%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET842-2 : 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 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(VAR_0,v_m,tc_set(tc_set(t_a))) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_1,plain,
( ~ c_in(A,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(A,v_m,tc_set(tc_set(t_a))) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_Set_OsubsetD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(c_3,plain,
( c_in(A,D,C)
| ~ c_lessequals(B,D,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetD_0]) ).
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]) ).
cnf(c_6,plain,
~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a)),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_8,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_10,plain,
( ~ c_in(B,v_Y,tc_set(tc_set(t_a)))
| c_in(A,v_m,tc_set(t_a))
| ~ c_in(A,B,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
fof(cls_Set_OUnionE_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Main_OUnionE__1(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ c_in(VAR_0,c_Union(VAR_1,VAR_2),VAR_2) ),
file('theBenchmark.p',cls_Set_OUnionE_1) ).
cnf(c_12,plain,
( c_in(A,c_Main_OUnionE__1(A,B,C),C)
| ~ c_in(A,c_Union(B,C),C) ),
inference(clausify,[status(thm)],[cls_Set_OUnionE_1]) ).
fof(cls_Set_OUnionE_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Main_OUnionE__1(VAR_0,VAR_1,VAR_2),VAR_1,tc_set(VAR_2))
| ~ c_in(VAR_0,c_Union(VAR_1,VAR_2),VAR_2) ),
file('theBenchmark.p',cls_Set_OUnionE_0) ).
cnf(c_13,plain,
( c_in(c_Main_OUnionE__1(A,B,C),B,tc_set(C))
| ~ c_in(A,c_Union(B,C),C) ),
inference(clausify,[status(thm)],[cls_Set_OUnionE_0]) ).
cnf(c_16,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_17,plain,
c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_22,plain,
( ~ c_in(A,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_23,plain,
~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_22,c_17]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_16,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET842-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.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 08:21:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3189051 was started by sandbox on n008,
% 0.11/0.37 % Sat Sep 26 08:21:09 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 13.
% 0.11/0.39 % Level of proof is 3.
% 0.11/0.39 % Maximum clause weight is 23.000.
% 0.11/0.39 % Given clauses 10.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------