%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET858-2 : 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 : n026.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 08:37:10 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 120 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 126 ( 51 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 64 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
c_in(v_n,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(v_n,v_m,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_4,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_Set_Osubset__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_3,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__trans_0) ).
cnf(c_5,plain,
( c_lessequals(D,B,tc_set(C))
| ~ c_lessequals(D,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__trans_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_6,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__linear__lemma1_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2),c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(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_OTFin__linear__lemma1_0) ).
cnf(c_7,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(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_OTFin__linear__lemma1_0]) ).
fof(cls_Zorn_OTFin__linear__lemma1_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2),VAR_0,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(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_OTFin__linear__lemma1_1) ).
cnf(c_8,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(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_OTFin__linear__lemma1_1]) ).
fof(cls_Zorn_OTFin__linear__lemma1_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2) != VAR_0
| ~ 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_OTFin__linear__lemma1_2) ).
cnf(c_9,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| c_Zorn_OTFin__linear__lemma1__1(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(clausify,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_2]) ).
fof(cls_Zorn_OTFin__linear__lemma1_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| ~ c_lessequals(c_Zorn_Osucc(VAR_1,c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2),VAR_2),VAR_0,tc_set(tc_set(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_OTFin__linear__lemma1_3) ).
cnf(c_10,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| ~ c_lessequals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(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_OTFin__linear__lemma1_3]) ).
fof(cls_Zorn_OTFin__linear__lemma2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| ~ c_lessequals(VAR_0,VAR_3,tc_set(tc_set(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_OTFin__linear__lemma2_0) ).
cnf(c_11,plain,
( A = D
| c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| ~ c_lessequals(A,D,tc_set(tc_set(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_OTFin__linear__lemma2_0]) ).
cnf(c_83,plain,
( c_lessequals(B,D,tc_set(tc_set(C)))
| ~ c_lessequals(c_Zorn_Osucc(A,B,C),D,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_21,plain,
~ c_lessequals(c_Zorn_Osucc(A,v_n,t_a),v_m,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_83,c_3]) ).
cnf(c_84,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_n,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),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_7,c_2]) ).
cnf(c_85,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_84,c_1]) ).
cnf(c_86,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_4,c_85]) ).
cnf(c_27,plain,
c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_21,c_86]) ).
cnf(c_87,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(A,v_n,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_8,c_2]) ).
cnf(c_88,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_87,c_1]) ).
cnf(c_89,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_4,c_88]) ).
cnf(c_34,plain,
c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_21,c_89]) ).
cnf(c_90,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,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_10,c_2]) ).
cnf(c_91,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_90,c_1]) ).
cnf(c_92,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_91,c_4]) ).
cnf(c_56,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_92,c_21]) ).
cnf(c_93,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_n,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_94,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n ),
inference(resolve,[status(thm)],[c_93,c_1]) ).
cnf(c_95,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n ),
inference(resolve,[status(thm)],[c_94,c_4]) ).
cnf(c_57,plain,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n,
inference(resolve,[status(thm)],[c_95,c_21]) ).
cnf(c_96,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = A
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),A,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),A,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_11,c_27]) ).
cnf(c_97,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_96,c_2]) ).
cnf(c_98,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_97,c_34]) ).
cnf(c_99,plain,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n,
inference(resolve,[status(thm)],[c_56,c_98]) ).
cnf(c_82,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:25:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 542345 was started by sandbox2 on n026,
% 0.11/0.38 % Sat Sep 26 08:25:26 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % Assigning unary symbol tc_set kb_weight 0 and highest precedence (11).
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 17.
% 0.11/0.40 % Level of proof is 3.
% 0.11/0.40 % Maximum clause weight is 83.000.
% 0.11/0.40 % Given clauses 24.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------