%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET843-2 : 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 : n018.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 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 78 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 36 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 55 ( 2 sgn 21 !; 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_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_3,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_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_4,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_5,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_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_6,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_7,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_8,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_7]) ).
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_9,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)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_10,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_55,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m ),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_11,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m ),
inference(copy,[status(thm)],[c_55]) ).
fof(cls_conjecture_2,axiom,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_12,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_56,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_13,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
( B = c_Zorn_Osucc(A,B,C)
| ~ c_lessequals(c_Zorn_Osucc(A,B,C),B,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_14,plain,
( c_Zorn_Osucc(A,B,C) = B
| ~ c_lessequals(c_Zorn_Osucc(A,B,C),B,tc_set(tc_set(C))) ),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_15,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_6,c_3]) ).
cnf(c_17,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_9,c_8]) ).
cnf(c_18,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_19,plain,
c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_25,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,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_18,c_1]) ).
cnf(c_58,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| ~ 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_19,c_2]) ).
cnf(c_26,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_36,plain,
( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_m,t_a) != v_m ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_46,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
| 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_36,c_13]) ).
cnf(c_59,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m ),
inference(resolve,[status(thm)],[c_46,c_26]) ).
cnf(c_48,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(copy,[status(thm)],[c_59]) ).
cnf(c_49,plain,
c_Zorn_Osucc(v_S,v_m,t_a) != v_m,
inference(resolve,[status(thm)],[c_48,c_11]) ).
cnf(c_50,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_14,c_49]) ).
cnf(c_60,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_48,c_25]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_50,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:23:12 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 4180581 was started by sandbox2 on n018,
% 0.09/5.38 % Sat Sep 26 08:23:12 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 26.
% 0.09/5.39 % Level of proof is 8.
% 0.09/5.39 % Maximum clause weight is 43.000.
% 0.09/5.39 % Given clauses 33.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------