%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM754^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n001.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 08:18:07 AM UTC 2026
% Result : Theorem 2.82s 2.01s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 2 ~; 0 |; 0 &; 74 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% 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(u_decl,type,
u: frac ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(moref_decl,type,
moref: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(4,axiom,
moref @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(10,plain,
moref @ z @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62g) ).
thf(14,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(9,plain,
eq @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz58) ).
thf(17,plain,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(11,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ u @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62h) ).
thf(2,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM754^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:56:59 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.85/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.95 % [INFO] Parsing done (184ms).
% 1.17/0.97 % [INFO] Running in sequential loop mode.
% 1.72/1.37 % [INFO] eprover registered as external prover.
% 1.72/1.37 % [INFO] Scanning for conjecture ...
% 1.91/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.91/1.49 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.04/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.52 % [INFO] Type checking passed.
% 2.04/1.52 % [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 ...
% 2.82/2.00 % External prover 'e' found a proof!
% 2.82/2.01 % [INFO] Killing All external provers ...
% 2.82/2.01 % Time passed: 1672ms (effective reasoning time: 1034ms)
% 2.82/2.01 % 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)>
% 2.82/2.01 % Axioms used in derivation (5): e, satz62g, satz44, m, satz58
% 2.82/2.01 % No. of inferences in proof: 14
% 2.82/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1672 ms resp. 1034 ms w/o parsing
% 3.14/2.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.14/2.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------