%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CSR002+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:00:00 AM UTC 2026
% Result : Theorem 6.24s 4.29s
% Output : Refutation 7.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 56
% Syntax : Number of formulae : 114 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 337 ( 101 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 967 ( 63 ~; 22 |; 123 &; 681 @)
% ( 18 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 16 con; 0-4 aty)
% Number of variables : 179 ( 0 ^; 148 !; 31 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(holdsAt_decl,type,
holdsAt: $i > $i > $o ).
thf(filling_decl,type,
filling: $i ).
thf(n4_decl,type,
n4: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(n1_decl,type,
n1: $i ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(n3_decl,type,
n3: $i ).
thf(n2_decl,type,
n2: $i ).
thf(stoppedIn_decl,type,
stoppedIn: $i > $i > $i > $o ).
thf(happens_decl,type,
happens: $i > $i > $o ).
thf(terminates_decl,type,
terminates: $i > $i > $i > $o ).
thf(releasedAt_decl,type,
releasedAt: $i > $i > $o ).
thf(initiates_decl,type,
initiates: $i > $i > $i > $o ).
thf(tapOff_decl,type,
tapOff: $i ).
thf(tapOn_decl,type,
tapOn: $i ).
thf(n6_decl,type,
n6: $i ).
thf(overflow_decl,type,
overflow: $i ).
thf(n5_decl,type,
n5: $i ).
thf(releases_decl,type,
releases: $i > $i > $i > $o ).
thf(n7_decl,type,
n7: $i ).
thf(waterLevel_decl,type,
waterLevel: $i > $i ).
thf(n8_decl,type,
n8: $i ).
thf(n9_decl,type,
n9: $i ).
thf(spilling_decl,type,
spilling: $i ).
thf(startedIn_decl,type,
startedIn: $i > $i > $i > $o ).
thf(antitrajectory_decl,type,
antitrajectory: $i > $i > $i > $i > $o ).
thf(trajectory_decl,type,
trajectory: $i > $i > $i > $i > $o ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ ( A @ terminates ) ) )
| ( B @ ( C @ ( A @ initiates ) ) ) )
& ( B @ ( A @ happens ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( C @ releasedAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_not_released) ).
thf(196,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ ( A @ terminates ) ) )
| ( B @ ( C @ ( A @ initiates ) ) ) )
& ( B @ ( A @ happens ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( C @ releasedAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(40,axiom,
( ( n3 @ ( n1 @ plus ) )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_3) ).
thf(224,plain,
( ( n3 @ ( n1 @ plus ) )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24,axiom,
( ( n3 @ ( n0 @ plus ) )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_3) ).
thf(169,plain,
( ( n3 @ ( n0 @ plus ) )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(35,axiom,
( ( n2 @ ( n1 @ plus ) )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_2) ).
thf(212,plain,
( ( n2 @ ( n1 @ plus ) )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
~ ( n0 @ ( spilling @ releasedAt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_released_spilling_0) ).
thf(173,plain,
~ ( n0 @ ( spilling @ releasedAt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ terminates ) ) )
<=> ( ( ( B = filling )
& ( A = overflow ) )
| ( ( B = filling )
& ( A = tapOff ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',terminates_all_defn) ).
thf(281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( B = filling )
& ( A = overflow ) )
| ( ( B = filling )
& ( A = tapOff ) ) )
=> ( C @ ( B @ ( A @ terminates ) ) ) )
& ( ( C @ ( B @ ( A @ terminates ) ) )
=> ( ( ( B = filling )
& ( A = overflow ) )
| ( ( B = filling )
& ( A = tapOff ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
! [A: $i] :
( ( n6 @ ( A @ less ) )
<=> ( n5 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less6) ).
thf(159,plain,
! [A: $i] :
( ( ( n5 @ ( A @ less_or_equal ) )
=> ( n6 @ ( A @ less ) ) )
& ( ( n6 @ ( A @ less ) )
=> ( n5 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
overflow != tapOn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',overflow_not_tapOn) ).
