TSTP Solution File: SWV884-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV884-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:24:50 EDT 2022
% Result : Unsatisfiable 0.73s 0.77s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 53 ( 12 unt; 13 typ; 0 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 248 ( 116 ~; 111 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 6 >; 11 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 169 ( 151 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(1,plain,
( ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(3,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(6,plain,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
( ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
( ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
tff(13,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
( c_in(v_pn,v_U,tc_Com_Opname)
<=> c_in(v_pn,v_U,tc_Com_Opname) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
c_in(v_pn,v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(26,plain,
c_in(v_pn,v_U,tc_Com_Opname),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
<=> ( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
rewrite(
( ( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| ~ c_in(V_x,V_A,T_a) )
<=> ( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| ~ c_in(V_x,V_A,T_a) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| ~ c_in(V_x,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
tff(33,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,36,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV884-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 09:05:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.73/0.77 % SZS status Unsatisfiable
% 0.73/0.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------