%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW321+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 01:30:06 PM UTC 2026
% Result : Theorem 1.75s 1.57s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 14 unt; 3 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 36 ~; 30 |; 2 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
=> c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))
& c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_derivs__insertD) ).
fof(f5228,axiom,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5231,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f5232,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f5233,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(f5234,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
inference(negated_conjecture,[status(cth)],[f5233]) ).
fof(f5235,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
inference(flattening,[],[f5234]) ).
fof(f5238,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
inference(ennf_transformation,[],[f5228]) ).
fof(f5239,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
inference(ennf_transformation,[],[f5231]) ).
fof(f5245,plain,
! [X0,X1,X2,X3] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))
& c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f5246,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool)))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f5247,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool)))) ),
inference(flattening,[],[f5246]) ).
fof(f5374,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
inference(cnf_transformation,[],[f5238]) ).
fof(f5377,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
inference(cnf_transformation,[],[f5239]) ).
fof(f5378,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))),
inference(cnf_transformation,[],[f5232]) ).
fof(f5379,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
inference(cnf_transformation,[],[f5235]) ).
fof(f5383,plain,
! [X2,X3,X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0) ),
inference(cnf_transformation,[],[f5245]) ).
fof(f5384,plain,
! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f5245]) ).
fof(f5385,plain,
! [X2,X3,X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f5247]) ).
fof(f5592,definition,
( spl23_1
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f5594,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
| spl23_1 ),
inference(avatar_component_clause,[],[f5592]) ).
fof(f5596,definition,
( spl23_2
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f5598,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f5596]) ).
fof(f5599,plain,
( ~ spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f5377,f5596,f5592]) ).
fof(f5610,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),X1)) ),
inference(resolution,[],[f5374,f5384]) ).
fof(f5617,plain,
! [X2,X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),X1))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),X2)) ),
inference(resolution,[],[f5610,f5385]) ).
fof(f5621,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)),
inference(resolution,[],[f5378,f5383]) ).
fof(f5625,plain,
( $false
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f5621,f5594]) ).
fof(f5626,plain,
spl23_1,
inference(avatar_contradiction_clause,[],[f5625]) ).
fof(f5666,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),X0)) ),
inference(resolution,[],[f5617,f5378]) ).
fof(f5685,definition,
( spl23_5
<=> ! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f5686,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),X0))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X0) )
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f5685]) ).
fof(f5688,plain,
spl23_5,
inference(avatar_split_clause,[],[f5666,f5685]) ).
fof(f5689,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))
| ~ spl23_5 ),
inference(resolution,[],[f5686,f5379]) ).
fof(f5712,plain,
( $false
| ~ spl23_2
| ~ spl23_5 ),
inference(forward_subsumption_resolution,[],[f5689,f5598]) ).
fof(f5713,plain,
( ~ spl23_2
| ~ spl23_5 ),
inference(avatar_contradiction_clause,[],[f5712]) ).
cnf(s1,plain,
( ~ spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f5599]) ).
cnf(s3,plain,
spl23_1,
inference(sat_conversion,[],[f5626]) ).
cnf(s5,plain,
spl23_5,
inference(sat_conversion,[],[f5688]) ).
cnf(s6,plain,
( ~ spl23_2
| ~ spl23_5 ),
inference(sat_conversion,[],[f5713]) ).
cnf(s7,plain,
~ spl23_2,
inference(rat,[],[s6,s5]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s3]) ).
fof(f5714,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW321+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n013.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 13:34:06 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.75/1.57 % (1180491)Detected formulas, will run a generic FOF schedule.
% 1.75/1.57 % (1180498)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=784507875:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 1.75/1.57 % (1180497)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4089869709:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 1.75/1.57 % (1180496)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2600413745:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 1.75/1.57 % (1180502)dis-21_1_sil=8000:lcm=predicate:random_seed=1462633045:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 1.75/1.57 % (1180501)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2785668728:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 1.75/1.57 % (1180500)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2174018051:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 1.75/1.57 % (1180499)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2397626419:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 1.75/1.57 % (1180499)First to succeed.
