%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU610_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 08:39:39 AM UTC 2026
% Result : Theorem 6.85s 3.27s
% Output : Refutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 24 unt; 0 typ; 3 def)
% Number of atoms : 148 ( 29 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 351 ( 34 ~; 27 |; 6 &; 246 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 77 ( 2 ^; 72 !; 0 ?; 77 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(in__Cong_decl,type,
in__Cong: $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetI2_decl,type,
subsetI2: $o ).
thf(setminus_decl,type,
setminus: $i > $i > $i ).
thf(setminusI_decl,type,
setminusI: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ setminus ) )
= emptyset )
=> ( B @ ( A @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ setminus ) )
= emptyset )
=> ( A @ ( sk1 @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ setminus ) )
= emptyset )
=> ( B @ ( A @ subset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ setminus ) )
= emptyset )
=> ( B @ ( A @ subset ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ setminus ) )
= emptyset )
=> ( B @ ( A @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ~ ( sk2 @ ( sk1 @ subset ) )
& ( ( sk2 @ ( sk1 @ setminus ) )
= emptyset )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
( ( sk2 @ ( sk1 @ setminus ) )
= emptyset ),
inference(cnfConj,[status(thm)],[8]) ).
thf(15,plain,
( ( sk2 @ ( sk1 @ setminus ) )
= emptyset ),
inference(lifteq,[status(thm)],[11]) ).
thf(4,axiom,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(18,plain,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(10,plain,
subsetI2,
inference(cnfConj,[status(thm)],[8]) ).
thf(61,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) ),
inference(rewrite,[status(thm)],[19,10]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) )
& ( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(12,plain,
~ ( sk2 @ ( sk1 @ subset ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ $true
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[63,12]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
sk1 @ ( sk1 @ ( sk2 @ sk3 ) @ in ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(3,axiom,
( setminusI
= ( ! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ setminus ) @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(16,plain,
( setminusI
= ( ! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ setminus ) @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
( setminusI
= ( ! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ setminus ) @ ( C @ in ) ) ) ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(14,plain,
setminusI,
inference(cnfConj,[status(thm)],[8]) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ setminus ) @ ( C @ in ) ) ) ),
inference(rewrite,[status(thm)],[17,14]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ setminus ) @ ( C @ in ) )
| ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ sk3 ) @ in ) )
!= ( A @ ( C @ in ) ) )
| ( B @ ( A @ setminus ) @ ( C @ in ) )
| ( B @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,58]) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ sk3 ) @ in ) )
!= ( A @ ( C @ in ) ) )
| ( B @ ( A @ setminus ) @ ( C @ in ) )
| ( B @ ( C @ in ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(284,plain,
! [A: $i] :
( ( A @ ( sk1 @ setminus ) @ ( sk1 @ ( sk2 @ sk3 ) @ in ) )
| ( A @ ( sk1 @ ( sk2 @ sk3 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk1 @ ( sk2 @ sk3 ) ))]]) ).
thf(301,plain,
! [A: $i] :
( ( A @ ( sk1 @ setminus ) @ ( sk1 @ ( sk2 @ sk3 ) @ in ) )
| ( A @ ( sk1 @ ( sk2 @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(317,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ setminus ) )
!= ( A @ ( sk1 @ setminus ) ) )
| ( emptyset @ ( sk1 @ ( sk2 @ sk3 ) @ in ) )
| ( A @ ( sk1 @ ( sk2 @ sk3 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[15,301]) ).
thf(318,plain,
( ( emptyset @ ( sk1 @ ( sk2 @ sk3 ) @ in ) )
| ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( sk2 ))]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[64,12]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(180,plain,
~ ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ in ) ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6,axiom,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(22,plain,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(9,plain,
emptysetE,
inference(cnfConj,[status(thm)],[8]) ).
thf(24,plain,
! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ),
inference(rewrite,[status(thm)],[23,9]) ).
thf(25,plain,
! [B: $o,A: $i] :
( B
| ~ ( emptyset @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(29,plain,
! [B: $o,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ $true
| ~ ( emptyset @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[25,12]) ).
thf(30,plain,
! [B: $o,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ ( emptyset @ ( A @ in ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
! [A: $i] :
~ ( emptyset @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ subset ) ))]]) ).
thf(338,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[318,180,31]) ).
thf(339,plain,
$false,
inference(simp,[status(thm)],[338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU610_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.39 % Computer : n013.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 10:12:21 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.20 % [INFO] Parsing done (189ms).
% 1.44/1.22 % [INFO] Running in sequential loop mode.
% 2.07/1.63 % [INFO] eprover registered as external prover.
% 2.07/1.63 % [INFO] Scanning for conjecture ...
% 2.27/1.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.46/1.81 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.46/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.46/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.46/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.46/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.46/1.82 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.46/1.83 % [INFO] Type checking passed.
% 2.46/1.83 % [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 ...
% 6.85/3.26 % [INFO] Killing All external provers ...
% 6.85/3.27 % Time passed: 2724ms (effective reasoning time: 2043ms)
% 6.85/3.27 % 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)>
% 6.85/3.27 % Axioms used in derivation (3): subsetI2, setminusI, emptysetE
% 6.85/3.27 % No. of inferences in proof: 44
% 6.85/3.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2724 ms resp. 2043 ms w/o parsing
% 6.37/3.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.37/3.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------