%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN073+1 : TPTP v9.0.0. Released v2.0.0.
% 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 05:38:09 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 76 ( 28 ~; 37 |; 0 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 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 : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 77 ( 64 !; 10 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_f_type,type,
big_f: ( $i * $i ) > $o ).
tff(tptp_fun_Y1_0_type,type,
tptp_fun_Y1_0: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1)
<=> ~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
=> ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) )
<=> ~ ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
=> ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel50) ).
tff(4,plain,
~ ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[7,1]) ).
tff(9,plain,
^ [X1: $i] :
sk($oeq(~ ! [Y1: $i] : big_f(X1,Y1),~ big_f(X1,tptp_fun_Y1_0(X1)))),
inference(bind,[status(th)],[]) ).
tff(10,plain,
! [X1: $i] : ~ big_f(X1,tptp_fun_Y1_0(X1)),
inference(nnf-neg,[status(sab)],[8,9]) ).
tff(11,plain,
( ~ ! [X1: $i] : ~ big_f(X1,tptp_fun_Y1_0(X1))
| ~ big_f(tptp_fun_Y1_0(a),tptp_fun_Y1_0(tptp_fun_Y1_0(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ big_f(tptp_fun_Y1_0(a),tptp_fun_Y1_0(tptp_fun_Y1_0(a))),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ ! [X1: $i] : ~ big_f(X1,tptp_fun_Y1_0(X1))
| ~ big_f(a,tptp_fun_Y1_0(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(14,plain,
~ big_f(a,tptp_fun_Y1_0(a)),
inference(unit_resolution,[status(thm)],[13,10]) ).
tff(15,plain,
^ [X: $i] :
refl(( ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
rewrite(( ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(or_elim,[status(thm)],[4]) ).
tff(22,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) )
<=> ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
( ~ ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y)
| big_f(tptp_fun_Y1_0(a),tptp_fun_Y1_0(tptp_fun_Y1_0(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,28,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN073+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:31:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------