%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO018^1 : 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 : 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 08:45:01 AM UTC 2026
% Result : Theorem 4.32s 2.40s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 117 ( 8 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 146 ( 13 ~; 8 |; 30 &; 92 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 6 ^; 0 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $o > $i > $i ).
thf(p_decl,type,
p: ( $i > $i ) > $o ).
thf(a_decl,type,
a: ( $i > $i ) > $o ).
thf(b_decl,type,
b: $o ).
thf(1,conjecture,
( ( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( ( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) )
& ~ ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
~ ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ~ $true
| ( ( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) )
!= ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(8,plain,
( ( p
@ ( f
@ ( ( a @ ( f @ b ) )
& b ) ) )
!= ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( ( f
@ ( ( a @ ( f @ b ) )
& b ) )
!= ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ^ [A: $i] :
( ( a @ ( f @ b ) )
& b ) )
!= ( ^ [A: $i] :
( b
& ( a @ ( f @ b ) ) ) ) )
| ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(12,plain,
( ( ^ [A: $i] :
( ( a @ ( f @ b ) )
& b ) )
!= ( ^ [A: $i] :
( b
& ( a @ ( f @ b ) ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(14,plain,
( ( ( a @ ( f @ b ) )
& b )
!= ( b
& ( a @ ( f @ b ) ) ) ),
inference(func_ext,[status(esa)],[12]) ).
thf(55,plain,
( ( ( a @ ( f @ b ) )
& b )
| ( b
& ( a @ ( f @ b ) ) ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(65,plain,
( ( ( a @ ( f @ b ) )
| b )
& ( ( a @ ( f @ b ) )
| ( a @ ( f @ b ) ) )
& ( b
| b )
& ( b
| ( a @ ( f @ b ) ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(68,plain,
( b
| b ),
inference(cnfConj,[status(thm)],[65]) ).
thf(70,plain,
b,
inference(simp,[status(thm)],[68]) ).
thf(77,plain,
( ( f
@ ( ( a @ ( f @ $true ) )
& $true ) )
!= ( f
@ ( $true
& ( a @ ( f @ $true ) ) ) ) ),
inference(rewrite,[status(thm)],[9,70]) ).
thf(78,plain,
$false,
inference(simp,[status(thm)],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO018^1 : 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
% 0.12/0.22 % Computer : n008.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 16:22:09 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (178ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.72/1.39 % [INFO] eprover registered as external prover.
% 1.72/1.40 % [INFO] Scanning for conjecture ...
% 1.90/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.06/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.06/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.52 % [INFO] Type checking passed.
% 2.06/1.53 % [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 ...
% 3.99/2.39 % [INFO] Killing All external provers ...
% 3.99/2.40 % Time passed: 2035ms (effective reasoning time: 1399ms)
% 3.99/2.40 % 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)>
% 4.32/2.40 % Axioms used in derivation (0):
% 4.32/2.40 % No. of inferences in proof: 18
% 4.32/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2035 ms resp. 1399 ms w/o parsing
% 4.32/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.32/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------