%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 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 : n007.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 07:19:44 AM UTC 2026
% Result : Theorem 5.41s 3.39s
% Output : Refutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 0 equ; 0 cnn)
% Maximal formula atoms : 16 ( 12 avg)
% Number of connectives : 209 ( 2 ~; 0 |; 33 &; 162 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 72 ( 0 ^; 69 !; 3 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( ! [B: $i] : ( A @ ( B @ ( B @ inverse @ product ) ) )
& ! [B: $i] : ( A @ ( B @ inverse @ ( B @ product ) ) )
& ! [B: $i] : ( B @ ( B @ ( A @ product ) ) )
& ! [B: $i] : ( B @ ( A @ ( B @ product ) ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( B @ product ) ) )
& ( F @ ( D @ ( C @ product ) ) )
& ( E @ ( C @ ( B @ product ) ) ) )
=> ( G @ ( D @ ( E @ product ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( D @ ( E @ product ) ) )
& ( F @ ( D @ ( C @ product ) ) )
& ( E @ ( C @ ( B @ product ) ) ) )
=> ( G @ ( F @ ( B @ product ) ) ) )
& ! [B: $i,C: $i] :
? [D: $i] : ( D @ ( C @ ( B @ product ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( B @ ( C @ product ) ) )
& ( D @ ( C @ inverse @ ( B @ inverse @ product ) ) ) )
=> ( A @ ( E @ inverse @ ( D @ inverse @ product ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distribution) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ! [B: $i] : ( A @ ( B @ ( B @ inverse @ product ) ) )
& ! [B: $i] : ( A @ ( B @ inverse @ ( B @ product ) ) )
& ! [B: $i] : ( B @ ( B @ ( A @ product ) ) )
& ! [B: $i] : ( B @ ( A @ ( B @ product ) ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( B @ product ) ) )
& ( F @ ( D @ ( C @ product ) ) )
& ( E @ ( C @ ( B @ product ) ) ) )
=> ( G @ ( D @ ( E @ product ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( D @ ( E @ product ) ) )
& ( F @ ( D @ ( C @ product ) ) )
& ( E @ ( C @ ( B @ product ) ) ) )
=> ( G @ ( F @ ( B @ product ) ) ) )
& ! [B: $i,C: $i] :
? [D: $i] : ( D @ ( C @ ( B @ product ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( B @ ( C @ product ) ) )
& ( D @ ( C @ inverse @ ( B @ inverse @ product ) ) ) )
=> ( A @ ( E @ inverse @ ( D @ inverse @ product ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
( ( ! [B: $i] : ( A @ ( B @ ( B @ inverse @ product ) ) )
& ! [B: $i] : ( A @ ( B @ inverse @ ( B @ product ) ) )
& ! [B: $i] : ( B @ ( B @ ( A @ product ) ) )
& ! [B: $i] : ( B @ ( A @ ( B @ product ) ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( B @ product ) ) )
& ( F @ ( D @ ( C @ product ) ) )
& ( E @ ( C @ ( B @ product ) ) ) )
=> ( G @ ( D @ ( E @ product ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( D @ ( E @ product ) ) )
& ( F @ ( D @ ( C @ product ) ) )
& ( E @ ( C @ ( B @ product ) ) ) )
=> ( G @ ( F @ ( B @ product ) ) ) )
& ! [B: $i,C: $i] :
? [D: $i] : ( D @ ( C @ ( B @ product ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( B @ ( C @ product ) ) )
& ( D @ ( C @ inverse @ ( B @ inverse @ product ) ) ) )
=> ( A @ ( E @ inverse @ ( D @ inverse @ product ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 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
% 0.23/0.48 % Computer : n007.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Fri Sep 25 14:14:24 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.40/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.76/1.57 % [INFO] Parsing done (257ms).
% 1.76/1.59 % [INFO] Running in sequential loop mode.
% 2.81/2.18 % [INFO] eprover registered as external prover.
% 2.81/2.20 % [INFO] Scanning for conjecture ...
% 3.11/2.36 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.30/2.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.30/2.43 % [INFO] Problem is first-order (TPTP FOF).
% 3.30/2.43 % [INFO] Type checking passed.
% 3.30/2.44 % [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 ...
% 5.41/3.38 % External prover 'e' found a proof!
% 5.41/3.38 % [INFO] Killing All external provers ...
% 5.41/3.38 % Time passed: 2694ms (effective reasoning time: 1785ms)
% 5.41/3.38 % 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)>
% 5.41/3.38 % Axioms used in derivation (0):
% 5.41/3.38 % No. of inferences in proof: 4
% 5.41/3.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2694 ms resp. 1785 ms w/o parsing
% 5.84/3.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.84/3.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------