%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM730^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : 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 08:18:04 AM UTC 2026
% Result : Theorem 1.40s 0.99s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 5 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 109 ( 2 ~; 0 |; 0 &; 107 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(orec3_decl,type,
orec3: $o > $o > $o > $o ).
thf(ts_decl,type,
ts: nat > nat > nat ).
thf(c1x_decl,type,
c1x: frac > nat ).
thf(c2y_decl,type,
c2y: frac > nat ).
thf(c1y_decl,type,
c1y: frac > nat ).
thf(c2x_decl,type,
c2x: frac > nat ).
thf(more_decl,type,
more: nat > nat > $o ).
thf(less_decl,type,
less: nat > nat > $o ).
thf(1,conjecture,
( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41) ).
thf(2,negated_conjecture,
~ ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: nat,B: nat] : ( orec3 @ ( A = B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10) ).
thf(5,plain,
! [A: nat,B: nat] : ( orec3 @ ( A = B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,plain,
$false,
inference(e,[status(thm)],[4,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM730^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % 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
% 0.07/0.11 % Computer : n012.cluster.edu
% 0.07/0.11 % Model : x86_64 x86_64
% 0.07/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.11 % Memory : 8046.5625MB
% 0.07/0.11 % OS : Linux 6.8.0-71-generic
% 0.07/0.11 % CPULimit : 300
% 0.07/0.11 % WCLimit : 300
% 0.07/0.11 % DateTime : Tue Sep 29 12:45:33 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 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
% 0.39/0.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.49 % [INFO] Parsing done (93ms).
% 0.56/0.50 % [INFO] Running in sequential loop mode.
% 0.85/0.68 % [INFO] eprover registered as external prover.
% 0.85/0.69 % [INFO] Scanning for conjecture ...
% 1.00/0.73 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.00/0.74 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.00/0.75 % [INFO] Problem is higher-order (TPTP THF).
% 1.00/0.75 % [INFO] Type checking passed.
% 1.00/0.76 % [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 ...
% 1.40/0.99 % External prover 'e' found a proof!
% 1.40/0.99 % [INFO] Killing All external provers ...
% 1.40/0.99 % Time passed: 803ms (effective reasoning time: 492ms)
% 1.40/0.99 % 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)>
% 1.40/0.99 % Axioms used in derivation (1): satz10
% 1.40/0.99 % No. of inferences in proof: 6
% 1.40/0.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 803 ms resp. 492 ms w/o parsing
% 1.71/1.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.71/1.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------