%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV857-1 : 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 : n014.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 09:09:14 AM UTC 2026
% Result : Unsatisfiable 6.53s 1.38s
% Output : CNFRefutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 4 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),VAR_0),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,VAR_0,t_a) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_215,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,A,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_216,plain,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_217,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_218,plain,
c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_mem__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(hAPP(c_in(VAR_2),VAR_1),VAR_0))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(c_220,plain,
( ~ hBOOL(hAPP(hAPP(c_in(C),B),A))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_mem__def_0]) ).
fof(cls_mem__def_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(VAR_2,VAR_1))
| hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),VAR_2)) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(c_221,plain,
( ~ hBOOL(hAPP(C,B))
| hBOOL(hAPP(hAPP(c_in(A),B),C)) ),
inference(clausify,[status(thm)],[cls_mem__def_1]) ).
fof(cls_predicate1D_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_lessequals(VAR_2,VAR_0,tc_fun(VAR_3,tc_bool))
| ~ hBOOL(hAPP(VAR_2,VAR_1))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_predicate1D_0) ).
cnf(c_229,plain,
( ~ c_lessequals(C,A,tc_fun(D,tc_bool))
| ~ hBOOL(hAPP(C,B))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_predicate1D_0]) ).
cnf(c_888,plain,
hBOOL(hAPP(v_tsa,v_xa)),
inference(resolve,[status(thm)],[c_220,c_217]) ).
cnf(c_901,plain,
( ~ hBOOL(hAPP(v_tsa,A))
| hBOOL(hAPP(v_Ga,A)) ),
inference(resolve,[status(thm)],[c_229,c_218]) ).
cnf(c_4136,plain,
hBOOL(hAPP(v_Ga,v_xa)),
inference(resolve,[status(thm)],[c_901,c_888]) ).
cnf(c_4140,plain,
hBOOL(hAPP(hAPP(c_in(A),v_xa),v_Ga)),
inference(resolve,[status(thm)],[c_4136,c_221]) ).
cnf(c_4217,plain,
c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
inference(resolve,[status(thm)],[c_4140,c_215]) ).
cnf(c_4216,plain,
$false,
inference(resolve,[status(thm)],[c_216,c_4217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV857-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 15:04:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3462214 was started by sandbox on n014,
% 0.09/0.35 % Sat Sep 26 15:04:01 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 6.53/1.38
% 6.53/1.38 % given #500 (I,wt=28): 734 -class_Orderings_Oorder(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(B,A),tc_fun(A,tc_bool)),tc_fun(A,tc_bool)) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A). [back_rewrite(570),rewrite([607(9)])].
% 6.53/1.38
% 6.53/1.38 % SZS status Unsatisfiable for theBenchmark
% 6.53/1.38
% 6.53/1.38 % Proof 1 at 0.62 (+ 0.13) seconds.
% 6.53/1.38 % Length of proof is 12.
% 6.53/1.38 % Level of proof is 4.
% 6.53/1.38 % Maximum clause weight is 14.000.
% 6.53/1.38 % Given clauses 658.
% 6.53/1.38
% 6.53/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------