%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN729-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:56 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of formulae : 70 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 329 ( 160 ~; 139 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 81 ( 73 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: $i > $o ).
tff(sk1_type,type,
sk1: $i > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(h_type,type,
h: $i > $i ).
tff(g_type,type,
g: $i > $i ).
tff(l_type,type,
l: ( $i * $i ) > $o ).
tff(1,plain,
( p(sk2)
<=> p(sk2) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm72_5) ).
tff(3,plain,
p(sk2),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [A: $i] :
refl(( ( ~ p(A)
| l(A,g(h(sk1(A)))) )
<=> ( ~ p(A)
| l(A,g(h(sk1(A)))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) )
<=> ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) )
<=> ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [A: $i] :
rewrite(( ( l(A,g(h(sk1(A))))
| ~ p(A) )
<=> ( ~ p(A)
| l(A,g(h(sk1(A)))) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [A: $i] :
( l(A,g(h(sk1(A))))
| ~ p(A) )
<=> ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [A: $i] :
( l(A,g(h(sk1(A))))
| ~ p(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm72_1) ).
tff(10,plain,
! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) )
| ~ p(sk2)
| l(sk2,g(h(sk1(sk2)))) )
<=> ( ~ ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) )
| ~ p(sk2)
| l(sk2,g(h(sk1(sk2)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) )
| ~ p(sk2)
| l(sk2,g(h(sk1(sk2)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [A: $i] :
( ~ p(A)
| l(A,g(h(sk1(A)))) )
| ~ p(sk2)
| l(sk2,g(h(sk1(sk2)))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
l(sk2,g(h(sk1(sk2)))),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [A: $i] :
refl(( ( ~ p(A)
| ~ l(sk2,A) )
<=> ( ~ p(A)
| ~ l(sk2,A) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) )
<=> ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) )
<=> ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm72_6) ).
tff(22,plain,
! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) )
| ~ p(g(h(sk1(sk2))))
| ~ l(sk2,g(h(sk1(sk2)))) )
<=> ( ~ ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) )
| ~ p(g(h(sk1(sk2))))
| ~ l(sk2,g(h(sk1(sk2)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) )
| ~ p(g(h(sk1(sk2))))
| ~ l(sk2,g(h(sk1(sk2)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [A: $i] :
( ~ p(A)
| ~ l(sk2,A) )
| ~ p(g(h(sk1(sk2))))
| ~ l(sk2,g(h(sk1(sk2)))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ p(g(h(sk1(sk2)))),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [A: $i] :
refl(( ( ~ p(A)
| p(g(A)) )
<=> ( ~ p(A)
| p(g(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [A: $i] :
( ~ p(A)
| p(g(A)) )
<=> ! [A: $i] :
( ~ p(A)
| p(g(A)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [A: $i] :
( ~ p(A)
| p(g(A)) )
<=> ! [A: $i] :
( ~ p(A)
| p(g(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [A: $i] :
rewrite(( ( p(g(A))
| ~ p(A) )
<=> ( ~ p(A)
| p(g(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [A: $i] :
( p(g(A))
| ~ p(A) )
<=> ! [A: $i] :
( ~ p(A)
| p(g(A)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [A: $i] :
( p(g(A))
| ~ p(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm72_3) ).
tff(35,plain,
! [A: $i] :
( ~ p(A)
| p(g(A)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [A: $i] :
( ~ p(A)
| p(g(A)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [A: $i] :
( ~ p(A)
| p(g(A)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [A: $i] :
( ~ p(A)
| p(g(A)) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [A: $i] :
( ~ p(A)
| p(g(A)) )
| ~ p(h(sk1(sk2)))
| p(g(h(sk1(sk2)))) )
<=> ( ~ ! [A: $i] :
( ~ p(A)
| p(g(A)) )
| ~ p(h(sk1(sk2)))
| p(g(h(sk1(sk2)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [A: $i] :
( ~ p(A)
| p(g(A)) )
| ~ p(h(sk1(sk2)))
| p(g(h(sk1(sk2)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [A: $i] :
( ~ p(A)
| p(g(A)) )
| ~ p(h(sk1(sk2)))
| p(g(h(sk1(sk2)))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ p(h(sk1(sk2))),
inference(unit_resolution,[status(thm)],[41,38,28]) ).
tff(43,plain,
^ [A: $i] :
refl(( ( ~ p(A)
| p(h(A)) )
<=> ( ~ p(A)
| p(h(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [A: $i] :
( ~ p(A)
| p(h(A)) )
<=> ! [A: $i] :
( ~ p(A)
| p(h(A)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [A: $i] :
( ~ p(A)
| p(h(A)) )
<=> ! [A: $i] :
( ~ p(A)
| p(h(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
^ [A: $i] :
rewrite(( ( p(h(A))
| ~ p(A) )
<=> ( ~ p(A)
| p(h(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [A: $i] :
( p(h(A))
| ~ p(A) )
<=> ! [A: $i] :
( ~ p(A)
| p(h(A)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [A: $i] :
( p(h(A))
| ~ p(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm72_4) ).
tff(49,plain,
! [A: $i] :
( ~ p(A)
| p(h(A)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [A: $i] :
( ~ p(A)
| p(h(A)) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [A: $i] :
( ~ p(A)
| p(h(A)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [A: $i] :
( ~ p(A)
| p(h(A)) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [A: $i] :
( ~ p(A)
| p(h(A)) )
| ~ p(sk1(sk2))
| p(h(sk1(sk2))) )
<=> ( ~ ! [A: $i] :
( ~ p(A)
| p(h(A)) )
| ~ p(sk1(sk2))
| p(h(sk1(sk2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [A: $i] :
( ~ p(A)
| p(h(A)) )
| ~ p(sk1(sk2))
| p(h(sk1(sk2))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [A: $i] :
( ~ p(A)
| p(h(A)) )
| ~ p(sk1(sk2))
| p(h(sk1(sk2))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ p(sk1(sk2)),
inference(unit_resolution,[status(thm)],[55,52,42]) ).
tff(57,plain,
^ [A: $i] :
refl(( ( p(sk1(A))
| ~ p(A) )
<=> ( p(sk1(A))
| ~ p(A) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
<=> ! [A: $i] :
( p(sk1(A))
| ~ p(A) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
<=> ! [A: $i] :
( p(sk1(A))
| ~ p(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [A: $i] :
( p(sk1(A))
| ~ p(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm72_2) ).
tff(61,plain,
! [A: $i] :
( p(sk1(A))
| ~ p(A) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [A: $i] :
( p(sk1(A))
| ~ p(A) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [A: $i] :
( p(sk1(A))
| ~ p(A) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| ~ p(sk2)
| p(sk1(sk2)) )
<=> ( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| ~ p(sk2)
| p(sk1(sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( p(sk1(sk2))
| ~ p(sk2) )
<=> ( ~ p(sk2)
| p(sk1(sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| p(sk1(sk2))
| ~ p(sk2) )
<=> ( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| ~ p(sk2)
| p(sk1(sk2)) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| p(sk1(sk2))
| ~ p(sk2) )
<=> ( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| ~ p(sk2)
| p(sk1(sk2)) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| p(sk1(sk2))
| ~ p(sk2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [A: $i] :
( p(sk1(A))
| ~ p(A) )
| ~ p(sk2)
| p(sk1(sk2)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,63,3,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN729-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 12:41:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------