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),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_OsuccI_0) ).
cnf(c_4,plain,
( c_in(c_Zorn_Osucc(B,A,C),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_OsuccI_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_5,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_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_6,plain,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_7,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_15,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,v_m,t_a),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_16,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),
inference(paramod,[status(thm)],[c_6,c_15]) ).
cnf(c_8,plain,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_9,plain,
c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_17,plain,
( c_Zorn_Osucc(A,B,C) = B
| ~ c_lessequals(c_Zorn_Osucc(A,B,C),B,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_10,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_11,plain,
c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_13,plain,
~ c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET845-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:21:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2892139 was started by sandbox2 on n010,
% 0.10/0.37 % Sat Sep 26 08:21:30 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 13.
% 0.10/0.38 % Level of proof is 4.
% 0.10/0.38 % Maximum clause weight is 19.000.
% 0.10/0.38 % Given clauses 8.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------