%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET844-1 : 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 : n008.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 25.52s 3.98s
% Output : CNFRefutation 25.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 38 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(c_2,plain,
( c_lessequals(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
fof(clsarity_set_2,axiom,
! [VAR_0] : class_Orderings_Oorder(tc_set(VAR_0)),
file('theBenchmark.p',clsarity_set_2) ).
cnf(c_9,plain,
class_Orderings_Oorder(tc_set(A)),
inference(clausify,[status(thm)],[clsarity_set_2]) ).
fof(cls_Zorn_OTFin__UnionI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Union(VAR_0,tc_set(VAR_2)),c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_lessequals(VAR_0,c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(tc_set(VAR_2)))) ),
file('theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
cnf(c_973,plain,
( c_in(c_Union(A,tc_set(C)),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(A,c_Zorn_OTFin(B,C),tc_set(tc_set(tc_set(C)))) ),
inference(clausify,[status(thm)],[cls_Zorn_OTFin__UnionI_0]) ).
fof(cls_Zorn_Oeq__succ__upper_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| VAR_0 != c_Zorn_Osucc(VAR_1,VAR_0,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_Oeq__succ__upper_0) ).
cnf(c_974,plain,
( c_lessequals(D,A,tc_set(tc_set(C)))
| A != c_Zorn_Osucc(B,A,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_Oeq__succ__upper_0]) ).
cnf(c_975,plain,
( c_lessequals(D,A,tc_set(tc_set(C)))
| c_Zorn_Osucc(B,A,C) != A
| ~ 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(copy,[status(thm)],[c_974]) ).
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_976,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_977,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_978,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(copy,[status(thm)],[c_977]) ).
fof(cls_conjecture_2,axiom,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_979,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_992,plain,
c_lessequals(A,A,tc_set(B)),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_4856,plain,
( c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_976,c_975]) ).
cnf(c_1955,plain,
( c_lessequals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_978,c_4856]) ).
cnf(c_1959,plain,
c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))),
inference(resolve,[status(thm)],[c_992,c_973]) ).
cnf(c_4857,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_1959,c_1955]) ).
cnf(c_4855,plain,
$false,
inference(resolve,[status(thm)],[c_979,c_4857]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET844-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.64 % Computer : n008.cluster.edu
% 0.18/0.64 % Model : x86_64 x86_64
% 0.18/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.64 % Memory : 8046.5625MB
% 0.18/0.64 % OS : Linux 6.8.0-71-generic
% 0.18/0.64 % CPULimit : 300
% 0.18/0.64 % WCLimit : 300
% 0.18/0.64 % DateTime : Sat Sep 26 08:21:25 UTC 2026
% 0.18/0.65 % CPUTime :
% 0.18/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.65 % Process 3189450 was started by sandbox on n008,
% 0.18/0.65 % Sat Sep 26 08:21:25 2026
% 0.18/0.65 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.22/0.70
% 0.22/0.70 % From the command line: assign(max_seconds, 300).
% 25.52/3.98
% 25.52/3.98 % given #500 (I,wt=23): 987 -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(8,a,3,a)].
% 25.52/3.98
% 25.52/3.98 % given #1000 (I,wt=7): 1487 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # tptp_name(clsarity_IntDef__Oint_51) # clausal_fof(1). [assumption].
% 25.52/3.98
% 25.52/3.98 % SZS status Unsatisfiable for theBenchmark
% 25.52/3.98
% 25.52/3.98 % Proof 1 at 2.97 (+ 0.24) seconds.
% 25.52/3.98 % Length of proof is 13.
% 25.52/3.98 % Level of proof is 3.
% 25.52/3.98 % Maximum clause weight is 43.000.
% 25.52/3.98 % Given clauses 1421.
% 25.52/3.98
% 25.52/3.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------