%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM283-1.005 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 : Sun Sep 27 08:08:29 AM UTC 2026
% Result : Unsatisfiable 17.86s 5.52s
% Output : Refutation 17.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 12 ~; 10 |; 0 &; 88 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(factorial_decl,type,
factorial: $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf(n0_decl,type,
n0: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(2,axiom,
! [A: $i] : ( A @ ( n0 @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_0) ).
thf(10,plain,
! [A: $i] : ( A @ ( n0 @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ s @ product ) ) )
| ~ ( A @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ s @ product ) ) )
| ~ ( A @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( A @ ( n0 @ s @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times1) ).
thf(13,plain,
! [A: $i] : ( A @ ( A @ ( n0 @ s @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ s @ factorial ) )
| ~ ( C @ ( B @ ( A @ s @ product ) ) )
| ~ ( B @ ( A @ factorial ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ s @ factorial ) )
| ~ ( C @ ( B @ ( A @ s @ product ) ) )
| ~ ( B @ ( A @ factorial ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
n0 @ s @ ( n0 @ factorial ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial_0) ).
thf(16,plain,
n0 @ s @ ( n0 @ factorial ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ s @ ( B @ s @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ s @ ( B @ s @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ ( n0 @ s @ s @ s @ s @ s @ factorial ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_factorial) ).
thf(8,plain,
! [A: $i] :
~ ( A @ ( n0 @ s @ s @ s @ s @ s @ factorial ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(1593,plain,
$false,
inference(e,[status(thm)],[10,14,13,17,16,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM283-1.005 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 02:24:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.88/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.15 % [INFO] Parsing done (181ms).
% 1.25/1.16 % [INFO] Running in sequential loop mode.
% 1.75/1.56 % [INFO] eprover registered as external prover.
% 1.75/1.57 % [INFO] Scanning for conjecture ...
% 1.93/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.93/1.69 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.09/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.09/1.71 % [INFO] Type checking passed.
% 2.09/1.71 % [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 ...
% 17.86/5.51 % External prover 'e' found a proof!
% 17.86/5.52 % [INFO] Killing All external provers ...
% 17.86/5.52 % Time passed: 4991ms (effective reasoning time: 4348ms)
% 17.86/5.52 % Axioms used in derivation (6): factorial, times1, factorial_0, add, add_0, times
% 17.86/5.52 % No. of inferences in proof: 15
% 17.86/5.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4991 ms resp. 4348 ms w/o parsing
% 17.86/5.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.86/5.55 % [INFO] Killing All external provers ...
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