TSTP Solution File: GRP401-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP401-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 11:13:54 EDT 2023
% Result : Unsatisfiable 42.68s 7.26s
% Output : Refutation 42.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 18 ( 9 unt; 5 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 94 ( 6 ~; 4 |; 0 &; 84 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(commutator_type,type,
commutator: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( commutator @ ( multiply @ A @ B ) @ C )
= ( multiply @ ( commutator @ A @ C ) @ ( commutator @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator_distributes_over_product) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( commutator @ ( multiply @ A @ B ) @ C )
= ( multiply @ ( commutator @ A @ C ) @ ( commutator @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancellation) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( multiply @ ( commutator @ a @ b ) @ c )
!= ( multiply @ c @ ( commutator @ a @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_nilpotency) ).
thf(7,plain,
( ( multiply @ ( commutator @ a @ b ) @ c )
!= ( multiply @ c @ ( commutator @ a @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12939,plain,
$false,
inference(e,[status(thm)],[10,20,22,12,7,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP401-1 : TPTP v8.1.2. Released v2.5.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n007.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 01:55:24 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.00/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.98 % [INFO] Parsing done (117ms).
% 1.26/0.99 % [INFO] Running in sequential loop mode.
% 1.63/1.17 % [INFO] eprover registered as external prover.
% 1.63/1.17 % [INFO] cvc4 registered as external prover.
% 1.72/1.18 % [INFO] Scanning for conjecture ...
% 1.72/1.22 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.88/1.24 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.88/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.25 % [INFO] Type checking passed.
% 1.94/1.26 % [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 ...
% 42.68/7.26 % External prover 'e' found a proof!
% 42.68/7.26 % [INFO] Killing All external provers ...
% 42.68/7.26 % Time passed: 6723ms (effective reasoning time: 6273ms)
% 42.68/7.26 % 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)>
% 42.68/7.26 % Axioms used in derivation (5): left_cancellation, right_cancellation, commutator, commutator_distributes_over_product, associativity_of_multiply
% 42.68/7.26 % No. of inferences in proof: 13
% 42.68/7.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6723 ms resp. 6273 ms w/o parsing
% 42.68/7.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.68/7.28 % [INFO] Killing All external provers ...
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