%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV861-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:36:14 AM UTC 2025
% Result : Unsatisfiable 0.36s 0.53s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 317 ( 148 ~; 144 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 114 ( 102 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_s1_type,type,
v_s1: $i ).
tff(v_Z_type,type,
v_Z: $i ).
tff(v_Q_type,type,
v_Q: $i ).
tff(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o ).
tff(v_n_type,type,
v_n: $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(v_s_type,type,
v_s: $i ).
tff(v_R_type,type,
v_R: $i ).
tff(v_d_type,type,
v_d: $i ).
tff(v_s_H_type,type,
v_s_H: $i ).
tff(1,plain,
^ [V_Z: $i,V_s_H: $i,V_s: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_Z: $i,V_s_H: $i,V_s: $i] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H) )
<=> ( ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) )),
( ( hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) )
<=> ( ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) ) )),
rewrite(( ( ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) )
<=> ( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) )),
( ( hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) )
<=> ( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(7,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( c_Natural_Oevaln(v_c,v_s,v_n,v_s1)
<=> c_Natural_Oevaln(v_c,v_s,v_n,v_s1) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(13,plain,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( hBOOL(hAPP(hAPP(v_P,v_Z),v_s))
<=> hBOOL(hAPP(hAPP(v_P,v_Z),v_s)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
hBOOL(hAPP(hAPP(v_P,v_Z),v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(16,plain,
hBOOL(hAPP(hAPP(v_P,v_Z),v_s)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_P,v_Z),v_s))
| ~ c_Natural_Oevaln(v_c,v_s,v_n,v_s1)
| hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) )
<=> ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_P,v_Z),v_s))
| ~ c_Natural_Oevaln(v_c,v_s,v_n,v_s1)
| hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_P,v_Z),v_s))
| ~ c_Natural_Oevaln(v_c,v_s,v_n,v_s1)
| hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_P,v_Z),v_s))
| ~ c_Natural_Oevaln(v_c,v_s,v_n,v_s1)
| hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)),
inference(unit_resolution,[status(thm)],[19,16,13,10]) ).
tff(21,plain,
^ [V_Z: $i,V_s_H: $i,V_s: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [V_Z: $i,V_s_H: $i,V_s: $i] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H) )
<=> ( ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) )),
( ( hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) )
<=> ( ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) ) )),
rewrite(( ( ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) )
<=> ( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) )),
( ( hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) )
<=> ( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(27,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
<=> ~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(33,plain,
~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
<=> c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(36,plain,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) )
<=> ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) )
<=> ( hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) )
<=> ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) )
<=> ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H)) )
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H))
| ~ c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,36,33,30,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV861-1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:02:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.36/0.53 % SZS status Unsatisfiable
% 0.36/0.53 % SZS output start Proof
% See solution above
% 0.38/0.57 % E exiting
%------------------------------------------------------------------------------