TSTP Solution File: GRP010-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP010-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:12:59 EDT 2023
% Result : Unsatisfiable 2.36s 1.47s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 16 ( 11 unt; 5 typ; 0 def)
% Number of atoms : 11 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 36 ( 2 ~; 0 |; 0 &; 34 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(identity_type,type,
identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(1,negated_conjecture,
( ( multiply @ b @ c )
!= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_c_is_e) ).
thf(6,plain,
( ( multiply @ b @ c )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(9,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(4,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(13,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(11,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( ( multiply @ c @ b )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_b_is_e) ).
thf(15,plain,
( ( multiply @ c @ b )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(cvc4,[status(thm)],[6,9,13,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP010-4 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 01:33:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.95/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.94 % [INFO] Parsing done (100ms).
% 1.18/0.95 % [INFO] Running in sequential loop mode.
% 1.56/1.14 % [INFO] eprover registered as external prover.
% 1.56/1.14 % [INFO] cvc4 registered as external prover.
% 1.56/1.15 % [INFO] Scanning for conjecture ...
% 1.64/1.19 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.64/1.21 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.64/1.21 % [INFO] Problem is propositional (TPTP CNF).
% 1.64/1.22 % [INFO] Type checking passed.
% 1.64/1.22 % [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 ...
% 2.36/1.47 % External prover 'cvc4' found a proof!
% 2.36/1.47 % [INFO] Killing All external provers ...
% 2.36/1.47 % Time passed: 951ms (effective reasoning time: 520ms)
% 2.36/1.47 % 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)>
% 2.36/1.47 % Axioms used in derivation (4): associativity, left_inverse, left_identity, c_times_b_is_e
% 2.36/1.47 % No. of inferences in proof: 11
% 2.36/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 951 ms resp. 520 ms w/o parsing
% 2.36/1.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.36/1.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------