%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO376^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 : Wed Sep 30 08:45:41 AM UTC 2026
% Result : Theorem 5.10s 2.59s
% Output : Refutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 1
% Syntax : Number of formulae : 61 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 278 ( 26 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 290 ( 87 ~; 64 |; 9 &; 127 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 19 ^; 0 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(cG_decl,type,
cG: $o > $o ).
thf(cF_decl,type,
cF: $o > $o ).
thf(cP_decl,type,
cP: ( $o > $o ) > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk4_decl,type,
sk4: $o ).
thf(1,conjecture,
( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
| ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM627) ).
thf(2,negated_conjecture,
~ ( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
| ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
| ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( cP @ cF )
& ( cP @ cG )
& ~ ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
& ~ ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
cP @ cG,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ~ $true
| ( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
!= ( cP @ cG ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
!= ( cP @ cG ) ),
inference(simp,[status(thm)],[11]) ).
thf(14,plain,
( ( ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
!= cG ),
inference(simp,[status(thm)],[12]) ).
thf(16,plain,
( ( ( cF @ sk2 )
| ( cG @ sk2 ) )
!= ( cG @ sk2 ) ),
inference(func_ext,[status(esa)],[14]) ).
thf(33,plain,
( ~ ( ( cF @ sk2 )
| ( cG @ sk2 ) )
| ~ ( cG @ sk2 ) ),
inference(bool_ext,[status(thm)],[16]) ).
thf(35,plain,
( ( ~ ( cF @ sk2 )
| ~ ( cG @ sk2 ) )
& ( ~ ( cG @ sk2 )
| ~ ( cG @ sk2 ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(37,plain,
( ~ ( cG @ sk2 )
| ~ ( cG @ sk2 ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(38,plain,
~ ( cG @ sk2 ),
inference(simp,[status(thm)],[37]) ).
thf(43,plain,
( ( cF @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[16,38]) ).
thf(44,plain,
cF @ sk2,
inference(simp,[status(thm)],[43]) ).
thf(8,plain,
~ ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(19,plain,
( ~ $true
| ( ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) )
!= ( cP @ cG ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(20,plain,
( ( cP
@ ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) )
!= ( cP @ cG ) ),
inference(simp,[status(thm)],[19]) ).
thf(22,plain,
( ( ^ [A: $o] :
( ~ ( cF @ A )
| ( cG @ A ) ) )
!= cG ),
inference(simp,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( cF @ sk4 )
| ( cG @ sk4 ) )
!= ( cG @ sk4 ) ),
inference(func_ext,[status(esa)],[22]) ).
thf(81,plain,
( ( ( ~ $true
| ( cG @ sk4 ) )
!= ( cG @ sk4 ) )
| ( ( cF @ sk4 )
!= ( cF @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[44,24]) ).
thf(82,plain,
( ( cF @ sk4 )
!= ( cF @ sk2 ) ),
inference(simp,[status(thm)],[81]) ).
thf(84,plain,
sk4 != sk2,
inference(simp,[status(thm)],[82]) ).
thf(5,plain,
cP @ cF,
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ~ $true
| ( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
!= ( cP @ cF ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(10,plain,
( ( cP
@ ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
!= ( cP @ cF ) ),
inference(simp,[status(thm)],[9]) ).
thf(13,plain,
( ( ^ [A: $o] :
( ( cF @ A )
| ( cG @ A ) ) )
!= cF ),
inference(simp,[status(thm)],[10]) ).
thf(15,plain,
( ( ( cF @ sk1 )
| ( cG @ sk1 ) )
!= ( cF @ sk1 ) ),
inference(func_ext,[status(esa)],[13]) ).
thf(25,plain,
( ~ ( ( cF @ sk1 )
| ( cG @ sk1 ) )
| ~ ( cF @ sk1 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(27,plain,
( ( ~ ( cF @ sk1 )
| ~ ( cF @ sk1 ) )
& ( ~ ( cG @ sk1 )
| ~ ( cF @ sk1 ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(28,plain,
( ~ ( cF @ sk1 )
| ~ ( cF @ sk1 ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(30,plain,
~ ( cF @ sk1 ),
inference(simp,[status(thm)],[28]) ).
