%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n017.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 07:21:57 AM UTC 2026
% Result : Theorem 5.98s 3.56s
% Output : Refutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 146 ( 2 ~; 0 |; 17 &; 114 @)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 26 !; 3 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_decl,type,
d: $i > $i > $o ).
thf(product_decl,type,
product: $i > $i > $i ).
thf(l_decl,type,
l: $i > $i > $o ).
thf(r_decl,type,
r: $i > $i > $o ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ l ) )
<=> ( ( ( A @ ( B @ product ) )
= B )
& ( ( B @ ( A @ product ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( ( ( ( A @ ( B @ product ) )
= B )
& ( ( B @ ( A @ product ) )
= A ) )
=> ( B @ ( A @ l ) ) )
& ( ( B @ ( A @ l ) )
=> ( ( ( A @ ( B @ product ) )
= B )
& ( ( B @ ( A @ product ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ d ) )
<=> ? [C: $i] :
( ( B @ ( C @ l ) )
& ( C @ ( A @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ l ) )
& ( C @ ( A @ r ) ) )
=> ( B @ ( A @ d ) ) )
& ( ( B @ ( A @ d ) )
=> ? [C: $i] :
( ( B @ ( C @ l ) )
& ( C @ ( A @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r ) )
<=> ( ( ( A @ ( B @ product ) )
= A )
& ( ( B @ ( A @ product ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( ( ( A @ ( B @ product ) )
= A )
& ( ( B @ ( A @ product ) )
= B ) )
=> ( B @ ( A @ r ) ) )
& ( ( B @ ( A @ r ) )
=> ( ( ( A @ ( B @ product ) )
= A )
& ( ( B @ ( A @ product ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ d ) )
<=> ( ( ( B @ ( A @ product ) @ ( B @ product ) )
= B )
& ( ( A @ ( B @ product ) @ ( A @ product ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ d ) )
<=> ( ( ( B @ ( A @ product ) @ ( B @ product ) )
= B )
& ( ( A @ ( B @ product ) @ ( A @ product ) )
= A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ product ) @ ( B @ product ) )
= B )
& ( ( A @ ( B @ product ) @ ( A @ product ) )
= A ) )
=> ( B @ ( A @ d ) ) )
& ( ( B @ ( A @ d ) )
=> ( ( ( B @ ( A @ product ) @ ( B @ product ) )
= B )
& ( ( A @ ( B @ product ) @ ( A @ product ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ product ) @ product ) )
= ( A @ ( B @ product ) @ ( C @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
thf(19,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ product ) @ product ) )
= ( A @ ( B @ product ) @ ( C @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[25,45,22,35,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.25/0.50 % Computer : n017.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Fri Sep 25 15:41:47 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 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
% 1.43/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.62 % [INFO] Parsing done (263ms).
% 1.98/1.64 % [INFO] Running in sequential loop mode.
% 2.91/2.25 % [INFO] eprover registered as external prover.
% 2.91/2.26 % [INFO] Scanning for conjecture ...
% 3.27/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 3.27/2.45 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 3.27/2.48 % [INFO] Problem is first-order (TPTP FOF).
% 3.27/2.48 % [INFO] Type checking passed.
% 3.27/2.49 % [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 ...
% 5.98/3.54 % External prover 'e' found a proof!
% 5.98/3.55 % [INFO] Killing All external provers ...
% 5.98/3.55 % Time passed: 2838ms (effective reasoning time: 1905ms)
% 5.98/3.55 % 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)>
% 5.98/3.56 % Axioms used in derivation (5): sos03, sos02, sos05, sos04, sos01
% 5.98/3.56 % No. of inferences in proof: 14
% 5.98/3.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2838 ms resp. 1905 ms w/o parsing
% 6.19/3.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.19/3.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------