%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU134+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 : 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 08:37:41 AM UTC 2026
% Result : Theorem 18.69s 6.73s
% Output : Refutation 19.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 136 ( 69 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 353 ( 47 ~; 47 |; 8 &; 236 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 50 !; 0 ?; 54 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ set_difference ) )
= empty_set )
=> ( A @ ( sk1 @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ( sk3 @ subset ) )
=> ( ( A @ ( sk3 @ set_difference ) )
= empty_set ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
~ ( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
( ( ( ( sk4 @ ( sk3 @ set_difference ) )
!= empty_set )
| ~ ( sk2 @ ( sk1 @ subset ) ) )
& ( ( sk4 @ ( sk3 @ subset ) )
| ~ ( sk2 @ ( sk1 @ subset ) ) )
& ( ( ( sk4 @ ( sk3 @ set_difference ) )
!= empty_set )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) )
& ( ( sk4 @ ( sk3 @ subset ) )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(20,plain,
( ( ( sk4 @ ( sk3 @ set_difference ) )
!= empty_set )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(24,plain,
( ( ( sk4 @ ( sk3 @ set_difference ) )
!= empty_set )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(19,plain,
( ( sk4 @ ( sk3 @ subset ) )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(23,plain,
( ( sk4 @ ( sk3 @ subset ) )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(55,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ set_difference ) )
= empty_set )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(889,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ set_difference ) )
!= ( B @ ( A @ set_difference ) ) )
| ( B @ ( A @ subset ) )
| ( empty_set != empty_set )
| ( sk4 @ ( sk3 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[23,59]) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ set_difference ) )
!= ( B @ ( A @ set_difference ) ) )
| ( B @ ( A @ subset ) )
| ( sk4 @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[889]) ).
thf(891,plain,
( ( sk2 @ ( sk1 @ subset ) )
| ( sk4 @ ( sk3 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set ) ),
inference(simp,[status(thm)],[60]) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ $true
| ( ( B @ ( A @ set_difference ) )
= empty_set )
| ( sk2 @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[891,61]) ).
thf(1133,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set )
| ( sk2 @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[1132]) ).
thf(1134,plain,
( ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set )
| ( sk2 @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[1133:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(21,plain,
( ( sk4 @ ( sk3 @ subset ) )
| ~ ( sk2 @ ( sk1 @ subset ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(1306,plain,
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ( sk4 @ ( sk3 @ subset ) )
| ~ $true
| ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ) ),
inference(paramod_ordered,[status(thm)],[1134,21]) ).
thf(1307,plain,
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ( sk4 @ ( sk3 @ subset ) )
| ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ) ),
inference(simp,[status(thm)],[1306]) ).
thf(1308,plain,
( ( sk4 @ ( sk3 @ subset ) )
| ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[1307:[]]) ).
thf(1532,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ $true
| ( ( B @ ( A @ set_difference ) )
= empty_set )
| ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ) ),
inference(paramod_ordered,[status(thm)],[1308,61]) ).
thf(1533,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set )
| ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ) ),
inference(simp,[status(thm)],[1532]) ).
thf(1534,plain,
( ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set )
| ( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[1533:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1585,plain,
( ( sk4 @ ( sk3 @ set_difference ) )
= empty_set ),
inference(simp,[status(thm)],[1534]) ).
thf(1612,plain,
( ( empty_set != empty_set )
| ( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ) ),
inference(rewrite,[status(thm)],[24,1585]) ).
thf(1613,plain,
( ( sk2 @ ( sk1 @ set_difference ) )
= empty_set ),
inference(simp,[status(thm)],[1612]) ).
thf(22,plain,
( ( ( sk4 @ ( sk3 @ set_difference ) )
!= empty_set )
| ~ ( sk2 @ ( sk1 @ subset ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(25,plain,
( ~ ( sk2 @ ( sk1 @ subset ) )
| ( ( sk4 @ ( sk3 @ set_difference ) )
!= empty_set ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(1614,plain,
( ~ ( sk2 @ ( sk1 @ subset ) )
| ( empty_set != empty_set ) ),
inference(rewrite,[status(thm)],[25,1585]) ).
thf(1615,plain,
~ ( sk2 @ ( sk1 @ subset ) ),
inference(simp,[status(thm)],[1614]) ).
thf(1756,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ $true
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[59,1615]) ).
thf(1757,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ),
inference(simp,[status(thm)],[1756]) ).
thf(1758,plain,
( ( sk2 @ ( sk1 @ set_difference ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1757:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1841,plain,
$false,
inference(simplifyReflect,[status(thm)],[1613,1758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU134+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.24/0.50 % Computer : n009.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Sat Sep 26 08:38:29 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.51/1.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.01/1.70 % [INFO] Parsing done (292ms).
% 2.01/1.72 % [INFO] Running in sequential loop mode.
% 2.87/2.37 % [INFO] eprover registered as external prover.
% 2.87/2.38 % [INFO] Scanning for conjecture ...
% 3.24/2.53 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 3.24/2.59 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 3.39/2.62 % [INFO] Problem is first-order (TPTP FOF).
% 3.39/2.63 % [INFO] Type checking passed.
% 3.39/2.63 % [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 ...
% 18.69/6.72 % [INFO] Killing All external provers ...
% 18.69/6.73 % Time passed: 5997ms (effective reasoning time: 4988ms)
% 18.69/6.73 % 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)>
% 18.69/6.73 % Axioms used in derivation (1): l32_xboole_1
% 18.69/6.73 % No. of inferences in proof: 42
% 18.69/6.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5997 ms resp. 4988 ms w/o parsing
% 19.23/6.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.23/6.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------