%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU155+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 : n007.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 08:37:47 AM UTC 2026
% Result : Theorem 37.77s 10.68s
% Output : Refutation 38.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 7 def)
% Number of atoms : 179 ( 30 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 547 ( 57 ~; 50 |; 31 &; 377 @)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 114 ( 11 ^; 85 !; 11 ?; 114 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ in ) )
=> ( A @ union @ ( sk1 @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( C @ ( D @ in ) )
& ( D @ ( A @ in ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( C @ in ) )
& ( C @ ( B @ ( A @ sk7 ) @ in ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ~ ( sk2 @ union @ ( sk1 @ subset ) )
& ( sk2 @ ( sk1 @ in ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
sk2 @ ( sk1 @ in ),
inference(cnfConj,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
=> ( ! [C: $i] :
( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ ( G @ sk7 ) @ in ) )
| ( G @ ( F @ sk5 ) ) )
& ( ( G
= ( F @ union ) )
| ( F @ ( F @ ( G @ sk8 ) @ in ) )
| ( G @ ( F @ sk5 ) ) )
& ( ( G
= ( F @ union ) )
| ( F @ ( G @ sk8 ) @ ( F @ ( G @ sk7 ) @ in ) )
| ( G @ ( F @ sk5 ) ) )
& ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ sk5 ) )
| ~ ( F @ ( H @ in ) )
| ~ ( H @ ( F @ ( G @ sk6 ) @ in ) ) )
& ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ sk5 ) )
| ( G @ ( F @ ( G @ sk6 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( E @ in ) )
| ~ ( E @ ( D @ in ) )
| ( B
!= ( A @ union ) ) )
& ( ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) )
& ( ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( D @ in ) )
| ~ ( D @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( D @ in ) )
| ~ ( D @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ union @ ( B @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( C @ ( B @ in ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(5086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( A @ ( C @ in ) ) )
| ( A @ union @ ( B @ in ) )
| ~ $true
| ~ ( C @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[10,48]) ).
thf(5087,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( A @ ( C @ in ) ) )
| ( A @ union @ ( B @ in ) )
| ~ ( C @ ( B @ in ) ) ),
inference(simp,[status(thm)],[5086]) ).
thf(5088,plain,
! [A: $i] :
( ( sk2 @ union @ ( A @ in ) )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[5087:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(5334,plain,
! [A: $i] :
( ( sk2 @ union @ ( A @ in ) )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[5088]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk3 ) @ in ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk3 ) @ in ) ) )
& ( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(11,plain,
~ ( sk2 @ union @ ( sk1 @ subset ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[21,11]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
~ ( sk2 @ union @ ( sk1 @ ( sk2 @ union @ sk3 ) @ in ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ union ))]]) ).
thf(7648,plain,
! [A: $i] :
( ( ( sk2 @ union @ ( A @ in ) )
!= ( sk2 @ union @ ( sk1 @ ( sk2 @ union @ sk3 ) @ in ) ) )
| ~ $true
| ~ ( sk1 @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[5334,285]) ).
thf(7649,plain,
! [A: $i] :
( ( ( sk2 @ union @ ( A @ in ) )
!= ( sk2 @ union @ ( sk1 @ ( sk2 @ union @ sk3 ) @ in ) ) )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[7648]) ).
thf(7650,plain,
~ ( sk1 @ ( sk1 @ ( sk2 @ union @ sk3 ) @ in ) ),
inference(pattern_uni,[status(thm)],[7649:[bind(A,$thf( sk1 @ ( sk2 @ union @ sk3 ) ))]]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ $true
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[20,11]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ( A @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
sk1 @ ( sk1 @ ( sk2 @ union @ sk3 ) @ in ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ union ))]]) ).
thf(8282,plain,
~ $true,
inference(rewrite,[status(thm)],[7650,77]) ).
thf(8283,plain,
$false,
inference(simp,[status(thm)],[8282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU155+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
% 0.13/0.40 % Computer : n007.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 08:39:39 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
% 0.92/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.18 % [INFO] Parsing done (180ms).
% 1.40/1.19 % [INFO] Running in sequential loop mode.
% 2.23/1.77 % [INFO] eprover registered as external prover.
% 2.23/1.79 % [INFO] Scanning for conjecture ...
% 2.62/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.62/1.96 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.62/1.98 % [INFO] Problem is first-order (TPTP FOF).
% 2.62/1.99 % [INFO] Type checking passed.
% 2.62/1.99 % [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 ...
% 37.77/10.67 % [INFO] Killing All external provers ...
% 37.77/10.68 % Time passed: 10123ms (effective reasoning time: 9478ms)
% 37.77/10.68 % 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)>
% 37.77/10.68 % Axioms used in derivation (2): d4_tarski, d3_tarski
% 37.77/10.68 % No. of inferences in proof: 36
% 37.77/10.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10123 ms resp. 9478 ms w/o parsing
% 38.19/10.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.19/10.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------