%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO303^5 : 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 : n018.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 3.96s 2.21s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 9 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 24 ~; 15 |; 9 &; 38 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_decl,type,
b: $i ).
thf(cS_decl,type,
cS: $i > $o ).
thf(a_decl,type,
a: $i ).
thf(cT_decl,type,
cT: $i > $o ).
thf(c0_decl,type,
c0: $i ).
thf(1,conjecture,
( ! [A: $i > $o] :
( ~ ( A @ c0 )
| ! [B: $i] : ( A @ B ) )
=> ( ~ ( ( cS @ c0 )
& ( cT @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cMIN_QUAN_BUG) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $o] :
( ~ ( A @ c0 )
| ! [B: $i] : ( A @ B ) )
=> ( ~ ( ( cS @ c0 )
& ( cT @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o] :
( ~ ( A @ c0 )
| ! [B: $i] : ( A @ B ) )
=> ( ~ ( ( cS @ c0 )
& ( cT @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i > $o] :
( ( ~ ( A @ c0 )
| ( A @ B ) )
& ( cS @ c0 )
& ( cT @ c0 )
& ( ~ ( cT @ a )
| ~ ( cS @ b ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
cT @ c0,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ~ ( cT @ a )
| ~ ( cS @ b ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(10,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(11,plain,
! [A: $i] : ( c0 = A ),
inference(simp,[status(thm)],[10]) ).
thf(6,plain,
cS @ c0,
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [A: $i] :
( ( cS @ A )
| ( c0 != c0 ) ),
inference(paramod_ordered,[status(thm)],[11,6]) ).
thf(13,plain,
! [A: $i] : ( cS @ A ),
inference(pattern_uni,[status(thm)],[12:[]]) ).
thf(21,plain,
( ~ ( cT @ a )
| ~ $true ),
inference(rewrite,[status(thm)],[8,13]) ).
thf(22,plain,
~ ( cT @ a ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( ~ $true
| ( ( cT @ c0 )
!= ( cT @ a ) ) ),
inference(paramod_ordered,[status(thm)],[7,22]) ).
thf(24,plain,
( ( cT @ c0 )
!= ( cT @ a ) ),
inference(simp,[status(thm)],[23]) ).
thf(26,plain,
c0 != a,
inference(simp,[status(thm)],[24]) ).
thf(27,plain,
$false,
inference(simplifyReflect,[status(thm)],[26,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO303^5 : 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
% 0.10/0.23 % Computer : n018.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 16:46:41 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 0.89/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (184ms).
% 1.23/1.00 % [INFO] Running in sequential loop mode.
% 2.04/1.40 % [INFO] eprover registered as external prover.
% 2.04/1.41 % [INFO] Scanning for conjecture ...
% 2.22/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.55 % [INFO] Type checking passed.
% 2.22/1.55 % [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 ...
% 2.60/1.74 % [INFO] [Domain constraints] Detected constraint on $i
% 2.60/1.74 % [INFO] [Domain constraints] dom($i) ⊆ {c0}
% 3.96/2.20 % [INFO] Killing All external provers ...
% 3.96/2.21 % Time passed: 1837ms (effective reasoning time: 1199ms)
% 3.96/2.21 % 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)>
% 3.96/2.21 % Axioms used in derivation (0):
% 3.96/2.21 % No. of inferences in proof: 19
% 3.96/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1837 ms resp. 1199 ms w/o parsing
% 3.96/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.96/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------