%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM747^1 : 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 : n011.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 08:18:05 AM UTC 2026
% Result : Theorem 3.70s 2.47s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 72 ( 2 ~; 0 |; 0 &; 68 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(frac_type,type,
frac: $tType ).
thf(x1_decl,type,
x1: nat ).
thf(x2_decl,type,
x2: nat ).
thf(n_decl,type,
n: nat ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(fr_decl,type,
fr: nat > nat > frac ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(1,conjecture,
eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57a) ).
thf(2,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
thf(6,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57) ).
thf(8,plain,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[5,6,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM747^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.22 % Computer : n011.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 12:49:01 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.18/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.70/1.23 % [INFO] Parsing done (268ms).
% 1.70/1.25 % [INFO] Running in sequential loop mode.
% 2.57/1.81 % [INFO] eprover registered as external prover.
% 2.57/1.82 % [INFO] Scanning for conjecture ...
% 2.73/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.73/1.93 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.73/1.95 % [INFO] Problem is higher-order (TPTP THF).
% 2.73/1.95 % [INFO] Type checking passed.
% 2.73/1.96 % [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 ...
% 3.70/2.47 % External prover 'e' found a proof!
% 3.70/2.47 % [INFO] Killing All external provers ...
% 3.70/2.47 % Time passed: 2098ms (effective reasoning time: 1205ms)
% 3.70/2.47 % 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)>
% 3.70/2.47 % Axioms used in derivation (2): satz38, satz57
% 3.70/2.47 % No. of inferences in proof: 8
% 3.70/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2098 ms resp. 1205 ms w/o parsing
% 3.90/2.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.90/2.50 % [INFO] Killing All external provers ...
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