%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN727+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:55 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 41 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 125 ( 61 ~; 41 |; 5 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 102 ( 78 !; 19 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(likes_type,type,
likes: ( $i * $i ) > $o ).
tff(bruce_type,type,
bruce: $i ).
tff(tptp_fun_V_0_type,type,
tptp_fun_V_0: $i > $i ).
tff(lyle_type,type,
lyle: $i ).
tff(1,plain,
( ~ ? [U: $i] :
! [V: $i] : likes(U,V)
<=> ~ ? [U: $i] :
! [V: $i] : likes(U,V) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( ! [X: $i] : likes(X,bruce)
& ! [Y: $i] :
( ? [Z: $i] : likes(Y,Z)
=> likes(lyle,Y) ) )
=> ? [U: $i] :
! [V: $i] : likes(U,V) )
<=> ~ ( ~ ( ! [X: $i] : likes(X,bruce)
& ! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) ) )
| ? [U: $i] :
! [V: $i] : likes(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( ! [X: $i] : likes(X,bruce)
& ! [Y: $i] :
( ? [Z: $i] : likes(Y,Z)
=> likes(lyle,Y) ) )
=> ? [U: $i] :
! [V: $i] : likes(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm68) ).
tff(4,plain,
~ ( ~ ( ! [X: $i] : likes(X,bruce)
& ! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) ) )
| ? [U: $i] :
! [V: $i] : likes(U,V) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ ? [U: $i] :
! [V: $i] : likes(U,V),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ ? [U: $i] :
! [V: $i] : likes(U,V),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
~ ? [U: $i] :
! [V: $i] : likes(U,V),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
~ ? [U: $i] :
! [V: $i] : likes(U,V),
inference(modus_ponens,[status(thm)],[7,1]) ).
tff(9,plain,
^ [U: $i] :
sk($oeq(~ ! [V: $i] : likes(U,V),~ likes(U,tptp_fun_V_0(U)))),
inference(bind,[status(th)],[]) ).
tff(10,plain,
! [U: $i] : ~ likes(U,tptp_fun_V_0(U)),
inference(nnf-neg,[status(sab)],[8,9]) ).
tff(11,plain,
( ~ ! [U: $i] : ~ likes(U,tptp_fun_V_0(U))
| ~ likes(lyle,tptp_fun_V_0(lyle)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ likes(lyle,tptp_fun_V_0(lyle)),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Y: $i] :
refl(( ( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
<=> ( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
<=> ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [Y: $i] :
rewrite(( ( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
<=> ( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
<=> ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
<=> ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
^ [Y: $i] :
rewrite(( ( ! [Z: $i] : ~ likes(Y,Z)
| likes(lyle,Y) )
<=> ( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Y: $i] :
( ! [Z: $i] : ~ likes(Y,Z)
| likes(lyle,Y) )
<=> ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) )
<=> ! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ! [X: $i] : likes(X,bruce)
& ! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(22,plain,
! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) ),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
! [Y: $i] :
( ~ ? [Z: $i] : likes(Y,Z)
| likes(lyle,Y) ),
inference(modus_ponens,[status(thm)],[22,20]) ).
tff(24,plain,
! [Y: $i] :
( ! [Z: $i] : ~ likes(Y,Z)
| likes(lyle,Y) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ),
inference(modus_ponens,[status(thm)],[24,19]) ).
tff(26,plain,
! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) ),
inference(modus_ponens,[status(thm)],[25,17]) ).
tff(27,plain,
( ( ~ ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
| likes(lyle,tptp_fun_V_0(lyle))
| ! [Z: $i] : ~ likes(tptp_fun_V_0(lyle),Z) )
<=> ( ~ ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
| likes(lyle,tptp_fun_V_0(lyle))
| ! [Z: $i] : ~ likes(tptp_fun_V_0(lyle),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
| likes(lyle,tptp_fun_V_0(lyle))
| ! [Z: $i] : ~ likes(tptp_fun_V_0(lyle),Z) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Y: $i] :
( likes(lyle,Y)
| ! [Z: $i] : ~ likes(Y,Z) )
| likes(lyle,tptp_fun_V_0(lyle))
| ! [Z: $i] : ~ likes(tptp_fun_V_0(lyle),Z) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i] : ~ likes(tptp_fun_V_0(lyle),Z),
inference(unit_resolution,[status(thm)],[29,26,12]) ).
tff(31,plain,
( ~ ! [Z: $i] : ~ likes(tptp_fun_V_0(lyle),Z)
| ~ likes(tptp_fun_V_0(lyle),bruce) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
~ likes(tptp_fun_V_0(lyle),bruce),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
^ [X: $i] :
refl(( likes(X,bruce)
<=> likes(X,bruce) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X: $i] : likes(X,bruce)
<=> ! [X: $i] : likes(X,bruce) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X: $i] : likes(X,bruce)
<=> ! [X: $i] : likes(X,bruce) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
! [X: $i] : likes(X,bruce),
inference(and_elim,[status(thm)],[21]) ).
tff(37,plain,
! [X: $i] : likes(X,bruce),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X: $i] : likes(X,bruce),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X: $i] : likes(X,bruce),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [X: $i] : likes(X,bruce)
| likes(tptp_fun_V_0(lyle),bruce) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,39,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN727+1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:40:25 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------