%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV836-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 09:09:12 AM UTC 2026
% Result : Unsatisfiable 0.15s 16.05s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 26 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 25 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Collect__def_0,axiom,
! [VAR_0,VAR_1] : c_Collect(VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Collect__def_0) ).
cnf(c_405,plain,
c_Collect(A,B) = A,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
fof(cls_singleton__conv2_0,axiom,
! [VAR_0,VAR_1] : c_Collect(c_fequal(VAR_0,VAR_1),VAR_1) = c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool)),VAR_1),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_456,plain,
c_Collect(c_fequal(A,B),B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_2340,plain,
c_fequal(A,B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),
inference(paramod,[status(thm)],[c_405,c_456]) ).
cnf(c_457,plain,
c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = c_fequal(A,B),
inference(copy,[status(thm)],[c_2340]) ).
fof(cls_hoare__derivs_Oinsert_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,c_Set_Oinsert(VAR_1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(VAR_3),tc_bool)),tc_Hoare__Mirabelle_Otriple(VAR_3)),VAR_3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,VAR_2,VAR_3)
| c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,c_Set_Oinsert(VAR_1,VAR_2,tc_Hoare__Mirabelle_Otriple(VAR_3)),VAR_3) ),
file('theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
cnf(c_502,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(D),tc_bool)),tc_Hoare__Mirabelle_Otriple(D)),D)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(A,C,D)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(B,C,tc_Hoare__Mirabelle_Otriple(D)),D) ),
inference(clausify,[status(thm)],[cls_hoare__derivs_Oinsert_0]) ).
cnf(c_503,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(B,tc_Hoare__Mirabelle_Otriple(D)),D)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(A,C,D)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(B,C,tc_Hoare__Mirabelle_Otriple(D)),D) ),
inference(paramod,[status(thm)],[c_457,c_502]) ).
fof(cls_conjecture_3,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_551,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_552,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(paramod,[status(thm)],[c_457,c_551]) ).
fof(cls_conjecture_4,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,v_tsa,t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_553,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,v_tsa,t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_554,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_2341,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_fequal(A,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(A,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(resolve,[status(thm)],[c_503,c_553]) ).
cnf(c_2342,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(resolve,[status(thm)],[c_2341,c_552]) ).
cnf(c_2339,plain,
$false,
inference(resolve,[status(thm)],[c_554,c_2342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n006.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Sat Sep 26 15:02:13 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/15.39 % Process 1530500 was started by sandbox on n006,
% 0.11/15.39 % Sat Sep 26 15:02:13 2026
% 0.11/15.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/15.42
% 0.15/15.42 % From the command line: assign(max_seconds, 300).
% 0.15/16.05
% 0.15/16.05 % SZS status Unsatisfiable for theBenchmark
% 0.15/16.05
% 0.15/16.05 % Proof 1 at 0.53 (+ 0.08) seconds.
% 0.15/16.05 % Length of proof is 10.
% 0.15/16.05 % Level of proof is 3.
% 0.15/16.05 % Maximum clause weight is 34.000.
% 0.15/16.05 % Given clauses 325.
% 0.15/16.05
% 0.15/16.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------