%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV839-1 : 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 : 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 09:09:12 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 37 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_166,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_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_256,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(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_291,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_437,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_256,c_291]) ).
cnf(c_292,plain,
c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = hAPP(c_fequal(B),A),
inference(copy,[status(thm)],[c_437]) ).
fof(cls_insert__is__Un_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Set_Oinsert(VAR_0,VAR_1,VAR_2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_2,tc_bool)),VAR_2),VAR_1,tc_fun(VAR_2,tc_bool)),
file('theBenchmark.p',cls_insert__is__Un_0) ).
cnf(c_331,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),B,tc_fun(C,tc_bool)),
inference(clausify,[status(thm)],[cls_insert__is__Un_0]) ).
cnf(c_332,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(C),A),B,tc_fun(C,tc_bool)),
inference(paramod,[status(thm)],[c_292,c_331]) ).
fof(cls_hoare__derivs_OSkip_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(VAR_1,c_Com_Ocom_OSKIP,VAR_1,VAR_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(VAR_2),tc_bool)),tc_Hoare__Mirabelle_Otriple(VAR_2)),VAR_2),
file('theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
cnf(c_395,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(B,c_Com_Ocom_OSKIP,B,C),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool)),tc_Hoare__Mirabelle_Otriple(C)),C),
inference(clausify,[status(thm)],[cls_hoare__derivs_OSkip_0]) ).
cnf(c_438,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(C)),c_Hoare__Mirabelle_Otriple_Otriple(B,c_Com_Ocom_OSKIP,B,C)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool)),C),
inference(paramod,[status(thm)],[c_332,c_395]) ).
cnf(c_396,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(B)),c_Hoare__Mirabelle_Otriple_Otriple(C,c_Com_Ocom_OSKIP,C,B)),B),
inference(paramod,[status(thm)],[c_166,c_438]) ).
fof(cls_conjecture_1,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_P,c_Com_Ocom_OSKIP,v_P,t_a),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_435,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_P,c_Com_Ocom_OSKIP,v_P,t_a),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_439,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,c_Com_Ocom_OSKIP,v_P,t_a)),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_332,c_435]) ).
cnf(c_440,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,c_Com_Ocom_OSKIP,v_P,t_a)),t_a),
inference(paramod,[status(thm)],[c_166,c_439]) ).
cnf(c_436,plain,
$false,
inference(resolve,[status(thm)],[c_396,c_440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV839-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n026.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 26 15:05:45 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 1310709 was started by sandbox on n026,
% 0.10/5.37 % Sat Sep 26 15:05:45 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/5.46
% 0.13/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.46
% 0.13/5.46 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.13/5.46 % Length of proof is 10.
% 0.13/5.46 % Level of proof is 4.
% 0.13/5.46 % Maximum clause weight is 34.000.
% 0.13/5.46 % Given clauses 0.
% 0.13/5.46
% 0.13/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------