%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS017-1 : TPTP v9.0.0. Released v2.0.0.
% 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 05:13:12 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 37 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 312 ( 148 ~; 144 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 80 ( 72 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
tff(r_type,type,
r: ( $i * $i ) > $o ).
tff(u0r3_type,type,
u0r3: $i > $i ).
tff(exists_type,type,
exists: $i ).
tff(e_type,type,
e: $i > $o ).
tff(a_type,type,
a: $i > $o ).
tff(1,plain,
^ [X1: $i] :
refl(( ( ~ e(X1)
| r(X1,u0r3(X1)) )
<=> ( ~ e(X1)
| r(X1,u0r3(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) )
<=> ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) )
<=> ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X1: $i] :
rewrite(( ( r(X1,u0r3(X1))
| ~ e(X1) )
<=> ( ~ e(X1)
| r(X1,u0r3(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X1: $i] :
( r(X1,u0r3(X1))
| ~ e(X1) )
<=> ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X1: $i] :
( r(X1,u0r3(X1))
| ~ e(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(7,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( e(exists)
<=> e(exists) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
e(exists),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(13,plain,
e(exists),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) )
| ~ e(exists)
| r(exists,u0r3(exists)) )
<=> ( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) )
| ~ e(exists)
| r(exists,u0r3(exists)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) )
| ~ e(exists)
| r(exists,u0r3(exists)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u0r3(X1)) )
| ~ e(exists)
| r(exists,u0r3(exists)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
r(exists,u0r3(exists)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
<=> ( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(monotonicity(rewrite(( ( a(X3)
| ~ e(X1)
| ~ r(X1,X2) )
<=> ( ~ e(X1)
| ~ r(X1,X2)
| a(X3) ) )),
( ( a(X3)
| ~ e(X1)
| ~ r(X1,X2)
| ~ r(X3,X2) )
<=> ( ~ e(X1)
| ~ r(X1,X2)
| a(X3)
| ~ r(X3,X2) ) )),
rewrite(( ( ~ e(X1)
| ~ r(X1,X2)
| a(X3)
| ~ r(X3,X2) )
<=> ( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ) )),
( ( a(X3)
| ~ e(X1)
| ~ r(X1,X2)
| ~ r(X3,X2) )
<=> ( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( a(X3)
| ~ e(X1)
| ~ r(X1,X2)
| ~ r(X3,X2) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X3: $i,X2: $i,X1: $i] :
( a(X3)
| ~ e(X1)
| ~ r(X1,X2)
| ~ r(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(24,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ~ a(exists)
<=> ~ a(exists) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
~ a(exists),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(30,plain,
~ a(exists),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| a(exists)
| ~ e(exists)
| ~ r(exists,u0r3(exists)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| a(exists)
| ~ e(exists)
| ~ r(exists,u0r3(exists)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ e(exists)
| ~ r(exists,u0r3(exists))
| ~ r(exists,u0r3(exists))
| a(exists) )
<=> ( a(exists)
| ~ e(exists)
| ~ r(exists,u0r3(exists)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| ~ e(exists)
| ~ r(exists,u0r3(exists))
| ~ r(exists,u0r3(exists))
| a(exists) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| a(exists)
| ~ e(exists)
| ~ r(exists,u0r3(exists)) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| ~ e(exists)
| ~ r(exists,u0r3(exists))
| ~ r(exists,u0r3(exists))
| a(exists) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| a(exists)
| ~ e(exists)
| ~ r(exists,u0r3(exists)) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| ~ e(exists)
| ~ r(exists,u0r3(exists))
| ~ r(exists,u0r3(exists))
| a(exists) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X3,X2)
| ~ r(X1,X2)
| a(X3) )
| a(exists)
| ~ e(exists)
| ~ r(exists,u0r3(exists)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,13,30,27,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS017-1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:09:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------