%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN009-2 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:37:57 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 56 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 404 ( 0 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 597 ( 272 ~; 293 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 180 ( 165 !; 0 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
tff(q_type,type,
q: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(t_type,type,
t: ( $i * $i * $i ) > $o ).
tff(p_type,type,
p: ( $i * $i * $i ) > $o ).
tff(r_type,type,
r: ( $i * $i * $i ) > $o ).
tff(s_type,type,
s: $i > $o ).
tff(1,plain,
( t(c,c,c)
<=> t(c,c,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
t(c,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(3,plain,
t(c,c,c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
<=> ( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(8,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
| ~ q(c,c,c)
| ~ t(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
| ~ q(c,c,c)
| ~ t(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
| ~ q(c,c,c)
| ~ t(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ t(Y,Z,X) )
| ~ q(c,c,c)
| ~ t(c,c,c) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ q(c,c,c),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
<=> ( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
| ~ p(c,c,c)
| ~ t(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
| ~ p(c,c,c)
| ~ t(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
| ~ p(c,c,c)
| ~ t(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ t(X,Y,Z) )
| ~ p(c,c,c)
| ~ t(c,c,c) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ p(c,c,c),
inference(unit_resolution,[status(thm)],[24,21,3]) ).
tff(26,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
<=> ( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
| ~ r(c,c,c)
| ~ t(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
| ~ r(c,c,c)
| ~ t(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
| ~ r(c,c,c)
| ~ t(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ t(Z,X,Y) )
| ~ r(c,c,c)
| ~ t(c,c,c) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ r(c,c,c),
inference(unit_resolution,[status(thm)],[35,32,3]) ).
tff(37,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ s(X)
| ~ s(Y)
| ~ s(Z) )
<=> ( ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z) )
<=> ( ~ s(Z)
| ~ s(Y)
| ~ s(X)
| p(X,Y,Z) ) )),
rewrite(( ( ~ s(Z)
| ~ s(Y)
| ~ s(X)
| p(X,Y,Z) )
<=> ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z) )
<=> ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(Y,Z,X) )
<=> ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| q(Y,Z,X) ) )),
rewrite(( ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| q(Y,Z,X) )
<=> ( p(X,Y,Z)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(Y,Z,X) )
<=> ( p(X,Y,Z)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(Y,Z,X)
| r(Z,X,Y) )
<=> ( p(X,Y,Z)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| r(Z,X,Y) ) )),
rewrite(( ( p(X,Y,Z)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| r(Z,X,Y) )
<=> ( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(Y,Z,X)
| r(Z,X,Y) )
<=> ( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(Y,Z,X)
| r(Z,X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(Y,Z,X)
| r(Z,X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(43,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( s(c)
<=> s(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
s(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(49,plain,
s(c),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| r(c,c,c)
| p(c,c,c)
| q(c,c,c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| r(c,c,c)
| p(c,c,c)
| q(c,c,c)
| ~ s(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( p(c,c,c)
| r(c,c,c)
| q(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( r(c,c,c)
| p(c,c,c)
| q(c,c,c)
| ~ s(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| p(c,c,c)
| r(c,c,c)
| q(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| r(c,c,c)
| p(c,c,c)
| q(c,c,c)
| ~ s(c) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| p(c,c,c)
| r(c,c,c)
| q(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| r(c,c,c)
| p(c,c,c)
| q(c,c,c)
| ~ s(c) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| p(c,c,c)
| r(c,c,c)
| q(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| r(Z,X,Y)
| q(Y,Z,X)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| r(c,c,c)
| p(c,c,c)
| q(c,c,c)
| ~ s(c) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,49,46,36,25,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN009-2 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:26:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------