thf(209,plain,
overflow != tapOn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ startedIn ) ) )
<=> ? [D: $i,E: $i] :
( ( E @ ( C @ ( D @ initiates ) ) )
& ( B @ ( E @ less ) )
& ( E @ ( A @ less ) )
& ( E @ ( D @ happens ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',startedin_defn) ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( ( E @ ( C @ ( D @ initiates ) ) )
& ( B @ ( E @ less ) )
& ( E @ ( A @ less ) )
& ( E @ ( D @ happens ) ) )
=> ( B @ ( C @ ( A @ startedIn ) ) ) )
& ( ( B @ ( C @ ( A @ startedIn ) ) )
=> ? [D: $i,E: $i] :
( ( E @ ( C @ ( D @ initiates ) ) )
& ( B @ ( E @ less ) )
& ( E @ ( A @ less ) )
& ( E @ ( D @ happens ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,axiom,
( ( n1 @ ( n1 @ plus ) )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).
thf(203,plain,
( ( n1 @ ( n1 @ plus ) )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
~ ( n0 @ ( filling @ holdsAt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_0) ).
thf(222,plain,
~ ( n0 @ ( filling @ holdsAt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [A: $i] :
( ( n3 @ ( A @ less ) )
<=> ( n2 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3) ).
thf(69,plain,
! [A: $i] :
( ( ( n2 @ ( A @ less_or_equal ) )
=> ( n3 @ ( A @ less ) ) )
& ( ( n3 @ ( A @ less ) )
=> ( n2 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
( ( n3 @ ( n3 @ plus ) )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus3_3) ).
thf(101,plain,
( ( n3 @ ( n3 @ plus ) )
= n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
<=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ~ ( A @ ( B @ less ) ) )
=> ( B @ ( A @ less ) ) )
& ( ( B @ ( A @ less ) )
=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C
= ( D @ ( A @ plus ) ) )
& ( B @ ( A @ waterLevel @ holdsAt ) ) )
=> ( D @ ( C @ waterLevel @ ( B @ ( filling @ trajectory ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',change_of_waterLevel) ).
thf(216,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C
= ( D @ ( A @ plus ) ) )
& ( B @ ( A @ waterLevel @ holdsAt ) ) )
=> ( D @ ( C @ waterLevel @ ( B @ ( filling @ trajectory ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(12,axiom,
( ( n3 @ ( n2 @ plus ) )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus2_3) ).
thf(106,plain,
( ( n3 @ ( n2 @ plus ) )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( ( B @ ( A @ ( C @ terminates ) ) )
| ( B @ ( A @ ( C @ initiates ) ) ) )
& ( B @ ( C @ happens ) ) )
& ( B @ ( A @ releasedAt ) ) )
=> ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_released) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( ( B @ ( A @ ( C @ terminates ) ) )
| ( B @ ( A @ ( C @ initiates ) ) ) )
& ( B @ ( C @ happens ) ) )
& ( B @ ( A @ releasedAt ) ) )
=> ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ less ) ) )
=> ( B @ ( A @ less_or_equal ) ) )
& ( ( B @ ( A @ less_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(46,axiom,
n0 @ ( n0 @ waterLevel @ holdsAt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_0) ).
thf(243,plain,
n0 @ ( n0 @ waterLevel @ holdsAt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(43,axiom,
! [A: $i] :
( ( n5 @ ( A @ less ) )
<=> ( n4 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less5) ).
thf(233,plain,
! [A: $i] :
( ( ( n4 @ ( A @ less_or_equal ) )
=> ( n5 @ ( A @ less ) ) )
& ( ( n5 @ ( A @ less ) )
=> ( n4 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ terminates ) ) )
& ( B @ ( A @ happens ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( C @ holdsAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_terminates_not_holds) ).
thf(220,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ terminates ) ) )
& ( B @ ( A @ happens ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( C @ holdsAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(56,axiom,
n3 @ ( n3 @ waterLevel @ holdsAt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_3) ).
thf(302,plain,
n3 @ ( n3 @ waterLevel @ holdsAt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(19,axiom,
! [A: $i] :
( ( n8 @ ( A @ less ) )
<=> ( n7 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less8) ).
thf(137,plain,
! [A: $i] :
( ( ( n7 @ ( A @ less_or_equal ) )
=> ( n8 @ ( A @ less ) ) )
& ( ( n8 @ ( A @ less ) )
=> ( n7 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( A @ ( C @ releases ) ) )
& ( B @ ( C @ happens ) ) )
& ~ ( B @ ( A @ releasedAt ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_not_released) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( A @ ( C @ releases ) ) )
& ( B @ ( C @ happens ) ) )
& ~ ( B @ ( A @ releasedAt ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [A: $i] :
~ ( n0 @ ( A @ waterLevel @ releasedAt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_released_waterLevel_0) ).
thf(134,plain,
! [A: $i] :
~ ( n0 @ ( A @ waterLevel @ releasedAt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(17,axiom,
! [A: $i] :
( ( n7 @ ( A @ less ) )
<=> ( n6 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less7) ).
