%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET840-2 : 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 : n011.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 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 51 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 19 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 58 ( 6 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_lessequals(v_S,c_insert(VAR_0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
~ c_lessequals(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),VAR_0,tc_set(t_b)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
( ~ c_in(A,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),A,tc_set(t_b)) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Set_OUnionI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_Union(VAR_3,VAR_2),VAR_2)
| ~ c_in(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OUnionI_0) ).
cnf(c_3,plain,
( c_in(A,c_Union(D,C),C)
| ~ c_in(B,D,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUnionI_0]) ).
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_5,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_7,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_8,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_9,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_15,plain,
( c_in(D,c_Union(A,C),C)
| ~ c_in(D,c_Main_OsubsetI__1(A,B,tc_set(C)),C)
| c_lessequals(A,B,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_17,plain,
( c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,A,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,A,tc_set(tc_set(t_b))) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_20,plain,
~ c_in(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_57,plain,
( c_lessequals(c_Main_OsubsetI__1(A,B,tc_set(C)),D,tc_set(C))
| c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(A,B,tc_set(C)),D,C),c_Union(A,C),C)
| c_lessequals(A,B,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_94,plain,
c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),tc_set(t_b)),
inference(resolve,[status(thm)],[c_17,c_1]) ).
cnf(c_561,plain,
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b))
| ~ c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)) ),
inference(resolve,[status(thm)],[c_94,c_9]) ).
cnf(c_243,plain,
( c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b)
| ~ c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)) ),
inference(copy,[status(thm)],[c_561]) ).
cnf(c_562,plain,
( c_lessequals(c_Main_OsubsetI__1(A,B,tc_set(C)),c_Union(A,C),tc_set(C))
| c_lessequals(c_Main_OsubsetI__1(A,B,tc_set(C)),c_Union(A,C),tc_set(C))
| c_lessequals(A,B,tc_set(tc_set(C))) ),
inference(resolve,[status(thm)],[c_57,c_8]) ).
cnf(c_528,plain,
( c_lessequals(c_Main_OsubsetI__1(A,B,tc_set(C)),c_Union(A,C),tc_set(C))
| c_lessequals(A,B,tc_set(tc_set(C))) ),
inference(copy,[status(thm)],[c_562]) ).
cnf(c_547,plain,
c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)),
inference(resolve,[status(thm)],[c_528,c_1]) ).
cnf(c_553,plain,
c_Main_OsubsetI__1(v_S,c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b),
inference(resolve,[status(thm)],[c_547,c_243]) ).
cnf(c_559,plain,
~ c_in(c_Union(v_S,t_b),c_insert(A,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(paramod,[status(thm)],[c_553,c_20]) ).
cnf(c_560,plain,
$false,
inference(resolve,[status(thm)],[c_559,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET840-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:20:14 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 25740 was started by sandbox on n011,
% 0.08/0.34 % Sat Sep 26 08:20:14 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.44
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.44
% 0.11/0.44 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.11/0.44 % Length of proof is 18.
% 0.11/0.44 % Level of proof is 7.
% 0.11/0.44 % Maximum clause weight is 48.000.
% 0.11/0.44 % Given clauses 89.
% 0.11/0.44
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------