%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV841-1 : 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 : n020.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 20.15s 3.53s
% Output : CNFRefutation 20.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 38 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 5 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_139,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_140,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_singleton__conv2_0,axiom,
! [VAR_0,VAR_1] : c_Collect(c_fequal(VAR_0,VAR_1),VAR_1) = hAPP(hAPP(c_Set_Oinsert(VAR_1),VAR_0),c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool))),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_181,plain,
c_Collect(c_fequal(A,B),B) = hAPP(hAPP(c_Set_Oinsert(B),A),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_182,plain,
hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = c_Collect(c_fequal(B,A),A),
inference(copy,[status(thm)],[c_181]) ).
fof(cls_weaken_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_fun(tc_Hoare__Mirabelle_Otriple(VAR_2),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_weaken_0) ).
cnf(c_219,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(A,D,C)
| ~ c_lessequals(B,D,tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(A,B,C) ),
inference(clausify,[status(thm)],[cls_weaken_0]) ).
fof(cls_subset__insertI_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_lessequals(VAR_0,hAPP(hAPP(c_Set_Oinsert(VAR_1),VAR_2),VAR_0),tc_fun(VAR_1,tc_bool)),
file('theBenchmark.p',cls_subset__insertI_0) ).
cnf(c_230,plain,
c_lessequals(A,hAPP(hAPP(c_Set_Oinsert(B),C),A),tc_fun(B,tc_bool)),
inference(clausify,[status(thm)],[cls_subset__insertI_0]) ).
fof(cls_insert__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_lessequals(VAR_2,VAR_3,tc_fun(VAR_0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Set_Oinsert(VAR_0),VAR_1),VAR_2),hAPP(hAPP(c_Set_Oinsert(VAR_0),VAR_1),VAR_3),tc_fun(VAR_0,tc_bool)) ),
file('theBenchmark.p',cls_insert__mono_0) ).
cnf(c_236,plain,
( ~ c_lessequals(C,D,tc_fun(A,tc_bool))
| c_lessequals(hAPP(hAPP(c_Set_Oinsert(A),B),C),hAPP(hAPP(c_Set_Oinsert(A),B),D),tc_fun(A,tc_bool)) ),
inference(clausify,[status(thm)],[cls_insert__mono_0]) ).
fof(cls_empty__subsetI_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_1,tc_fun(VAR_0,tc_bool)),
file('theBenchmark.p',cls_empty__subsetI_0) ).
cnf(c_353,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)),
inference(clausify,[status(thm)],[cls_empty__subsetI_0]) ).
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_484,plain,
c_Collect(A,B) = A,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
cnf(c_12952,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Collect(c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a) ),
inference(paramod,[status(thm)],[c_182,c_139]) ).
cnf(c_602,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a) ),
inference(paramod,[status(thm)],[c_484,c_12952]) ).
cnf(c_637,plain,
hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = c_fequal(B,A),
inference(paramod,[status(thm)],[c_484,c_182]) ).
cnf(c_725,plain,
( ~ c_lessequals(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,A,t_a) ),
inference(resolve,[status(thm)],[c_219,c_140]) ).
cnf(c_12953,plain,
c_lessequals(hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),hAPP(hAPP(c_Set_Oinsert(A),B),C),tc_fun(A,tc_bool)),
inference(resolve,[status(thm)],[c_353,c_236]) ).
cnf(c_935,plain,
c_lessequals(c_fequal(A,B),hAPP(hAPP(c_Set_Oinsert(B),A),C),tc_fun(B,tc_bool)),
inference(paramod,[status(thm)],[c_637,c_12953]) ).
cnf(c_9536,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a),
inference(resolve,[status(thm)],[c_725,c_230]) ).
cnf(c_9538,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(resolve,[status(thm)],[c_9536,c_602]) ).
cnf(c_12954,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(resolve,[status(thm)],[c_935,c_725]) ).
cnf(c_12951,plain,
$false,
inference(resolve,[status(thm)],[c_9538,c_12954]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV841-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n020.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sat Sep 26 15:03:35 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.58 % Process 1850034 was started by sandbox on n020,
% 0.09/0.58 % Sat Sep 26 15:03:35 2026
% 0.09/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.61
% 0.09/0.61 % From the command line: assign(max_seconds, 300).
% 20.15/3.53
% 20.15/3.53 % given #500 (F,wt=49): 1913 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(B,hAPP(c_Set_Ovimage(C,D,E),c_fequal(hAPP(C,A),E)),tc_fun(D,tc_bool)),D)). [resolve(616,a,475,a)].
% 20.15/3.53
% 20.15/3.53 % given #1000 (W,wt=33): 3684 c_lessequals(A,B,tc_fun(C,tc_bool)) | -c_lessequals(A,c_Complete__Lattice_OInf__class_OInf(c_fequal(B,D),tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [resolve(3191,a,296,d),unit_del(a,705)].
% 20.15/3.53
% 20.15/3.53 % SZS status Unsatisfiable for theBenchmark
% 20.15/3.53
% 20.15/3.53 % Proof 1 at 2.18 (+ 0.54) seconds.
% 20.15/3.53 % Length of proof is 16.
% 20.15/3.53 % Level of proof is 4.
% 20.15/3.53 % Maximum clause weight is 46.000.
% 20.15/3.53 % Given clauses 1243.
% 20.15/3.53
% 20.15/3.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------