thf(128,plain,
! [A: $i] :
( ( ( n6 @ ( A @ less_or_equal ) )
=> ( n7 @ ( A @ less ) ) )
& ( ( n7 @ ( A @ less ) )
=> ( n6 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ ( B @ plus ) @ ( C @ ( B @ stoppedIn ) ) )
& ( E @ ( D @ ( B @ ( C @ trajectory ) ) ) )
& ( E @ ( n0 @ less ) )
& ( B @ ( C @ ( A @ initiates ) ) )
& ( B @ ( A @ happens ) ) )
=> ( E @ ( B @ plus ) @ ( D @ holdsAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',change_holding) ).
thf(244,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ ( B @ plus ) @ ( C @ ( B @ stoppedIn ) ) )
& ( E @ ( D @ ( B @ ( C @ trajectory ) ) ) )
& ( E @ ( n0 @ less ) )
& ( B @ ( C @ ( A @ initiates ) ) )
& ( B @ ( A @ happens ) ) )
=> ( E @ ( B @ plus ) @ ( D @ holdsAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(33,axiom,
! [A: $i] :
( spilling
!= ( A @ waterLevel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spilling_not_waterLevel) ).
thf(205,plain,
! [A: $i] :
( spilling
!= ( A @ waterLevel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,axiom,
( ( n2 @ ( n2 @ plus ) )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus2_2) ).
thf(279,plain,
( ( n2 @ ( n2 @ plus ) )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( A @ waterLevel )
= ( B @ waterLevel ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_waterLevels) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ waterLevel )
= ( B @ waterLevel ) ) )
& ( ( ( A @ waterLevel )
= ( B @ waterLevel ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ waterLevel @ holdsAt ) )
& ( A @ ( B @ waterLevel @ holdsAt ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',same_waterLevel) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ waterLevel @ holdsAt ) )
& ( A @ ( B @ waterLevel @ holdsAt ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(51,axiom,
! [A: $i] :
( ( n4 @ ( A @ less ) )
<=> ( n3 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less4) ).
thf(271,plain,
! [A: $i] :
( ( ( n3 @ ( A @ less_or_equal ) )
=> ( n4 @ ( A @ less ) ) )
& ( ( n4 @ ( A @ less ) )
=> ( n3 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(9,axiom,
tapOff != tapOn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tapOff_not_tapOn) ).
thf(98,plain,
tapOff != tapOn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ initiates ) ) )
<=> ( ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = overflow )
& ( C @ ( D @ waterLevel @ holdsAt ) ) )
| ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = tapOff )
& ( C @ ( D @ waterLevel @ holdsAt ) ) )
| ( ( B = spilling )
& ( A = overflow ) )
| ( ( B = filling )
& ( A = tapOn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initiates_all_defn) ).
thf(303,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = overflow )
& ( C @ ( D @ waterLevel @ holdsAt ) ) )
| ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = tapOff )
& ( C @ ( D @ waterLevel @ holdsAt ) ) )
| ( ( B = spilling )
& ( A = overflow ) )
| ( ( B = filling )
& ( A = tapOn ) ) )
=> ( C @ ( B @ ( A @ initiates ) ) ) )
& ( ( C @ ( B @ ( A @ initiates ) ) )
=> ( ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = overflow )
& ( C @ ( D @ waterLevel @ holdsAt ) ) )
| ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = tapOff )
& ( C @ ( D @ waterLevel @ holdsAt ) ) )
| ( ( B = spilling )
& ( A = overflow ) )
| ( ( B = filling )
& ( A = tapOn ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11,axiom,
tapOff != overflow,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tapOff_not_overflow) ).
thf(103,plain,
tapOff != overflow,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( n2 @ ( A @ less ) )
<=> ( n1 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).
thf(108,plain,
! [A: $i] :
( ( ( n1 @ ( A @ less_or_equal ) )
=> ( n2 @ ( A @ less ) ) )
& ( ( n2 @ ( A @ less ) )
=> ( n1 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(55,axiom,
filling != spilling,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',filling_not_spilling) ).
thf(299,plain,
filling != spilling,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [A: $i] :
( filling
!= ( A @ waterLevel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',filling_not_waterLevel) ).
