%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN732+1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n020.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 : Sun Sep 27 09:18:16 AM UTC 2026
% Result : Theorem 2.69s 2.22s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 35 ( 2 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 9 ~; 5 |; 3 &; 66 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 2 ^; 26 !; 14 ?; 44 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: $i > $i > $o ).
thf(q_decl,type,
q: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] :
~ ( A @ ( B @ p ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ p ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i] :
( ! [B: $i] : ( A @ ( B @ p ) )
=> ! [B: $i] : ( A @ ( B @ q ) ) )
=> ? [A: $i] :
( ? [B: $i] : ( A @ ( B @ p ) )
=> ? [B: $i] :
( ( A @ ( B @ q ) )
| ( B @ ( A @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x3411) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ! [B: $i] : ( A @ ( B @ p ) )
=> ! [B: $i] : ( A @ ( B @ q ) ) )
=> ? [A: $i] :
( ? [B: $i] : ( A @ ( B @ p ) )
=> ? [B: $i] :
( ( A @ ( B @ q ) )
| ( B @ ( A @ p ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ! [B: $i] : ( A @ ( B @ p ) )
=> ! [B: $i] : ( A @ ( B @ q ) ) )
=> ? [A: $i] :
( ? [B: $i] : ( A @ ( B @ p ) )
=> ? [B: $i] :
( ( A @ ( B @ q ) )
| ( B @ ( A @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i] :
( ! [B: $i] : ( A @ ( B @ p ) )
=> ! [B: $i] : ( A @ ( B @ q ) ) )
=> ( ! [A: $i] :
? [B: $i] : ( A @ ( B @ p ) )
=> ( ? [A: $i,B: $i] : ( A @ ( B @ q ) )
| ? [A: $i,B: $i] : ( B @ ( A @ p ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( G @ q ) )
& ~ ( E @ ( D @ p ) )
& ( C @ ( C @ sk2 @ p ) )
& ( ( A @ ( B @ q ) )
| ~ ( A @ ( A @ sk1 @ p ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [A: $i] : ( A @ ( A @ sk2 @ p ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [A: $i] : ( A @ ( A @ sk2 @ p ) ),
inference(simp,[status(thm)],[7]) ).
thf(8,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ p ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ p ) ),
inference(simp,[status(thm)],[8]) ).
thf(13,plain,
$false,
inference(rewrite,[status(thm)],[10,11]) ).
thf(14,plain,
$false,
inference(simp,[status(thm)],[13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN732+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % 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
% 0.13/0.38 % Computer : n020.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 18:23:33 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 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
% 0.81/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.17 % [INFO] Parsing done (181ms).
% 1.17/1.19 % [INFO] Running in sequential loop mode.
% 1.70/1.74 % [INFO] eprover registered as external prover.
% 1.70/1.76 % [INFO] Scanning for conjecture ...
% 1.84/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.98/1.93 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.98/1.93 % [INFO] Problem is first-order (TPTP FOF).
% 1.98/1.94 % [INFO] Type checking passed.
% 1.98/1.94 % [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 ...
% 2.69/2.21 % [INFO] Killing All external provers ...
% 2.69/2.21 % Time passed: 1693ms (effective reasoning time: 1009ms)
% 2.69/2.21 % 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)>
% 2.69/2.21 % Axioms used in derivation (0):
% 2.69/2.21 % No. of inferences in proof: 11
% 2.69/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1693 ms resp. 1009 ms w/o parsing
% 2.69/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.69/2.25 % [INFO] Killing All external provers ...
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