thf(41,plain,
( $false
| ( cG @ sk1 ) ),
inference(rewrite,[status(thm)],[15,30]) ).
thf(42,plain,
cG @ sk1,
inference(simp,[status(thm)],[41]) ).
thf(77,plain,
( ~ ( ~ ( cF @ sk4 )
| ( cG @ sk4 ) )
| ~ ( cG @ sk4 ) ),
inference(bool_ext,[status(thm)],[24]) ).
thf(85,plain,
( ( ( cF @ sk4 )
| ~ ( cG @ sk4 ) )
& ( ~ ( cG @ sk4 )
| ~ ( cG @ sk4 ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(87,plain,
( ~ ( cG @ sk4 )
| ~ ( cG @ sk4 ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(88,plain,
~ ( cG @ sk4 ),
inference(simp,[status(thm)],[87]) ).
thf(95,plain,
( ~ $true
| ( ( cG @ sk4 )
!= ( cG @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,88]) ).
thf(96,plain,
( ( cG @ sk4 )
!= ( cG @ sk1 ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
sk4 != sk1,
inference(simp,[status(thm)],[96]) ).
thf(104,plain,
( ~ sk4
| ~ sk1 ),
inference(bool_ext,[status(thm)],[97]) ).
thf(105,plain,
( sk4
| sk1 ),
inference(bool_ext,[status(thm)],[97]) ).
thf(45,plain,
( ~ $true
| ( ( cG @ sk2 )
!= ( cG @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,38]) ).
thf(46,plain,
( ( cG @ sk2 )
!= ( cG @ sk1 ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
sk2 != sk1,
inference(simp,[status(thm)],[46]) ).
thf(52,plain,
( sk2
| sk1 ),
inference(bool_ext,[status(thm)],[47]) ).
thf(91,plain,
( ~ sk4
| ~ sk2 ),
inference(bool_ext,[status(thm)],[84]) ).
thf(101,plain,
( sk1
| ~ sk4
| ~ $true
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[52,91]) ).
thf(102,plain,
( sk1
| ~ sk4
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( sk1
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[102:[]]) ).
thf(136,plain,
( sk1
| sk1
| ~ $true
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[105,103]) ).
thf(137,plain,
( sk1
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
sk1,
inference(pattern_uni,[status(thm)],[137:[]]) ).
thf(143,plain,
( ~ sk4
| ~ $true ),
inference(rewrite,[status(thm)],[104,138]) ).
thf(144,plain,
~ sk4,
inference(simp,[status(thm)],[143]) ).
thf(150,plain,
sk2,
inference(rewrite,[status(thm)],[84,144]) ).
thf(145,plain,
~ sk2,
inference(rewrite,[status(thm)],[47,138]) ).
thf(159,plain,
$false,
inference(rewrite,[status(thm)],[150,145]) ).
thf(160,plain,
$false,
inference(simp,[status(thm)],[159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO376^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.22 % Computer : n007.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:47:41 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.90/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.98 % [INFO] Parsing done (178ms).
% 1.26/0.99 % [INFO] Running in sequential loop mode.
% 2.08/1.40 % [INFO] eprover registered as external prover.
% 2.08/1.41 % [INFO] Scanning for conjecture ...
% 2.08/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.25/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.25/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.53 % [INFO] Type checking passed.
% 2.25/1.53 % [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 ...
% 5.10/2.58 % [INFO] Killing All external provers ...
% 5.10/2.58 % Time passed: 2211ms (effective reasoning time: 1583ms)
% 5.10/2.58 % 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)>
% 5.10/2.58 % Axioms used in derivation (0):
% 5.10/2.59 % No. of inferences in proof: 61
% 5.10/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2211 ms resp. 1583 ms w/o parsing
% 4.89/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.89/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------