%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET786-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:26:20 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 46 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 354 ( 176 ~; 154 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 84 ( 78 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(element_type,type,
element: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
<=> ( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
<=> ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
<=> ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [B: $i,A: $i] :
trans(monotonicity(rewrite(( ( ~ element(B,A)
| ~ element(A,B) )
<=> ( ~ element(A,B)
| ~ element(B,A) ) )),
( ( ~ element(B,A)
| ~ element(A,B)
| ~ element(A,sk1) )
<=> ( ~ element(A,B)
| ~ element(B,A)
| ~ element(A,sk1) ) )),
rewrite(( ( ~ element(A,B)
| ~ element(B,A)
| ~ element(A,sk1) )
<=> ( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ) )),
( ( ~ element(B,A)
| ~ element(A,B)
| ~ element(A,sk1) )
<=> ( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i] :
( ~ element(B,A)
| ~ element(A,B)
| ~ element(A,sk1) )
<=> ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,A: $i] :
( ~ element(B,A)
| ~ element(A,B)
| ~ element(A,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm25_1) ).
tff(7,plain,
! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( ~ element(sk1,sk1)
| ~ element(sk1,sk1)
| ~ element(sk1,sk1) )
<=> ~ element(sk1,sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1)
| ~ element(sk1,sk1)
| ~ element(sk1,sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1)
| ~ element(sk1,sk1)
| ~ element(sk1,sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1)
| ~ element(sk1,sk1)
| ~ element(sk1,sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk1,sk1) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ element(sk1,sk1),
inference(unit_resolution,[status(thm)],[16,10]) ).
tff(18,plain,
^ [A: $i] :
refl(( ( element(A,sk1)
| element(sk2(A),A) )
<=> ( element(A,sk1)
| element(sk2(A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) )
<=> ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) )
<=> ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm25_3) ).
tff(22,plain,
! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) )
| element(sk1,sk1)
| element(sk2(sk1),sk1) )
<=> ( ~ ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) )
| element(sk1,sk1)
| element(sk2(sk1),sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) )
| element(sk1,sk1)
| element(sk2(sk1),sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [A: $i] :
( element(A,sk1)
| element(sk2(A),A) )
| element(sk1,sk1)
| element(sk2(sk1),sk1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
element(sk2(sk1),sk1),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [A: $i] :
refl(( ( element(A,sk1)
| element(A,sk2(A)) )
<=> ( element(A,sk1)
| element(A,sk2(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) )
<=> ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) )
<=> ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm25_2) ).
tff(33,plain,
! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) )
| element(sk1,sk1)
| element(sk1,sk2(sk1)) )
<=> ( ~ ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) )
| element(sk1,sk1)
| element(sk1,sk2(sk1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) )
| element(sk1,sk1)
| element(sk1,sk2(sk1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [A: $i] :
( element(A,sk1)
| element(A,sk2(A)) )
| element(sk1,sk1)
| element(sk1,sk2(sk1)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
element(sk1,sk2(sk1)),
inference(unit_resolution,[status(thm)],[38,35,17]) ).
tff(40,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ element(sk2(sk1),sk1)
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) )
<=> ( ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] :
( ~ element(A,sk1)
| ~ element(A,B)
| ~ element(B,A) )
| ~ element(sk2(sk1),sk1)
| ~ element(sk1,sk2(sk1)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,10,39,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET786-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 05:42:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------