TSTP Solution File: GRP775+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP775+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:15:22 EDT 2023
% Result : Theorem 3.37s 1.82s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 18 ( 5 unt; 4 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 : 8 ( 8 >; 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_type,type,
d: $i > $i > $o ).
thf(product_type,type,
product: $i > $i > $i ).
thf(l_type,type,
l: $i > $i > $o ).
thf(r_type,type,
r: $i > $i > $o ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( product @ ( product @ C @ B ) @ A )
= ( product @ C @ ( product @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( product @ ( product @ C @ B ) @ A )
= ( product @ C @ ( product @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( d @ A @ B )
<=> ( ( ( product @ A @ ( product @ B @ A ) )
= A )
& ( ( product @ B @ ( product @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( d @ A @ B )
<=> ( ( ( product @ A @ ( product @ B @ A ) )
= A )
& ( ( product @ B @ ( product @ A @ B ) )
= B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( d @ A @ B )
=> ( ( ( product @ A @ ( product @ B @ A ) )
= A )
& ( ( product @ B @ ( product @ A @ B ) )
= B ) ) )
& ( ( ( ( product @ A @ ( product @ B @ A ) )
= A )
& ( ( product @ B @ ( product @ A @ B ) )
= B ) )
=> ( d @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( d @ A @ B )
<=> ? [C: $i] :
( ( r @ A @ C )
& ( l @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( d @ A @ B )
=> ? [C: $i] :
( ( r @ A @ C )
& ( l @ C @ B ) ) )
& ( ? [C: $i] :
( ( r @ A @ C )
& ( l @ C @ B ) )
=> ( d @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( l @ A @ B )
<=> ( ( ( product @ A @ B )
= A )
& ( ( product @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ( l @ A @ B )
=> ( ( ( product @ A @ B )
= A )
& ( ( product @ B @ A )
= B ) ) )
& ( ( ( ( product @ A @ B )
= A )
& ( ( product @ B @ A )
= B ) )
=> ( l @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
thf(21,plain,
! [A: $i] :
( ( product @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( r @ A @ B )
<=> ( ( ( product @ A @ B )
= B )
& ( ( product @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( r @ A @ B )
=> ( ( ( product @ A @ B )
= B )
& ( ( product @ B @ A )
= A ) ) )
& ( ( ( ( product @ A @ B )
= B )
& ( ( product @ B @ A )
= A ) )
=> ( r @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(59,plain,
$false,
inference(cvc4,[status(thm)],[18,8,42,24,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP775+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n009.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 02:03:48 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.91/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.05 % [INFO] Parsing done (116ms).
% 1.17/1.06 % [INFO] Running in sequential loop mode.
% 1.69/1.25 % [INFO] eprover registered as external prover.
% 1.69/1.26 % [INFO] cvc4 registered as external prover.
% 1.69/1.26 % [INFO] Scanning for conjecture ...
% 1.80/1.31 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.80/1.34 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.98/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 1.98/1.35 % [INFO] Type checking passed.
% 1.98/1.35 % [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 ...
% 3.37/1.82 % External prover 'cvc4' found a proof!
% 3.37/1.82 % [INFO] Killing All external provers ...
% 3.37/1.82 % Time passed: 1252ms (effective reasoning time: 760ms)
% 3.37/1.82 % 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)>
% 3.37/1.82 % Axioms used in derivation (5): sos03, sos02, sos05, sos04, sos01
% 3.37/1.82 % No. of inferences in proof: 14
% 3.37/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1252 ms resp. 760 ms w/o parsing
% 3.37/1.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.37/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------