%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET850-1 : 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 : n007.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 22.21s 3.27s
% Output : CNFRefutation 22.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 19 ( 3 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1571,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_1572,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_conjecture_0,axiom,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1573,plain,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1574,plain,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_3571,plain,
( c_lessequals(A,c_Zorn_Osucc(D,B,C),tc_set(tc_set(C)))
| ~ c_lessequals(A,B,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_1571,c_1572]) ).
cnf(c_3569,plain,
c_lessequals(v_x,c_Zorn_Osucc(A,v_y,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_3571,c_1573]) ).
cnf(c_3570,plain,
$false,
inference(resolve,[status(thm)],[c_3569,c_1574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET850-1 : 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 : n007.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 08:19:08 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 3279082 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 08:19:08 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 22.21/3.27
% 22.21/3.27 % given #500 (I,wt=12): 995 c_less(c_0,A,tc_nat) | c_0 = A. [copy(994),flip(b)].
% 22.21/3.27
% 22.21/3.27 % given #1000 (I,wt=9): 1541 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # tptp_name(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) # clausal_fof(1). [assumption].
% 22.21/3.27
% 22.21/3.27 % SZS status Unsatisfiable for theBenchmark
% 22.21/3.27
% 22.21/3.27 % Proof 1 at 2.69 (+ 0.14) seconds.
% 22.21/3.27 % Length of proof is 6.
% 22.21/3.27 % Level of proof is 2.
% 22.21/3.27 % Maximum clause weight is 29.000.
% 22.21/3.27 % Given clauses 1032.
% 22.21/3.27
% 22.21/3.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------