%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET820-2 : 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 08:37:01 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 27 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 8 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_OemptyE_0,axiom,
! [VAR_0,VAR_1] : ~ c_in(VAR_0,c_emptyset,VAR_1),
file('theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(c_1,plain,
~ c_in(A,c_emptyset,B),
inference(clausify,[status(thm)],[cls_Set_OemptyE_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_2,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
fof(cls_Set_OinsertE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_1
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(c_3,plain,
( A = B
| c_in(A,C,D)
| ~ c_in(A,c_insert(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OinsertE_0]) ).
fof(cls_conjecture_0,axiom,
v_P(v_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_4,plain,
v_P(v_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0,VAR_1] :
( c_in(v_x(VAR_1),VAR_1,tc_IntDef_Oint)
| ~ c_in(VAR_0,VAR_1,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_5,plain,
( c_in(v_x(B),B,tc_IntDef_Oint)
| ~ c_in(A,B,tc_IntDef_Oint) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0,VAR_1] :
( ~ v_P(v_x(VAR_1))
| ~ c_in(VAR_0,VAR_1,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_6,plain,
( ~ v_P(v_x(B))
| ~ c_in(A,B,tc_IntDef_Oint) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_7,plain,
c_in(v_x(c_insert(A,B,tc_IntDef_Oint)),c_insert(A,B,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_8,plain,
~ v_P(v_x(c_insert(A,B,tc_IntDef_Oint))),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_9,plain,
( v_x(c_insert(A,B,tc_IntDef_Oint)) = A
| c_in(v_x(c_insert(A,B,tc_IntDef_Oint)),B,tc_IntDef_Oint) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_13,plain,
v_x(c_insert(A,c_emptyset,tc_IntDef_Oint)) = A,
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_15,plain,
~ v_P(A),
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_16,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n026.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 08:21:10 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 533955 was started by sandbox2 on n026,
% 0.15/0.42 % Sat Sep 26 08:21:10 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.44
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.44
% 0.15/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.44 % Length of proof is 12.
% 0.15/0.44 % Level of proof is 5.
% 0.15/0.44 % Maximum clause weight is 15.000.
% 0.15/0.44 % Given clauses 10.
% 0.15/0.44
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------