%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO304^5 : 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 : n008.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 08:45:34 AM UTC 2026
% Result : Theorem 7.04s 3.34s
% Output : Refutation 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 59 ( 38 equ; 9 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 141 ( 34 ~; 19 |; 2 &; 67 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 18 ^; 19 !; 0 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: ( a > a > $o ) > $o ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( a > a > $o ) > $o] :
~ ( ( A
@ ^ [B: a,C: a] :
! [D: a > $o] :
( ( D @ B )
=> ( D @ C ) ) )
=> ( A @ ( (=) @ a ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a > $o] :
~ ( ( A @ sk2 )
=> ( A @ sk3 ) ) ) ) ).
thf(1,conjecture,
! [A: ( a > a > $o ) > $o] :
( ( A
@ ^ [B: a,C: a] :
! [D: a > $o] :
( ( D @ B )
=> ( D @ C ) ) )
=> ( A @ ( (=) @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE2_eq__pme) ).
thf(2,negated_conjecture,
~ ! [A: ( a > a > $o ) > $o] :
( ( A
@ ^ [B: a,C: a] :
! [D: a > $o] :
( ( D @ B )
=> ( D @ C ) ) )
=> ( A @ ( (=) @ a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( a > a > $o ) > $o] :
( ( A
@ ^ [B: a,C: a] :
! [D: a > $o] :
( ( D @ B )
=> ( D @ C ) ) )
=> ( A @ ( (=) @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1
@ ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
& ~ ( sk1 @ ( (=) @ a ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( sk1
@ ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
~ ( sk1 @ ( (=) @ a ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ~ $true
| ( ( sk1
@ ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
!= ( sk1 @ ( (=) @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(8,plain,
( ( sk1
@ ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
!= ( sk1 @ ( (=) @ a ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( ( ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
!= ( (=) @ a ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [A: a > $o] :
( ( A @ sk2 )
=> ( A @ sk3 ) ) )
!= ( sk2 = sk3 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(12,plain,
( ! [A: a > $o] :
( ( A @ sk2 )
=> ( A @ sk3 ) )
| ( sk2 = sk3 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(14,plain,
( ( sk3 = sk2 )
| ! [A: a > $o] :
( ( A @ sk2 )
=> ( A @ sk3 ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(18,plain,
! [A: a > $o] :
( ( sk3 = sk2 )
| ~ ( A @ sk2 )
| ( A @ sk3 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(11,plain,
( ~ ! [A: a > $o] :
( ( A @ sk2 )
=> ( A @ sk3 ) )
| ( sk2 != sk3 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(13,plain,
( ( sk3 != sk2 )
| ~ ! [A: a > $o] :
( ( A @ sk2 )
=> ( A @ sk3 ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(15,plain,
( ( ( sk3 != sk2 )
| ( sk4 @ sk2 ) )
& ( ( sk3 != sk2 )
| ~ ( sk4 @ sk3 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(16,plain,
( ( sk3 != sk2 )
| ( sk4 @ sk2 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(17,plain,
( ( sk3 != sk2 )
| ~ ( sk4 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(19,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 )
| ~ $true
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,17]) ).
thf(20,plain,
( ( sk3 != sk2 )
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
sk3 != sk2,
inference(simp,[status(thm)],[21]) ).
thf(105,plain,
! [A: a > $o] :
( ~ ( A @ sk2 )
| ( A @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[18,22]) ).
thf(106,plain,
( ( sk2 != sk2 )
| ( sk2 = sk3 ) ),
inference(replace_leibeq,[status(thm)],[105:[bind(A,$thf( (=) @ a @ sk2 ))]]) ).
thf(107,plain,
( ( sk2 != sk2 )
| ( sk3 = sk2 ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(108,plain,
sk3 = sk2,
inference(pattern_uni,[status(thm)],[107:[]]) ).
thf(109,plain,
$false,
inference(simplifyReflect,[status(thm)],[108,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO304^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.11/0.25 % Computer : n008.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 16:45:09 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 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
% 1.23/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.12 % [INFO] Parsing done (185ms).
% 1.51/1.13 % [INFO] Running in sequential loop mode.
% 2.39/1.68 % [INFO] eprover registered as external prover.
% 2.39/1.69 % [INFO] Scanning for conjecture ...
% 2.43/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.60/1.84 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.60/1.85 % [INFO] Problem is higher-order (TPTP THF).
% 2.60/1.86 % [INFO] Type checking passed.
% 2.60/1.87 % [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 ...
% 7.04/3.33 % [INFO] Killing All external provers ...
% 7.04/3.34 % Time passed: 2932ms (effective reasoning time: 2193ms)
% 7.04/3.34 % 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)>
% 7.04/3.34 % Axioms used in derivation (0):
% 7.04/3.34 % No. of inferences in proof: 27
% 7.04/3.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2932 ms resp. 2193 ms w/o parsing
% 6.81/3.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.81/3.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------