%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO026^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n014.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 08:45:02 AM UTC 2026
% Result : Theorem 5.81s 2.85s
% Output : Refutation 5.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of formulae : 74 ( 18 unt; 0 typ; 1 def)
% Number of atoms : 305 ( 41 equ; 8 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 268 ( 107 ~; 68 |; 13 &; 77 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 24 ^; 3 !; 0 ?; 28 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: ( $o > $o ) > $o ).
thf(sk1_decl,type,
sk1: $o > $o ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $o > $o] :
~ ( p @ A ) ) ) ).
thf(1,conjecture,
( ( ( p
@ ^ [A: $o] : A )
& ( p @ (~) )
& ( p
@ ^ [A: $o] : $false )
& ( p
@ ^ [A: $o] : $true ) )
=> ! [A: $o > $o] : ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( ( ( p
@ ^ [A: $o] : A )
& ( p @ (~) )
& ( p
@ ^ [A: $o] : $false )
& ( p
@ ^ [A: $o] : $true ) )
=> ! [A: $o > $o] : ( p @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( p
@ ^ [A: $o] : A )
& ( p @ (~) )
& ( p
@ ^ [A: $o] : $false )
& ( p
@ ^ [A: $o] : $true ) )
=> ! [A: $o > $o] : ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( p
@ ^ [A: $o] : A )
& ( p @ (~) )
& ( p
@ ^ [A: $o] : $false )
& ( p
@ ^ [A: $o] : $true )
& ~ ( p @ sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
p @ (~),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
~ ( p @ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(16,plain,
( ~ $true
| ( ( p @ sk1 )
!= ( p @ (~) ) ) ),
inference(paramod_ordered,[status(thm)],[8,9]) ).
thf(17,plain,
( ( p @ sk1 )
!= ( p @ (~) ) ),
inference(simp,[status(thm)],[16]) ).
thf(21,plain,
sk1 != (~),
inference(simp,[status(thm)],[17]) ).
thf(25,plain,
( ( sk1 @ sk5 )
!= ( ~ sk5 ) ),
inference(func_ext,[status(esa)],[21]) ).
thf(36,plain,
( ( sk1 @ sk5 )
| ~ sk5 ),
inference(bool_ext,[status(thm)],[25]) ).
thf(41,plain,
( ( sk1 @ sk5 )
| ~ sk5 ),
inference(cnf,[status(esa)],[36]) ).
thf(5,plain,
( p
@ ^ [A: $o] : $true ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ~ $true
| ( ( p @ sk1 )
!= ( p
@ ^ [A: $o] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[5,9]) ).
thf(11,plain,
( ( p @ sk1 )
!= ( p
@ ^ [A: $o] : $true ) ),
inference(simp,[status(thm)],[10]) ).
thf(18,plain,
( sk1
!= ( ^ [A: $o] : $true ) ),
inference(simp,[status(thm)],[11]) ).
thf(23,plain,
~ ( sk1 @ sk3 ),
inference(func_ext,[status(esa)],[18]) ).
thf(132,plain,
( ~ sk5
| ~ $true
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[41,23]) ).
thf(133,plain,
( ~ sk5
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(134,plain,
( ~ sk5
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[133]) ).
thf(7,plain,
( p
@ ^ [A: $o] : A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
( ~ $true
| ( ( p @ sk1 )
!= ( p
@ ^ [A: $o] : A ) ) ),
inference(paramod_ordered,[status(thm)],[7,9]) ).
thf(15,plain,
( ( p @ sk1 )
!= ( p
@ ^ [A: $o] : A ) ),
inference(simp,[status(thm)],[14]) ).
thf(20,plain,
( sk1
!= ( ^ [A: $o] : A ) ),
inference(simp,[status(thm)],[15]) ).
thf(22,plain,
( ( sk1 @ sk2 )
!= sk2 ),
inference(func_ext,[status(esa)],[20]) ).
thf(27,plain,
( ( sk1 @ sk2 )
| sk2 ),
inference(bool_ext,[status(thm)],[22]) ).
thf(59,plain,
( sk2
| ~ $true
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[27,23]) ).
thf(60,plain,
( sk2
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(62,plain,
( sk2
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[60]) ).
thf(6,plain,
( p
@ ^ [A: $o] : $false ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
( ~ $true
| ( ( p @ sk1 )
!= ( p
@ ^ [A: $o] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(13,plain,
( ( p @ sk1 )
!= ( p
@ ^ [A: $o] : $false ) ),
inference(simp,[status(thm)],[12]) ).
thf(19,plain,
( sk1
!= ( ^ [A: $o] : $false ) ),
inference(simp,[status(thm)],[13]) ).
