%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV840-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.23s 0.72s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 29 unt; 0 def)
% Number of atoms : 37 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 12 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 48 ( 4 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Un__upper2_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_lessequals(VAR_0,c_Lattices_Oupper__semilattice__class_Osup(VAR_1,VAR_0,tc_fun(VAR_2,tc_bool)),tc_fun(VAR_2,tc_bool)),
file('theBenchmark.p',cls_Un__upper2_0) ).
cnf(c_35,plain,
c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)),
inference(clausify,[status(thm)],[cls_Un__upper2_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_111,plain,
c_Collect(A,B) = A,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
fof(cls_insert__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Set_Oinsert(VAR_0,VAR_1,VAR_2) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(VAR_2),VAR_2,VAR_2,tc_bool),VAR_0),VAR_2),VAR_1,tc_fun(VAR_2,tc_bool)),
file('theBenchmark.p',cls_insert__def_0) ).
cnf(c_165,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(C),C,C,tc_bool),A),C),B,tc_fun(C,tc_bool)),
inference(clausify,[status(thm)],[cls_insert__def_0]) ).
cnf(c_166,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(C),C,C,tc_bool),A),B,tc_fun(C,tc_bool)),
inference(paramod,[status(thm)],[c_111,c_165]) ).
fof(cls_Un__empty__right_0,axiom,
! [VAR_0,VAR_1] : c_Lattices_Oupper__semilattice__class_Osup(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool)),tc_fun(VAR_1,tc_bool)) = VAR_0,
file('theBenchmark.p',cls_Un__empty__right_0) ).
cnf(c_212,plain,
c_Lattices_Oupper__semilattice__class_Osup(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) = A,
inference(clausify,[status(thm)],[cls_Un__empty__right_0]) ).
fof(cls_thin_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(VAR_3,VAR_1,VAR_2)
| ~ c_lessequals(VAR_3,VAR_0,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_thin_0) ).
cnf(c_360,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(D,B,C)
| ~ c_lessequals(D,A,tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(A,B,C) ),
inference(clausify,[status(thm)],[cls_thin_0]) ).
fof(cls_singleton__conv2_0,axiom,
! [VAR_0,VAR_1] : c_Collect(hAPP(c_fequal(VAR_0),VAR_1),VAR_0) = c_Set_Oinsert(VAR_1,c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_0),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_379,plain,
c_Collect(hAPP(c_fequal(A),B),A) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_1310,plain,
hAPP(c_fequal(A),B) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),
inference(paramod,[status(thm)],[c_111,c_379]) ).
cnf(c_1311,plain,
hAPP(c_fequal(A),B) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),tc_fun(A,tc_bool)),
inference(paramod,[status(thm)],[c_166,c_1310]) ).
cnf(c_1312,plain,
hAPP(c_fequal(A),B) = hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B),
inference(paramod,[status(thm)],[c_212,c_1311]) ).
cnf(c_380,plain,
hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B) = hAPP(c_fequal(A),B),
inference(copy,[status(thm)],[c_1312]) ).
fof(cls_conjecture_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),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_0) ).
cnf(c_492,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),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_0]) ).
cnf(c_1313,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference(paramod,[status(thm)],[c_166,c_492]) ).
cnf(c_1314,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference(paramod,[status(thm)],[c_380,c_1313]) ).
cnf(c_493,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a),
inference(paramod,[status(thm)],[c_212,c_1314]) ).
fof(cls_conjecture_1,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),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_1) ).
cnf(c_494,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),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_1]) ).
cnf(c_1315,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(paramod,[status(thm)],[c_166,c_494]) ).
cnf(c_1316,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(paramod,[status(thm)],[c_380,c_1315]) ).
cnf(c_1317,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference(paramod,[status(thm)],[c_166,c_1316]) ).
cnf(c_1318,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference(paramod,[status(thm)],[c_380,c_1317]) ).
cnf(c_495,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a),
inference(paramod,[status(thm)],[c_212,c_1318]) ).
cnf(c_1319,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(B,D,C)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool)),D,C) ),
inference(resolve,[status(thm)],[c_360,c_35]) ).
cnf(c_1308,plain,
c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a),
inference(resolve,[status(thm)],[c_1319,c_493]) ).
cnf(c_1309,plain,
$false,
inference(resolve,[status(thm)],[c_1308,c_495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV840-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 15:00:40 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 4023726 was started by sandbox2 on n007,
% 0.17/0.44 % Sat Sep 26 15:00:40 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.23/0.72
% 0.23/0.72 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.72
% 0.23/0.72 % Proof 1 at 0.18 (+ 0.05) seconds.
% 0.23/0.72 % Length of proof is 14.
% 0.23/0.72 % Level of proof is 5.
% 0.23/0.72 % Maximum clause weight is 119.000.
% 0.23/0.72 % Given clauses 278.
% 0.23/0.72
% 0.23/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------