%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM759^1 : 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 : n010.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 08:18:08 AM UTC 2026
% Result : Theorem 2.33s 1.28s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 2 ~; 0 |; 0 &; 58 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(z_decl,type,
z: frac ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(4,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
=> ( eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz63b) ).
thf(9,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
=> ( eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(12,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz63e) ).
thf(2,negated_conjecture,
~ ( eq @ x @ y ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( eq @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(8,plain,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).
thf(15,plain,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[9,12,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM759^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.21 % Computer : n010.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 12:53:38 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.61 % [INFO] Parsing done (93ms).
% 0.88/0.61 % [INFO] Running in sequential loop mode.
% 1.13/0.79 % [INFO] eprover registered as external prover.
% 1.36/0.80 % [INFO] Scanning for conjecture ...
% 1.36/0.84 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.36/0.85 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.36/0.86 % [INFO] Problem is higher-order (TPTP THF).
% 1.36/0.87 % [INFO] Type checking passed.
% 1.36/0.87 % [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 ...
% 2.33/1.28 % External prover 'e' found a proof!
% 2.33/1.28 % [INFO] Killing All external provers ...
% 2.33/1.28 % Time passed: 970ms (effective reasoning time: 662ms)
% 2.33/1.28 % 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)>
% 2.33/1.28 % Axioms used in derivation (4): satz63b, satz39, e, satz58
% 2.33/1.28 % No. of inferences in proof: 12
% 2.33/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 970 ms resp. 662 ms w/o parsing
% 2.67/1.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.67/1.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------