thf(226,plain,
! [A: $i] :
( filling
!= ( A @ waterLevel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( A @ ( C @ terminates ) ) )
& ( B @ ( C @ happens ) ) )
& ~ ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) )
& ( B @ ( A @ holdsAt ) ) )
=> ( n1 @ ( B @ plus ) @ ( A @ holdsAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_holding) ).
thf(267,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( A @ ( C @ terminates ) ) )
& ( B @ ( C @ happens ) ) )
& ~ ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) )
& ( B @ ( A @ holdsAt ) ) )
=> ( n1 @ ( B @ plus ) @ ( A @ holdsAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(45,axiom,
~ ( n0 @ ( filling @ releasedAt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_released_filling_0) ).
thf(241,plain,
~ ( n0 @ ( filling @ releasedAt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4,axiom,
! [A: $i] :
( ( n1 @ ( A @ less ) )
<=> ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less1) ).
thf(63,plain,
! [A: $i] :
( ( ( n0 @ ( A @ less_or_equal ) )
=> ( n1 @ ( A @ less ) ) )
& ( ( n1 @ ( A @ less ) )
=> ( n0 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( A @ ( C @ initiates ) ) )
& ( B @ ( C @ happens ) ) )
& ~ ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) )
& ~ ( B @ ( A @ holdsAt ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( A @ holdsAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_not_holding) ).
thf(263,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( A @ ( C @ initiates ) ) )
& ( B @ ( C @ happens ) ) )
& ~ ( n1 @ ( B @ plus ) @ ( A @ releasedAt ) )
& ~ ( B @ ( A @ holdsAt ) ) )
=> ~ ( n1 @ ( B @ plus ) @ ( A @ holdsAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(27,axiom,
( ( n2 @ ( n0 @ plus ) )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_2) ).
thf(175,plain,
( ( n2 @ ( n0 @ plus ) )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(20,axiom,
! [A: $i] :
( ( n9 @ ( A @ less ) )
<=> ( n8 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less9) ).
thf(143,plain,
! [A: $i] :
( ( ( n8 @ ( A @ less_or_equal ) )
=> ( n9 @ ( A @ less ) ) )
& ( ( n9 @ ( A @ less ) )
=> ( n8 @ ( A @ less_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ releases ) ) )
<=> ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = tapOn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',releases_all_defn) ).
thf(186,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = tapOn ) )
=> ( C @ ( B @ ( A @ releases ) ) ) )
& ( ( C @ ( B @ ( A @ releases ) ) )
=> ? [D: $i] :
( ( B
= ( D @ waterLevel ) )
& ( A = tapOn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ releases ) ) )
& ( B @ ( A @ happens ) ) )
=> ( n1 @ ( B @ plus ) @ ( C @ releasedAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_releases) ).
thf(114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ releases ) ) )
& ( B @ ( A @ happens ) ) )
=> ( n1 @ ( B @ plus ) @ ( C @ releasedAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,axiom,
( ( n0 @ ( n0 @ plus ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_0) ).
thf(171,plain,
( ( n0 @ ( n0 @ plus ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ stoppedIn ) ) )
<=> ? [D: $i,E: $i] :
( ( E @ ( B @ ( D @ terminates ) ) )
& ( C @ ( E @ less ) )
& ( E @ ( A @ less ) )
& ( E @ ( D @ happens ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stoppedin_defn) ).
thf(75,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( ( E @ ( B @ ( D @ terminates ) ) )
& ( C @ ( E @ less ) )
& ( E @ ( A @ less ) )
& ( E @ ( D @ happens ) ) )
=> ( C @ ( B @ ( A @ stoppedIn ) ) ) )
& ( ( C @ ( B @ ( A @ stoppedIn ) ) )
=> ? [D: $i,E: $i] :
( ( E @ ( B @ ( D @ terminates ) ) )
& ( C @ ( E @ less ) )
& ( E @ ( A @ less ) )
& ( E @ ( D @ happens ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
~ ( n4 @ ( filling @ holdsAt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_4) ).
thf(2,negated_conjecture,
~ ~ ( n4 @ ( filling @ holdsAt ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(58,plain,
~ ~ ( n4 @ ( filling @ holdsAt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ happens ) )
<=> ( ( ( A = overflow )
& ( B @ ( filling @ holdsAt ) )
& ( B @ ( n3 @ waterLevel @ holdsAt ) ) )
| ( ( B = n0 )
& ( A = tapOn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_all_defn) ).