% 1.75/1.57 % (1180499)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1180491"
% 1.75/1.57 % (1180501)Instruction limit reached!
% 1.75/1.57 % (1180501)------------------------------
% 1.75/1.57 % (1180501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.57 % (1180501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.57 % (1180501)CaDiCaL version: 2.1.3
% 1.75/1.57 % (1180501)Termination reason: Instruction limit
% 1.75/1.57 % (1180501)Termination phase: SInE selection
% 1.75/1.57 % (1180501)Time elapsed: 0.057 s
% 1.75/1.57 % (1180501)Peak memory usage: 90 MB
% 1.75/1.57 % (1180501)Instructions burned: 140 (million)
% 1.75/1.57 % (1180500)Instruction limit reached!
% 1.75/1.57 % (1180500)------------------------------
% 1.75/1.57 % (1180500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.57 % (1180500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.57 % (1180500)CaDiCaL version: 2.1.3
% 1.75/1.57 % (1180500)Termination reason: Instruction limit
% 1.75/1.57 % (1180500)Termination phase: Equality resolution with deletion
% 1.75/1.57 % (1180500)Time elapsed: 0.067 s
% 1.75/1.57 % (1180500)Peak memory usage: 92 MB
% 1.75/1.57 % (1180500)Instructions burned: 120 (million)
% 1.75/1.57 % (1180502)Instruction limit reached!
% 1.75/1.57 % (1180502)------------------------------
% 1.75/1.57 % (1180502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.57 % (1180502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.57 % (1180502)CaDiCaL version: 2.1.3
% 1.75/1.57 % (1180502)Termination reason: Instruction limit
% 1.75/1.57 % (1180502)Termination phase: Preprocessing 3
% 1.75/1.57 % (1180502)Time elapsed: 0.105 s
% 1.75/1.57 % (1180502)Peak memory usage: 93 MB
% 1.75/1.57 % (1180502)Instructions burned: 129 (million)
% 1.75/1.57 % (1180510)lrs+10_1_sil=8000:sp=occurrence:random_seed=3822194734:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 1.75/1.57 % (1180511)lrs+10_1_sil=32000:urr=on:br=off:random_seed=793543558:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 1.75/1.57 % (1180512)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1487427170:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 1.75/1.57 % (1180511)Instruction limit reached!
% 1.75/1.57 % (1180511)------------------------------
% 1.75/1.57 % (1180511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.57 % (1180511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.57 % (1180511)CaDiCaL version: 2.1.3
% 1.75/1.57 % (1180511)Termination reason: Instruction limit
% 1.75/1.57 % (1180511)Termination phase: Equality resolution with deletion
% 1.75/1.57 % (1180511)Time elapsed: 0.072 s
% 1.75/1.57 % (1180511)Peak memory usage: 92 MB
% 1.75/1.57 % (1180511)Instructions burned: 160 (million)
% 1.75/1.57 % (1180499)Refutation found. Thanks to Tanya!
% 1.75/1.57 % SZS status Theorem for theBenchmark
% 1.75/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.80 % (1180499)------------------------------
% 0.21/1.80 % (1180499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.80 % (1180499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.80 % (1180499)CaDiCaL version: 2.1.3
% 0.21/1.80 % (1180499)Termination reason: Refutation
% 0.21/1.80 % (1180499)Time elapsed: 0.052 s
% 0.21/1.80 % (1180499)Peak memory usage: 96 MB
% 0.21/1.80 % (1180499)Instructions burned: 82 (million)
% 0.21/1.80 % (1180499)------------------------------
% 0.21/1.80 % (1180499)------------------------------
% 0.21/1.80 % (1180491)Success in time 0.887 s
% 0.21/1.80 % Vampire exiting
%------------------------------------------------------------------------------