thf(24,plain,
sk1 @ sk4,
inference(func_ext,[status(esa)],[19]) ).
thf(37,plain,
( ~ ~ sk5
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24,25]) ).
thf(38,plain,
( sk5
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
( sk5
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[38]) ).
thf(70,plain,
( sk5
| sk5
| sk4 ),
inference(bool_ext,[status(thm)],[39]) ).
thf(71,plain,
( sk5
| sk4 ),
inference(simp,[status(thm)],[70]) ).
thf(29,plain,
( ~ $true
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[24,23]) ).
thf(30,plain,
( ( sk1 @ sk4 )
!= ( sk1 @ sk3 ) ),
inference(simp,[status(thm)],[29]) ).
thf(32,plain,
sk4 != sk3,
inference(simp,[status(thm)],[30]) ).
thf(34,plain,
( sk4
| sk3 ),
inference(bool_ext,[status(thm)],[32]) ).
thf(28,plain,
( ~ sk2
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[24,22]) ).
thf(31,plain,
( ~ sk2
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28]) ).
thf(65,plain,
( sk3
| ~ sk2
| ~ sk2
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[34,31]) ).
thf(66,plain,
( sk3
| ~ sk2
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
( sk3
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[66:[]]) ).
thf(75,plain,
( ~ sk2
| ~ ( sk1 @ $true )
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[67,23]) ).
thf(76,plain,
( ~ sk2
| ~ ( sk1 @ $true ) ),
inference(pattern_uni,[status(thm)],[75:[]]) ).
thf(125,plain,
( ~ sk5
| ~ sk2
| ~ $true
| ( ( sk1 @ sk5 )
!= ( sk1 @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[41,76]) ).
thf(126,plain,
( ~ sk5
| ~ sk2
| ( ( sk1 @ sk5 )
!= ( sk1 @ $true ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(136,plain,
( ~ sk5
| ~ sk2
| ~ sk5 ),
inference(simp,[status(thm)],[126]) ).
thf(138,plain,
( ~ sk5
| ~ sk2 ),
inference(simp,[status(thm)],[136]) ).
thf(144,plain,
( sk4
| ~ $true
| ~ sk2
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[71,138]) ).
thf(145,plain,
( sk4
| ~ sk2
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[144]) ).
thf(146,plain,
( sk4
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[145:[]]) ).
thf(63,plain,
( ~ sk2
| ~ sk4
| ~ sk2 ),
inference(bool_ext,[status(thm)],[31]) ).
thf(68,plain,
( ~ sk2
| ~ sk4 ),
inference(simp,[status(thm)],[63]) ).
thf(161,plain,
( ~ sk2
| ~ sk2
| ~ $true
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[146,68]) ).
thf(162,plain,
( ~ sk2
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
~ sk2,
inference(pattern_uni,[status(thm)],[162:[]]) ).
thf(189,plain,
( $false
| sk3 ),
inference(rewrite,[status(thm)],[62,163]) ).
thf(190,plain,
sk3,
inference(simp,[status(thm)],[189]) ).
thf(52,plain,
( sk2
| ~ ~ sk5
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[27,25]) ).
thf(53,plain,
( sk2
| sk5
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(61,plain,
( sk2
| sk5
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[53]) ).
thf(140,plain,
( sk2
| sk5
| sk5
| sk2 ),
inference(bool_ext,[status(thm)],[61]) ).
thf(143,plain,
( sk2
| sk5 ),
inference(simp,[status(thm)],[140]) ).
thf(174,plain,
( $false
| sk5 ),
inference(rewrite,[status(thm)],[143,163]) ).
thf(175,plain,
sk5,
inference(simp,[status(thm)],[174]) ).
thf(202,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[134,190,175]) ).
thf(203,plain,
$false,
inference(simp,[status(thm)],[202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO026^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.11/0.21 % Computer : n014.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:22:19 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (182ms).
% 1.19/0.99 % [INFO] Running in sequential loop mode.
% 1.78/1.36 % [INFO] eprover registered as external prover.
% 1.78/1.37 % [INFO] Scanning for conjecture ...
% 1.97/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.50 % [INFO] Type checking passed.
% 2.12/1.50 % [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 ...
% 5.81/2.84 % [INFO] Killing All external provers ...
% 5.81/2.84 % Time passed: 2492ms (effective reasoning time: 1848ms)
% 5.81/2.84 % 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)>
% 5.81/2.85 % Axioms used in derivation (0):
% 5.81/2.85 % No. of inferences in proof: 73
% 5.81/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2492 ms resp. 1848 ms w/o parsing
% 5.81/2.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.81/2.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------