%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV838-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 : Fri Sep 25 03:24:19 PM UTC 2026
% Result : Unsatisfiable 113.20s 18.81s
% Output : CNFRefutation 113.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 17 unt; 0 def)
% Number of atoms : 127 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 130 ( 57 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-6 aty)
% Number of variables : 142 ( 0 sgn 142 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X0),X2),X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
fof(f226,axiom,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f365,axiom,
! [X0,X1] : c_Collect(X0,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f404,axiom,
! [X0,X1] : c_Collect(hAPP(c_fequal(X0),X1),X0) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f405,plain,
! [X0,X1] : c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Collect(hAPP(c_fequal(X0),X1),X0),
inference(reorient_equations,[],[f404]) ).
fof(f445,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,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)
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X1,X3,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(f446,axiom,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(f447,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,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)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X1,X3,X2,X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(f514,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f515,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f517,negated_conjecture,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f518,negated_conjecture,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X2),v_sa(X0,X2,X1)),X2))
| hBOOL(hAPP(hAPP(v_Q,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f519,negated_conjecture,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X2),v_sa(X0,X2,X1)),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f603,plain,
! [X0,X1] : c_Collect(hAPP(c_fequal(X0),X1),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f405,f46]) ).
fof(f636,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,t_a)),tc_Hoare__Mirabelle_Otriple(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)
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X1,X3,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(definition_unfolding,[],[f445,f46,f46]) ).
fof(f637,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(definition_unfolding,[],[f446,f46]) ).
fof(f638,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,t_a)),tc_Hoare__Mirabelle_Otriple(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)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X1,X3,X2,X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(definition_unfolding,[],[f447,f46,f46]) ).
fof(f670,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),tc_Hoare__Mirabelle_Otriple(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(definition_unfolding,[],[f515,f46]) ).
fof(f672,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a)),tc_Hoare__Mirabelle_Otriple(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(definition_unfolding,[],[f517,f46]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[],[f226]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i] : c_Collect(X0,X1) = X0,
inference(cnf_transformation,[],[f365]) ).
tcf(c_845,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_fequal(X0),X1),X0),
inference(cnf_transformation,[],[f603]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( hBOOL(hAPP(hAPP(X3,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X5,X6,X2,X1,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X5,X2,X6,t_a)),tc_Hoare__Mirabelle_Otriple(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)
| ~ hBOOL(hAPP(hAPP(X1,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X5,X6,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(cnf_transformation,[],[f636]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(cnf_transformation,[],[f637]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X5,X2,X4,t_a)),tc_Hoare__Mirabelle_Otriple(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)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X5,X4,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X5,X4,X2,X1,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(cnf_transformation,[],[f638]) ).
tcf(c_943,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(cnf_transformation,[],[f514]) ).
tcf(c_944,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),tc_Hoare__Mirabelle_Otriple(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(cnf_transformation,[],[f670]) ).
tcf(c_946,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a)),tc_Hoare__Mirabelle_Otriple(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)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X0)) ),
inference(cnf_transformation,[],[f672]) ).
tcf(c_947,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1)) ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_948,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f519]) ).
tcf(c_1529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(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),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(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(prop_impl_just,[status(thm)],[c_881]) ).
tcf(c_3489,plain,
! [X0: $i,X1: $i] : hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = hAPP(c_fequal(X0),X1),
inference(demodulation,[status(thm)],[c_845,c_703,c_813]) ).
tcf(c_3509,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,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(demodulation,[status(thm)],[c_944,c_703,c_813,c_3489]) ).
tcf(c_3546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X3,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X0,X2,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X0,X2,X3))) ),
inference(demodulation,[status(thm)],[c_1529,c_703,c_813,c_3489]) ).
tcf(c_3563,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X0)) ),
inference(demodulation,[status(thm)],[c_946,c_703,c_813,c_3489]) ).
tcf(c_3590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X0,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X3,X5,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X0,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X0,X3,X4,X5))) ),
inference(demodulation,[status(thm)],[c_882,c_703,c_813,c_3489]) ).
tcf(c_3592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X2,X6,t_a)),t_a)
| hBOOL(hAPP(hAPP(X3,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X5,X6,X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(X1,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X5,X6,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a) ),
inference(demodulation,[status(thm)],[c_880,c_703,c_813,c_3489]) ).
tcf(c_7493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X3,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X0,X2,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X0,X2,X3))) ),
inference(prop_impl_just,[status(thm)],[c_3546]) ).
tcf(c_15641,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,X2,X1,t_a)),t_a)
| hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2))) ),
inference(instantiation,[status(thm)],[c_7493]) ).
tcf(c_15643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2)),X3))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2)))
| ~ hBOOL(hAPP(hAPP(v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2),X3)),X3)) ),
inference(instantiation,[status(thm)],[c_948]) ).