thf(246,plain,
! [A: $i,B: $i] :
( ( ( ( ( A = overflow )
& ( B @ ( filling @ holdsAt ) )
& ( B @ ( n3 @ waterLevel @ holdsAt ) ) )
| ( ( B = n0 )
& ( A = tapOn ) ) )
=> ( B @ ( A @ happens ) ) )
& ( ( B @ ( A @ happens ) )
=> ( ( ( A = overflow )
& ( B @ ( filling @ holdsAt ) )
& ( B @ ( n3 @ waterLevel @ holdsAt ) ) )
| ( ( B = n0 )
& ( A = tapOn ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( B @ plus ) @ ( C @ ( B @ startedIn ) ) )
& ( D @ ( E @ ( B @ ( C @ antitrajectory ) ) ) )
& ( D @ ( n0 @ less ) )
& ( B @ ( C @ ( A @ terminates ) ) )
& ( B @ ( A @ happens ) ) )
=> ( D @ ( B @ plus ) @ ( E @ holdsAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antitrajectory) ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( B @ plus ) @ ( C @ ( B @ startedIn ) ) )
& ( D @ ( E @ ( B @ ( C @ antitrajectory ) ) ) )
& ( D @ ( n0 @ less ) )
& ( B @ ( C @ ( A @ terminates ) ) )
& ( B @ ( A @ happens ) ) )
=> ( D @ ( B @ plus ) @ ( E @ holdsAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ initiates ) ) )
& ( B @ ( A @ happens ) ) )
=> ( n1 @ ( B @ plus ) @ ( C @ holdsAt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_holds) ).
thf(239,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ initiates ) ) )
& ( B @ ( A @ happens ) ) )
=> ( n1 @ ( B @ plus ) @ ( C @ holdsAt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(16,axiom,
( ( n1 @ ( n0 @ plus ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
thf(126,plain,
( ( n1 @ ( n0 @ plus ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(31,axiom,
~ ? [A: $i] : ( n0 @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less0) ).
thf(200,plain,
~ ? [A: $i] : ( n0 @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,axiom,
~ ( n0 @ ( spilling @ holdsAt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_spilling_0) ).
thf(277,plain,
~ ( n0 @ ( spilling @ holdsAt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(365,plain,
$false,
inference(e,[status(thm)],[196,224,169,212,173,281,159,209,177,203,222,69,101,88,216,106,84,116,243,233,60,220,302,137,165,134,128,244,205,279,149,230,271,98,303,103,108,299,226,267,241,63,263,175,143,186,114,171,75,58,246,214,239,126,200,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR002+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 23:54:30 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.77/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.32 % [INFO] Parsing done (304ms).
% 1.34/1.34 % [INFO] Running in sequential loop mode.
% 2.02/1.88 % [INFO] eprover registered as external prover.
% 2.02/1.90 % [INFO] Scanning for conjecture ...
% 2.20/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 55 axioms. Running axiom selection ...
% 2.40/2.09 % [INFO] Axiom selection finished. Selected 55 axioms (removed 0 axioms).
% 2.62/2.18 % [INFO] Problem is first-order (TPTP FOF).
% 2.62/2.19 % [INFO] Type checking passed.
% 2.70/2.20 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.24/4.28 % External prover 'e' found a proof!
% 6.24/4.28 % [INFO] Killing All external provers ...
% 6.24/4.28 % Time passed: 3703ms (effective reasoning time: 2930ms)
% 6.24/4.28 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.24/4.29 % Axioms used in derivation (55): keep_not_holding, same_waterLevel, plus1_1, stoppedin_defn, happens_all_defn, plus3_3, happens_holds, plus2_2, less9, waterLevel_3, keep_holding, not_filling_0, releases_all_defn, spilling_not_waterLevel, less8, less_property, antitrajectory, tapOff_not_overflow, less0, plus0_0, happens_terminates_not_holds, waterLevel_0, distinct_waterLevels, less4, less1, keep_released, plus2_3, less3, filling_not_waterLevel, plus0_1, not_spilling_0, plus0_3, not_released_filling_0, plus1_2, overflow_not_tapOn, filling_not_spilling, tapOff_not_tapOn, symmetry_of_plus, less7, initiates_all_defn, keep_not_released, not_released_waterLevel_0, terminates_all_defn, less2, change_of_waterLevel, plus0_2, plus1_3, change_holding, less6, happens_releases, less5, startedin_defn, happens_not_released, less_or_equal, not_released_spilling_0
% 6.24/4.29 % No. of inferences in proof: 114
% 6.24/4.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3703 ms resp. 2930 ms w/o parsing
% 7.03/4.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.03/4.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------