%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET839-2 : 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 08:37:06 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 35 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 15 |; 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 11 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_lessequals(v_S,c_insert(VAR_0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
~ c_lessequals(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0,VAR_1] :
( ~ c_in(VAR_0,v_S,tc_set(t_a))
| ~ c_in(VAR_1,v_S,tc_set(t_a))
| c_lessequals(VAR_0,VAR_1,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| ~ c_in(B,v_S,tc_set(t_a))
| c_lessequals(A,B,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Set_OinsertCI_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(VAR_0,c_insert(VAR_0,VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c_3,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
fof(cls_Set_OsubsetI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_0,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(c_4,plain,
( c_lessequals(A,B,tc_set(C))
| c_in(c_Main_OsubsetI__1(A,B,C),A,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_0]) ).
fof(cls_Set_OsubsetI_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| ~ c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(c_5,plain,
( c_lessequals(A,B,tc_set(C))
| ~ c_in(c_Main_OsubsetI__1(A,B,C),B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_1]) ).
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_6,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]) ).
cnf(c_8,plain,
c_in(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),v_S,tc_set(t_a)),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_13,plain,
( ~ c_in(B,v_S,tc_set(t_a))
| c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),B,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_20,plain,
c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_Main_OsubsetI__1(v_S,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_27,plain,
( c_Main_OsubsetI__1(v_S,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_Main_OsubsetI__1(v_S,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_20,c_6]) ).
cnf(c_24,plain,
c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_20,c_27]) ).
cnf(c_28,plain,
( c_lessequals(v_S,c_insert(B,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_24,c_5]) ).
cnf(c_25,plain,
~ c_in(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(B,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_1,c_28]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET839-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:20:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3187534 was started by sandbox on n008,
% 0.08/0.36 % Sat Sep 26 08:20:54 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 12.
% 0.08/0.38 % Level of proof is 6.
% 0.08/0.38 % Maximum clause weight is 21.000.
% 0.08/0.38 % Given clauses 16.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------