%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS093+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 64 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 261 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 347 ( 168 ~; 103 |; 10 &)
% ( 57 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 18 ( 18 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 : 65 ( 57 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(cc_type,type,
cc: $i > $o ).
tff(i2003_11_14_17_20_07201_type,type,
i2003_11_14_17_20_07201: $i ).
tff(ce3_type,type,
ce3: $i > $o ).
tff(cf_type,type,
cf: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) )
<=> ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) )
<=> ! [X: $i] :
~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ( cf(X)
& ce3(X) )
<=> ~ ( ~ ce3(X)
| ~ cf(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) )
<=> ( cUnsatisfiable(X)
<=> ~ ( ~ ce3(X)
| ~ cf(X) ) ) )),
rewrite(( ( cUnsatisfiable(X)
<=> ~ ( ~ ce3(X)
| ~ cf(X) ) )
<=> ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) )
<=> ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) )),
rewrite(( ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) )
<=> ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) )
<=> ~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) )
<=> ! [X: $i] :
~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(7,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cf(X)
& ce3(X) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] :
~ ( ( ~ ce3(X)
| ~ cf(X) )
<=> cUnsatisfiable(X) )
| ~ ( ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) )
<=> cUnsatisfiable(i2003_11_14_17_20_07201) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) )
<=> cUnsatisfiable(i2003_11_14_17_20_07201) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( cUnsatisfiable(i2003_11_14_17_20_07201)
<=> cUnsatisfiable(i2003_11_14_17_20_07201) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
cUnsatisfiable(i2003_11_14_17_20_07201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(15,plain,
cUnsatisfiable(i2003_11_14_17_20_07201),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ( ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) )
<=> cUnsatisfiable(i2003_11_14_17_20_07201) )
| ~ ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) )
| ~ cUnsatisfiable(i2003_11_14_17_20_07201) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ( ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) )
<=> cUnsatisfiable(i2003_11_14_17_20_07201) )
| ~ ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) ) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
~ ( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) ),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201)
| ce3(i2003_11_14_17_20_07201) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
ce3(i2003_11_14_17_20_07201),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( cc(X)
| ~ ce3(X) )
<=> ( cc(X)
| ~ ce3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( cc(X)
| ~ ce3(X) )
<=> ! [X: $i] :
( cc(X)
| ~ ce3(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( cc(X)
| ~ ce3(X) )
<=> ! [X: $i] :
( cc(X)
| ~ ce3(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [X: $i] :
rewrite(( ( ce3(X)
=> cc(X) )
<=> ( cc(X)
| ~ ce3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] :
( ce3(X)
=> cc(X) )
<=> ! [X: $i] :
( cc(X)
| ~ ce3(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [X: $i] :
( ce3(X)
=> cc(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(27,plain,
! [X: $i] :
( cc(X)
| ~ ce3(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( cc(X)
| ~ ce3(X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i] :
( cc(X)
| ~ ce3(X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] :
( cc(X)
| ~ ce3(X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( cc(X)
| ~ ce3(X) )
| cc(i2003_11_14_17_20_07201)
| ~ ce3(i2003_11_14_17_20_07201) )
<=> ( ~ ! [X: $i] :
( cc(X)
| ~ ce3(X) )
| cc(i2003_11_14_17_20_07201)
| ~ ce3(i2003_11_14_17_20_07201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i] :
( cc(X)
| ~ ce3(X) )
| cc(i2003_11_14_17_20_07201)
| ~ ce3(i2003_11_14_17_20_07201) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i] :
( cc(X)
| ~ ce3(X) )
| cc(i2003_11_14_17_20_07201)
| ~ ce3(i2003_11_14_17_20_07201) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
cc(i2003_11_14_17_20_07201),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( ~ ce3(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201)
| cf(i2003_11_14_17_20_07201) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
cf(i2003_11_14_17_20_07201),
inference(unit_resolution,[status(thm)],[35,18]) ).
tff(37,plain,
^ [X: $i] :
refl(( ( cd(X)
| ~ cf(X) )
<=> ( cd(X)
| ~ cf(X) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [X: $i] :
( cd(X)
| ~ cf(X) )
<=> ! [X: $i] :
( cd(X)
| ~ cf(X) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X: $i] :
( cd(X)
| ~ cf(X) )
<=> ! [X: $i] :
( cd(X)
| ~ cf(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [X: $i] :
rewrite(( ( cf(X)
=> cd(X) )
<=> ( cd(X)
| ~ cf(X) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i] :
( cf(X)
=> cd(X) )
<=> ! [X: $i] :
( cd(X)
| ~ cf(X) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [X: $i] :
( cf(X)
=> cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(43,plain,
! [X: $i] :
( cd(X)
| ~ cf(X) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] :
( cd(X)
| ~ cf(X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [X: $i] :
( cd(X)
| ~ cf(X) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i] :
( cd(X)
| ~ cf(X) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [X: $i] :
( cd(X)
| ~ cf(X) )
| cd(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) )
<=> ( ~ ! [X: $i] :
( cd(X)
| ~ cf(X) )
| cd(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i] :
( cd(X)
| ~ cf(X) )
| cd(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X: $i] :
( cd(X)
| ~ cf(X) )
| cd(i2003_11_14_17_20_07201)
| ~ cf(i2003_11_14_17_20_07201) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
cd(i2003_11_14_17_20_07201),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
^ [X: $i] :
refl(( ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i] :
( cc(X)
=> ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [X: $i] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(57,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_07201)
| ~ cd(i2003_11_14_17_20_07201) )
<=> ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_07201)
| ~ cd(i2003_11_14_17_20_07201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_07201)
| ~ cd(i2003_11_14_17_20_07201) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(i2003_11_14_17_20_07201)
| ~ cd(i2003_11_14_17_20_07201) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,60,50,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KRS093+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 : Thu Jun 19 19:12:46 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
%------------------------------------------------------------------------------