TSTP Solution File: GRP001+6 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:12:58 EDT 2023
% Result : Theorem 2.51s 1.50s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 1 unt; 2 typ; 0 def)
% Number of atoms : 49 ( 0 equ; 0 cnn)
% Maximal formula atoms : 16 ( 12 avg)
% Number of connectives : 197 ( 2 ~; 0 |; 30 &; 150 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 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_type,type,
product: $i > $i > $i > $o ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( ! [B: $i,C: $i] :
? [D: $i] : ( product @ B @ C @ D )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( product @ B @ C @ E )
& ( product @ C @ D @ F )
& ( product @ E @ D @ G ) )
=> ( product @ B @ F @ G ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( product @ B @ C @ E )
& ( product @ C @ D @ F )
& ( product @ B @ F @ G ) )
=> ( product @ E @ D @ G ) )
& ! [B: $i] : ( product @ B @ A @ B )
& ! [B: $i] : ( product @ A @ B @ B )
& ! [B: $i] : ( product @ B @ ( inverse @ B ) @ A )
& ! [B: $i] : ( product @ ( inverse @ B ) @ B @ A ) )
=> ( ! [B: $i] : ( product @ B @ B @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( product @ B @ C @ D )
=> ( product @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ! [B: $i,C: $i] :
? [D: $i] : ( product @ B @ C @ D )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( product @ B @ C @ E )
& ( product @ C @ D @ F )
& ( product @ E @ D @ G ) )
=> ( product @ B @ F @ G ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( product @ B @ C @ E )
& ( product @ C @ D @ F )
& ( product @ B @ F @ G ) )
=> ( product @ E @ D @ G ) )
& ! [B: $i] : ( product @ B @ A @ B )
& ! [B: $i] : ( product @ A @ B @ B )
& ! [B: $i] : ( product @ B @ ( inverse @ B ) @ A )
& ! [B: $i] : ( product @ ( inverse @ B ) @ B @ A ) )
=> ( ! [B: $i] : ( product @ B @ B @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( product @ B @ C @ D )
=> ( product @ C @ B @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
( ( ! [B: $i,C: $i] :
? [D: $i] : ( product @ B @ C @ D )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( product @ B @ C @ E )
& ( product @ C @ D @ F )
& ( product @ E @ D @ G ) )
=> ( product @ B @ F @ G ) )
& ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( product @ B @ C @ E )
& ( product @ C @ D @ F )
& ( product @ B @ F @ G ) )
=> ( product @ E @ D @ G ) )
& ! [B: $i] : ( product @ B @ A @ B )
& ! [B: $i] : ( product @ A @ B @ B )
& ! [B: $i] : ( product @ B @ ( inverse @ B ) @ A )
& ! [B: $i] : ( product @ ( inverse @ B ) @ B @ A ) )
=> ( ! [B: $i] : ( product @ B @ B @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( product @ B @ C @ D )
=> ( product @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.02/0.10 % Command : run_Leo-III %s %d
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Fri May 19 01:46:12 EDT 2023
% 0.11/0.29 % CPUTime :
% 0.75/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.84/0.86 % [INFO] Parsing done (119ms).
% 1.06/0.87 % [INFO] Running in sequential loop mode.
% 1.31/1.06 % [INFO] eprover registered as external prover.
% 1.31/1.06 % [INFO] cvc4 registered as external prover.
% 1.31/1.07 % [INFO] Scanning for conjecture ...
% 1.49/1.13 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.49/1.15 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.49/1.16 % [INFO] Problem is first-order (TPTP FOF).
% 1.49/1.16 % [INFO] Type checking passed.
% 1.49/1.16 % [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 ...
% 2.26/1.47 % External prover 'e' found a proof!
% 2.26/1.47 % [INFO] Killing All external provers ...
% 2.26/1.47 % Time passed: 1050ms (effective reasoning time: 598ms)
% 2.26/1.47 % 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)>
% 2.51/1.50 % Axioms used in derivation (0):
% 2.51/1.50 % No. of inferences in proof: 4
% 2.51/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1050 ms resp. 598 ms w/o parsing
% 2.51/1.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.51/1.53 % [INFO] Killing All external provers ...
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