%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU416+3 : TPTP v9.3.1. Released v3.4.0.
% 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 : n009.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 08:38:46 AM UTC 2026
% Result : Theorem 52.20s 13.09s
% Output : Refutation 52.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 28 unt; 0 typ; 3 def)
% Number of atoms : 52 ( 51 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 184 ( 18 ~; 9 |; 0 &; 155 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 55 !; 1 ?; 59 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k3_pua2mss1_decl,type,
k3_pua2mss1: $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( A @ ( sk1 @ k4_xboole_0 ) @ k3_pua2mss1 )
!= ( A @ k3_pua2mss1 @ ( sk1 @ k3_pua2mss1 @ k4_xboole_0 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(146,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(147,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[146]) ).
thf(148,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[147]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
( ( sk2 @ ( sk1 @ k4_xboole_0 ) @ k3_pua2mss1 )
!= ( sk2 @ k3_pua2mss1 @ ( sk1 @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
( ( sk2 @ k3_pua2mss1 @ ( sk1 @ k3_pua2mss1 @ k4_xboole_0 ) )
!= ( sk2 @ ( sk1 @ k4_xboole_0 ) @ k3_pua2mss1 ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(184,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( sk2 @ k3_pua2mss1 @ ( sk1 @ k3_pua2mss1 @ k4_xboole_0 ) ) )
| ( ( sk2 @ ( sk1 @ k4_xboole_0 ) @ k3_pua2mss1 )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[148,46]) ).
thf(189,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k3_pua2mss1 ) )
| ( ( sk1 @ k3_pua2mss1 )
!= k1_xboole_0 )
| ( ( sk2 @ ( sk1 @ k4_xboole_0 ) @ k3_pua2mss1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[184]) ).
thf(190,plain,
( ( ( sk1 @ k3_pua2mss1 )
!= k1_xboole_0 )
| ( ( sk2 @ ( sk1 @ k4_xboole_0 ) @ k3_pua2mss1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[189]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(113,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(114,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[113]) ).
thf(115,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[114]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[141]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2_xboole_0 ) )
!= ( C @ ( B @ k2_xboole_0 ) ) )
| ( ( A @ ( B @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[115,142]) ).
thf(281,plain,
! [A: $i] :
( ( A @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(158,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[157]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk4 ) )
= A ),
inference(cnf,[status(esa)],[158]) ).
thf(10399,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk4 ) )
= A ),
inference(lifteq,[status(thm)],[159]) ).
thf(10436,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk4 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[281,10399]) ).
thf(10437,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk4 ) )
= A ),
inference(pattern_uni,[status(thm)],[10436:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(10402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk4 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[148,10399]) ).
thf(10403,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk4 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[10402:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(11668,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[10437,10403]) ).
thf(11682,plain,
$false,
inference(simplifyReflect,[status(thm)],[190,11668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU416+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.13 % 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
% 0.23/0.49 % Computer : n009.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 09:34:36 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 0.90/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 11.11/4.68 % [INFO] Parsing done (3691ms).
% 11.24/4.72 % [INFO] Running in sequential loop mode.
% 12.12/5.32 % [INFO] eprover registered as external prover.
% 12.12/5.33 % [INFO] Scanning for conjecture ...
% 18.11/6.81 % [INFO] Found a conjecture (or negated_conjecture) and 19071 axioms. Running axiom selection ...
% 19.13/7.09 % [INFO] Axiom selection finished. Selected 41 axioms (removed 19030 axioms).
% 19.13/7.14 % [INFO] Problem is first-order (TPTP FOF).
% 19.49/7.15 % [INFO] Type checking passed.
% 19.49/7.16 % [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 ...
% 52.20/13.08 % [INFO] Killing All external provers ...
% 52.20/13.08 % Time passed: 12456ms (effective reasoning time: 8353ms)
% 52.20/13.08 % 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)>
% 52.20/13.09 % Axioms used in derivation (4): t4_boole, idempotence_k2_xboole_0, t46_xboole_1, t32_xboole_1
% 52.20/13.09 % No. of inferences in proof: 35
% 52.20/13.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12456 ms resp. 8353 ms w/o parsing
% 52.20/13.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.20/13.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------