tcf(c_15644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2)),X3))
| hBOOL(hAPP(hAPP(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2),X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2)))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,v_P,X1,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,v_P,X1,X2))) ),
inference(instantiation,[status(thm)],[c_947]) ).
tcf(c_16830,plain,
! [X0: $i,X1: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,X0,X1))) ),
inference(instantiation,[status(thm)],[c_3590]) ).
tcf(c_16842,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,X0,X1)))
| ~ hBOOL(hAPP(hAPP(X0,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),t_a) ),
inference(instantiation,[status(thm)],[c_3592]) ).
tcf(c_17128,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))) ),
inference(instantiation,[status(thm)],[c_15641]) ).
tcf(c_22445,plain,
! [X0: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_c,v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X0))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))) ),
inference(instantiation,[status(thm)],[c_3563]) ).
tcf(c_22448,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),X0))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))
| ~ hBOOL(hAPP(hAPP(v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c),X0)),X0)) ),
inference(instantiation,[status(thm)],[c_15643]) ).
tcf(c_28329,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_c,v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))) ),
inference(instantiation,[status(thm)],[c_22445]) ).
tcf(c_28670,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,X0,v_c)),X1))
| hBOOL(hAPP(hAPP(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,X0,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,X0,v_c)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,X0,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,X0,v_c),X1)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,X0,v_c)))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,X0,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,X0,v_c))) ),
inference(instantiation,[status(thm)],[c_15644]) ).
tcf(c_36767,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_c,v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))))) ),
inference(instantiation,[status(thm)],[c_16830]) ).
tcf(c_36771,plain,
! [X0: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| hBOOL(hAPP(hAPP(v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))))
| ~ hBOOL(hAPP(hAPP(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_c,v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),t_a)),t_a) ),
inference(instantiation,[status(thm)],[c_16842]) ).
tcf(c_45922,plain,
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))))
| hBOOL(hAPP(hAPP(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))) ),
inference(instantiation,[status(thm)],[c_28670]) ).
tcf(c_64683,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| hBOOL(hAPP(hAPP(v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_c,v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))) ),
inference(instantiation,[status(thm)],[c_36771]) ).
tcf(c_75871,plain,
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)))
| ~ hBOOL(hAPP(hAPP(v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_sa(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_Ga,v_P,v_Q,v_c,v_Z(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c)),v_s(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_Ga,v_P,v_Q,v_c),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_Ga,v_P,v_Q,v_c))))) ),
inference(instantiation,[status(thm)],[c_22448]) ).
tcf(c_75872,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_75871,c_64683,c_45922,c_36767,c_28329,c_17128,c_3509,c_943]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV838-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 21:11:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 113.20/18.81 % SZS status Started for theBenchmark.p
% 113.20/18.81 % SZS status Unsatisfiable for theBenchmark.p
% 113.20/18.81
% 113.20/18.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 113.20/18.81
% 113.20/18.81 % ------ iProver source info
% 113.20/18.81
% 113.20/18.81 % git: date: 2026-07-19 20:42:38 +0200
% 113.20/18.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 113.20/18.81 % git: non_committed_changes: false
% 113.20/18.81
% 113.20/18.81 % ------ Parsing...% successful
% 113.20/18.81
% 113.20/18.81
% 113.20/18.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 113.20/18.81
% 113.20/18.81 % ------ Preprocessing... sup_sim: 98 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sup_sim: 7 sf_s rm: 4 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 113.20/18.81
% 113.20/18.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 113.20/18.81
% 113.20/18.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 113.20/18.81 % ------ Proving...
% 113.20/18.81 % ------ Problem Properties
% 113.20/18.81
% 113.20/18.81 %
% 113.20/18.81 % clauses 334
% 113.20/18.81 % conjectures 3
% 113.20/18.81 % EPR 31
% 113.20/18.81 % Horn 274
% 113.20/18.81 % unary 84
% 113.20/18.81 % binary 117
% 113.20/18.81 % lits 752
% 113.20/18.81 % lits eq 162
% 113.20/18.81 % fd_pure 0
% 113.20/18.81 % fd_pseudo 0
% 113.20/18.81 % fd_cond 4
% 113.20/18.81 % fd_pseudo_cond 34
% 113.20/18.81 % AC symbols 0
% 113.20/18.81
% 113.20/18.81 % ------ Input Options Time Limit: Unbounded
% 113.20/18.81
% 113.20/18.81
% 113.20/18.81 % ------
% 113.20/18.81 % Current options:
% 113.20/18.81 % ------
% 113.20/18.81
% 113.20/18.81
% 113.20/18.81 %
% 113.20/18.81
% 113.20/18.81 % ------ Proving...
% 113.20/18.81 %
% 113.20/18.81
% 113.20/18.81 % SZS status Unsatisfiable for theBenchmark.p
% 113.20/18.81
% 113.20/18.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 113.20/18.82
%------------------------------------------------------------------------------