%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU123+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 08:37:38 AM UTC 2026
% Result : Theorem 4.91s 2.94s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 65 ( 26 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 23 ~; 17 |; 10 &; 72 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 28 !; 0 ?; 29 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
( ( sk1 != empty_set )
& ( empty_set @ ( sk1 @ subset ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
empty_set @ ( sk1 @ subset ),
inference(cnfConj,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ subset ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A @ ( B @ subset ) )
| ( A != B ) )
& ( ( B @ ( A @ subset ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[31]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( sk1 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[16,32]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( sk1 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( A @ ( B @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
( ~ ( sk1 @ ( empty_set @ subset ) )
| ( sk1 = empty_set ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( sk1 )),bind(B,$thf( empty_set ))]]) ).
thf(10,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(42,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[42]) ).
thf(237,plain,
( ~ $true
| ( sk1 = empty_set ) ),
inference(rewrite,[status(thm)],[135,43]) ).
thf(238,plain,
sk1 = empty_set,
inference(simp,[status(thm)],[237]) ).
thf(17,plain,
sk1 != empty_set,
inference(cnfConj,[status(thm)],[15]) ).
thf(18,plain,
sk1 != empty_set,
inference(lifteq,[status(thm)],[17]) ).
thf(239,plain,
$false,
inference(simplifyReflect,[status(thm)],[238,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU123+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 08:37:43 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.86/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.21 % [INFO] Parsing done (205ms).
% 1.28/1.22 % [INFO] Running in sequential loop mode.
% 1.75/1.68 % [INFO] eprover registered as external prover.
% 1.75/1.69 % [INFO] Scanning for conjecture ...
% 2.06/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.06/1.86 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.06/1.88 % [INFO] Problem is first-order (TPTP FOF).
% 2.06/1.89 % [INFO] Type checking passed.
% 2.06/1.90 % [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 ...
% 4.91/2.93 % [INFO] Killing All external provers ...
% 4.91/2.94 % Time passed: 2400ms (effective reasoning time: 1700ms)
% 4.91/2.94 % 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)>
% 4.91/2.94 % Axioms used in derivation (2): d10_xboole_0, t2_xboole_1
% 4.91/2.94 % No. of inferences in proof: 23
% 4.91/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2400 ms resp. 1700 ms w/o parsing
% 4.91/2.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.91/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------