TSTP Solution File: BOO001-1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : BOO001-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n029.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 : Mon Jun 24 04:37:37 EDT 2024
% Result : Unsatisfiable 2.34s 1.67s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 16 ( 13 unt; 3 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 64 ( 2 ~; 0 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-3 aty)
% Number of variables : 26 ( 0 ^ 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i > $i ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B @ C ) @ D @ ( multiply @ A @ B @ E ) )
= ( multiply @ A @ B @ ( multiply @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(10,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B @ C ) @ D @ ( multiply @ A @ B @ E ) )
= ( multiply @ A @ B @ ( multiply @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( inverse @ ( inverse @ a ) )
!= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
thf(7,plain,
( ( inverse @ ( inverse @ a ) )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B @ ( inverse @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B @ ( inverse @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ A ) @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ A ) @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : BOO001-1 : TPTP v8.2.0. Released v1.0.0.
% 0.02/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.31 % Computer : n029.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Jun 18 19:36:40 EDT 2024
% 0.12/0.31 % CPUTime :
% 0.94/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.02 % [INFO] Parsing done (109ms).
% 1.25/1.03 % [INFO] Running in sequential loop mode.
% 1.58/1.27 % [INFO] eprover registered as external prover.
% 1.58/1.28 % [INFO] Scanning for conjecture ...
% 1.77/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.77/1.35 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.77/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.36 % [INFO] Type checking passed.
% 1.77/1.36 % [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 ...
% 2.34/1.67 % External prover 'e' found a proof!
% 2.34/1.67 % [INFO] Killing All external provers ...
% 2.34/1.67 % Time passed: 1176ms (effective reasoning time: 642ms)
% 2.34/1.67 % Axioms used in derivation (5): associativity, ternary_multiply_1, right_inverse, ternary_multiply_2, left_inverse
% 2.34/1.67 % No. of inferences in proof: 13
% 2.34/1.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1176 ms resp. 642 ms w/o parsing
% 2.52/1.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.52/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------