%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN984^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n012.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 08:41:34 AM UTC 2026
% Result : Theorem 1.73s 1.09s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 8 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 66 ( 14 ~; 6 |; 20 &; 23 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 29 ^; 0 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $o ).
thf(b_decl,type,
b: $o ).
thf(p_decl,type,
p: ( $i > $o ) > $o ).
thf(1,conjecture,
( ( ( p
@ ^ [A: $i] : a )
& ( p
@ ^ [A: $i] : b ) )
=> ( p
@ ^ [A: $i] :
( a
& b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ( ( ( p
@ ^ [A: $i] : a )
& ( p
@ ^ [A: $i] : b ) )
=> ( p
@ ^ [A: $i] :
( a
& b ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( p
@ ^ [A: $i] : a )
& ( p
@ ^ [A: $i] : b ) )
=> ( p
@ ^ [A: $i] :
( a
& b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( p
@ ^ [A: $i] : a )
& ( p
@ ^ [A: $i] : b )
& ~ ( p
@ ^ [A: $i] :
( a
& b ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( p
@ ^ [A: $i] : b ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( p
@ ^ [A: $i] :
( a
& b ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ~ $true
| ( ( p
@ ^ [A: $i] :
( a
& b ) )
!= ( p
@ ^ [A: $i] : b ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(11,plain,
( ( p
@ ^ [A: $i] :
( a
& b ) )
!= ( p
@ ^ [A: $i] : b ) ),
inference(simp,[status(thm)],[10]) ).
thf(13,plain,
( ( ^ [A: $i] :
( a
& b ) )
!= ( ^ [A: $i] : b ) ),
inference(simp,[status(thm)],[11]) ).
thf(5,plain,
( p
@ ^ [A: $i] : a ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ~ $true
| ( ( p
@ ^ [A: $i] :
( a
& b ) )
!= ( p
@ ^ [A: $i] : a ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(9,plain,
( ( p
@ ^ [A: $i] :
( a
& b ) )
!= ( p
@ ^ [A: $i] : a ) ),
inference(simp,[status(thm)],[8]) ).
thf(12,plain,
( ( ^ [A: $i] :
( a
& b ) )
!= ( ^ [A: $i] : a ) ),
inference(simp,[status(thm)],[9]) ).
thf(14,plain,
( ( a
& b )
!= a ),
inference(func_ext,[status(esa)],[12]) ).
thf(17,plain,
( ( a
& b )
| a ),
inference(bool_ext,[status(thm)],[14]) ).
thf(20,plain,
( ( a
| a )
& ( b
| a ) ),
inference(cnf,[status(esa)],[17]) ).
thf(21,plain,
( a
| a ),
inference(cnfConj,[status(thm)],[20]) ).
thf(23,plain,
a,
inference(simp,[status(thm)],[21]) ).
thf(27,plain,
( ( ^ [A: $i] :
( $true
& b ) )
!= ( ^ [A: $i] : b ) ),
inference(rewrite,[status(thm)],[13,23]) ).
thf(28,plain,
$false,
inference(simp,[status(thm)],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN984^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % 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
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 16:19:18 UTC 2026
% 0.08/0.12 % CPUTime :
% 0.08/0.12 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
% 0.40/0.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.56/0.49 % [INFO] Parsing done (87ms).
% 0.56/0.49 % [INFO] Running in sequential loop mode.
% 0.84/0.68 % [INFO] eprover registered as external prover.
% 0.84/0.68 % [INFO] Scanning for conjecture ...
% 1.00/0.72 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.00/0.73 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.00/0.74 % [INFO] Problem is higher-order (TPTP THF).
% 1.00/0.74 % [INFO] Type checking passed.
% 1.00/0.74 % [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 ...
% 1.73/1.09 % [INFO] Killing All external provers ...
% 1.73/1.09 % Time passed: 897ms (effective reasoning time: 592ms)
% 1.73/1.09 % 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)>
% 1.73/1.09 % Axioms used in derivation (0):
% 1.73/1.09 % No. of inferences in proof: 20
% 1.73/1.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 897 ms resp. 592 ms w/o parsing
% 1.73/1.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.73/1.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------