%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CSR004+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:01:12 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 269 ( 118 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 462 ( 231 ~; 141 |; 36 &)
% ( 54 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 50 ( 44 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(holdsAt_type,type,
holdsAt: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i ).
tff(filling_type,type,
filling: $i ).
tff(waterLevel_type,type,
waterLevel: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(tapOn_type,type,
tapOn: $i ).
tff(overflow_type,type,
overflow: $i ).
tff(happens_type,type,
happens: ( $i * $i ) > $o ).
tff(1,plain,
( holdsAt(filling,n3)
<=> holdsAt(filling,n3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
holdsAt(filling,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',filling_3) ).
tff(3,plain,
holdsAt(filling,n3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( holdsAt(waterLevel(n3),n3)
<=> holdsAt(waterLevel(n3),n3) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
holdsAt(waterLevel(n3),n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_3) ).
tff(6,plain,
holdsAt(waterLevel(n3),n3),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) )
| ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ),
inference(tautology,[status(thm)],[]) ).
tff(8,plain,
~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ),
inference(unit_resolution,[status(thm)],[7,6,3]) ).
tff(9,plain,
( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) )
| ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ),
inference(tautology,[status(thm)],[]) ).
tff(10,plain,
( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
( ~ happens(overflow,n3)
<=> ~ happens(overflow,n3) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ happens(overflow,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',overflow_3) ).
tff(13,plain,
~ happens(overflow,n3),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ~ ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) )
| happens(overflow,n3)
| ~ ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(15,plain,
~ ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ),
inference(unit_resolution,[status(thm)],[14,13,10]) ).
tff(16,plain,
^ [Event: $i,Time: $i] :
refl(( ( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
<=> ( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
<=> ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [Event: $i,Time: $i] :
rewrite(( ( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) )
<=> ( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) )
<=> ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) )
<=> ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [Event: $i,Time: $i] :
rewrite(( ( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) )
<=> ( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) )
<=> ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',happens_all_defn) ).
tff(24,plain,
! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ( ( Event = tapOn )
& ( Time = n0 ) )
| ( holdsAt(waterLevel(n3),Time)
& holdsAt(filling,Time)
& ( Event = overflow ) ) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) ),
inference(modus_ponens,[status(thm)],[27,17]) ).
tff(29,plain,
( ( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ) )
<=> ( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3)
| ( overflow != overflow ) ) ) )
<=> ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3)
| ( overflow != overflow ) ) ) ) )
<=> ( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3)
| ( overflow != overflow ) ) ) ) )
<=> ( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3)
| ( overflow != overflow ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Event: $i,Time: $i] :
( happens(Event,Time)
<=> ( ~ ( ( Event != tapOn )
| ( Time != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),Time)
| ~ holdsAt(filling,Time)
| ( Event != overflow ) ) ) )
| ( happens(overflow,n3)
<=> ( ~ ( ( overflow != tapOn )
| ( n3 != n0 ) )
| ~ ( ~ holdsAt(waterLevel(n3),n3)
| ~ holdsAt(filling,n3) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,28,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CSR004+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n015.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
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 12:26:55 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% See solution above
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------