%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO173^5 : 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 : n009.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 08:45:20 AM UTC 2026
% Result : Theorem 4.42s 3.00s
% Output : Refutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 143 ( 14 ~; 6 |; 12 &; 111 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 27 !; 3 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(nt_decl,type,
nt: $i > $i ).
thf(imp_decl,type,
imp: $i > $i > $i ).
thf(cT_decl,type,
cT: $i > $o ).
thf(1,conjecture,
~ ( ! [A: $i,B: $i] :
( ~ ( cT @ ( imp @ A @ B ) )
| ~ ( cT @ A )
| ( cT @ B ) )
& ! [A: $i,B: $i] : ( cT @ ( imp @ A @ ( imp @ B @ A ) ) )
& ! [A: $i,B: $i,C: $i] : ( cT @ ( imp @ ( imp @ A @ ( imp @ B @ C ) ) @ ( imp @ ( imp @ A @ B ) @ ( imp @ A @ C ) ) ) )
& ! [A: $i,B: $i] : ( cT @ ( imp @ ( imp @ ( nt @ A ) @ ( nt @ B ) ) @ ( imp @ B @ A ) ) )
& ? [A: $i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLCL077_1) ).
thf(2,negated_conjecture,
~ ~ ( ! [A: $i,B: $i] :
( ~ ( cT @ ( imp @ A @ B ) )
| ~ ( cT @ A )
| ( cT @ B ) )
& ! [A: $i,B: $i] : ( cT @ ( imp @ A @ ( imp @ B @ A ) ) )
& ! [A: $i,B: $i,C: $i] : ( cT @ ( imp @ ( imp @ A @ ( imp @ B @ C ) ) @ ( imp @ ( imp @ A @ B ) @ ( imp @ A @ C ) ) ) )
& ! [A: $i,B: $i] : ( cT @ ( imp @ ( imp @ ( nt @ A ) @ ( nt @ B ) ) @ ( imp @ B @ A ) ) )
& ? [A: $i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ A ) ) @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ! [A: $i,B: $i] :
( ~ ( cT @ ( imp @ A @ B ) )
| ~ ( cT @ A )
| ( cT @ B ) )
& ! [A: $i,B: $i] : ( cT @ ( imp @ A @ ( imp @ B @ A ) ) )
& ! [A: $i,B: $i,C: $i] : ( cT @ ( imp @ ( imp @ A @ ( imp @ B @ C ) ) @ ( imp @ ( imp @ A @ B ) @ ( imp @ A @ C ) ) ) )
& ! [A: $i,B: $i] : ( cT @ ( imp @ ( imp @ ( nt @ A ) @ ( nt @ B ) ) @ ( imp @ B @ A ) ) )
& ? [A: $i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO173^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.26/0.31 % Computer : n009.cluster.edu
% 0.26/0.31 % Model : x86_64 x86_64
% 0.26/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.31 % Memory : 8046.5625MB
% 0.26/0.31 % OS : Linux 6.8.0-71-generic
% 0.26/0.31 % CPULimit : 300
% 0.26/0.31 % WCLimit : 300
% 0.26/0.31 % DateTime : Tue Sep 29 16:37:00 UTC 2026
% 0.26/0.31 % CPUTime :
% 0.26/0.31 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
% 1.28/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.69/1.38 % [INFO] Parsing done (252ms).
% 1.89/1.40 % [INFO] Running in sequential loop mode.
% 2.60/1.98 % [INFO] eprover registered as external prover.
% 2.60/1.99 % [INFO] Scanning for conjecture ...
% 2.86/2.13 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.04/2.18 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.04/2.18 % [INFO] Problem is higher-order (TPTP THF).
% 3.04/2.19 % [INFO] Type checking passed.
% 3.11/2.20 % [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 ...
% 4.42/3.00 % External prover 'e' found a proof!
% 4.42/3.00 % [INFO] Killing All external provers ...
% 4.42/3.00 % Time passed: 2487ms (effective reasoning time: 1592ms)
% 4.42/3.00 % 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)>
% 4.42/3.00 % Axioms used in derivation (0):
% 4.42/3.00 % No. of inferences in proof: 4
% 4.42/3.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2487 ms resp. 1592 ms w/o parsing
% 4.89/3.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.89/3.05 % [INFO] Killing All external provers ...
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