%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV911-1 : 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 : n017.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 09:09:19 AM UTC 2026
% Result : Unsatisfiable 82.81s 11.98s
% Output : CNFRefutation 82.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 49 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% Number of variables : 35 ( 1 sgn 11 !; 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_306,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) = hAPP(hAPP(c_Set_Oinsert(VAR_0),VAR_1),c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool))),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_535,plain,
c_Collect(hAPP(c_fequal(A),B),A) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_5809,plain,
hAPP(c_fequal(A),B) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),
inference(paramod,[status(thm)],[c_306,c_535]) ).
cnf(c_536,plain,
hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = hAPP(c_fequal(A),B),
inference(copy,[status(thm)],[c_5809]) ).
fof(cls_conjecture_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_647,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_648,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a),
inference(paramod,[status(thm)],[c_536,c_647]) ).
fof(cls_conjecture_1,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_649,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_650,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),t_a),
inference(paramod,[status(thm)],[c_536,c_649]) ).
fof(cls_conjecture_2,axiom,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_651,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0,VAR_1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(VAR_0,v_c,VAR_1,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(VAR_0,VAR_1))) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_652,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(A,B))) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_653,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(A,B))) ),
inference(paramod,[status(thm)],[c_536,c_652]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0,VAR_1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(VAR_0,v_c,VAR_1,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(VAR_0,VAR_1))) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_654,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(A,B))) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_655,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(A,B))) ),
inference(paramod,[status(thm)],[c_536,c_654]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(VAR_2,v_c,VAR_0,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(VAR_2,VAR_1),v_xa))
| hBOOL(hAPP(hAPP(VAR_0,VAR_1),v_xb(VAR_2,VAR_0))) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_656,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(C,v_c,A,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(C,B),v_xa))
| hBOOL(hAPP(hAPP(A,B),v_xb(C,A))) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_657,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(C,v_c,A,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(C,B),v_xa))
| hBOOL(hAPP(hAPP(A,B),v_xb(C,A))) ),
inference(paramod,[status(thm)],[c_536,c_656]) ).
cnf(c_2364,plain,
~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))),
inference(resolve,[status(thm)],[c_653,c_648]) ).
cnf(c_2368,plain,
~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))),
inference(resolve,[status(thm)],[c_655,c_650]) ).
cnf(c_5810,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,A,t_a)),t_a)
| hBOOL(hAPP(hAPP(A,v_x),v_xb(v_P_H,A))) ),
inference(resolve,[status(thm)],[c_657,c_651]) ).
cnf(c_5811,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))) ),
inference(resolve,[status(thm)],[c_5810,c_650]) ).
cnf(c_2378,plain,
hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(resolve,[status(thm)],[c_2368,c_5811]) ).
cnf(c_5812,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,A,t_a)),t_a)
| hBOOL(hAPP(hAPP(A,v_x),v_xb(v_P,A))) ),
inference(resolve,[status(thm)],[c_657,c_2378]) ).
cnf(c_5813,plain,
hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))),
inference(resolve,[status(thm)],[c_5812,c_648]) ).
cnf(c_5808,plain,
$false,
inference(resolve,[status(thm)],[c_2364,c_5813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV911-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.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 15:04:34 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1018715 was started by sandbox on n017,
% 0.17/0.44 % Sat Sep 26 15:04:34 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 82.81/11.98
% 82.81/11.98 % given #500 (A,wt=36): 756 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A). [para(89(a,1),83(a,1,2)),flip(a)].
% 82.81/11.98
% 82.81/11.98 % SZS status Unsatisfiable for theBenchmark
% 82.81/11.98
% 82.81/11.98 % Proof 1 at 2.89 (+ 0.49) seconds.
% 82.81/11.98 % Length of proof is 18.
% 82.81/11.98 % Level of proof is 5.
% 82.81/11.98 % Maximum clause weight is 38.000.
% 82.81/11.98 % Given clauses 651.
% 82.81/11.98
% 82.81/11.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------