%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET592^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n010.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 : Wed Sep 30 08:22:58 AM UTC 2026
% Result : Theorem 3.56s 2.24s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 105 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 185 ( 37 ~; 18 |; 27 &; 85 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 28 ^; 39 !; 5 ?; 75 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ( ? [B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
& ? [C: a > $o] :
( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ( ( ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) )
= ( ^ [D: a] : $false ) ) ) )
=> ( A
= ( ^ [B: a] : $false ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) )
& ? [B: a > $o] :
( ! [C: a] :
( ( sk1 @ C )
=> ( B @ C ) )
& ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) )
& ( ( ^ [B: a] :
( ( sk2 @ B )
& ( A @ B ) ) )
= ( ^ [B: a] : $false ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) )
& ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ( ( ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) )
= ( ^ [D: a] : $false ) ) )
=> ( A
= ( ^ [D: a] : $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_51_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) )
& ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ( ( ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) )
= ( ^ [D: a] : $false ) ) )
=> ( A
= ( ^ [D: a] : $false ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) )
& ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ( ( ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) )
= ( ^ [D: a] : $false ) ) )
=> ( A
= ( ^ [D: a] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > $o] :
( ? [B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
& ? [C: a > $o] :
( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ( ( ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) )
= ( ^ [D: a] : $false ) ) ) )
=> ( A
= ( ^ [B: a] : $false ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [B: a,A: a] :
( ( ~ ( sk1 @ A )
| ( sk2 @ A ) )
& ( ~ ( sk1 @ B )
| ( sk3 @ B ) )
& ( ( ^ [C: a] :
( ( sk2 @ C )
& ( sk3 @ C ) ) )
= ( ^ [C: a] : $false ) )
& ( sk1
!= ( ^ [C: a] : $false ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(12,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(13,plain,
sk1 @ sk4,
inference(func_ext,[status(esa)],[12]) ).
thf(6,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
( ( ^ [A: a] :
( ( sk2 @ A )
& ( sk3 @ A ) ) )
= ( ^ [A: a] : $false ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
( ( ^ [A: a] :
( ( sk2 @ A )
& ( sk3 @ A ) ) )
= ( ^ [A: a] : $false ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(14,plain,
! [A: a] :
~ ( ( sk2 @ A )
& ( sk3 @ A ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(15,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ~ ( sk3 @ A ) ),
inference(cnf,[status(esa)],[14]) ).
thf(19,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ $true
| ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6,15]) ).
thf(20,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= ( sk2 @ B ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(22,plain,
! [A: a] :
( ~ $true
| ~ ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,21]) ).
thf(23,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
~ ( sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk4 ))]]) ).
thf(29,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ $true
| ( ( sk3 @ A )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[10,24]) ).
thf(30,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( sk3 @ A )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
~ ( sk1 @ sk4 ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk4 ))]]) ).
thf(42,plain,
~ $true,
inference(rewrite,[status(thm)],[31,13]) ).
thf(43,plain,
$false,
inference(simp,[status(thm)],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET592^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.19 % Computer : n010.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:38:48 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.87/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.94 % [INFO] Parsing done (178ms).
% 1.18/0.95 % [INFO] Running in sequential loop mode.
% 1.74/1.35 % [INFO] eprover registered as external prover.
% 1.74/1.36 % [INFO] Scanning for conjecture ...
% 1.92/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.92/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.92/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 1.92/1.49 % [INFO] Type checking passed.
% 2.08/1.50 % [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 ...
% 3.56/2.23 % [INFO] Killing All external provers ...
% 3.56/2.23 % Time passed: 1901ms (effective reasoning time: 1271ms)
% 3.56/2.23 % 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)>
% 3.56/2.23 % Axioms used in derivation (0):
% 3.56/2.23 % No. of inferences in proof: 26
% 3.56/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1901 ms resp. 1271 ms w/o parsing
% 3.79/2.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.79/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------