%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS091+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:13:21 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 36 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 233 ( 120 ~; 55 |; 10 &)
% ( 45 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 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 : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 31 ( 27 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(cc_type,type,
cc: $i > $o ).
tff(i2003_11_14_17_20_00819_type,type,
i2003_11_14_17_20_00819: $i ).
tff(cd_type,type,
cd: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) )
<=> ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) )
<=> ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ( cd(X)
& cc(X) )
<=> ~ ( ~ cd(X)
| ~ cc(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) )
<=> ( cUnsatisfiable(X)
<=> ~ ( ~ cd(X)
| ~ cc(X) ) ) )),
rewrite(( ( cUnsatisfiable(X)
<=> ~ ( ~ cd(X)
| ~ cc(X) ) )
<=> ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) )
<=> ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) )),
rewrite(( ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) )
<=> ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) )
<=> ~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) )
<=> ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(7,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cc(X) )
<=> cUnsatisfiable(X) )
| ~ ( ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) )
<=> cUnsatisfiable(i2003_11_14_17_20_00819) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) )
<=> cUnsatisfiable(i2003_11_14_17_20_00819) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( cUnsatisfiable(i2003_11_14_17_20_00819)
<=> cUnsatisfiable(i2003_11_14_17_20_00819) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
cUnsatisfiable(i2003_11_14_17_20_00819),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(15,plain,
cUnsatisfiable(i2003_11_14_17_20_00819),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ( ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) )
<=> cUnsatisfiable(i2003_11_14_17_20_00819) )
| ~ ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) )
| ~ cUnsatisfiable(i2003_11_14_17_20_00819) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ( ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) )
<=> cUnsatisfiable(i2003_11_14_17_20_00819) )
| ~ ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) ) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
~ ( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819) ),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819)
| cc(i2003_11_14_17_20_00819) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
cc(i2003_11_14_17_20_00819),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ cd(i2003_11_14_17_20_00819)
| ~ cc(i2003_11_14_17_20_00819)
| cd(i2003_11_14_17_20_00819) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
cd(i2003_11_14_17_20_00819),
inference(unit_resolution,[status(thm)],[21,18]) ).
tff(23,plain,
^ [X: $i] :
refl(( ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [X: $i] :
( cc(X)
=> ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [X: $i] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(29,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_00819)
| ~ cd(i2003_11_14_17_20_00819) )
<=> ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_00819)
| ~ cd(i2003_11_14_17_20_00819) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_00819)
| ~ cd(i2003_11_14_17_20_00819) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_00819)
| ~ cd(i2003_11_14_17_20_00819) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,32,22,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS091+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 : Thu Jun 19 19:10:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.36 % SZS status Unsatisfiable
% 0.20/0.36 % SZS output start Proof
% See solution above
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------