%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET158-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 05:25:22 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 51 ~; 27 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(1,plain,
( ( y = z )
<=> ( y = z ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
y = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_complement_axiom_3) ).
tff(3,plain,
y = z,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
z = y,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( member(z,x)
<=> member(y,x) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( member(y,x)
<=> member(z,x) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( member(y,x)
<=> member(y,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
member(y,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_complement_axiom_1) ).
tff(9,plain,
member(y,x),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
member(z,x),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( member(z,complement(x))
<=> member(z,complement(x)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
member(z,complement(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_complement_axiom_2) ).
tff(13,plain,
member(z,complement(x)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [Z: $i,X: $i] :
refl(( ( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ( ~ member(Z,X)
| ~ member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [Z: $i,X: $i] :
rewrite(( ( ~ member(Z,complement(X))
| ~ member(Z,X) )
<=> ( ~ member(Z,X)
| ~ member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,complement(X))
| ~ member(Z,X) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
tff(20,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(z,x)
| ~ member(z,complement(x)) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(z,x)
| ~ member(z,complement(x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(z,x)
| ~ member(z,complement(x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(z,x)
| ~ member(z,complement(x)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
~ member(z,x),
inference(unit_resolution,[status(thm)],[26,23,13]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET158-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:26:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42 % SZS output start Proof
% See solution above
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------