%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW375+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:36:53 AM UTC 2025
% Result : Theorem 17.28s 17.43s
% Output : Proof 17.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 43 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 176 ( 77 ~; 73 |; 0 &)
% ( 15 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_Com_OWT_type,type,
c_Com_OWT: $i ).
tff(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
tff(1,plain,
( ~ hBOOL(hAPP(c_Com_OWT,v_y))
<=> ~ hBOOL(hAPP(c_Com_OWT,v_y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_Com_OWT,v_y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(3,plain,
~ hBOOL(hAPP(c_Com_OWT,v_y)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
<=> ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
tff(6,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_Com_OWT__bodies
<=> c_Com_OWT__bodies ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(9,plain,
c_Com_OWT__bodies,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_b: $i,V_pn: $i] :
refl(( ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_b: $i,V_pn: $i] :
trans(monotonicity(rewrite(( ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )),
( ( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) )
<=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) ) )),
rewrite(( ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) )),
( ( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_b: $i,V_pn: $i] :
( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_b: $i,V_pn: $i] :
( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
tff(16,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) )
<=> ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
| ~ c_Com_OWT__bodies )
<=> ( hBOOL(hAPP(c_Com_OWT,v_y))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
| ~ c_Com_OWT__bodies )
<=> ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
| ~ c_Com_OWT__bodies )
<=> ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
| ~ c_Com_OWT__bodies ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW375+1 : TPTP v9.0.0. Released v5.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:34:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 17.28/17.43 % SZS status Theorem
% 17.28/17.43 % SZS output start Proof
% See solution above
% 17.72/17.89 % E exiting
%------------------------------------------------------------------------------